1,1,273,137,0.852000," ","int((a+a*sec(d*x+c))*tan(d*x+c)^9,x)","\frac{a \left(\tan^{8}\left(d x +c \right)\right)}{8 d}-\frac{a \left(\tan^{6}\left(d x +c \right)\right)}{6 d}+\frac{a \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a \left(\sin^{10}\left(d x +c \right)\right)}{9 d \cos \left(d x +c \right)^{9}}-\frac{a \left(\sin^{10}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)^{7}}+\frac{a \left(\sin^{10}\left(d x +c \right)\right)}{105 d \cos \left(d x +c \right)^{5}}-\frac{a \left(\sin^{10}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)^{3}}+\frac{a \left(\sin^{10}\left(d x +c \right)\right)}{9 d \cos \left(d x +c \right)}+\frac{128 a \cos \left(d x +c \right)}{315 d}+\frac{\cos \left(d x +c \right) \left(\sin^{8}\left(d x +c \right)\right) a}{9 d}+\frac{8 a \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{63 d}+\frac{16 a \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{105 d}+\frac{64 a \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{315 d}"," ",0,"1/8/d*a*tan(d*x+c)^8-1/6/d*a*tan(d*x+c)^6+1/4*a*tan(d*x+c)^4/d-1/2*a*tan(d*x+c)^2/d-a*ln(cos(d*x+c))/d+1/9/d*a*sin(d*x+c)^10/cos(d*x+c)^9-1/63/d*a*sin(d*x+c)^10/cos(d*x+c)^7+1/105/d*a*sin(d*x+c)^10/cos(d*x+c)^5-1/63/d*a*sin(d*x+c)^10/cos(d*x+c)^3+1/9/d*a*sin(d*x+c)^10/cos(d*x+c)+128/315*a*cos(d*x+c)/d+1/9/d*cos(d*x+c)*sin(d*x+c)^8*a+8/63/d*a*cos(d*x+c)*sin(d*x+c)^6+16/105/d*a*cos(d*x+c)*sin(d*x+c)^4+64/315/d*a*cos(d*x+c)*sin(d*x+c)^2","A"
2,1,216,108,0.859000," ","int((a+a*sec(d*x+c))*tan(d*x+c)^7,x)","\frac{a \left(\tan^{6}\left(d x +c \right)\right)}{6 d}-\frac{a \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a \left(\sin^{8}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{7}}-\frac{a \left(\sin^{8}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{5}}+\frac{a \left(\sin^{8}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{3}}-\frac{a \left(\sin^{8}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)}-\frac{16 a \cos \left(d x +c \right)}{35 d}-\frac{a \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{7 d}-\frac{6 a \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{35 d}-\frac{8 a \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{35 d}"," ",0,"1/6/d*a*tan(d*x+c)^6-1/4*a*tan(d*x+c)^4/d+1/2*a*tan(d*x+c)^2/d+a*ln(cos(d*x+c))/d+1/7/d*a*sin(d*x+c)^8/cos(d*x+c)^7-1/35/d*a*sin(d*x+c)^8/cos(d*x+c)^5+1/35/d*a*sin(d*x+c)^8/cos(d*x+c)^3-1/7/d*a*sin(d*x+c)^8/cos(d*x+c)-16/35*a*cos(d*x+c)/d-1/7/d*a*cos(d*x+c)*sin(d*x+c)^6-6/35/d*a*cos(d*x+c)*sin(d*x+c)^4-8/35/d*a*cos(d*x+c)*sin(d*x+c)^2","A"
3,1,161,81,0.737000," ","int((a+a*sec(d*x+c))*tan(d*x+c)^5,x)","\frac{a \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a \left(\sin^{6}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}-\frac{a \left(\sin^{6}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{3}}+\frac{a \left(\sin^{6}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)}+\frac{8 a \cos \left(d x +c \right)}{15 d}+\frac{a \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 a \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}"," ",0,"1/4*a*tan(d*x+c)^4/d-1/2*a*tan(d*x+c)^2/d-a*ln(cos(d*x+c))/d+1/5/d*a*sin(d*x+c)^6/cos(d*x+c)^5-1/15/d*a*sin(d*x+c)^6/cos(d*x+c)^3+1/5/d*a*sin(d*x+c)^6/cos(d*x+c)+8/15*a*cos(d*x+c)/d+1/5/d*a*cos(d*x+c)*sin(d*x+c)^4+4/15/d*a*cos(d*x+c)*sin(d*x+c)^2","A"
4,1,104,53,0.729000," ","int((a+a*sec(d*x+c))*tan(d*x+c)^3,x)","\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{a \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}-\frac{a \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}-\frac{2 a \cos \left(d x +c \right)}{3 d}"," ",0,"1/2*a*tan(d*x+c)^2/d+a*ln(cos(d*x+c))/d+1/3/d*a*sin(d*x+c)^4/cos(d*x+c)^3-1/3/d*a*sin(d*x+c)^4/cos(d*x+c)-1/3/d*a*cos(d*x+c)*sin(d*x+c)^2-2/3*a*cos(d*x+c)/d","A"
5,1,25,25,0.282000," ","int((a+a*sec(d*x+c))*tan(d*x+c),x)","\frac{a \sec \left(d x +c \right)}{d}+\frac{a \ln \left(\sec \left(d x +c \right)\right)}{d}"," ",0,"a*sec(d*x+c)/d+a/d*ln(sec(d*x+c))","A"
6,1,29,16,0.442000," ","int(cot(d*x+c)*(a+a*sec(d*x+c)),x)","-\frac{a \ln \left(\sec \left(d x +c \right)\right)}{d}+\frac{a \ln \left(-1+\sec \left(d x +c \right)\right)}{d}"," ",0,"-a/d*ln(sec(d*x+c))+a/d*ln(-1+sec(d*x+c))","A"
7,1,60,51,0.658000," ","int(cot(d*x+c)^3*(a+a*sec(d*x+c)),x)","\frac{a \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a}{2 d \left(-1+\sec \left(d x +c \right)\right)}-\frac{3 a \ln \left(-1+\sec \left(d x +c \right)\right)}{4 d}-\frac{a \ln \left(1+\sec \left(d x +c \right)\right)}{4 d}"," ",0,"a/d*ln(sec(d*x+c))-1/2*a/d/(-1+sec(d*x+c))-3/4*a/d*ln(-1+sec(d*x+c))-1/4*a/d*ln(1+sec(d*x+c))","A"
8,1,93,85,0.546000," ","int(cot(d*x+c)^5*(a+a*sec(d*x+c)),x)","-\frac{a \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a}{8 d \left(-1+\sec \left(d x +c \right)\right)^{2}}+\frac{a}{2 d \left(-1+\sec \left(d x +c \right)\right)}+\frac{11 a \ln \left(-1+\sec \left(d x +c \right)\right)}{16 d}-\frac{a}{8 d \left(1+\sec \left(d x +c \right)\right)}+\frac{5 a \ln \left(1+\sec \left(d x +c \right)\right)}{16 d}"," ",0,"-a/d*ln(sec(d*x+c))-1/8*a/d/(-1+sec(d*x+c))^2+1/2*a/d/(-1+sec(d*x+c))+11/16*a/d*ln(-1+sec(d*x+c))-1/8*a/d/(1+sec(d*x+c))+5/16*a/d*ln(1+sec(d*x+c))","A"
9,1,124,119,0.612000," ","int(cot(d*x+c)^7*(a+a*sec(d*x+c)),x)","\frac{a \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a}{24 d \left(-1+\sec \left(d x +c \right)\right)^{3}}+\frac{5 a}{32 d \left(-1+\sec \left(d x +c \right)\right)^{2}}-\frac{a}{2 d \left(-1+\sec \left(d x +c \right)\right)}-\frac{21 a \ln \left(-1+\sec \left(d x +c \right)\right)}{32 d}+\frac{a}{32 d \left(1+\sec \left(d x +c \right)\right)^{2}}+\frac{3 a}{16 d \left(1+\sec \left(d x +c \right)\right)}-\frac{11 a \ln \left(1+\sec \left(d x +c \right)\right)}{32 d}"," ",0,"a/d*ln(sec(d*x+c))-1/24*a/d/(-1+sec(d*x+c))^3+5/32*a/d/(-1+sec(d*x+c))^2-1/2*a/d/(-1+sec(d*x+c))-21/32*a/d*ln(-1+sec(d*x+c))+1/32*a/d/(1+sec(d*x+c))^2+3/16*a/d/(1+sec(d*x+c))-11/32*a/d*ln(1+sec(d*x+c))","A"
10,1,227,119,0.543000," ","int((a+a*sec(d*x+c))*tan(d*x+c)^8,x)","\frac{a \left(\tan^{7}\left(d x +c \right)\right)}{7 d}-\frac{a \left(\tan^{5}\left(d x +c \right)\right)}{5 d}+\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \tan \left(d x +c \right)}{d}+a x +\frac{c a}{d}+\frac{a \left(\sin^{9}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{8}}-\frac{a \left(\sin^{9}\left(d x +c \right)\right)}{48 d \cos \left(d x +c \right)^{6}}+\frac{a \left(\sin^{9}\left(d x +c \right)\right)}{64 d \cos \left(d x +c \right)^{4}}-\frac{5 a \left(\sin^{9}\left(d x +c \right)\right)}{128 d \cos \left(d x +c \right)^{2}}-\frac{5 a \left(\sin^{7}\left(d x +c \right)\right)}{128 d}-\frac{7 a \left(\sin^{5}\left(d x +c \right)\right)}{128 d}-\frac{35 a \left(\sin^{3}\left(d x +c \right)\right)}{384 d}-\frac{35 a \sin \left(d x +c \right)}{128 d}+\frac{35 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{128 d}"," ",0,"1/7*a*tan(d*x+c)^7/d-1/5*a*tan(d*x+c)^5/d+1/3*a*tan(d*x+c)^3/d-a*tan(d*x+c)/d+a*x+1/d*c*a+1/8/d*a*sin(d*x+c)^9/cos(d*x+c)^8-1/48/d*a*sin(d*x+c)^9/cos(d*x+c)^6+1/64/d*a*sin(d*x+c)^9/cos(d*x+c)^4-5/128/d*a*sin(d*x+c)^9/cos(d*x+c)^2-5/128*a*sin(d*x+c)^7/d-7/128*a*sin(d*x+c)^5/d-35/384*a*sin(d*x+c)^3/d-35/128*a*sin(d*x+c)/d+35/128/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
11,1,178,94,0.510000," ","int((a+a*sec(d*x+c))*tan(d*x+c)^6,x)","\frac{a \left(\tan^{5}\left(d x +c \right)\right)}{5 d}-\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \tan \left(d x +c \right)}{d}-a x -\frac{c a}{d}+\frac{a \left(\sin^{7}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}-\frac{a \left(\sin^{7}\left(d x +c \right)\right)}{24 d \cos \left(d x +c \right)^{4}}+\frac{a \left(\sin^{7}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{a \left(\sin^{5}\left(d x +c \right)\right)}{16 d}+\frac{5 a \left(\sin^{3}\left(d x +c \right)\right)}{48 d}+\frac{5 a \sin \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,"1/5*a*tan(d*x+c)^5/d-1/3*a*tan(d*x+c)^3/d+a*tan(d*x+c)/d-a*x-1/d*c*a+1/6/d*a*sin(d*x+c)^7/cos(d*x+c)^6-1/24/d*a*sin(d*x+c)^7/cos(d*x+c)^4+1/16/d*a*sin(d*x+c)^7/cos(d*x+c)^2+1/16*a*sin(d*x+c)^5/d+5/48*a*sin(d*x+c)^3/d+5/16*a*sin(d*x+c)/d-5/16/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
12,1,127,67,0.481000," ","int((a+a*sec(d*x+c))*tan(d*x+c)^4,x)","\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \tan \left(d x +c \right)}{d}+a x +\frac{c a}{d}+\frac{a \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{3 a \sin \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,"1/3*a*tan(d*x+c)^3/d-a*tan(d*x+c)/d+a*x+1/d*c*a+1/4/d*a*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*a*sin(d*x+c)^5/cos(d*x+c)^2-1/8*a*sin(d*x+c)^3/d-3/8*a*sin(d*x+c)/d+3/8/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
13,1,78,41,0.464000," ","int((a+a*sec(d*x+c))*tan(d*x+c)^2,x)","-a x +\frac{a \tan \left(d x +c \right)}{d}-\frac{c a}{d}+\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a \sin \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,"-a*x+a*tan(d*x+c)/d-1/d*c*a+1/2/d*a*sin(d*x+c)^3/cos(d*x+c)^2+1/2*a*sin(d*x+c)/d-1/2/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
14,1,35,26,0.476000," ","int(cot(d*x+c)^2*(a+a*sec(d*x+c)),x)","\frac{a \left(-\cot \left(d x +c \right)-d x -c \right)-\frac{a}{\sin \left(d x +c \right)}}{d}"," ",0,"1/d*(a*(-cot(d*x+c)-d*x-c)-a/sin(d*x+c))","A"
15,1,86,51,0.788000," ","int(cot(d*x+c)^4*(a+a*sec(d*x+c)),x)","\frac{a \left(-\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}+\cot \left(d x +c \right)+d x +c \right)+a \left(-\frac{\cos^{4}\left(d x +c \right)}{3 \sin \left(d x +c \right)^{3}}+\frac{\cos^{4}\left(d x +c \right)}{3 \sin \left(d x +c \right)}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}\right)}{d}"," ",0,"1/d*(a*(-1/3*cot(d*x+c)^3+cot(d*x+c)+d*x+c)+a*(-1/3/sin(d*x+c)^3*cos(d*x+c)^4+1/3/sin(d*x+c)*cos(d*x+c)^4+1/3*(2+cos(d*x+c)^2)*sin(d*x+c)))","A"
16,1,129,78,0.812000," ","int(cot(d*x+c)^6*(a+a*sec(d*x+c)),x)","\frac{a \left(-\frac{\left(\cot^{5}\left(d x +c \right)\right)}{5}+\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}-\cot \left(d x +c \right)-d x -c \right)+a \left(-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{15 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)}-\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)}{5}\right)}{d}"," ",0,"1/d*(a*(-1/5*cot(d*x+c)^5+1/3*cot(d*x+c)^3-cot(d*x+c)-d*x-c)+a*(-1/5/sin(d*x+c)^5*cos(d*x+c)^6+1/15/sin(d*x+c)^3*cos(d*x+c)^6-1/5/sin(d*x+c)*cos(d*x+c)^6-1/5*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","A"
17,1,162,103,0.951000," ","int(cot(d*x+c)^8*(a+a*sec(d*x+c)),x)","\frac{a \left(-\frac{\left(\cot^{7}\left(d x +c \right)\right)}{7}+\frac{\left(\cot^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}+\cot \left(d x +c \right)+d x +c \right)+a \left(-\frac{\cos^{8}\left(d x +c \right)}{7 \sin \left(d x +c \right)^{7}}+\frac{\cos^{8}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{5}}-\frac{\cos^{8}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{3}}+\frac{\cos^{8}\left(d x +c \right)}{7 \sin \left(d x +c \right)}+\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)}{7}\right)}{d}"," ",0,"1/d*(a*(-1/7*cot(d*x+c)^7+1/5*cot(d*x+c)^5-1/3*cot(d*x+c)^3+cot(d*x+c)+d*x+c)+a*(-1/7/sin(d*x+c)^7*cos(d*x+c)^8+1/35/sin(d*x+c)^5*cos(d*x+c)^8-1/35/sin(d*x+c)^3*cos(d*x+c)^8+1/7/sin(d*x+c)*cos(d*x+c)^8+1/7*(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"
18,1,205,130,0.973000," ","int(cot(d*x+c)^10*(a+a*sec(d*x+c)),x)","\frac{a \left(-\frac{\left(\cot^{9}\left(d x +c \right)\right)}{9}+\frac{\left(\cot^{7}\left(d x +c \right)\right)}{7}-\frac{\left(\cot^{5}\left(d x +c \right)\right)}{5}+\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}-\cot \left(d x +c \right)-d x -c \right)+a \left(-\frac{\cos^{10}\left(d x +c \right)}{9 \sin \left(d x +c \right)^{9}}+\frac{\cos^{10}\left(d x +c \right)}{63 \sin \left(d x +c \right)^{7}}-\frac{\cos^{10}\left(d x +c \right)}{105 \sin \left(d x +c \right)^{5}}+\frac{\cos^{10}\left(d x +c \right)}{63 \sin \left(d x +c \right)^{3}}-\frac{\cos^{10}\left(d x +c \right)}{9 \sin \left(d x +c \right)}-\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)}{9}\right)}{d}"," ",0,"1/d*(a*(-1/9*cot(d*x+c)^9+1/7*cot(d*x+c)^7-1/5*cot(d*x+c)^5+1/3*cot(d*x+c)^3-cot(d*x+c)-d*x-c)+a*(-1/9/sin(d*x+c)^9*cos(d*x+c)^10+1/63/sin(d*x+c)^7*cos(d*x+c)^10-1/105/sin(d*x+c)^5*cos(d*x+c)^10+1/63/sin(d*x+c)^3*cos(d*x+c)^10-1/9/sin(d*x+c)*cos(d*x+c)^10-1/9*(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"
19,1,327,174,0.855000," ","int((a+a*sec(d*x+c))^2*tan(d*x+c)^9,x)","\frac{a^{2} \left(\tan^{8}\left(d x +c \right)\right)}{8 d}-\frac{a^{2} \left(\tan^{6}\left(d x +c \right)\right)}{6 d}+\frac{a^{2} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{2 a^{2} \left(\sin^{10}\left(d x +c \right)\right)}{9 d \cos \left(d x +c \right)^{9}}-\frac{2 a^{2} \left(\sin^{10}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)^{7}}+\frac{2 a^{2} \left(\sin^{10}\left(d x +c \right)\right)}{105 d \cos \left(d x +c \right)^{5}}-\frac{2 a^{2} \left(\sin^{10}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)^{3}}+\frac{2 a^{2} \left(\sin^{10}\left(d x +c \right)\right)}{9 d \cos \left(d x +c \right)}+\frac{256 a^{2} \cos \left(d x +c \right)}{315 d}+\frac{2 a^{2} \cos \left(d x +c \right) \left(\sin^{8}\left(d x +c \right)\right)}{9 d}+\frac{16 a^{2} \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{63 d}+\frac{32 a^{2} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{105 d}+\frac{128 a^{2} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{315 d}+\frac{a^{2} \left(\sin^{10}\left(d x +c \right)\right)}{10 d \cos \left(d x +c \right)^{10}}"," ",0,"1/8/d*a^2*tan(d*x+c)^8-1/6/d*a^2*tan(d*x+c)^6+1/4*a^2*tan(d*x+c)^4/d-1/2*a^2*tan(d*x+c)^2/d-a^2*ln(cos(d*x+c))/d+2/9/d*a^2*sin(d*x+c)^10/cos(d*x+c)^9-2/63/d*a^2*sin(d*x+c)^10/cos(d*x+c)^7+2/105/d*a^2*sin(d*x+c)^10/cos(d*x+c)^5-2/63/d*a^2*sin(d*x+c)^10/cos(d*x+c)^3+2/9/d*a^2*sin(d*x+c)^10/cos(d*x+c)+256/315*a^2*cos(d*x+c)/d+2/9/d*a^2*cos(d*x+c)*sin(d*x+c)^8+16/63/d*a^2*cos(d*x+c)*sin(d*x+c)^6+32/105/d*a^2*cos(d*x+c)*sin(d*x+c)^4+128/315/d*a^2*cos(d*x+c)*sin(d*x+c)^2+1/10/d*a^2*sin(d*x+c)^10/cos(d*x+c)^10","A"
20,1,264,124,0.782000," ","int((a+a*sec(d*x+c))^2*tan(d*x+c)^7,x)","\frac{a^{2} \left(\tan^{6}\left(d x +c \right)\right)}{6 d}-\frac{a^{2} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{2 a^{2} \left(\sin^{8}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{7}}-\frac{2 a^{2} \left(\sin^{8}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{5}}+\frac{2 a^{2} \left(\sin^{8}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{3}}-\frac{2 a^{2} \left(\sin^{8}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)}-\frac{32 a^{2} \cos \left(d x +c \right)}{35 d}-\frac{2 a^{2} \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{7 d}-\frac{12 a^{2} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{35 d}-\frac{16 a^{2} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{35 d}+\frac{a^{2} \left(\sin^{8}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{8}}"," ",0,"1/6/d*a^2*tan(d*x+c)^6-1/4*a^2*tan(d*x+c)^4/d+1/2*a^2*tan(d*x+c)^2/d+a^2*ln(cos(d*x+c))/d+2/7/d*a^2*sin(d*x+c)^8/cos(d*x+c)^7-2/35/d*a^2*sin(d*x+c)^8/cos(d*x+c)^5+2/35/d*a^2*sin(d*x+c)^8/cos(d*x+c)^3-2/7/d*a^2*sin(d*x+c)^8/cos(d*x+c)-32/35*a^2*cos(d*x+c)/d-2/7/d*a^2*cos(d*x+c)*sin(d*x+c)^6-12/35/d*a^2*cos(d*x+c)*sin(d*x+c)^4-16/35/d*a^2*cos(d*x+c)*sin(d*x+c)^2+1/8/d*a^2*sin(d*x+c)^8/cos(d*x+c)^8","B"
21,1,203,110,0.736000," ","int((a+a*sec(d*x+c))^2*tan(d*x+c)^5,x)","\frac{a^{2} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{2 a^{2} \left(\sin^{6}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}-\frac{2 a^{2} \left(\sin^{6}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{3}}+\frac{2 a^{2} \left(\sin^{6}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)}+\frac{16 a^{2} \cos \left(d x +c \right)}{15 d}+\frac{2 a^{2} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{5 d}+\frac{8 a^{2} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}+\frac{a^{2} \left(\sin^{6}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}"," ",0,"1/4*a^2*tan(d*x+c)^4/d-1/2*a^2*tan(d*x+c)^2/d-a^2*ln(cos(d*x+c))/d+2/5/d*a^2*sin(d*x+c)^6/cos(d*x+c)^5-2/15/d*a^2*sin(d*x+c)^6/cos(d*x+c)^3+2/5/d*a^2*sin(d*x+c)^6/cos(d*x+c)+16/15*a^2*cos(d*x+c)/d+2/5/d*a^2*cos(d*x+c)*sin(d*x+c)^4+8/15/d*a^2*cos(d*x+c)*sin(d*x+c)^2+1/6/d*a^2*sin(d*x+c)^6/cos(d*x+c)^6","A"
22,1,140,61,0.719000," ","int((a+a*sec(d*x+c))^2*tan(d*x+c)^3,x)","\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{2 a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{2 a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}-\frac{2 a^{2} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}-\frac{4 a^{2} \cos \left(d x +c \right)}{3 d}+\frac{a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/2*a^2*tan(d*x+c)^2/d+a^2*ln(cos(d*x+c))/d+2/3/d*a^2*sin(d*x+c)^4/cos(d*x+c)^3-2/3/d*a^2*sin(d*x+c)^4/cos(d*x+c)-2/3/d*a^2*cos(d*x+c)*sin(d*x+c)^2-4/3*a^2*cos(d*x+c)/d+1/4/d*a^2*sin(d*x+c)^4/cos(d*x+c)^4","B"
23,1,46,46,0.297000," ","int((a+a*sec(d*x+c))^2*tan(d*x+c),x)","\frac{a^{2} \left(\sec^{2}\left(d x +c \right)\right)}{2 d}+\frac{2 a^{2} \sec \left(d x +c \right)}{d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)\right)}{d}"," ",0,"1/2*a^2*sec(d*x+c)^2/d+2*a^2*sec(d*x+c)/d+a^2/d*ln(sec(d*x+c))","A"
24,1,34,35,0.532000," ","int(cot(d*x+c)*(a+a*sec(d*x+c))^2,x)","-\frac{a^{2} \ln \left(\sec \left(d x +c \right)\right)}{d}+\frac{2 a^{2} \ln \left(-1+\sec \left(d x +c \right)\right)}{d}"," ",0,"-a^2/d*ln(sec(d*x+c))+2*a^2/d*ln(-1+sec(d*x+c))","A"
25,1,51,40,0.680000," ","int(cot(d*x+c)^3*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a^{2}}{d \left(-1+\sec \left(d x +c \right)\right)}-\frac{a^{2} \ln \left(-1+\sec \left(d x +c \right)\right)}{d}"," ",0,"a^2/d*ln(sec(d*x+c))-a^2/d/(-1+sec(d*x+c))-a^2/d*ln(-1+sec(d*x+c))","A"
26,1,87,77,0.582000," ","int(cot(d*x+c)^5*(a+a*sec(d*x+c))^2,x)","-\frac{a^{2} \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a^{2}}{4 d \left(-1+\sec \left(d x +c \right)\right)^{2}}+\frac{3 a^{2}}{4 d \left(-1+\sec \left(d x +c \right)\right)}+\frac{7 a^{2} \ln \left(-1+\sec \left(d x +c \right)\right)}{8 d}+\frac{a^{2} \ln \left(1+\sec \left(d x +c \right)\right)}{8 d}"," ",0,"-a^2/d*ln(sec(d*x+c))-1/4*a^2/d/(-1+sec(d*x+c))^2+3/4*a^2/d/(-1+sec(d*x+c))+7/8*a^2/d*ln(-1+sec(d*x+c))+1/8*a^2/d*ln(1+sec(d*x+c))","A"
27,1,122,115,0.628000," ","int(cot(d*x+c)^7*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a^{2}}{12 d \left(-1+\sec \left(d x +c \right)\right)^{3}}+\frac{a^{2}}{4 d \left(-1+\sec \left(d x +c \right)\right)^{2}}-\frac{11 a^{2}}{16 d \left(-1+\sec \left(d x +c \right)\right)}-\frac{13 a^{2} \ln \left(-1+\sec \left(d x +c \right)\right)}{16 d}+\frac{a^{2}}{16 d \left(1+\sec \left(d x +c \right)\right)}-\frac{3 a^{2} \ln \left(1+\sec \left(d x +c \right)\right)}{16 d}"," ",0,"a^2/d*ln(sec(d*x+c))-1/12*a^2/d/(-1+sec(d*x+c))^3+1/4*a^2/d/(-1+sec(d*x+c))^2-11/16*a^2/d/(-1+sec(d*x+c))-13/16*a^2/d*ln(-1+sec(d*x+c))+1/16*a^2/d/(1+sec(d*x+c))-3/16*a^2/d*ln(1+sec(d*x+c))","A"
28,1,159,153,0.705000," ","int(cot(d*x+c)^9*(a+a*sec(d*x+c))^2,x)","-\frac{a^{2} \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a^{2}}{32 d \left(-1+\sec \left(d x +c \right)\right)^{4}}+\frac{5 a^{2}}{48 d \left(-1+\sec \left(d x +c \right)\right)^{3}}-\frac{a^{2}}{4 d \left(-1+\sec \left(d x +c \right)\right)^{2}}+\frac{21 a^{2}}{32 d \left(-1+\sec \left(d x +c \right)\right)}+\frac{99 a^{2} \ln \left(-1+\sec \left(d x +c \right)\right)}{128 d}-\frac{a^{2}}{64 d \left(1+\sec \left(d x +c \right)\right)^{2}}-\frac{7 a^{2}}{64 d \left(1+\sec \left(d x +c \right)\right)}+\frac{29 a^{2} \ln \left(1+\sec \left(d x +c \right)\right)}{128 d}"," ",0,"-a^2/d*ln(sec(d*x+c))-1/32*a^2/d/(-1+sec(d*x+c))^4+5/48*a^2/d/(-1+sec(d*x+c))^3-1/4*a^2/d/(-1+sec(d*x+c))^2+21/32*a^2/d/(-1+sec(d*x+c))+99/128*a^2/d*ln(-1+sec(d*x+c))-1/64*a^2/d/(1+sec(d*x+c))^2-7/64*a^2/d/(1+sec(d*x+c))+29/128*a^2/d*ln(1+sec(d*x+c))","A"
29,1,226,147,0.540000," ","int((a+a*sec(d*x+c))^2*tan(d*x+c)^6,x)","\frac{a^{2} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}-\frac{a^{2} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \tan \left(d x +c \right)}{d}-a^{2} x -\frac{a^{2} c}{d}+\frac{a^{2} \left(\sin^{7}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{6}}-\frac{a^{2} \left(\sin^{7}\left(d x +c \right)\right)}{12 d \cos \left(d x +c \right)^{4}}+\frac{a^{2} \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{8 d}+\frac{5 a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{24 d}+\frac{5 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{a^{2} \left(\sin^{7}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{7}}"," ",0,"1/5*a^2*tan(d*x+c)^5/d-1/3*a^2*tan(d*x+c)^3/d+a^2*tan(d*x+c)/d-a^2*x-1/d*a^2*c+1/3/d*a^2*sin(d*x+c)^7/cos(d*x+c)^6-1/12/d*a^2*sin(d*x+c)^7/cos(d*x+c)^4+1/8/d*a^2*sin(d*x+c)^7/cos(d*x+c)^2+1/8*a^2*sin(d*x+c)^5/d+5/24*a^2*sin(d*x+c)^3/d+5/8*a^2*sin(d*x+c)/d-5/8/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/7/d*a^2*sin(d*x+c)^7/cos(d*x+c)^7","A"
30,1,169,109,0.519000," ","int((a+a*sec(d*x+c))^2*tan(d*x+c)^4,x)","\frac{a^{2} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} \tan \left(d x +c \right)}{d}+a^{2} x +\frac{a^{2} c}{d}+\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}-\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}-\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{2} \sin \left(d x +c \right)}{4 d}+\frac{3 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}"," ",0,"1/3*a^2*tan(d*x+c)^3/d-a^2*tan(d*x+c)/d+a^2*x+1/d*a^2*c+1/2/d*a^2*sin(d*x+c)^5/cos(d*x+c)^4-1/4/d*a^2*sin(d*x+c)^5/cos(d*x+c)^2-1/4*a^2*sin(d*x+c)^3/d-3/4*a^2*sin(d*x+c)/d+3/4/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/5/d*a^2*sin(d*x+c)^5/cos(d*x+c)^5","A"
31,1,112,70,0.493000," ","int((a+a*sec(d*x+c))^2*tan(d*x+c)^2,x)","-a^{2} x +\frac{a^{2} \tan \left(d x +c \right)}{d}-\frac{a^{2} c}{d}+\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{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}+\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}"," ",0,"-a^2*x+a^2*tan(d*x+c)/d-1/d*a^2*c+1/d*a^2*sin(d*x+c)^3/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))+1/3/d*a^2*sin(d*x+c)^3/cos(d*x+c)^3","A"
32,1,50,35,0.725000," ","int(cot(d*x+c)^2*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \left(-\cot \left(d x +c \right)-d x -c \right)-\frac{2 a^{2}}{\sin \left(d x +c \right)}-a^{2} \cot \left(d x +c \right)}{d}"," ",0,"1/d*(a^2*(-cot(d*x+c)-d*x-c)-2*a^2/sin(d*x+c)-a^2*cot(d*x+c))","A"
33,1,112,65,0.890000," ","int(cot(d*x+c)^4*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}+\cot \left(d x +c \right)+d x +c \right)+2 a^{2} \left(-\frac{\cos^{4}\left(d x +c \right)}{3 \sin \left(d x +c \right)^{3}}+\frac{\cos^{4}\left(d x +c \right)}{3 \sin \left(d x +c \right)}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}\right)-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 \sin \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(a^2*(-1/3*cot(d*x+c)^3+cot(d*x+c)+d*x+c)+2*a^2*(-1/3/sin(d*x+c)^3*cos(d*x+c)^4+1/3/sin(d*x+c)*cos(d*x+c)^4+1/3*(2+cos(d*x+c)^2)*sin(d*x+c))-1/3*a^2/sin(d*x+c)^3*cos(d*x+c)^3)","A"
34,1,155,99,1.038000," ","int(cot(d*x+c)^6*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\cot^{5}\left(d x +c \right)\right)}{5}+\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}-\cot \left(d x +c \right)-d x -c \right)+2 a^{2} \left(-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{15 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)}-\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)}{5}\right)-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5 \sin \left(d x +c \right)^{5}}}{d}"," ",0,"1/d*(a^2*(-1/5*cot(d*x+c)^5+1/3*cot(d*x+c)^3-cot(d*x+c)-d*x-c)+2*a^2*(-1/5/sin(d*x+c)^5*cos(d*x+c)^6+1/15/sin(d*x+c)^3*cos(d*x+c)^6-1/5/sin(d*x+c)*cos(d*x+c)^6-1/5*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/5*a^2/sin(d*x+c)^5*cos(d*x+c)^5)","A"
35,1,188,129,1.103000," ","int(cot(d*x+c)^8*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\cot^{7}\left(d x +c \right)\right)}{7}+\frac{\left(\cot^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}+\cot \left(d x +c \right)+d x +c \right)+2 a^{2} \left(-\frac{\cos^{8}\left(d x +c \right)}{7 \sin \left(d x +c \right)^{7}}+\frac{\cos^{8}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{5}}-\frac{\cos^{8}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{3}}+\frac{\cos^{8}\left(d x +c \right)}{7 \sin \left(d x +c \right)}+\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)}{7}\right)-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{7 \sin \left(d x +c \right)^{7}}}{d}"," ",0,"1/d*(a^2*(-1/7*cot(d*x+c)^7+1/5*cot(d*x+c)^5-1/3*cot(d*x+c)^3+cot(d*x+c)+d*x+c)+2*a^2*(-1/7/sin(d*x+c)^7*cos(d*x+c)^8+1/35/sin(d*x+c)^5*cos(d*x+c)^8-1/35/sin(d*x+c)^3*cos(d*x+c)^8+1/7/sin(d*x+c)*cos(d*x+c)^8+1/7*(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))-1/7*a^2/sin(d*x+c)^7*cos(d*x+c)^7)","A"
36,1,231,163,1.029000," ","int(cot(d*x+c)^10*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\cot^{9}\left(d x +c \right)\right)}{9}+\frac{\left(\cot^{7}\left(d x +c \right)\right)}{7}-\frac{\left(\cot^{5}\left(d x +c \right)\right)}{5}+\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}-\cot \left(d x +c \right)-d x -c \right)+2 a^{2} \left(-\frac{\cos^{10}\left(d x +c \right)}{9 \sin \left(d x +c \right)^{9}}+\frac{\cos^{10}\left(d x +c \right)}{63 \sin \left(d x +c \right)^{7}}-\frac{\cos^{10}\left(d x +c \right)}{105 \sin \left(d x +c \right)^{5}}+\frac{\cos^{10}\left(d x +c \right)}{63 \sin \left(d x +c \right)^{3}}-\frac{\cos^{10}\left(d x +c \right)}{9 \sin \left(d x +c \right)}-\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)}{9}\right)-\frac{a^{2} \left(\cos^{9}\left(d x +c \right)\right)}{9 \sin \left(d x +c \right)^{9}}}{d}"," ",0,"1/d*(a^2*(-1/9*cot(d*x+c)^9+1/7*cot(d*x+c)^7-1/5*cot(d*x+c)^5+1/3*cot(d*x+c)^3-cot(d*x+c)-d*x-c)+2*a^2*(-1/9/sin(d*x+c)^9*cos(d*x+c)^10+1/63/sin(d*x+c)^7*cos(d*x+c)^10-1/105/sin(d*x+c)^5*cos(d*x+c)^10+1/63/sin(d*x+c)^3*cos(d*x+c)^10-1/9/sin(d*x+c)*cos(d*x+c)^10-1/9*(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))-1/9*a^2/sin(d*x+c)^9*cos(d*x+c)^9)","A"
37,1,351,190,0.868000," ","int((a+a*sec(d*x+c))^3*tan(d*x+c)^9,x)","\frac{4352 a^{3} \cos \left(d x +c \right)}{3465 d}+\frac{34 a^{3} \left(\sin^{10}\left(d x +c \right)\right)}{99 d \cos \left(d x +c \right)^{9}}-\frac{34 a^{3} \left(\sin^{10}\left(d x +c \right)\right)}{693 d \cos \left(d x +c \right)^{7}}+\frac{34 a^{3} \left(\sin^{10}\left(d x +c \right)\right)}{1155 d \cos \left(d x +c \right)^{5}}-\frac{34 a^{3} \left(\sin^{10}\left(d x +c \right)\right)}{693 d \cos \left(d x +c \right)^{3}}+\frac{34 a^{3} \left(\sin^{10}\left(d x +c \right)\right)}{99 d \cos \left(d x +c \right)}+\frac{a^{3} \left(\sin^{10}\left(d x +c \right)\right)}{11 d \cos \left(d x +c \right)^{11}}+\frac{3 a^{3} \left(\sin^{10}\left(d x +c \right)\right)}{10 d \cos \left(d x +c \right)^{10}}+\frac{34 a^{3} \cos \left(d x +c \right) \left(\sin^{8}\left(d x +c \right)\right)}{99 d}+\frac{272 a^{3} \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{693 d}+\frac{544 a^{3} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{1155 d}+\frac{2176 a^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3465 d}+\frac{a^{3} \left(\tan^{8}\left(d x +c \right)\right)}{8 d}-\frac{a^{3} \left(\tan^{6}\left(d x +c \right)\right)}{6 d}+\frac{a^{3} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"4352/3465*a^3*cos(d*x+c)/d+34/99/d*a^3*sin(d*x+c)^10/cos(d*x+c)^9-34/693/d*a^3*sin(d*x+c)^10/cos(d*x+c)^7+34/1155/d*a^3*sin(d*x+c)^10/cos(d*x+c)^5-34/693/d*a^3*sin(d*x+c)^10/cos(d*x+c)^3+34/99/d*a^3*sin(d*x+c)^10/cos(d*x+c)+1/11/d*a^3*sin(d*x+c)^10/cos(d*x+c)^11+3/10/d*a^3*sin(d*x+c)^10/cos(d*x+c)^10+34/99/d*a^3*cos(d*x+c)*sin(d*x+c)^8+272/693/d*a^3*cos(d*x+c)*sin(d*x+c)^6+544/1155/d*a^3*cos(d*x+c)*sin(d*x+c)^4+2176/3465/d*a^3*cos(d*x+c)*sin(d*x+c)^2+1/8/d*a^3*tan(d*x+c)^8-1/6/d*a^3*tan(d*x+c)^6+1/4*a^3*tan(d*x+c)^4/d-1/2*a^3*tan(d*x+c)^2/d-a^3*ln(cos(d*x+c))/d","A"
38,1,288,125,0.806000," ","int((a+a*sec(d*x+c))^3*tan(d*x+c)^7,x)","\frac{a^{3} \left(\tan^{6}\left(d x +c \right)\right)}{6 d}-\frac{a^{3} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{4 a^{3} \left(\sin^{8}\left(d x +c \right)\right)}{9 d \cos \left(d x +c \right)^{7}}-\frac{4 a^{3} \left(\sin^{8}\left(d x +c \right)\right)}{45 d \cos \left(d x +c \right)^{5}}+\frac{4 a^{3} \left(\sin^{8}\left(d x +c \right)\right)}{45 d \cos \left(d x +c \right)^{3}}-\frac{4 a^{3} \left(\sin^{8}\left(d x +c \right)\right)}{9 d \cos \left(d x +c \right)}-\frac{64 a^{3} \cos \left(d x +c \right)}{45 d}-\frac{4 a^{3} \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{9 d}-\frac{8 a^{3} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{15 d}-\frac{32 a^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{45 d}+\frac{3 a^{3} \left(\sin^{8}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{8}}+\frac{a^{3} \left(\sin^{8}\left(d x +c \right)\right)}{9 d \cos \left(d x +c \right)^{9}}"," ",0,"1/6/d*a^3*tan(d*x+c)^6-1/4*a^3*tan(d*x+c)^4/d+1/2*a^3*tan(d*x+c)^2/d+a^3*ln(cos(d*x+c))/d+4/9/d*a^3*sin(d*x+c)^8/cos(d*x+c)^7-4/45/d*a^3*sin(d*x+c)^8/cos(d*x+c)^5+4/45/d*a^3*sin(d*x+c)^8/cos(d*x+c)^3-4/9/d*a^3*sin(d*x+c)^8/cos(d*x+c)-64/45*a^3*cos(d*x+c)/d-4/9/d*a^3*cos(d*x+c)*sin(d*x+c)^6-8/15/d*a^3*cos(d*x+c)*sin(d*x+c)^4-32/45/d*a^3*cos(d*x+c)*sin(d*x+c)^2+3/8/d*a^3*sin(d*x+c)^8/cos(d*x+c)^8+1/9/d*a^3*sin(d*x+c)^8/cos(d*x+c)^9","B"
39,1,227,126,0.792000," ","int((a+a*sec(d*x+c))^3*tan(d*x+c)^5,x)","\frac{a^{3} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{22 a^{3} \left(\sin^{6}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{5}}-\frac{22 a^{3} \left(\sin^{6}\left(d x +c \right)\right)}{105 d \cos \left(d x +c \right)^{3}}+\frac{22 a^{3} \left(\sin^{6}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)}+\frac{176 a^{3} \cos \left(d x +c \right)}{105 d}+\frac{22 a^{3} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{35 d}+\frac{88 a^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{105 d}+\frac{a^{3} \left(\sin^{6}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{6}}+\frac{a^{3} \left(\sin^{6}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{7}}"," ",0,"1/4*a^3*tan(d*x+c)^4/d-1/2*a^3*tan(d*x+c)^2/d-a^3*ln(cos(d*x+c))/d+22/35/d*a^3*sin(d*x+c)^6/cos(d*x+c)^5-22/105/d*a^3*sin(d*x+c)^6/cos(d*x+c)^3+22/35/d*a^3*sin(d*x+c)^6/cos(d*x+c)+176/105*a^3*cos(d*x+c)/d+22/35/d*a^3*cos(d*x+c)*sin(d*x+c)^4+88/105/d*a^3*cos(d*x+c)*sin(d*x+c)^2+1/2/d*a^3*sin(d*x+c)^6/cos(d*x+c)^6+1/7/d*a^3*sin(d*x+c)^6/cos(d*x+c)^7","A"
40,1,164,93,0.784000," ","int((a+a*sec(d*x+c))^3*tan(d*x+c)^3,x)","\frac{a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{16 a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{3}}-\frac{16 a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)}-\frac{16 a^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}-\frac{32 a^{3} \cos \left(d x +c \right)}{15 d}+\frac{3 a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}"," ",0,"1/2*a^3*tan(d*x+c)^2/d+a^3*ln(cos(d*x+c))/d+16/15/d*a^3*sin(d*x+c)^4/cos(d*x+c)^3-16/15/d*a^3*sin(d*x+c)^4/cos(d*x+c)-16/15/d*a^3*cos(d*x+c)*sin(d*x+c)^2-32/15*a^3*cos(d*x+c)/d+3/4/d*a^3*sin(d*x+c)^4/cos(d*x+c)^4+1/5/d*a^3*sin(d*x+c)^4/cos(d*x+c)^5","A"
41,1,62,62,0.304000," ","int((a+a*sec(d*x+c))^3*tan(d*x+c),x)","\frac{a^{3} \left(\sec^{3}\left(d x +c \right)\right)}{3 d}+\frac{3 a^{3} \left(\sec^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a^{3} \sec \left(d x +c \right)}{d}+\frac{a^{3} \ln \left(\sec \left(d x +c \right)\right)}{d}"," ",0,"1/3*a^3*sec(d*x+c)^3/d+3/2*a^3*sec(d*x+c)^2/d+3*a^3*sec(d*x+c)/d+a^3/d*ln(sec(d*x+c))","A"
42,1,47,48,0.514000," ","int(cot(d*x+c)*(a+a*sec(d*x+c))^3,x)","\frac{a^{3} \sec \left(d x +c \right)}{d}-\frac{a^{3} \ln \left(\sec \left(d x +c \right)\right)}{d}+\frac{4 a^{3} \ln \left(-1+\sec \left(d x +c \right)\right)}{d}"," ",0,"a^3*sec(d*x+c)/d-a^3/d*ln(sec(d*x+c))+4*a^3/d*ln(-1+sec(d*x+c))","A"
43,1,51,40,0.728000," ","int(cot(d*x+c)^3*(a+a*sec(d*x+c))^3,x)","\frac{a^{3} \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{2 a^{3}}{d \left(-1+\sec \left(d x +c \right)\right)}-\frac{a^{3} \ln \left(-1+\sec \left(d x +c \right)\right)}{d}"," ",0,"a^3/d*ln(sec(d*x+c))-2*a^3/d/(-1+sec(d*x+c))-a^3/d*ln(-1+sec(d*x+c))","A"
44,1,68,59,0.617000," ","int(cot(d*x+c)^5*(a+a*sec(d*x+c))^3,x)","-\frac{a^{3} \ln \left(\sec \left(d x +c \right)\right)}{d}+\frac{a^{3}}{d \left(-1+\sec \left(d x +c \right)\right)}-\frac{a^{3}}{2 d \left(-1+\sec \left(d x +c \right)\right)^{2}}+\frac{a^{3} \ln \left(-1+\sec \left(d x +c \right)\right)}{d}"," ",0,"-a^3/d*ln(sec(d*x+c))+a^3/d/(-1+sec(d*x+c))-1/2*a^3/d/(-1+sec(d*x+c))^2+a^3/d*ln(-1+sec(d*x+c))","A"
45,1,104,97,0.625000," ","int(cot(d*x+c)^7*(a+a*sec(d*x+c))^3,x)","\frac{a^{3} \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a^{3}}{6 d \left(-1+\sec \left(d x +c \right)\right)^{3}}+\frac{3 a^{3}}{8 d \left(-1+\sec \left(d x +c \right)\right)^{2}}-\frac{7 a^{3}}{8 d \left(-1+\sec \left(d x +c \right)\right)}-\frac{15 a^{3} \ln \left(-1+\sec \left(d x +c \right)\right)}{16 d}-\frac{a^{3} \ln \left(1+\sec \left(d x +c \right)\right)}{16 d}"," ",0,"a^3/d*ln(sec(d*x+c))-1/6*a^3/d/(-1+sec(d*x+c))^3+3/8*a^3/d/(-1+sec(d*x+c))^2-7/8*a^3/d/(-1+sec(d*x+c))-15/16*a^3/d*ln(-1+sec(d*x+c))-1/16*a^3/d*ln(1+sec(d*x+c))","A"
46,1,141,135,0.750000," ","int(cot(d*x+c)^9*(a+a*sec(d*x+c))^3,x)","-\frac{a^{3} \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a^{3}}{16 d \left(-1+\sec \left(d x +c \right)\right)^{4}}+\frac{a^{3}}{6 d \left(-1+\sec \left(d x +c \right)\right)^{3}}-\frac{11 a^{3}}{32 d \left(-1+\sec \left(d x +c \right)\right)^{2}}+\frac{13 a^{3}}{16 d \left(-1+\sec \left(d x +c \right)\right)}+\frac{57 a^{3} \ln \left(-1+\sec \left(d x +c \right)\right)}{64 d}-\frac{a^{3}}{32 d \left(1+\sec \left(d x +c \right)\right)}+\frac{7 a^{3} \ln \left(1+\sec \left(d x +c \right)\right)}{64 d}"," ",0,"-a^3/d*ln(sec(d*x+c))-1/16*a^3/d/(-1+sec(d*x+c))^4+1/6*a^3/d/(-1+sec(d*x+c))^3-11/32*a^3/d/(-1+sec(d*x+c))^2+13/16*a^3/d/(-1+sec(d*x+c))+57/64*a^3/d*ln(-1+sec(d*x+c))-1/32*a^3/d/(1+sec(d*x+c))+7/64*a^3/d*ln(1+sec(d*x+c))","A"
47,1,250,217,0.585000," ","int((a+a*sec(d*x+c))^3*tan(d*x+c)^6,x)","\frac{a^{3} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}-\frac{a^{3} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{3} \tan \left(d x +c \right)}{d}-a^{3} x -\frac{a^{3} c}{d}+\frac{25 a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{48 d \cos \left(d x +c \right)^{6}}-\frac{25 a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{192 d \cos \left(d x +c \right)^{4}}+\frac{25 a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{128 d \cos \left(d x +c \right)^{2}}+\frac{25 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{128 d}+\frac{125 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{384 d}+\frac{125 a^{3} \sin \left(d x +c \right)}{128 d}-\frac{125 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{128 d}+\frac{3 a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{7}}+\frac{a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{8}}"," ",0,"1/5*a^3*tan(d*x+c)^5/d-1/3*a^3*tan(d*x+c)^3/d+a^3*tan(d*x+c)/d-a^3*x-1/d*a^3*c+25/48/d*a^3*sin(d*x+c)^7/cos(d*x+c)^6-25/192/d*a^3*sin(d*x+c)^7/cos(d*x+c)^4+25/128/d*a^3*sin(d*x+c)^7/cos(d*x+c)^2+25/128*a^3*sin(d*x+c)^5/d+125/384*a^3*sin(d*x+c)^3/d+125/128*a^3*sin(d*x+c)/d-125/128/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/7/d*a^3*sin(d*x+c)^7/cos(d*x+c)^7+1/8/d*a^3*sin(d*x+c)^7/cos(d*x+c)^8","A"
48,1,193,155,0.568000," ","int((a+a*sec(d*x+c))^3*tan(d*x+c)^4,x)","\frac{a^{3} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{3} \tan \left(d x +c \right)}{d}+a^{3} x +\frac{a^{3} c}{d}+\frac{19 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{24 d \cos \left(d x +c \right)^{4}}-\frac{19 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{48 d \cos \left(d x +c \right)^{2}}-\frac{19 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{48 d}-\frac{19 a^{3} \sin \left(d x +c \right)}{16 d}+\frac{19 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{3 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}+\frac{a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}"," ",0,"1/3*a^3*tan(d*x+c)^3/d-a^3*tan(d*x+c)/d+a^3*x+1/d*a^3*c+19/24/d*a^3*sin(d*x+c)^5/cos(d*x+c)^4-19/48/d*a^3*sin(d*x+c)^5/cos(d*x+c)^2-19/48*a^3*sin(d*x+c)^3/d-19/16*a^3*sin(d*x+c)/d+19/16/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/5/d*a^3*sin(d*x+c)^5/cos(d*x+c)^5+1/6/d*a^3*sin(d*x+c)^5/cos(d*x+c)^6","A"
49,1,137,92,0.544000," ","int((a+a*sec(d*x+c))^3*tan(d*x+c)^2,x)","-a^{3} x +\frac{a^{3} \tan \left(d x +c \right)}{d}-\frac{a^{3} c}{d}+\frac{13 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{13 a^{3} \sin \left(d x +c \right)}{8 d}-\frac{13 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{3}}+\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"-a^3*x+a^3*tan(d*x+c)/d-1/d*a^3*c+13/8/d*a^3*sin(d*x+c)^3/cos(d*x+c)^2+13/8*a^3*sin(d*x+c)/d-13/8/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^3*sin(d*x+c)^3/cos(d*x+c)^3+1/4/d*a^3*sin(d*x+c)^3/cos(d*x+c)^4","A"
50,1,68,49,0.833000," ","int(cot(d*x+c)^2*(a+a*sec(d*x+c))^3,x)","-a^{3} x -\frac{4 a^{3} \cot \left(d x +c \right)}{d}-\frac{a^{3} c}{d}-\frac{4 a^{3}}{d \sin \left(d x +c \right)}+\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-a^3*x-4*a^3*cot(d*x+c)/d-1/d*a^3*c-4/d*a^3/sin(d*x+c)+1/d*a^3*ln(sec(d*x+c)+tan(d*x+c))","A"
51,1,125,65,0.854000," ","int(cot(d*x+c)^4*(a+a*sec(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}+\cot \left(d x +c \right)+d x +c \right)+3 a^{3} \left(-\frac{\cos^{4}\left(d x +c \right)}{3 \sin \left(d x +c \right)^{3}}+\frac{\cos^{4}\left(d x +c \right)}{3 \sin \left(d x +c \right)}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}\right)-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{\sin \left(d x +c \right)^{3}}-\frac{a^{3}}{3 \sin \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(a^3*(-1/3*cot(d*x+c)^3+cot(d*x+c)+d*x+c)+3*a^3*(-1/3/sin(d*x+c)^3*cos(d*x+c)^4+1/3/sin(d*x+c)*cos(d*x+c)^4+1/3*(2+cos(d*x+c)^2)*sin(d*x+c))-a^3/sin(d*x+c)^3*cos(d*x+c)^3-1/3*a^3/sin(d*x+c)^3)","A"
52,1,232,99,1.066000," ","int(cot(d*x+c)^6*(a+a*sec(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\cot^{5}\left(d x +c \right)\right)}{5}+\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}-\cot \left(d x +c \right)-d x -c \right)+3 a^{3} \left(-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{15 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)}-\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)}{5}\right)-\frac{3 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5 \sin \left(d x +c \right)^{5}}+a^{3} \left(-\frac{\cos^{4}\left(d x +c \right)}{5 \sin \left(d x +c \right)^{5}}-\frac{\cos^{4}\left(d x +c \right)}{15 \sin \left(d x +c \right)^{3}}+\frac{\cos^{4}\left(d x +c \right)}{15 \sin \left(d x +c \right)}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)}{d}"," ",0,"1/d*(a^3*(-1/5*cot(d*x+c)^5+1/3*cot(d*x+c)^3-cot(d*x+c)-d*x-c)+3*a^3*(-1/5/sin(d*x+c)^5*cos(d*x+c)^6+1/15/sin(d*x+c)^3*cos(d*x+c)^6-1/5/sin(d*x+c)*cos(d*x+c)^6-1/5*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-3/5*a^3/sin(d*x+c)^5*cos(d*x+c)^5+a^3*(-1/5/sin(d*x+c)^5*cos(d*x+c)^4-1/15/sin(d*x+c)^3*cos(d*x+c)^4+1/15/sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c)))","B"
53,1,293,129,1.183000," ","int(cot(d*x+c)^8*(a+a*sec(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\cot^{7}\left(d x +c \right)\right)}{7}+\frac{\left(\cot^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}+\cot \left(d x +c \right)+d x +c \right)+3 a^{3} \left(-\frac{\cos^{8}\left(d x +c \right)}{7 \sin \left(d x +c \right)^{7}}+\frac{\cos^{8}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{5}}-\frac{\cos^{8}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{3}}+\frac{\cos^{8}\left(d x +c \right)}{7 \sin \left(d x +c \right)}+\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)}{7}\right)-\frac{3 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{7 \sin \left(d x +c \right)^{7}}+a^{3} \left(-\frac{\cos^{6}\left(d x +c \right)}{7 \sin \left(d x +c \right)^{7}}-\frac{\cos^{6}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{35 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)}{d}"," ",0,"1/d*(a^3*(-1/7*cot(d*x+c)^7+1/5*cot(d*x+c)^5-1/3*cot(d*x+c)^3+cot(d*x+c)+d*x+c)+3*a^3*(-1/7/sin(d*x+c)^7*cos(d*x+c)^8+1/35/sin(d*x+c)^5*cos(d*x+c)^8-1/35/sin(d*x+c)^3*cos(d*x+c)^8+1/7/sin(d*x+c)*cos(d*x+c)^8+1/7*(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))-3/7*a^3/sin(d*x+c)^7*cos(d*x+c)^7+a^3*(-1/7/sin(d*x+c)^7*cos(d*x+c)^6-1/35/sin(d*x+c)^5*cos(d*x+c)^6+1/105/sin(d*x+c)^3*cos(d*x+c)^6-1/35/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)))","B"
54,1,364,163,1.204000," ","int(cot(d*x+c)^10*(a+a*sec(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\cot^{9}\left(d x +c \right)\right)}{9}+\frac{\left(\cot^{7}\left(d x +c \right)\right)}{7}-\frac{\left(\cot^{5}\left(d x +c \right)\right)}{5}+\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}-\cot \left(d x +c \right)-d x -c \right)+3 a^{3} \left(-\frac{\cos^{10}\left(d x +c \right)}{9 \sin \left(d x +c \right)^{9}}+\frac{\cos^{10}\left(d x +c \right)}{63 \sin \left(d x +c \right)^{7}}-\frac{\cos^{10}\left(d x +c \right)}{105 \sin \left(d x +c \right)^{5}}+\frac{\cos^{10}\left(d x +c \right)}{63 \sin \left(d x +c \right)^{3}}-\frac{\cos^{10}\left(d x +c \right)}{9 \sin \left(d x +c \right)}-\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)}{9}\right)-\frac{a^{3} \left(\cos^{9}\left(d x +c \right)\right)}{3 \sin \left(d x +c \right)^{9}}+a^{3} \left(-\frac{\cos^{8}\left(d x +c \right)}{9 \sin \left(d x +c \right)^{9}}-\frac{\cos^{8}\left(d x +c \right)}{63 \sin \left(d x +c \right)^{7}}+\frac{\cos^{8}\left(d x +c \right)}{315 \sin \left(d x +c \right)^{5}}-\frac{\cos^{8}\left(d x +c \right)}{315 \sin \left(d x +c \right)^{3}}+\frac{\cos^{8}\left(d x +c \right)}{63 \sin \left(d x +c \right)}+\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)}{d}"," ",0,"1/d*(a^3*(-1/9*cot(d*x+c)^9+1/7*cot(d*x+c)^7-1/5*cot(d*x+c)^5+1/3*cot(d*x+c)^3-cot(d*x+c)-d*x-c)+3*a^3*(-1/9/sin(d*x+c)^9*cos(d*x+c)^10+1/63/sin(d*x+c)^7*cos(d*x+c)^10-1/105/sin(d*x+c)^5*cos(d*x+c)^10+1/63/sin(d*x+c)^3*cos(d*x+c)^10-1/9/sin(d*x+c)*cos(d*x+c)^10-1/9*(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))-1/3*a^3/sin(d*x+c)^9*cos(d*x+c)^9+a^3*(-1/9/sin(d*x+c)^9*cos(d*x+c)^8-1/63/sin(d*x+c)^7*cos(d*x+c)^8+1/315/sin(d*x+c)^5*cos(d*x+c)^8-1/315/sin(d*x+c)^3*cos(d*x+c)^8+1/63/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)))","B"
55,1,425,193,1.273000," ","int(cot(d*x+c)^12*(a+a*sec(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\cot^{11}\left(d x +c \right)\right)}{11}+\frac{\left(\cot^{9}\left(d x +c \right)\right)}{9}-\frac{\left(\cot^{7}\left(d x +c \right)\right)}{7}+\frac{\left(\cot^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}+\cot \left(d x +c \right)+d x +c \right)+3 a^{3} \left(-\frac{\cos^{12}\left(d x +c \right)}{11 \sin \left(d x +c \right)^{11}}+\frac{\cos^{12}\left(d x +c \right)}{99 \sin \left(d x +c \right)^{9}}-\frac{\cos^{12}\left(d x +c \right)}{231 \sin \left(d x +c \right)^{7}}+\frac{\cos^{12}\left(d x +c \right)}{231 \sin \left(d x +c \right)^{5}}-\frac{\cos^{12}\left(d x +c \right)}{99 \sin \left(d x +c \right)^{3}}+\frac{\cos^{12}\left(d x +c \right)}{11 \sin \left(d x +c \right)}+\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)}{11}\right)-\frac{3 a^{3} \left(\cos^{11}\left(d x +c \right)\right)}{11 \sin \left(d x +c \right)^{11}}+a^{3} \left(-\frac{\cos^{10}\left(d x +c \right)}{11 \sin \left(d x +c \right)^{11}}-\frac{\cos^{10}\left(d x +c \right)}{99 \sin \left(d x +c \right)^{9}}+\frac{\cos^{10}\left(d x +c \right)}{693 \sin \left(d x +c \right)^{7}}-\frac{\cos^{10}\left(d x +c \right)}{1155 \sin \left(d x +c \right)^{5}}+\frac{\cos^{10}\left(d x +c \right)}{693 \sin \left(d x +c \right)^{3}}-\frac{\cos^{10}\left(d x +c \right)}{99 \sin \left(d x +c \right)}-\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)}{d}"," ",0,"1/d*(a^3*(-1/11*cot(d*x+c)^11+1/9*cot(d*x+c)^9-1/7*cot(d*x+c)^7+1/5*cot(d*x+c)^5-1/3*cot(d*x+c)^3+cot(d*x+c)+d*x+c)+3*a^3*(-1/11/sin(d*x+c)^11*cos(d*x+c)^12+1/99/sin(d*x+c)^9*cos(d*x+c)^12-1/231/sin(d*x+c)^7*cos(d*x+c)^12+1/231/sin(d*x+c)^5*cos(d*x+c)^12-1/99/sin(d*x+c)^3*cos(d*x+c)^12+1/11/sin(d*x+c)*cos(d*x+c)^12+1/11*(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))-3/11*a^3/sin(d*x+c)^11*cos(d*x+c)^11+a^3*(-1/11/sin(d*x+c)^11*cos(d*x+c)^10-1/99/sin(d*x+c)^9*cos(d*x+c)^10+1/693/sin(d*x+c)^7*cos(d*x+c)^10-1/1155/sin(d*x+c)^5*cos(d*x+c)^10+1/693/sin(d*x+c)^3*cos(d*x+c)^10-1/99/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)))","B"
56,1,125,125,0.626000," ","int(tan(d*x+c)^9/(a+a*sec(d*x+c)),x)","\frac{\sec^{7}\left(d x +c \right)}{7 d a}-\frac{\sec^{6}\left(d x +c \right)}{6 d a}-\frac{3 \left(\sec^{5}\left(d x +c \right)\right)}{5 d a}+\frac{3 \left(\sec^{4}\left(d x +c \right)\right)}{4 d a}+\frac{\sec^{3}\left(d x +c \right)}{d a}-\frac{3 \left(\sec^{2}\left(d x +c \right)\right)}{2 d a}-\frac{\sec \left(d x +c \right)}{d a}+\frac{\ln \left(\sec \left(d x +c \right)\right)}{a d}"," ",0,"1/7*sec(d*x+c)^7/d/a-1/6*sec(d*x+c)^6/d/a-3/5*sec(d*x+c)^5/d/a+3/4*sec(d*x+c)^4/d/a+sec(d*x+c)^3/d/a-3/2*sec(d*x+c)^2/d/a-sec(d*x+c)/d/a+1/a/d*ln(sec(d*x+c))","A"
57,1,93,91,0.558000," ","int(tan(d*x+c)^7/(a+a*sec(d*x+c)),x)","\frac{\sec^{5}\left(d x +c \right)}{5 d a}-\frac{\sec^{4}\left(d x +c \right)}{4 d a}-\frac{2 \left(\sec^{3}\left(d x +c \right)\right)}{3 d a}+\frac{\sec^{2}\left(d x +c \right)}{d a}+\frac{\sec \left(d x +c \right)}{d a}-\frac{\ln \left(\sec \left(d x +c \right)\right)}{a d}"," ",0,"1/5*sec(d*x+c)^5/d/a-1/4*sec(d*x+c)^4/d/a-2/3*sec(d*x+c)^3/d/a+sec(d*x+c)^2/d/a+sec(d*x+c)/d/a-1/a/d*ln(sec(d*x+c))","A"
58,1,62,62,0.536000," ","int(tan(d*x+c)^5/(a+a*sec(d*x+c)),x)","\frac{\sec^{3}\left(d x +c \right)}{3 d a}-\frac{\sec^{2}\left(d x +c \right)}{2 d a}-\frac{\sec \left(d x +c \right)}{d a}+\frac{\ln \left(\sec \left(d x +c \right)\right)}{a d}"," ",0,"1/3*sec(d*x+c)^3/d/a-1/2*sec(d*x+c)^2/d/a-sec(d*x+c)/d/a+1/a/d*ln(sec(d*x+c))","A"
59,1,30,28,0.313000," ","int(tan(d*x+c)^3/(a+a*sec(d*x+c)),x)","\frac{\sec \left(d x +c \right)}{d a}-\frac{\ln \left(\sec \left(d x +c \right)\right)}{a d}"," ",0,"sec(d*x+c)/d/a-1/a/d*ln(sec(d*x+c))","A"
60,1,33,17,0.115000," ","int(tan(d*x+c)/(a+a*sec(d*x+c)),x)","\frac{\ln \left(\sec \left(d x +c \right)\right)}{a d}-\frac{\ln \left(1+\sec \left(d x +c \right)\right)}{d a}"," ",0,"1/a/d*ln(sec(d*x+c))-1/d/a*ln(1+sec(d*x+c))","A"
61,1,54,55,0.613000," ","int(cot(d*x+c)/(a+a*sec(d*x+c)),x)","\frac{\ln \left(-1+\cos \left(d x +c \right)\right)}{4 d a}+\frac{1}{2 a d \left(1+\cos \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\cos \left(d x +c \right)\right)}{4 d a}"," ",0,"1/4/d/a*ln(-1+cos(d*x+c))+1/2/a/d/(1+cos(d*x+c))+3/4*ln(1+cos(d*x+c))/d/a","A"
62,1,90,93,0.805000," ","int(cot(d*x+c)^3/(a+a*sec(d*x+c)),x)","\frac{1}{8 a d \left(-1+\cos \left(d x +c \right)\right)}-\frac{5 \ln \left(-1+\cos \left(d x +c \right)\right)}{16 d a}+\frac{1}{8 a d \left(1+\cos \left(d x +c \right)\right)^{2}}-\frac{3}{4 a d \left(1+\cos \left(d x +c \right)\right)}-\frac{11 \ln \left(1+\cos \left(d x +c \right)\right)}{16 d a}"," ",0,"1/8/a/d/(-1+cos(d*x+c))-5/16/d/a*ln(-1+cos(d*x+c))+1/8/a/d/(1+cos(d*x+c))^2-3/4/a/d/(1+cos(d*x+c))-11/16*ln(1+cos(d*x+c))/d/a","A"
63,1,126,131,0.690000," ","int(cot(d*x+c)^5/(a+a*sec(d*x+c)),x)","-\frac{1}{32 a d \left(-1+\cos \left(d x +c \right)\right)^{2}}-\frac{1}{4 a d \left(-1+\cos \left(d x +c \right)\right)}+\frac{11 \ln \left(-1+\cos \left(d x +c \right)\right)}{32 d a}+\frac{1}{24 a d \left(1+\cos \left(d x +c \right)\right)^{3}}-\frac{9}{32 a d \left(1+\cos \left(d x +c \right)\right)^{2}}+\frac{15}{16 a d \left(1+\cos \left(d x +c \right)\right)}+\frac{21 \ln \left(1+\cos \left(d x +c \right)\right)}{32 d a}"," ",0,"-1/32/a/d/(-1+cos(d*x+c))^2-1/4/a/d/(-1+cos(d*x+c))+11/32/d/a*ln(-1+cos(d*x+c))+1/24/a/d/(1+cos(d*x+c))^3-9/32/a/d/(1+cos(d*x+c))^2+15/16/a/d/(1+cos(d*x+c))+21/32*ln(1+cos(d*x+c))/d/a","A"
64,1,312,97,0.538000," ","int(tan(d*x+c)^8/(a+a*sec(d*x+c)),x)","\frac{1}{6 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{6}}+\frac{7}{10 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{5}}+\frac{3}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}-\frac{5}{12 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{9}{16 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{21}{16 a 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)}{16 a d}-\frac{1}{6 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{7}{10 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{3}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{5}{12 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{9}{16 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{21}{16 a 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)}{16 a d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"1/6/a/d/(tan(1/2*d*x+1/2*c)-1)^6+7/10/a/d/(tan(1/2*d*x+1/2*c)-1)^5+3/4/a/d/(tan(1/2*d*x+1/2*c)-1)^4-5/12/a/d/(tan(1/2*d*x+1/2*c)-1)^3-9/16/a/d/(tan(1/2*d*x+1/2*c)-1)^2+21/16/a/d/(tan(1/2*d*x+1/2*c)-1)+5/16/a/d*ln(tan(1/2*d*x+1/2*c)-1)-1/6/a/d/(tan(1/2*d*x+1/2*c)+1)^6+7/10/a/d/(tan(1/2*d*x+1/2*c)+1)^5-3/4/a/d/(tan(1/2*d*x+1/2*c)+1)^4-5/12/a/d/(tan(1/2*d*x+1/2*c)+1)^3+9/16/a/d/(tan(1/2*d*x+1/2*c)+1)^2+21/16/a/d/(tan(1/2*d*x+1/2*c)+1)-5/16/a/d*ln(tan(1/2*d*x+1/2*c)+1)+2/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
65,1,228,72,0.530000," ","int(tan(d*x+c)^6/(a+a*sec(d*x+c)),x)","\frac{1}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{5}{6 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{3}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{11}{8 a 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)}{8 a d}-\frac{1}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{5}{6 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{3}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{11}{8 a 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)}{8 a d}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"1/4/a/d/(tan(1/2*d*x+1/2*c)-1)^4+5/6/a/d/(tan(1/2*d*x+1/2*c)-1)^3+3/8/a/d/(tan(1/2*d*x+1/2*c)-1)^2-11/8/a/d/(tan(1/2*d*x+1/2*c)-1)-3/8/a/d*ln(tan(1/2*d*x+1/2*c)-1)-1/4/a/d/(tan(1/2*d*x+1/2*c)+1)^4+5/6/a/d/(tan(1/2*d*x+1/2*c)+1)^3-3/8/a/d/(tan(1/2*d*x+1/2*c)+1)^2-11/8/a/d/(tan(1/2*d*x+1/2*c)+1)+3/8/a/d*ln(tan(1/2*d*x+1/2*c)+1)-2/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
66,1,144,45,0.499000," ","int(tan(d*x+c)^4/(a+a*sec(d*x+c)),x)","\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{3}{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{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{3}{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{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"1/2/a/d/(tan(1/2*d*x+1/2*c)-1)^2+3/2/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)-1/2/a/d/(tan(1/2*d*x+1/2*c)+1)^2+3/2/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)+2/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
67,1,59,21,0.324000," ","int(tan(d*x+c)^2/(a+a*sec(d*x+c)),x)","-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a d}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"-1/a/d*ln(tan(1/2*d*x+1/2*c)-1)+1/a/d*ln(tan(1/2*d*x+1/2*c)+1)-2/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
68,1,74,57,0.616000," ","int(cot(d*x+c)^2/(a+a*sec(d*x+c)),x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{12 a d}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{1}{4 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"-1/12/a/d*tan(1/2*d*x+1/2*c)^3+1/a/d*tan(1/2*d*x+1/2*c)-1/4/a/d/tan(1/2*d*x+1/2*c)-2/a/d*arctan(tan(1/2*d*x+1/2*c))","A"
69,1,113,82,0.659000," ","int(cot(d*x+c)^4/(a+a*sec(d*x+c)),x)","-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{80 a d}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{1}{48 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{3}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"-1/80/a/d*tan(1/2*d*x+1/2*c)^5+1/8/a/d*tan(1/2*d*x+1/2*c)^3-1/a/d*tan(1/2*d*x+1/2*c)-1/48/a/d/tan(1/2*d*x+1/2*c)^3+3/8/a/d/tan(1/2*d*x+1/2*c)+2/a/d*arctan(tan(1/2*d*x+1/2*c))","A"
70,1,150,109,0.771000," ","int(cot(d*x+c)^6/(a+a*sec(d*x+c)),x)","-\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{448 a d}+\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{40 a d}-\frac{29 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 a d}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{1}{320 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{24 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{29}{64 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"-1/448/a/d*tan(1/2*d*x+1/2*c)^7+1/40/a/d*tan(1/2*d*x+1/2*c)^5-29/192/a/d*tan(1/2*d*x+1/2*c)^3+1/a/d*tan(1/2*d*x+1/2*c)-1/320/a/d/tan(1/2*d*x+1/2*c)^5+1/24/a/d/tan(1/2*d*x+1/2*c)^3-29/64/a/d/tan(1/2*d*x+1/2*c)-2/a/d*arctan(tan(1/2*d*x+1/2*c))","A"
71,1,110,110,0.627000," ","int(tan(d*x+c)^9/(a+a*sec(d*x+c))^2,x)","\frac{\sec^{6}\left(d x +c \right)}{6 a^{2} d}-\frac{2 \left(\sec^{5}\left(d x +c \right)\right)}{5 a^{2} d}-\frac{\sec^{4}\left(d x +c \right)}{4 a^{2} d}+\frac{4 \left(\sec^{3}\left(d x +c \right)\right)}{3 a^{2} d}-\frac{\sec^{2}\left(d x +c \right)}{2 a^{2} d}-\frac{2 \sec \left(d x +c \right)}{a^{2} d}+\frac{\ln \left(\sec \left(d x +c \right)\right)}{a^{2} d}"," ",0,"1/6*sec(d*x+c)^6/a^2/d-2/5*sec(d*x+c)^5/a^2/d-1/4*sec(d*x+c)^4/a^2/d+4/3*sec(d*x+c)^3/a^2/d-1/2*sec(d*x+c)^2/a^2/d-2*sec(d*x+c)/a^2/d+1/a^2/d*ln(sec(d*x+c))","A"
72,1,63,61,0.605000," ","int(tan(d*x+c)^7/(a+a*sec(d*x+c))^2,x)","\frac{\sec^{4}\left(d x +c \right)}{4 a^{2} d}-\frac{2 \left(\sec^{3}\left(d x +c \right)\right)}{3 a^{2} d}+\frac{2 \sec \left(d x +c \right)}{a^{2} d}-\frac{\ln \left(\sec \left(d x +c \right)\right)}{a^{2} d}"," ",0,"1/4*sec(d*x+c)^4/a^2/d-2/3*sec(d*x+c)^3/a^2/d+2*sec(d*x+c)/a^2/d-1/a^2/d*ln(sec(d*x+c))","A"
73,1,46,46,0.545000," ","int(tan(d*x+c)^5/(a+a*sec(d*x+c))^2,x)","\frac{\sec^{2}\left(d x +c \right)}{2 a^{2} d}-\frac{2 \sec \left(d x +c \right)}{a^{2} d}+\frac{\ln \left(\sec \left(d x +c \right)\right)}{a^{2} d}"," ",0,"1/2*sec(d*x+c)^2/a^2/d-2*sec(d*x+c)/a^2/d+1/a^2/d*ln(sec(d*x+c))","A"
74,1,34,33,0.515000," ","int(tan(d*x+c)^3/(a+a*sec(d*x+c))^2,x)","-\frac{\ln \left(\sec \left(d x +c \right)\right)}{a^{2} d}+\frac{2 \ln \left(1+\sec \left(d x +c \right)\right)}{a^{2} d}"," ",0,"-1/a^2/d*ln(sec(d*x+c))+2/a^2/d*ln(1+sec(d*x+c))","A"
75,1,50,36,0.189000," ","int(tan(d*x+c)/(a+a*sec(d*x+c))^2,x)","\frac{\ln \left(\sec \left(d x +c \right)\right)}{a^{2} d}+\frac{1}{a^{2} d \left(1+\sec \left(d x +c \right)\right)}-\frac{\ln \left(1+\sec \left(d x +c \right)\right)}{a^{2} d}"," ",0,"1/a^2/d*ln(sec(d*x+c))+1/a^2/d/(1+sec(d*x+c))-1/a^2/d*ln(1+sec(d*x+c))","A"
76,1,72,73,0.699000," ","int(cot(d*x+c)/(a+a*sec(d*x+c))^2,x)","\frac{\ln \left(-1+\cos \left(d x +c \right)\right)}{8 a^{2} d}-\frac{1}{4 a^{2} d \left(1+\cos \left(d x +c \right)\right)^{2}}+\frac{5}{4 a^{2} d \left(1+\cos \left(d x +c \right)\right)}+\frac{7 \ln \left(1+\cos \left(d x +c \right)\right)}{8 a^{2} d}"," ",0,"1/8/a^2/d*ln(-1+cos(d*x+c))-1/4/a^2/d/(1+cos(d*x+c))^2+5/4/a^2/d/(1+cos(d*x+c))+7/8*ln(1+cos(d*x+c))/a^2/d","A"
77,1,108,111,0.936000," ","int(cot(d*x+c)^3/(a+a*sec(d*x+c))^2,x)","\frac{1}{16 a^{2} d \left(-1+\cos \left(d x +c \right)\right)}-\frac{3 \ln \left(-1+\cos \left(d x +c \right)\right)}{16 a^{2} d}-\frac{1}{12 a^{2} d \left(1+\cos \left(d x +c \right)\right)^{3}}+\frac{1}{2 a^{2} d \left(1+\cos \left(d x +c \right)\right)^{2}}-\frac{23}{16 a^{2} d \left(1+\cos \left(d x +c \right)\right)}-\frac{13 \ln \left(1+\cos \left(d x +c \right)\right)}{16 a^{2} d}"," ",0,"1/16/a^2/d/(-1+cos(d*x+c))-3/16/a^2/d*ln(-1+cos(d*x+c))-1/12/a^2/d/(1+cos(d*x+c))^3+1/2/a^2/d/(1+cos(d*x+c))^2-23/16/a^2/d/(1+cos(d*x+c))-13/16*ln(1+cos(d*x+c))/a^2/d","A"
78,1,144,149,1.016000," ","int(cot(d*x+c)^5/(a+a*sec(d*x+c))^2,x)","-\frac{1}{64 a^{2} d \left(-1+\cos \left(d x +c \right)\right)^{2}}-\frac{9}{64 a^{2} d \left(-1+\cos \left(d x +c \right)\right)}+\frac{29 \ln \left(-1+\cos \left(d x +c \right)\right)}{128 a^{2} d}-\frac{1}{32 a^{2} d \left(1+\cos \left(d x +c \right)\right)^{4}}+\frac{11}{48 a^{2} d \left(1+\cos \left(d x +c \right)\right)^{3}}-\frac{3}{4 a^{2} d \left(1+\cos \left(d x +c \right)\right)^{2}}+\frac{51}{32 a^{2} d \left(1+\cos \left(d x +c \right)\right)}+\frac{99 \ln \left(1+\cos \left(d x +c \right)\right)}{128 a^{2} d}"," ",0,"-1/64/a^2/d/(-1+cos(d*x+c))^2-9/64/a^2/d/(-1+cos(d*x+c))+29/128/a^2/d*ln(-1+cos(d*x+c))-1/32/a^2/d/(1+cos(d*x+c))^4+11/48/a^2/d/(1+cos(d*x+c))^3-3/4/a^2/d/(1+cos(d*x+c))^2+51/32/a^2/d/(1+cos(d*x+c))+99/128*ln(1+cos(d*x+c))/a^2/d","A"
79,1,269,109,0.661000," ","int(tan(d*x+c)^8/(a+a*sec(d*x+c))^2,x)","-\frac{1}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{5}}-\frac{1}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}-\frac{19}{12 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{7}{4 a^{2} 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)}{4 a^{2} d}-\frac{1}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{19}{12 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{7}{4 a^{2} 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)}{4 a^{2} d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d}"," ",0,"-1/5/a^2/d/(tan(1/2*d*x+1/2*c)-1)^5-1/a^2/d/(tan(1/2*d*x+1/2*c)-1)^4-19/12/a^2/d/(tan(1/2*d*x+1/2*c)-1)^3-1/8/a^2/d/(tan(1/2*d*x+1/2*c)-1)^2+7/4/a^2/d/(tan(1/2*d*x+1/2*c)-1)+3/4/a^2/d*ln(tan(1/2*d*x+1/2*c)-1)-1/5/a^2/d/(tan(1/2*d*x+1/2*c)+1)^5+1/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4-19/12/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3+1/8/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2+7/4/a^2/d/(tan(1/2*d*x+1/2*c)+1)-3/4/a^2/d*ln(tan(1/2*d*x+1/2*c)+1)+2/a^2/d*arctan(tan(1/2*d*x+1/2*c))","B"
80,1,185,70,0.602000," ","int(tan(d*x+c)^6/(a+a*sec(d*x+c))^2,x)","-\frac{1}{3 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{3}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{2}{a^{2} 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^{2} d}-\frac{1}{3 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{3}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{2}{a^{2} 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^{2} d}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d}"," ",0,"-1/3/a^2/d/(tan(1/2*d*x+1/2*c)-1)^3-3/2/a^2/d/(tan(1/2*d*x+1/2*c)-1)^2-2/a^2/d/(tan(1/2*d*x+1/2*c)-1)-1/a^2/d*ln(tan(1/2*d*x+1/2*c)-1)-1/3/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3+3/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2-2/a^2/d/(tan(1/2*d*x+1/2*c)+1)+1/a^2/d*ln(tan(1/2*d*x+1/2*c)+1)-2/a^2/d*arctan(tan(1/2*d*x+1/2*c))","B"
81,1,102,34,0.404000," ","int(tan(d*x+c)^4/(a+a*sec(d*x+c))^2,x)","-\frac{1}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a^{2} d}-\frac{1}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a^{2} d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d}"," ",0,"-1/a^2/d/(tan(1/2*d*x+1/2*c)-1)+2/a^2/d*ln(tan(1/2*d*x+1/2*c)-1)-1/a^2/d/(tan(1/2*d*x+1/2*c)+1)-2/a^2/d*ln(tan(1/2*d*x+1/2*c)+1)+2/a^2/d*arctan(tan(1/2*d*x+1/2*c))","B"
82,1,37,33,0.476000," ","int(tan(d*x+c)^2/(a+a*sec(d*x+c))^2,x)","\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{2} d}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d}"," ",0,"2/a^2/d*tan(1/2*d*x+1/2*c)-2/a^2/d*arctan(tan(1/2*d*x+1/2*c))","A"
83,1,94,99,0.703000," ","int(cot(d*x+c)^2/(a+a*sec(d*x+c))^2,x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{40 a^{2} d}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a^{2} d}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d}-\frac{1}{8 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d}"," ",0,"1/40/a^2/d*tan(1/2*d*x+1/2*c)^5-5/24/a^2/d*tan(1/2*d*x+1/2*c)^3+11/8/a^2/d*tan(1/2*d*x+1/2*c)-1/8/a^2/d/tan(1/2*d*x+1/2*c)-2/a^2/d*arctan(tan(1/2*d*x+1/2*c))","A"
84,1,132,129,0.825000," ","int(cot(d*x+c)^4/(a+a*sec(d*x+c))^2,x)","\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{224 a^{2} d}-\frac{7 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{160 a^{2} d}+\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{48 a^{2} d}-\frac{21 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 a^{2} d}-\frac{1}{96 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{7}{32 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d}"," ",0,"1/224/a^2/d*tan(1/2*d*x+1/2*c)^7-7/160/a^2/d*tan(1/2*d*x+1/2*c)^5+11/48/a^2/d*tan(1/2*d*x+1/2*c)^3-21/16/a^2/d*tan(1/2*d*x+1/2*c)-1/96/a^2/d/tan(1/2*d*x+1/2*c)^3+7/32/a^2/d/tan(1/2*d*x+1/2*c)+2/a^2/d*arctan(tan(1/2*d*x+1/2*c))","A"
85,1,170,163,0.852000," ","int(cot(d*x+c)^6/(a+a*sec(d*x+c))^2,x)","\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{1152 a^{2} d}-\frac{9 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{896 a^{2} d}+\frac{37 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{640 a^{2} d}-\frac{31 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a^{2} d}+\frac{163 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a^{2} d}-\frac{1}{640 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{3}{128 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{37}{128 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d}"," ",0,"1/1152/a^2/d*tan(1/2*d*x+1/2*c)^9-9/896/a^2/d*tan(1/2*d*x+1/2*c)^7+37/640/a^2/d*tan(1/2*d*x+1/2*c)^5-31/128/a^2/d*tan(1/2*d*x+1/2*c)^3+163/128/a^2/d*tan(1/2*d*x+1/2*c)-1/640/a^2/d/tan(1/2*d*x+1/2*c)^5+3/128/a^2/d/tan(1/2*d*x+1/2*c)^3-37/128/a^2/d/tan(1/2*d*x+1/2*c)-2/a^2/d*arctan(tan(1/2*d*x+1/2*c))","A"
86,1,127,125,0.799000," ","int(tan(d*x+c)^11/(a+a*sec(d*x+c))^3,x)","\frac{\sec^{7}\left(d x +c \right)}{7 a^{3} d}-\frac{\sec^{6}\left(d x +c \right)}{2 a^{3} d}+\frac{\sec^{5}\left(d x +c \right)}{5 a^{3} d}+\frac{5 \left(\sec^{4}\left(d x +c \right)\right)}{4 a^{3} d}-\frac{5 \left(\sec^{3}\left(d x +c \right)\right)}{3 a^{3} d}-\frac{\sec^{2}\left(d x +c \right)}{2 a^{3} d}+\frac{3 \sec \left(d x +c \right)}{a^{3} d}-\frac{\ln \left(\sec \left(d x +c \right)\right)}{d \,a^{3}}"," ",0,"1/7*sec(d*x+c)^7/a^3/d-1/2*sec(d*x+c)^6/a^3/d+1/5*sec(d*x+c)^5/a^3/d+5/4*sec(d*x+c)^4/a^3/d-5/3*sec(d*x+c)^3/a^3/d-1/2*sec(d*x+c)^2/a^3/d+3*sec(d*x+c)/a^3/d-1/d/a^3*ln(sec(d*x+c))","A"
87,1,93,93,0.648000," ","int(tan(d*x+c)^9/(a+a*sec(d*x+c))^3,x)","\frac{\sec^{5}\left(d x +c \right)}{5 a^{3} d}-\frac{3 \left(\sec^{4}\left(d x +c \right)\right)}{4 a^{3} d}+\frac{2 \left(\sec^{3}\left(d x +c \right)\right)}{3 a^{3} d}+\frac{\sec^{2}\left(d x +c \right)}{a^{3} d}-\frac{3 \sec \left(d x +c \right)}{a^{3} d}+\frac{\ln \left(\sec \left(d x +c \right)\right)}{d \,a^{3}}"," ",0,"1/5*sec(d*x+c)^5/a^3/d-3/4*sec(d*x+c)^4/a^3/d+2/3*sec(d*x+c)^3/a^3/d+sec(d*x+c)^2/a^3/d-3*sec(d*x+c)/a^3/d+1/d/a^3*ln(sec(d*x+c))","A"
88,1,63,61,0.558000," ","int(tan(d*x+c)^7/(a+a*sec(d*x+c))^3,x)","\frac{\sec^{3}\left(d x +c \right)}{3 a^{3} d}-\frac{3 \left(\sec^{2}\left(d x +c \right)\right)}{2 a^{3} d}+\frac{3 \sec \left(d x +c \right)}{a^{3} d}-\frac{\ln \left(\sec \left(d x +c \right)\right)}{d \,a^{3}}"," ",0,"1/3*sec(d*x+c)^3/a^3/d-3/2*sec(d*x+c)^2/a^3/d+3*sec(d*x+c)/a^3/d-1/d/a^3*ln(sec(d*x+c))","A"
89,1,46,46,0.521000," ","int(tan(d*x+c)^5/(a+a*sec(d*x+c))^3,x)","\frac{\sec \left(d x +c \right)}{a^{3} d}+\frac{\ln \left(\sec \left(d x +c \right)\right)}{d \,a^{3}}-\frac{4 \ln \left(1+\sec \left(d x +c \right)\right)}{d \,a^{3}}"," ",0,"sec(d*x+c)/a^3/d+1/d/a^3*ln(sec(d*x+c))-4/d/a^3*ln(1+sec(d*x+c))","A"
90,1,51,35,0.630000," ","int(tan(d*x+c)^3/(a+a*sec(d*x+c))^3,x)","-\frac{\ln \left(\sec \left(d x +c \right)\right)}{d \,a^{3}}-\frac{2}{d \,a^{3} \left(1+\sec \left(d x +c \right)\right)}+\frac{\ln \left(1+\sec \left(d x +c \right)\right)}{d \,a^{3}}"," ",0,"-1/d/a^3*ln(sec(d*x+c))-2/d/a^3/(1+sec(d*x+c))+1/d/a^3*ln(1+sec(d*x+c))","A"
91,1,68,54,0.303000," ","int(tan(d*x+c)/(a+a*sec(d*x+c))^3,x)","\frac{\ln \left(\sec \left(d x +c \right)\right)}{d \,a^{3}}+\frac{1}{2 a^{3} d \left(1+\sec \left(d x +c \right)\right)^{2}}+\frac{1}{d \,a^{3} \left(1+\sec \left(d x +c \right)\right)}-\frac{\ln \left(1+\sec \left(d x +c \right)\right)}{d \,a^{3}}"," ",0,"1/d/a^3*ln(sec(d*x+c))+1/2/a^3/d/(1+sec(d*x+c))^2+1/d/a^3/(1+sec(d*x+c))-1/d/a^3*ln(1+sec(d*x+c))","A"
92,1,90,91,0.815000," ","int(cot(d*x+c)/(a+a*sec(d*x+c))^3,x)","\frac{\ln \left(-1+\cos \left(d x +c \right)\right)}{16 d \,a^{3}}+\frac{1}{6 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)^{3}}-\frac{7}{8 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)^{2}}+\frac{17}{8 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)}+\frac{15 \ln \left(1+\cos \left(d x +c \right)\right)}{16 a^{3} d}"," ",0,"1/16/d/a^3*ln(-1+cos(d*x+c))+1/6/d/a^3/(1+cos(d*x+c))^3-7/8/d/a^3/(1+cos(d*x+c))^2+17/8/d/a^3/(1+cos(d*x+c))+15/16*ln(1+cos(d*x+c))/a^3/d","A"
93,1,126,129,0.925000," ","int(cot(d*x+c)^3/(a+a*sec(d*x+c))^3,x)","\frac{1}{32 a^{3} d \left(-1+\cos \left(d x +c \right)\right)}-\frac{7 \ln \left(-1+\cos \left(d x +c \right)\right)}{64 d \,a^{3}}+\frac{1}{16 a^{3} d \left(1+\cos \left(d x +c \right)\right)^{4}}-\frac{5}{12 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)^{3}}+\frac{39}{32 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)^{2}}-\frac{9}{4 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)}-\frac{57 \ln \left(1+\cos \left(d x +c \right)\right)}{64 a^{3} d}"," ",0,"1/32/a^3/d/(-1+cos(d*x+c))-7/64/d/a^3*ln(-1+cos(d*x+c))+1/16/a^3/d/(1+cos(d*x+c))^4-5/12/d/a^3/(1+cos(d*x+c))^3+39/32/d/a^3/(1+cos(d*x+c))^2-9/4/d/a^3/(1+cos(d*x+c))-57/64*ln(1+cos(d*x+c))/a^3/d","A"
94,1,162,167,0.864000," ","int(cot(d*x+c)^5/(a+a*sec(d*x+c))^3,x)","-\frac{1}{128 a^{3} d \left(-1+\cos \left(d x +c \right)\right)^{2}}-\frac{5}{64 a^{3} d \left(-1+\cos \left(d x +c \right)\right)}+\frac{37 \ln \left(-1+\cos \left(d x +c \right)\right)}{256 d \,a^{3}}+\frac{1}{40 a^{3} d \left(1+\cos \left(d x +c \right)\right)^{5}}-\frac{13}{64 a^{3} d \left(1+\cos \left(d x +c \right)\right)^{4}}+\frac{35}{48 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)^{3}}-\frac{99}{64 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)^{2}}+\frac{303}{128 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)}+\frac{219 \ln \left(1+\cos \left(d x +c \right)\right)}{256 a^{3} d}"," ",0,"-1/128/a^3/d/(-1+cos(d*x+c))^2-5/64/a^3/d/(-1+cos(d*x+c))+37/256/d/a^3*ln(-1+cos(d*x+c))+1/40/a^3/d/(1+cos(d*x+c))^5-13/64/a^3/d/(1+cos(d*x+c))^4+35/48/d/a^3/(1+cos(d*x+c))^3-99/64/d/a^3/(1+cos(d*x+c))^2+303/128/d/a^3/(1+cos(d*x+c))+219/256*ln(1+cos(d*x+c))/a^3/d","A"
95,1,396,217,0.848000," ","int(tan(d*x+c)^12/(a+a*sec(d*x+c))^3,x)","\frac{1}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{8}}+\frac{13}{14 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{7}}+\frac{65}{24 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{6}}+\frac{143}{40 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{5}}+\frac{79}{64 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}-\frac{49}{32 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{29}{128 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{253}{128 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{125 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{128 a^{3} d}-\frac{1}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}+\frac{13}{14 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{65}{24 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{143}{40 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{79}{64 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{49}{32 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{29}{128 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{253}{128 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{125 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{128 a^{3} d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"1/8/a^3/d/(tan(1/2*d*x+1/2*c)-1)^8+13/14/a^3/d/(tan(1/2*d*x+1/2*c)-1)^7+65/24/a^3/d/(tan(1/2*d*x+1/2*c)-1)^6+143/40/a^3/d/(tan(1/2*d*x+1/2*c)-1)^5+79/64/a^3/d/(tan(1/2*d*x+1/2*c)-1)^4-49/32/a^3/d/(tan(1/2*d*x+1/2*c)-1)^3-29/128/a^3/d/(tan(1/2*d*x+1/2*c)-1)^2+253/128/a^3/d/(tan(1/2*d*x+1/2*c)-1)+125/128/a^3/d*ln(tan(1/2*d*x+1/2*c)-1)-1/8/a^3/d/(tan(1/2*d*x+1/2*c)+1)^8+13/14/a^3/d/(tan(1/2*d*x+1/2*c)+1)^7-65/24/a^3/d/(tan(1/2*d*x+1/2*c)+1)^6+143/40/a^3/d/(tan(1/2*d*x+1/2*c)+1)^5-79/64/a^3/d/(tan(1/2*d*x+1/2*c)+1)^4-49/32/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3+29/128/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2+253/128/a^3/d/(tan(1/2*d*x+1/2*c)+1)-125/128/a^3/d*ln(tan(1/2*d*x+1/2*c)+1)+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))","A"
96,1,312,155,0.820000," ","int(tan(d*x+c)^10/(a+a*sec(d*x+c))^3,x)","\frac{1}{6 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{6}}+\frac{11}{10 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{5}}+\frac{11}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{11}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{5}{16 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{35}{16 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{19 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{16 a^{3} d}-\frac{1}{6 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{11}{10 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{11}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{11}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{5}{16 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{35}{16 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{19 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{16 a^{3} d}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"1/6/a^3/d/(tan(1/2*d*x+1/2*c)-1)^6+11/10/a^3/d/(tan(1/2*d*x+1/2*c)-1)^5+11/4/a^3/d/(tan(1/2*d*x+1/2*c)-1)^4+11/4/a^3/d/(tan(1/2*d*x+1/2*c)-1)^3-5/16/a^3/d/(tan(1/2*d*x+1/2*c)-1)^2-35/16/a^3/d/(tan(1/2*d*x+1/2*c)-1)-19/16/a^3/d*ln(tan(1/2*d*x+1/2*c)-1)-1/6/a^3/d/(tan(1/2*d*x+1/2*c)+1)^6+11/10/a^3/d/(tan(1/2*d*x+1/2*c)+1)^5-11/4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^4+11/4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3+5/16/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2-35/16/a^3/d/(tan(1/2*d*x+1/2*c)+1)+19/16/a^3/d*ln(tan(1/2*d*x+1/2*c)+1)-2/d/a^3*arctan(tan(1/2*d*x+1/2*c))","B"
97,1,228,93,0.621000," ","int(tan(d*x+c)^8/(a+a*sec(d*x+c))^3,x)","\frac{1}{4 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{27}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{21}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{13 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{8 a^{3} d}-\frac{1}{4 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{27}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{21}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{13 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{8 a^{3} d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"1/4/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+27/8/a^3/d/(tan(1/2*d*x+1/2*c)-1)^2+21/8/a^3/d/(tan(1/2*d*x+1/2*c)-1)+13/8/a^3/d*ln(tan(1/2*d*x+1/2*c)-1)-1/4/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)^3-27/8/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2+21/8/a^3/d/(tan(1/2*d*x+1/2*c)+1)-13/8/a^3/d*ln(tan(1/2*d*x+1/2*c)+1)+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))","B"
98,1,144,60,0.600000," ","int(tan(d*x+c)^6/(a+a*sec(d*x+c))^3,x)","\frac{1}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{7}{2 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)}{2 a^{3} d}-\frac{1}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{7}{2 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)}{2 a^{3} d}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"1/2/a^3/d/(tan(1/2*d*x+1/2*c)-1)^2+7/2/a^3/d/(tan(1/2*d*x+1/2*c)-1)-7/2/a^3/d*ln(tan(1/2*d*x+1/2*c)-1)-1/2/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2+7/2/a^3/d/(tan(1/2*d*x+1/2*c)+1)+7/2/a^3/d*ln(tan(1/2*d*x+1/2*c)+1)-2/d/a^3*arctan(tan(1/2*d*x+1/2*c))","B"
99,1,76,46,0.600000," ","int(tan(d*x+c)^4/(a+a*sec(d*x+c))^3,x)","-\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a^{3} d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a^{3} d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"-4/d/a^3*tan(1/2*d*x+1/2*c)-1/a^3/d*ln(tan(1/2*d*x+1/2*c)-1)+1/a^3/d*ln(tan(1/2*d*x+1/2*c)+1)+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))","A"
100,1,56,58,0.584000," ","int(tan(d*x+c)^2/(a+a*sec(d*x+c))^3,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{3 d \,a^{3}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"-1/3/d/a^3*tan(1/2*d*x+1/2*c)^3+2/d/a^3*tan(1/2*d*x+1/2*c)-2/d/a^3*arctan(tan(1/2*d*x+1/2*c))","A"
101,1,113,131,0.805000," ","int(cot(d*x+c)^2/(a+a*sec(d*x+c))^3,x)","-\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{112 a^{3} d}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{3}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{3 d \,a^{3}}+\frac{13 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}-\frac{1}{16 a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"-1/112/a^3/d*tan(1/2*d*x+1/2*c)^7+3/40/d/a^3*tan(1/2*d*x+1/2*c)^5-1/3/d/a^3*tan(1/2*d*x+1/2*c)^3+13/8/d/a^3*tan(1/2*d*x+1/2*c)-1/16/a^3/d/tan(1/2*d*x+1/2*c)-2/d/a^3*arctan(tan(1/2*d*x+1/2*c))","A"
102,1,151,161,0.882000," ","int(cot(d*x+c)^4/(a+a*sec(d*x+c))^3,x)","-\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{576 a^{3} d}+\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{56 a^{3} d}-\frac{29 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{320 d \,a^{3}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{3 d \,a^{3}}-\frac{99 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d \,a^{3}}-\frac{1}{192 a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{8 a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"-1/576/a^3/d*tan(1/2*d*x+1/2*c)^9+1/56/a^3/d*tan(1/2*d*x+1/2*c)^7-29/320/d/a^3*tan(1/2*d*x+1/2*c)^5+1/3/d/a^3*tan(1/2*d*x+1/2*c)^3-99/64/d/a^3*tan(1/2*d*x+1/2*c)-1/192/a^3/d/tan(1/2*d*x+1/2*c)^3+1/8/a^3/d/tan(1/2*d*x+1/2*c)+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))","A"
103,1,189,195,1.017000," ","int(cot(d*x+c)^6/(a+a*sec(d*x+c))^3,x)","-\frac{\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2816 a^{3} d}+\frac{5 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{1152 a^{3} d}-\frac{23 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{896 a^{3} d}+\frac{13 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{3}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{3 d \,a^{3}}+\frac{191 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 d \,a^{3}}-\frac{1}{1280 a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{5}{384 a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{23}{128 a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"-1/2816/a^3/d*tan(1/2*d*x+1/2*c)^11+5/1152/a^3/d*tan(1/2*d*x+1/2*c)^9-23/896/a^3/d*tan(1/2*d*x+1/2*c)^7+13/128/d/a^3*tan(1/2*d*x+1/2*c)^5-1/3/d/a^3*tan(1/2*d*x+1/2*c)^3+191/128/d/a^3*tan(1/2*d*x+1/2*c)-1/1280/a^3/d/tan(1/2*d*x+1/2*c)^5+5/384/a^3/d/tan(1/2*d*x+1/2*c)^3-23/128/a^3/d/tan(1/2*d*x+1/2*c)-2/d/a^3*arctan(tan(1/2*d*x+1/2*c))","A"
104,1,1495,274,1.900000," ","int((a+a*sec(d*x+c))*(e*tan(d*x+c))^(5/2),x)","\frac{a \left(-1+\cos \left(d x +c \right)\right)^{2} \left(-15 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+15 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-36 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+18 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+15 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+15 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-15 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+15 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-36 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+18 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+15 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+15 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+8 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-24 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+10 \cos \left(d x +c \right) \sqrt{2}+6 \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}}{30 d \sin \left(d x +c \right)^{7}}"," ",0,"1/30*a/d*(-1+cos(d*x+c))^2*(15*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-15*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-36*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+18*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+15*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+15*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+15*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-15*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-36*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+18*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+15*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+15*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+8*2^(1/2)*cos(d*x+c)^3-24*cos(d*x+c)^2*2^(1/2)+10*cos(d*x+c)*2^(1/2)+6*2^(1/2))*(1+cos(d*x+c))^2*(e*sin(d*x+c)/cos(d*x+c))^(5/2)/sin(d*x+c)^7*2^(1/2)","C"
105,1,688,250,1.799000," ","int((a+a*sec(d*x+c))*(e*tan(d*x+c))^(3/2),x)","\frac{a \left(-1+\cos \left(d x +c \right)\right) \left(-3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-4 \cos \left(d x +c \right) \sqrt{2}-2 \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}}{6 d \sin \left(d x +c \right)^{5}}"," ",0,"1/6*a/d*(-1+cos(d*x+c))*(-3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-4*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+6*cos(d*x+c)^2*2^(1/2)-4*cos(d*x+c)*2^(1/2)-2*2^(1/2))*(1+cos(d*x+c))^2*(e*sin(d*x+c)/cos(d*x+c))^(3/2)/sin(d*x+c)^5*2^(1/2)","C"
106,1,1409,244,1.968000," ","int((a+a*sec(d*x+c))*(e*tan(d*x+c))^(1/2),x)","\frac{a \sqrt{\frac{e \sin \left(d x +c \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(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+4 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+4 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-2 \cos \left(d x +c \right) \sqrt{2}+2 \sqrt{2}\right) \sqrt{2}}{2 d \sin \left(d x +c \right)^{5}}"," ",0,"1/2*a/d*(e*sin(d*x+c)/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+4*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+4*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-2*cos(d*x+c)*2^(1/2)+2*2^(1/2))/sin(d*x+c)^5*2^(1/2)","C"
107,1,284,219,1.803000," ","int((a+a*sec(d*x+c))/(e*tan(d*x+c))^(1/2),x)","-\frac{a \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}}}"," ",0,"-1/2*a/d*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-1+cos(d*x+c))/sin(d*x+c)^2/cos(d*x+c)*(1+cos(d*x+c))^2/(e*sin(d*x+c)/cos(d*x+c))^(1/2)*2^(1/2)","C"
108,1,1390,275,1.776000," ","int((a+a*sec(d*x+c))/(e*tan(d*x+c))^(3/2),x)","-\frac{a \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-4 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-4 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+4 \cos \left(d x +c \right) \sqrt{2}\right) \sin \left(d x +c \right) \sqrt{2}}{2 d \cos \left(d x +c \right)^{2} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/2*a/d*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-4*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-4*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+4*cos(d*x+c)*2^(1/2))*sin(d*x+c)/cos(d*x+c)^2/(e*sin(d*x+c)/cos(d*x+c))^(3/2)*2^(1/2)","C"
109,1,648,250,1.697000," ","int((a+a*sec(d*x+c))/(e*tan(d*x+c))^(5/2),x)","\frac{a \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-4 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \cos \left(d x +c \right) \sqrt{2}\right) \sqrt{2}}{6 d \cos \left(d x +c \right)^{3} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)}"," ",0,"1/6*a/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-4*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+2*cos(d*x+c)*2^(1/2))/cos(d*x+c)^3/(e*sin(d*x+c)/cos(d*x+c))^(5/2)/sin(d*x+c)*2^(1/2)","C"
110,1,1427,306,1.764000," ","int((a+a*sec(d*x+c))/(e*tan(d*x+c))^(7/2),x)","\frac{a \left(5 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-5 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-12 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-5 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+5 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+12 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+5 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+5 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-6 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+18 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-16 \cos \left(d x +c \right) \sqrt{2}\right) \left(\sin^{3}\left(d x +c \right)\right) \sqrt{2}}{10 d \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{4} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}"," ",0,"1/10*a/d*(5*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-5*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-12*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-5*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-5*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+6*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-5*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+5*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+5*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+5*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-6*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+18*cos(d*x+c)^2*2^(1/2)-16*cos(d*x+c)*2^(1/2))*sin(d*x+c)^3/(-1+cos(d*x+c))/cos(d*x+c)^4/(e*sin(d*x+c)/cos(d*x+c))^(7/2)*2^(1/2)","C"
111,1,1518,322,1.959000," ","int((a+a*sec(d*x+c))^2*(e*tan(d*x+c))^(5/2),x)","\frac{a^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(-105 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+105 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+105 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)-105 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+105 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+105 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+252 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)-504 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+105 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+105 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+252 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-504 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+212 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-336 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+10 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+84 \cos \left(d x +c \right) \sqrt{2}+30 \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}}{210 d \sin \left(d x +c \right)^{7} \cos \left(d x +c \right)}"," ",0,"1/210*a^2/d*(-1+cos(d*x+c))^2*(-105*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4+105*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4+105*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4+105*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+105*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4-105*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+252*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4-504*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4+105*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+105*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+252*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-504*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+212*cos(d*x+c)^4*2^(1/2)-336*2^(1/2)*cos(d*x+c)^3+10*cos(d*x+c)^2*2^(1/2)+84*cos(d*x+c)*2^(1/2)+30*2^(1/2))*(1+cos(d*x+c))^2*(e*sin(d*x+c)/cos(d*x+c))^(5/2)/sin(d*x+c)^7/cos(d*x+c)*2^(1/2)","C"
112,1,721,297,1.946000," ","int((a+a*sec(d*x+c))^2*(e*tan(d*x+c))^(3/2),x)","\frac{a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(-15 i \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+15 i \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+15 \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+15 \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-10 \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+24 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-14 \cos \left(d x +c \right) \sqrt{2}-6 \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}}{30 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}"," ",0,"1/30*a^2/d*(-1+cos(d*x+c))*(-15*I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-10*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+24*2^(1/2)*cos(d*x+c)^3-4*cos(d*x+c)^2*2^(1/2)-14*cos(d*x+c)*2^(1/2)-6*2^(1/2))*(1+cos(d*x+c))^2*(e*sin(d*x+c)/cos(d*x+c))^(3/2)/sin(d*x+c)^5/cos(d*x+c)*2^(1/2)","C"
113,1,1480,277,2.038000," ","int((a+a*sec(d*x+c))^2*(e*tan(d*x+c))^(1/2),x)","\frac{a^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+24 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-12 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+24 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-12 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-14 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+12 \cos \left(d x +c \right) \sqrt{2}+2 \sqrt{2}\right) \sqrt{2}}{6 d \cos \left(d x +c \right) \sin \left(d x +c \right)^{5}}"," ",0,"1/6*a^2/d*(1+cos(d*x+c))^2*(e*sin(d*x+c)/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+24*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-12*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-3*I*cos(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+24*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-12*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-14*cos(d*x+c)^2*2^(1/2)+12*cos(d*x+c)*2^(1/2)+2*2^(1/2))/cos(d*x+c)/sin(d*x+c)^5*2^(1/2)","C"
114,1,653,250,1.995000," ","int((a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(1/2),x)","-\frac{a^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \cos \left(d x +c \right) \sqrt{2}+2 \sqrt{2}\right) \sqrt{2}}{2 d \cos \left(d x +c \right) \sin \left(d x +c \right)^{3} \sqrt{\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}}}"," ",0,"-1/2*a^2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-2*cos(d*x+c)*2^(1/2)+2*2^(1/2))/cos(d*x+c)/sin(d*x+c)^3/(e*sin(d*x+c)/cos(d*x+c))^(1/2)*2^(1/2)","C"
115,1,1392,280,1.816000," ","int((a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(3/2),x)","-\frac{a^{2} \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+4 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-8 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+4 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-8 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+8 \cos \left(d x +c \right) \sqrt{2}\right) \sin \left(d x +c \right) \sqrt{2}}{2 d \cos \left(d x +c \right)^{2} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/2*a^2/d*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+4*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-8*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+4*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-8*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+8*cos(d*x+c)*2^(1/2))*sin(d*x+c)/cos(d*x+c)^2/(e*sin(d*x+c)/cos(d*x+c))^(3/2)*2^(1/2)","C"
116,1,650,280,1.808000," ","int((a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(5/2),x)","\frac{a^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 \cos \left(d x +c \right) \sqrt{2}\right) \sqrt{2}}{6 d \cos \left(d x +c \right)^{3} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)}"," ",0,"1/6*a^2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+4*cos(d*x+c)*2^(1/2))/cos(d*x+c)^3/(e*sin(d*x+c)/cos(d*x+c))^(5/2)/sin(d*x+c)*2^(1/2)","C"
117,1,1429,328,1.899000," ","int((a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(7/2),x)","-\frac{a^{2} \left(5 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-5 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+24 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-12 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+5 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-5 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+5 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-5 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-24 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+12 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-5 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-26 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+22 \cos \left(d x +c \right) \sqrt{2}\right) \left(\sin^{3}\left(d x +c \right)\right) \sqrt{2}}{10 d \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{4} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}"," ",0,"-1/10*a^2/d*(5*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)^2-5*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)^2+5*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+24*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-12*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+5*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-5*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+5*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-5*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-24*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+12*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-5*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-26*cos(d*x+c)^2*2^(1/2)+22*cos(d*x+c)*2^(1/2))*sin(d*x+c)^3/(-1+cos(d*x+c))/cos(d*x+c)^4/(e*sin(d*x+c)/cos(d*x+c))^(7/2)*2^(1/2)","C"
118,1,734,294,1.733000," ","int((e*tan(d*x+c))^(11/2)/(a+a*sec(d*x+c)),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(-105 i \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+105 i \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+105 \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+105 \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-260 \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+252 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-332 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+38 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+72 \cos \left(d x +c \right) \sqrt{2}-30 \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{2}}{210 a d \sin \left(d x +c \right)^{9}}"," ",0,"1/210/a/d*(-1+cos(d*x+c))*(-105*I*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+105*I*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+105*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+105*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-260*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+252*cos(d*x+c)^4*2^(1/2)-332*2^(1/2)*cos(d*x+c)^3+38*cos(d*x+c)^2*2^(1/2)+72*cos(d*x+c)*2^(1/2)-30*2^(1/2))*cos(d*x+c)^2*(1+cos(d*x+c))^2*(e*sin(d*x+c)/cos(d*x+c))^(11/2)/sin(d*x+c)^9*2^(1/2)","C"
119,1,1505,290,1.689000," ","int((e*tan(d*x+c))^(9/2)/(a+a*sec(d*x+c)),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(-15 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+15 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-36 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+18 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+15 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-15 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-36 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+18 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+28 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-24 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-10 \cos \left(d x +c \right) \sqrt{2}+6 \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}}{30 a d \sin \left(d x +c \right)^{9}}"," ",0,"1/30/a/d*(-1+cos(d*x+c))^2*(-15*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+15*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-15*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-15*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-36*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+18*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-15*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+15*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-15*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-15*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-36*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+18*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+28*2^(1/2)*cos(d*x+c)^3-24*cos(d*x+c)^2*2^(1/2)-10*cos(d*x+c)*2^(1/2)+6*2^(1/2))*cos(d*x+c)^2*(1+cos(d*x+c))^2*(e*sin(d*x+c)/cos(d*x+c))^(9/2)/sin(d*x+c)^9*2^(1/2)","C"
120,1,698,263,1.699000," ","int((e*tan(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-8 \cos \left(d x +c \right) \sqrt{2}+2 \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{2}}{6 a d \sin \left(d x +c \right)^{7}}"," ",0,"-1/6/a/d*(-1+cos(d*x+c))*(3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-8*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+6*cos(d*x+c)^2*2^(1/2)-8*cos(d*x+c)*2^(1/2)+2*2^(1/2))*cos(d*x+c)^2*(1+cos(d*x+c))^2*(e*sin(d*x+c)/cos(d*x+c))^(7/2)/sin(d*x+c)^7*2^(1/2)","C"
121,1,1419,257,2.087000," ","int((e*tan(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-4 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-4 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 \cos \left(d x +c \right) \sqrt{2}-2 \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}}{2 a d \sin \left(d x +c \right)^{7}}"," ",0,"-1/2/a/d*(-1+cos(d*x+c))^2*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-4*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-4*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+2*cos(d*x+c)*2^(1/2)-2*2^(1/2))*cos(d*x+c)^2*(1+cos(d*x+c))^2*(e*sin(d*x+c)/cos(d*x+c))^(5/2)/sin(d*x+c)^7*2^(1/2)","C"
122,1,319,232,1.829000," ","int((e*tan(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x)","\frac{\left(1+\cos \left(d x +c \right)\right)^{2} \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{2}}{2 a d \sin \left(d x +c \right)^{4}}"," ",0,"1/2/a/d*(1+cos(d*x+c))^2*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-4*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-1+cos(d*x+c))*(e*sin(d*x+c)/cos(d*x+c))^(3/2)*cos(d*x+c)/sin(d*x+c)^4*2^(1/2)","C"
123,1,352,285,1.766000," ","int((e*tan(d*x+c))^(1/2)/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{e \sin \left(d x +c \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) \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+4 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{2}}{2 a d \sin \left(d x +c \right)^{3}}"," ",0,"-1/2/a/d*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(e*sin(d*x+c)/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+4*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2)))/sin(d*x+c)^3*2^(1/2)","C"
124,1,1269,258,1.731000," ","int(1/(a+a*sec(d*x+c))/(e*tan(d*x+c))^(1/2),x)","\frac{\left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-2 \cos \left(d x +c \right) \sqrt{2}\right) \sqrt{2}}{6 a d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right) \sqrt{\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}}}"," ",0,"1/6/a/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-8*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-8*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+2*cos(d*x+c)^2*2^(1/2)-2*cos(d*x+c)*2^(1/2))/sin(d*x+c)^5/cos(d*x+c)/(e*sin(d*x+c)/cos(d*x+c))^(1/2)*2^(1/2)","C"
125,1,2113,319,1.618000," ","int(1/(a+a*sec(d*x+c))/(e*tan(d*x+c))^(3/2),x)","\text{Expression too large to display}"," ",0,"1/10/a/d*(-1+cos(d*x+c))*(-10*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)+5*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+5*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-5*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-5*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-5*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-6*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-5*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+10*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-10*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-10*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+24*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-12*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-5*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-5*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+12*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-6*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+6*cos(d*x+c)^2*2^(1/2)+4*cos(d*x+c)*2^(1/2))/cos(d*x+c)^2/(e*sin(d*x+c)/cos(d*x+c))^(3/2)/sin(d*x+c)*2^(1/2)","C"
126,1,1896,292,1.682000," ","int(1/(a+a*sec(d*x+c))/(e*tan(d*x+c))^(5/2),x)","-\frac{\left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{3} \left(42 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-21 i \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-21 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+21 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-21 \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-21 \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+52 \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+21 i \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-42 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-42 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-42 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+104 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-21 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-21 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+52 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-20 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+10 \cos \left(d x +c \right) \sqrt{2}\right) \sqrt{2}}{42 a d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)^{3} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/42/a/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^3*(-21*I*sin(d*x+c)*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+42*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+21*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-21*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-21*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-21*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+52*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-42*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+21*I*sin(d*x+c)*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-42*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-42*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+104*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-21*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-21*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+52*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-20*2^(1/2)*cos(d*x+c)^3-4*cos(d*x+c)^2*2^(1/2)+10*cos(d*x+c)*2^(1/2))/sin(d*x+c)^5/cos(d*x+c)^3/(e*sin(d*x+c)/cos(d*x+c))^(5/2)*2^(1/2)","C"
127,1,1518,328,1.760000," ","int((e*tan(d*x+c))^(13/2)/(a+a*sec(d*x+c))^2,x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(-105 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+105 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+105 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)-105 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+105 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+105 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+504 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)-252 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+105 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+105 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+504 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-252 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-292 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}+336 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+10 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-84 \cos \left(d x +c \right) \sqrt{2}+30 \sqrt{2}\right) \left(\cos^{3}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{13}{2}} \sqrt{2}}{210 a^{2} d \sin \left(d x +c \right)^{11}}"," ",0,"1/210/a^2/d*(-1+cos(d*x+c))^2*(105*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4-105*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4+105*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3-105*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3+105*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4+105*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4+504*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4-252*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^4+105*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+105*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+504*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-252*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-292*cos(d*x+c)^4*2^(1/2)+336*2^(1/2)*cos(d*x+c)^3+10*cos(d*x+c)^2*2^(1/2)-84*cos(d*x+c)*2^(1/2)+30*2^(1/2))*cos(d*x+c)^3*(1+cos(d*x+c))^2*(e*sin(d*x+c)/cos(d*x+c))^(13/2)/sin(d*x+c)^11*2^(1/2)","C"
128,1,721,301,1.692000," ","int((e*tan(d*x+c))^(11/2)/(a+a*sec(d*x+c))^2,x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(-15 i \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+15 i \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+15 \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+15 \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-50 \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+24 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-44 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+26 \cos \left(d x +c \right) \sqrt{2}-6 \sqrt{2}\right) \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \left(\cos^{3}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{30 a^{2} d \sin \left(d x +c \right)^{9}}"," ",0,"1/30/a^2/d*(-1+cos(d*x+c))*(-15*I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+15*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-50*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+24*2^(1/2)*cos(d*x+c)^3-44*cos(d*x+c)^2*2^(1/2)+26*cos(d*x+c)*2^(1/2)-6*2^(1/2))*(e*sin(d*x+c)/cos(d*x+c))^(11/2)*cos(d*x+c)^3*(1+cos(d*x+c))^2/sin(d*x+c)^9*2^(1/2)","C"
129,1,1480,280,1.734000," ","int((e*tan(d*x+c))^(9/2)/(a+a*sec(d*x+c))^2,x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+12 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-24 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+12 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-24 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+10 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-12 \cos \left(d x +c \right) \sqrt{2}+2 \sqrt{2}\right) \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\cos^{3}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{6 a^{2} d \sin \left(d x +c \right)^{9}}"," ",0,"1/6/a^2/d*(-1+cos(d*x+c))^2*(3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-3*I*cos(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-24*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+12*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-24*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+10*cos(d*x+c)^2*2^(1/2)-12*cos(d*x+c)*2^(1/2)+2*2^(1/2))*(e*sin(d*x+c)/cos(d*x+c))^(9/2)*cos(d*x+c)^3*(1+cos(d*x+c))^2/sin(d*x+c)^9*2^(1/2)","C"
130,1,653,253,1.778000," ","int((e*tan(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-6 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \cos \left(d x +c \right) \sqrt{2}+2 \sqrt{2}\right) \left(-1+\cos \left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{2}}{2 a^{2} d \sin \left(d x +c \right)^{7}}"," ",0,"-1/2/a^2/d*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-6*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-2*cos(d*x+c)*2^(1/2)+2*2^(1/2))*(-1+cos(d*x+c))*cos(d*x+c)^3*(1+cos(d*x+c))^2*(e*sin(d*x+c)/cos(d*x+c))^(7/2)/sin(d*x+c)^7*2^(1/2)","C"
131,1,360,280,1.715000," ","int((e*tan(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x)","\frac{\left(1+\cos \left(d x +c \right)\right)^{2} \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+8 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}}{2 a^{2} d \sin \left(d x +c \right)^{5}}"," ",0,"1/2/a^2/d*(1+cos(d*x+c))^2*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-4*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+8*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-1+cos(d*x+c))*(e*sin(d*x+c)/cos(d*x+c))^(5/2)*cos(d*x+c)^2/sin(d*x+c)^5*2^(1/2)","C"
132,1,1267,280,1.842000," ","int((e*tan(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-10 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-10 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-4 \cos \left(d x +c \right) \sqrt{2}\right) \cos \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}}{6 a^{2} d \sin \left(d x +c \right)^{7}}"," ",0,"-1/6/a^2/d*(-1+cos(d*x+c))^2*(3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-10*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-10*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+4*cos(d*x+c)^2*2^(1/2)-4*cos(d*x+c)*2^(1/2))*cos(d*x+c)*(1+cos(d*x+c))^2*(e*sin(d*x+c)/cos(d*x+c))^(3/2)/sin(d*x+c)^7*2^(1/2)","C"
133,1,2117,321,1.875000," ","int((e*tan(d*x+c))^(1/2)/(a+a*sec(d*x+c))^2,x)","\text{Expression too large to display}"," ",0,"-1/10/a^2/d*(e*sin(d*x+c)/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^3*(-10*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)+5*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+5*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-5*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-5*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-5*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+24*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-12*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-5*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+10*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-10*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-10*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+48*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-24*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-5*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-5*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+24*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-12*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+2*cos(d*x+c)^2*2^(1/2)-2*cos(d*x+c)*2^(1/2))/sin(d*x+c)^7*2^(1/2)","C"
134,1,1896,321,1.901000," ","int(1/(a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(1/2),x)","\frac{\left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{3} \left(-42 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-21 i \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+42 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-21 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-21 \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-21 \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+62 \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+21 i \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+21 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-42 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-42 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+124 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-21 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-21 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+62 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-26 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+20 \cos \left(d x +c \right) \sqrt{2}\right) \sqrt{2}}{42 a^{2} d \sin \left(d x +c \right)^{7} \cos \left(d x +c \right) \sqrt{\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}}}"," ",0,"1/42/a^2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^3*(-21*I*sin(d*x+c)*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+42*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+21*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-21*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-21*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-21*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+62*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-42*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+21*I*sin(d*x+c)*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-42*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-42*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+124*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-21*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-21*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+62*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-26*2^(1/2)*cos(d*x+c)^3+6*cos(d*x+c)^2*2^(1/2)+20*cos(d*x+c)*2^(1/2))/sin(d*x+c)^7/cos(d*x+c)/(e*sin(d*x+c)/cos(d*x+c))^(1/2)*2^(1/2)","C"
135,1,359,123,1.377000," ","int((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^5,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(315 \left(\cos^{4}\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{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)+1260 \left(\cos^{3}\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{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)+1890 \left(\cos^{2}\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{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)+1260 \cos \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}} \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\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{9}{2}}+12256 \left(\cos^{4}\left(d x +c \right)\right)-1088 \left(\cos^{3}\left(d x +c \right)\right)-4224 \left(\cos^{2}\left(d x +c \right)\right)+160 \cos \left(d x +c \right)+1120\right)}{5040 d \cos \left(d x +c \right)^{4}}"," ",0,"1/5040/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(315*cos(d*x+c)^4*2^(1/2)*(-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))+1260*cos(d*x+c)^3*2^(1/2)*(-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))+1890*cos(d*x+c)^2*2^(1/2)*(-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))+1260*cos(d*x+c)*2^(1/2)*(-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))+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)))^(9/2)+12256*cos(d*x+c)^4-1088*cos(d*x+c)^3-4224*cos(d*x+c)^2+160*cos(d*x+c)+1120)/cos(d*x+c)^4","B"
136,1,221,83,1.262000," ","int((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^3,x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(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{5}{2}} \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+30 \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}\, \cos \left(d x +c \right)+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}}+136 \left(\cos^{2}\left(d x +c \right)\right)-8 \cos \left(d x +c \right)-24\right)}{60 d \cos \left(d x +c \right)^{2}}"," ",0,"-1/60/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(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)))^(5/2)*2^(1/2)*cos(d*x+c)^2+30*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)*cos(d*x+c)+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)+136*cos(d*x+c)^2-8*cos(d*x+c)-24)/cos(d*x+c)^2","B"
137,1,42,43,0.239000," ","int((a+a*sec(d*x+c))^(1/2)*tan(d*x+c),x)","\frac{2 \sqrt{a +a \sec \left(d x +c \right)}-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{a +a \sec \left(d x +c \right)}}{\sqrt{a}}\right)}{d}"," ",0,"1/d*(2*(a+a*sec(d*x+c))^(1/2)-2*a^(1/2)*arctanh((a+a*sec(d*x+c))^(1/2)/a^(1/2)))","A"
138,1,98,58,1.142000," ","int(cot(d*x+c)*(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\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)\right)}{d}"," ",0,"-1/d*(a*(1+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*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)))","A"
139,1,267,106,1.376000," ","int(cot(d*x+c)^3*(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(8 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+7 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)-8 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-7 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+6 \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)-1\right)}{8 d \sin \left(d x +c \right)^{4}}"," ",0,"1/8/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(8*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+7*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-8*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-7*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+6*cos(d*x+c)^2-2*cos(d*x+c))/sin(d*x+c)^4*(cos(d*x+c)^2-1)","B"
140,1,407,160,1.469000," ","int(cot(d*x+c)^5*(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\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(384 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+321 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-768 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+410 \left(\cos^{4}\left(d x +c \right)\right)-642 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)-142 \left(\cos^{3}\left(d x +c \right)\right)+384 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-298 \left(\cos^{2}\left(d x +c \right)\right)+321 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+126 \cos \left(d x +c \right)\right)}{384 d \sin \left(d x +c \right)^{8}}"," ",0,"-1/384/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(384*cos(d*x+c)^4*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+321*cos(d*x+c)^4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-768*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+410*cos(d*x+c)^4-642*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-142*cos(d*x+c)^3+384*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-298*cos(d*x+c)^2+321*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+126*cos(d*x+c))/sin(d*x+c)^8","B"
141,1,566,196,1.436000," ","int((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^6,x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(495 \sqrt{2}\, \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}}+2475 \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}}+4950 \sqrt{2}\, \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}}+4950 \sqrt{2}\, \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}}+2475 \sqrt{2}\, \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}}+495 \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{11}{2}} \sin \left(d x +c \right)+31616 \left(\cos^{6}\left(d x +c \right)\right)-15808 \left(\cos^{5}\left(d x +c \right)\right)-27712 \left(\cos^{4}\left(d x +c \right)\right)+1984 \left(\cos^{3}\left(d x +c \right)\right)+13120 \left(\cos^{2}\left(d x +c \right)\right)-320 \cos \left(d x +c \right)-2880\right)}{15840 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{5}}"," ",0,"-1/15840/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(495*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)+2475*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)+4950*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)+4950*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)+2475*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)+495*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)+31616*cos(d*x+c)^6-15808*cos(d*x+c)^5-27712*cos(d*x+c)^4+1984*cos(d*x+c)^3+13120*cos(d*x+c)^2-320*cos(d*x+c)-2880)/sin(d*x+c)/cos(d*x+c)^5","B"
142,1,317,140,1.360000," ","int((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^4,x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(105 \sqrt{2}\, \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{5}{2}}+210 \sqrt{2}\, \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{5}{2}}+105 \sqrt{2}\, \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{5}{2}}-736 \left(\cos^{4}\left(d x +c \right)\right)+368 \left(\cos^{3}\left(d x +c \right)\right)+512 \left(\cos^{2}\left(d x +c \right)\right)-24 \cos \left(d x +c \right)-120\right)}{420 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3}}"," ",0,"-1/420/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(105*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)))^(5/2)+210*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)))^(5/2)+105*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)))^(5/2)-736*cos(d*x+c)^4+368*cos(d*x+c)^3+512*cos(d*x+c)^2-24*cos(d*x+c)-120)/sin(d*x+c)/cos(d*x+c)^3","B"
143,1,210,84,1.065000," ","int((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^2,x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 \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) \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)+3 \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{3}{2}} \sin \left(d x +c \right)+8 \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right)-4\right)}{6 d \sin \left(d x +c \right) \cos \left(d x +c \right)}"," ",0,"-1/6/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*(-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))*cos(d*x+c)*2^(1/2)*sin(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)))^(3/2)*sin(d*x+c)+8*cos(d*x+c)^2-4*cos(d*x+c)-4)/sin(d*x+c)/cos(d*x+c)","B"
144,1,188,93,1.236000," ","int(cot(d*x+c)^2*(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(2 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-2 \cos \left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)}"," ",0,"1/2/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(2*2^(1/2)*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)))^(1/2)+sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-2*cos(d*x+c))/sin(d*x+c)","B"
145,1,381,166,1.250000," ","int(cot(d*x+c)^4*(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(48 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+27 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-48 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-27 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-62 \left(\cos^{3}\left(d x +c \right)\right)+4 \left(\cos^{2}\left(d x +c \right)\right)+42 \cos \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)-1\right)}{48 d \sin \left(d x +c \right)^{5}}"," ",0,"-1/48/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(48*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)+27*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-48*2^(1/2)*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)))^(1/2)-27*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-62*cos(d*x+c)^3+4*cos(d*x+c)^2+42*cos(d*x+c))/sin(d*x+c)^5*(cos(d*x+c)^2-1)","B"
146,1,573,241,1.584000," ","int(cot(d*x+c)^6*(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\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(-3840 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \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)-2265 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+7680 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+5642 \left(\cos^{5}\left(d x +c \right)\right)+4530 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-556 \left(\cos^{4}\left(d x +c \right)\right)-3840 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-7928 \left(\cos^{3}\left(d x +c \right)\right)-2265 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+460 \left(\cos^{2}\left(d x +c \right)\right)+3150 \cos \left(d x +c \right)\right)}{3840 d \sin \left(d x +c \right)^{9}}"," ",0,"-1/3840/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(1+cos(d*x+c))^2*(-3840*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(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))-2265*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+7680*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)+5642*cos(d*x+c)^5+4530*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-556*cos(d*x+c)^4-3840*2^(1/2)*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)))^(1/2)-7928*cos(d*x+c)^3-2265*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+460*cos(d*x+c)^2+3150*cos(d*x+c))/sin(d*x+c)^9","B"
147,1,429,141,1.207000," ","int((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^5,x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(1155 \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{11}{2}} \left(\cos^{5}\left(d x +c \right)\right)+5775 \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{11}{2}} \left(\cos^{4}\left(d x +c \right)\right)+11550 \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{11}{2}} \left(\cos^{3}\left(d x +c \right)\right)+11550 \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{11}{2}} \left(\cos^{2}\left(d x +c \right)\right)+5775 \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{11}{2}} \cos \left(d x +c \right)+1155 \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{11}{2}}-105984 \left(\cos^{5}\left(d x +c \right)\right)-20928 \left(\cos^{4}\left(d x +c \right)\right)+34176 \left(\cos^{3}\left(d x +c \right)\right)+20800 \left(\cos^{2}\left(d x +c \right)\right)-8960 \cos \left(d x +c \right)-6720\right) a}{36960 d \cos \left(d x +c \right)^{5}}"," ",0,"-1/36960/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1155*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)))^(11/2)*cos(d*x+c)^5+5775*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)))^(11/2)*cos(d*x+c)^4+11550*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)))^(11/2)*cos(d*x+c)^3+11550*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)))^(11/2)*cos(d*x+c)^2+5775*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)))^(11/2)*cos(d*x+c)+1155*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)))^(11/2)-105984*cos(d*x+c)^5-20928*cos(d*x+c)^4+34176*cos(d*x+c)^3+20800*cos(d*x+c)^2-8960*cos(d*x+c)-6720)/cos(d*x+c)^5*a","B"
148,1,291,101,1.138000," ","int((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^3,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(105 \left(\cos^{3}\left(d x +c \right)\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}+315 \left(\cos^{2}\left(d x +c \right)\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}+315 \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) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{2}+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}}-2336 \left(\cos^{3}\left(d x +c \right)\right)-512 \left(\cos^{2}\left(d x +c \right)\right)+384 \cos \left(d x +c \right)+240\right) a}{840 d \cos \left(d x +c \right)^{3}}"," ",0,"1/840/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(105*cos(d*x+c)^3*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)+315*cos(d*x+c)^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)*2^(1/2)+315*cos(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)+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)-2336*cos(d*x+c)^3-512*cos(d*x+c)^2+384*cos(d*x+c)+240)/cos(d*x+c)^3*a","B"
149,1,57,61,0.174000," ","int((a+a*sec(d*x+c))^(3/2)*tan(d*x+c),x)","\frac{\frac{2 \left(a +a \sec \left(d x +c \right)\right)^{\frac{3}{2}}}{3}+2 a \sqrt{a +a \sec \left(d x +c \right)}-2 a^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{a +a \sec \left(d x +c \right)}}{\sqrt{a}}\right)}{d}"," ",0,"1/d*(2/3*(a+a*sec(d*x+c))^(3/2)+2*a*(a+a*sec(d*x+c))^(1/2)-2*a^(3/2)*arctanh((a+a*sec(d*x+c))^(1/2)/a^(1/2)))","A"
150,1,101,58,1.019000," ","int(cot(d*x+c)*(a+a*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\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)+2 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)\right) a}{d}"," ",0,"-1/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+2*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)))*a","A"
151,1,258,88,1.181000," ","int(cot(d*x+c)^3*(a+a*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(4 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+5 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)-4 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+2 \left(\cos^{2}\left(d x +c \right)\right)-5 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+2 \cos \left(d x +c \right)\right) a}{4 d \sin \left(d x +c \right)^{2}}"," ",0,"-1/4/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+2*cos(d*x+c)^2-5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+2*cos(d*x+c))/sin(d*x+c)^2*a","B"
152,1,502,142,1.270000," ","int(cot(d*x+c)^5*(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(64 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+71 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-64 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-71 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)-64 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+54 \left(\cos^{3}\left(d x +c \right)\right)-71 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+64 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-24 \left(\cos^{2}\left(d x +c \right)\right)+71 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-14 \cos \left(d x +c \right)\right) a}{64 d \sin \left(d x +c \right)^{6}}"," ",0,"1/64/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))^2*(64*cos(d*x+c)^3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+71*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-64*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2-71*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-64*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+54*cos(d*x+c)^3-71*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+64*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-24*cos(d*x+c)^2+71*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-14*cos(d*x+c))/sin(d*x+c)^6*a","B"
153,1,656,226,1.356000," ","int((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^6,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(45045 \sin \left(d x +c \right) \left(\cos^{6}\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{13}{2}} \sqrt{2}+270270 \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{13}{2}} \sqrt{2}+675675 \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{13}{2}} \sqrt{2}+900900 \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{13}{2}} \sqrt{2}+675675 \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{13}{2}} \sqrt{2}+270270 \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{13}{2}} \sqrt{2}+45045 \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)-4150912 \left(\cos^{7}\left(d x +c \right)\right)-807424 \left(\cos^{6}\left(d x +c \right)\right)+5563904 \left(\cos^{5}\left(d x +c \right)\right)+2781952 \left(\cos^{4}\left(d x +c \right)\right)-2585600 \left(\cos^{3}\left(d x +c \right)\right)-1809920 \left(\cos^{2}\left(d x +c \right)\right)+564480 \cos \left(d x +c \right)+443520\right) a}{2882880 d \cos \left(d x +c \right)^{6} \sin \left(d x +c \right)}"," ",0,"1/2882880/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(45045*sin(d*x+c)*cos(d*x+c)^6*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)*2^(1/2)+270270*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)))^(13/2)*2^(1/2)+675675*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)))^(13/2)*2^(1/2)+900900*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)))^(13/2)*2^(1/2)+675675*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)))^(13/2)*2^(1/2)+270270*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)))^(13/2)*2^(1/2)+45045*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)-4150912*cos(d*x+c)^7-807424*cos(d*x+c)^6+5563904*cos(d*x+c)^5+2781952*cos(d*x+c)^4-2585600*cos(d*x+c)^3-1809920*cos(d*x+c)^2+564480*cos(d*x+c)+443520)/cos(d*x+c)^6/sin(d*x+c)*a","B"
154,1,407,170,1.279000," ","int((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^4,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(315 \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}} \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+945 \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}} \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+945 \sqrt{2}\, \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{7}{2}}+315 \sqrt{2}\, \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{7}{2}}+2704 \left(\cos^{5}\left(d x +c \right)\right)+1168 \left(\cos^{4}\left(d x +c \right)\right)-3488 \left(\cos^{3}\left(d x +c \right)\right)-1744 \left(\cos^{2}\left(d x +c \right)\right)+800 \cos \left(d x +c \right)+560\right) a}{2520 d \cos \left(d x +c \right)^{4} \sin \left(d x +c \right)}"," ",0,"1/2520/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(315*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)*2^(1/2)*sin(d*x+c)*cos(d*x+c)^4+945*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)*2^(1/2)*sin(d*x+c)*cos(d*x+c)^3+945*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)))^(7/2)+315*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)))^(7/2)+2704*cos(d*x+c)^5+1168*cos(d*x+c)^4-3488*cos(d*x+c)^3-1744*cos(d*x+c)^2+800*cos(d*x+c)+560)/cos(d*x+c)^4/sin(d*x+c)*a","B"
155,1,300,114,1.024000," ","int((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^2,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(5 \sqrt{2}\, \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{5}{2}}+10 \sqrt{2}\, \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{5}{2}}+5 \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)-8 \left(\cos^{3}\left(d x +c \right)\right)-16 \left(\cos^{2}\left(d x +c \right)\right)+16 \cos \left(d x +c \right)+8\right) a}{20 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}"," ",0,"1/20/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(5*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)))^(5/2)+10*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)))^(5/2)+5*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)-8*cos(d*x+c)^3-16*cos(d*x+c)^2+16*cos(d*x+c)+8)/sin(d*x+c)/cos(d*x+c)^2*a","B"
156,1,113,56,1.044000," ","int(cot(d*x+c)^2*(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-2 \cos \left(d x +c \right)\right) a}{d \sin \left(d x +c \right)}"," ",0,"1/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(2^(1/2)*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)))^(1/2)-2*cos(d*x+c))/sin(d*x+c)*a","A"
157,1,372,119,1.107000," ","int(cot(d*x+c)^4*(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(12 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-12 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-3 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-22 \left(\cos^{3}\left(d x +c \right)\right)-4 \left(\cos^{2}\left(d x +c \right)\right)+18 \cos \left(d x +c \right)\right) a}{12 d \sin \left(d x +c \right)^{3}}"," ",0,"1/12/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(12*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)+3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-12*2^(1/2)*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)))^(1/2)-3*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-22*cos(d*x+c)^3-4*cos(d*x+c)^2+18*cos(d*x+c))/sin(d*x+c)^3*a","B"
158,1,720,192,1.611000," ","int(cot(d*x+c)^6*(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(-480 \left(\cos^{3}\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)}}\, \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)-165 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+480 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+165 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+480 \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)}}\, \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)+898 \left(\cos^{4}\left(d x +c \right)\right)+165 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-480 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-702 \left(\cos^{3}\left(d x +c \right)\right)-165 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-730 \left(\cos^{2}\left(d x +c \right)\right)+630 \cos \left(d x +c \right)\right) a}{480 d \sin \left(d x +c \right)^{7}}"," ",0,"1/480/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))^2*(-480*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-165*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+480*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)+165*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+480*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+898*cos(d*x+c)^4+165*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-480*2^(1/2)*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)))^(1/2)-702*cos(d*x+c)^3-165*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-730*cos(d*x+c)^2+630*cos(d*x+c))/sin(d*x+c)^7*a","B"
159,1,500,161,1.319000," ","int((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^5,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(45045 \left(\cos^{6}\left(d x +c \right)\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{13}{2}}+270270 \left(\cos^{5}\left(d x +c \right)\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{13}{2}}+675675 \left(\cos^{4}\left(d x +c \right)\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{13}{2}}+900900 \left(\cos^{3}\left(d x +c \right)\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{13}{2}}+675675 \left(\cos^{2}\left(d x +c \right)\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{13}{2}}+270270 \cos \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{13}{2}}+45045 \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}}+9176192 \left(\cos^{6}\left(d x +c \right)\right)+4060544 \left(\cos^{5}\left(d x +c \right)\right)-1603968 \left(\cos^{4}\left(d x +c \right)\right)-3468160 \left(\cos^{3}\left(d x +c \right)\right)-568960 \left(\cos^{2}\left(d x +c \right)\right)+1088640 \cos \left(d x +c \right)+443520\right) a^{2}}{2882880 d \cos \left(d x +c \right)^{6}}"," ",0,"1/2882880/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(45045*cos(d*x+c)^6*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)+270270*cos(d*x+c)^5*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)+675675*cos(d*x+c)^4*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)+900900*cos(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)))^(13/2)+675675*cos(d*x+c)^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)))^(13/2)+270270*cos(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)))^(13/2)+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)))^(13/2)+9176192*cos(d*x+c)^6+4060544*cos(d*x+c)^5-1603968*cos(d*x+c)^4-3468160*cos(d*x+c)^3-568960*cos(d*x+c)^2+1088640*cos(d*x+c)+443520)/cos(d*x+c)^6*a^2","B"
160,1,362,121,1.244000," ","int((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^3,x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(315 \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\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{9}{2}}+1260 \left(\cos^{3}\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{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)+1890 \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\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{9}{2}}+1260 \sqrt{2}\, \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) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}}+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{9}{2}}+15776 \left(\cos^{4}\left(d x +c \right)\right)+7232 \left(\cos^{3}\left(d x +c \right)\right)-384 \left(\cos^{2}\left(d x +c \right)\right)-3040 \cos \left(d x +c \right)-1120\right) a^{2}}{5040 d \cos \left(d x +c \right)^{4}}"," ",0,"-1/5040/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(315*2^(1/2)*cos(d*x+c)^4*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)+1260*2^(1/2)*cos(d*x+c)^3*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)+1890*2^(1/2)*cos(d*x+c)^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)))^(9/2)+1260*2^(1/2)*cos(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)))^(9/2)+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)))^(9/2)+15776*cos(d*x+c)^4+7232*cos(d*x+c)^3-384*cos(d*x+c)^2-3040*cos(d*x+c)-1120)/cos(d*x+c)^4*a^2","B"
161,1,74,81,0.194000," ","int((a+a*sec(d*x+c))^(5/2)*tan(d*x+c),x)","\frac{\frac{2 \left(a +a \sec \left(d x +c \right)\right)^{\frac{5}{2}}}{5}+\frac{2 a \left(a +a \sec \left(d x +c \right)\right)^{\frac{3}{2}}}{3}+2 a^{2} \sqrt{a +a \sec \left(d x +c \right)}-2 a^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{a +a \sec \left(d x +c \right)}}{\sqrt{a}}\right)}{d}"," ",0,"1/d*(2/5*(a+a*sec(d*x+c))^(5/2)+2/3*a*(a+a*sec(d*x+c))^(3/2)+2*a^2*(a+a*sec(d*x+c))^(1/2)-2*a^(5/2)*arctanh((a+a*sec(d*x+c))^(1/2)/a^(1/2)))","A"
162,1,124,78,1.008000," ","int(cot(d*x+c)*(a+a*sec(d*x+c))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+4 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-2\right) a^{2}}{d}"," ",0,"-1/d*(a*(1+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*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-2)*a^2","A"
163,1,248,89,1.133000," ","int(cot(d*x+c)^3*(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(2 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-2 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-3 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+2 \cos \left(d x +c \right)\right) a^{2}}{2 d \left(-1+\cos \left(d x +c \right)\right)}"," ",0,"1/2/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(2*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+3*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+2*cos(d*x+c))/(-1+cos(d*x+c))*a^2","B"
164,1,376,122,1.327000," ","int(cot(d*x+c)^5*(a+a*sec(d*x+c))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(32 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+43 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)-64 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-86 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+32 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+30 \left(\cos^{2}\left(d x +c \right)\right)+43 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-22 \cos \left(d x +c \right)\right) a^{2}}{32 d \sin \left(d x +c \right)^{4}}"," ",0,"-1/32/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(32*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+43*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-64*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-86*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+32*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+30*cos(d*x+c)^2+43*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-22*cos(d*x+c))/sin(d*x+c)^4*a^2","B"
165,1,747,254,1.668000," ","int((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^6,x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(45045 \sin \left(d x +c \right) \left(\cos^{7}\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{15}{2}} \sqrt{2}+315315 \sin \left(d x +c \right) \left(\cos^{6}\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{15}{2}} \sqrt{2}+945945 \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{15}{2}} \sqrt{2}+1576575 \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{15}{2}} \sqrt{2}+1576575 \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{15}{2}} \sqrt{2}+945945 \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{15}{2}} \sqrt{2}+315315 \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{15}{2}} \sqrt{2}+45045 \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{15}{2}} \sin \left(d x +c \right)+4112896 \left(\cos^{8}\left(d x +c \right)\right)+9475072 \left(\cos^{7}\left(d x +c \right)\right)-9162752 \left(\cos^{6}\left(d x +c \right)\right)-12269056 \left(\cos^{5}\left(d x +c \right)\right)+980480 \left(\cos^{4}\left(d x +c \right)\right)+7605248 \left(\cos^{3}\left(d x +c \right)\right)+1860096 \left(\cos^{2}\left(d x +c \right)\right)-1833216 \cos \left(d x +c \right)-768768\right) a^{2}}{5765760 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{7}}"," ",0,"-1/5765760/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(45045*sin(d*x+c)*cos(d*x+c)^7*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)))^(15/2)*2^(1/2)+315315*sin(d*x+c)*cos(d*x+c)^6*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)))^(15/2)*2^(1/2)+945945*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)))^(15/2)*2^(1/2)+1576575*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)))^(15/2)*2^(1/2)+1576575*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)))^(15/2)*2^(1/2)+945945*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)))^(15/2)*2^(1/2)+315315*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)))^(15/2)*2^(1/2)+45045*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)))^(15/2)*sin(d*x+c)+4112896*cos(d*x+c)^8+9475072*cos(d*x+c)^7-9162752*cos(d*x+c)^6-12269056*cos(d*x+c)^5+980480*cos(d*x+c)^4+7605248*cos(d*x+c)^3+1860096*cos(d*x+c)^2-1833216*cos(d*x+c)-768768)/sin(d*x+c)/cos(d*x+c)^7*a^2","B"
166,1,498,198,1.425000," ","int((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^4,x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(693 \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{9}{2}} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)+2772 \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{9}{2}} \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)+4158 \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{9}{2}} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+2772 \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}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+693 \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}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-1664 \left(\cos^{6}\left(d x +c \right)\right)-21344 \left(\cos^{5}\left(d x +c \right)\right)+11296 \left(\cos^{4}\left(d x +c \right)\right)+16736 \left(\cos^{3}\left(d x +c \right)\right)+2144 \left(\cos^{2}\left(d x +c \right)\right)-5152 \cos \left(d x +c \right)-2016\right) a^{2}}{11088 d \cos \left(d x +c \right)^{5} \sin \left(d x +c \right)}"," ",0,"-1/11088/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(693*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)*cos(d*x+c)^5*sin(d*x+c)+2772*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)*cos(d*x+c)^4*sin(d*x+c)+4158*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)*cos(d*x+c)^3*sin(d*x+c)+2772*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)*cos(d*x+c)^2*sin(d*x+c)+693*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)*cos(d*x+c)*sin(d*x+c)-1664*cos(d*x+c)^6-21344*cos(d*x+c)^5+11296*cos(d*x+c)^4+16736*cos(d*x+c)^3+2144*cos(d*x+c)^2-5152*cos(d*x+c)-2016)/cos(d*x+c)^5/sin(d*x+c)*a^2","B"
167,1,391,142,1.061000," ","int((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^2,x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(21 \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}} \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+63 \sqrt{2}\, \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{7}{2}}+63 \sqrt{2}\, \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{7}{2}}+21 \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)-160 \left(\cos^{4}\left(d x +c \right)\right)+416 \left(\cos^{3}\left(d x +c \right)\right)-64 \left(\cos^{2}\left(d x +c \right)\right)-144 \cos \left(d x +c \right)-48\right) a^{2}}{168 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3}}"," ",0,"-1/168/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(21*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)*2^(1/2)*sin(d*x+c)*cos(d*x+c)^3+63*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)))^(7/2)+63*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)))^(7/2)+21*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)-160*cos(d*x+c)^4+416*cos(d*x+c)^3-64*cos(d*x+c)^2-144*cos(d*x+c)-48)/sin(d*x+c)/cos(d*x+c)^3*a^2","B"
168,1,192,58,1.007000," ","int(cot(d*x+c)^2*(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-\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)+4 \cos \left(d x +c \right) \sin \left(d x +c \right)\right) a^{2}}{d \left(\cos^{2}\left(d x +c \right)-1\right)}"," ",0,"1/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(cos(d*x+c)^2*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-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))+4*cos(d*x+c)*sin(d*x+c))/(cos(d*x+c)^2-1)*a^2","B"
169,1,214,84,1.184000," ","int(cot(d*x+c)^4*(a+a*sec(d*x+c))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 \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)}}\, \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 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-8 \left(\cos^{2}\left(d x +c \right)\right)+6 \cos \left(d x +c \right)\right) a^{2}}{3 d \sin \left(d x +c \right) \left(-1+\cos \left(d x +c \right)\right)}"," ",0,"-1/3/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-3*2^(1/2)*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)))^(1/2)-8*cos(d*x+c)^2+6*cos(d*x+c))/sin(d*x+c)/(-1+cos(d*x+c))*a^2","B"
170,1,542,147,1.409000," ","int(cot(d*x+c)^6*(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(40 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-80 \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)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+5 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+40 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-10 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-98 \left(\cos^{3}\left(d x +c \right)\right)+5 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+160 \left(\cos^{2}\left(d x +c \right)\right)-70 \cos \left(d x +c \right)\right) a^{2}}{40 d \sin \left(d x +c \right)^{5}}"," ",0,"1/40/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(40*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)-80*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+40*2^(1/2)*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)))^(1/2)-10*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-98*cos(d*x+c)^3+5*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+160*cos(d*x+c)^2-70*cos(d*x+c))/sin(d*x+c)^5*a^2","B"
171,1,293,106,1.329000," ","int(tan(d*x+c)^5/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(105 \left(\cos^{3}\left(d x +c \right)\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}+315 \left(\cos^{2}\left(d x +c \right)\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}+315 \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) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{2}+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}}-1472 \left(\cos^{3}\left(d x +c \right)\right)+736 \left(\cos^{2}\left(d x +c \right)\right)+288 \cos \left(d x +c \right)-240\right)}{840 d \cos \left(d x +c \right)^{3} a}"," ",0,"-1/840/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(105*cos(d*x+c)^3*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)+315*cos(d*x+c)^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)*2^(1/2)+315*cos(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)+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)-1472*cos(d*x+c)^3+736*cos(d*x+c)^2+288*cos(d*x+c)-240)/cos(d*x+c)^3/a","B"
172,1,155,66,1.327000," ","int(tan(d*x+c)^3/(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 \cos \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}}+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}}-8 \cos \left(d x +c \right)+4\right)}{6 d \cos \left(d x +c \right) a}"," ",0,"1/6/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*cos(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)+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)-8*cos(d*x+c)+4)/cos(d*x+c)/a","B"
173,1,26,25,0.172000," ","int(tan(d*x+c)/(a+a*sec(d*x+c))^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{a +a \sec \left(d x +c \right)}}{\sqrt{a}}\right)}{d \sqrt{a}}"," ",0,"-2*arctanh((a+a*sec(d*x+c))^(1/2)/a^(1/2))/d/a^(1/2)","A"
174,1,259,75,1.320000," ","int(cot(d*x+c)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(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) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\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)-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) \sqrt{2}-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+2 \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \sin \left(d x +c \right)^{2} a}"," ",0,"1/2/d*(2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+2*cos(d*x+c)^2-2*cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^2/a","B"
175,1,504,123,1.519000," ","int(cot(d*x+c)^3/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2} \left(48 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+48 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+27 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-48 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+27 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)-48 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+62 \left(\cos^{3}\left(d x +c \right)\right)-27 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+4 \left(\cos^{2}\left(d x +c \right)\right)-27 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-42 \cos \left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{6} a}"," ",0,"-1/48/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))*(-1+cos(d*x+c))^2*(48*cos(d*x+c)^3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+48*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+27*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-48*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+27*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-48*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+62*cos(d*x+c)^3-27*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+4*cos(d*x+c)^2-27*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-42*cos(d*x+c))/sin(d*x+c)^6/a","B"
176,1,746,177,1.854000," ","int(cot(d*x+c)^5/(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\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)^{3} \left(3840 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+2265 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+3840 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+2265 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-7680 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+5642 \left(\cos^{5}\left(d x +c \right)\right)-4530 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-7680 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+556 \left(\cos^{4}\left(d x +c \right)\right)-4530 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)+3840 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-7928 \left(\cos^{3}\left(d x +c \right)\right)+2265 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+3840 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-460 \left(\cos^{2}\left(d x +c \right)\right)+2265 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+3150 \cos \left(d x +c \right)\right)}{3840 d \sin \left(d x +c \right)^{10} a}"," ",0,"1/3840/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^3*(3840*cos(d*x+c)^5*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))+2265*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+3840*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+2265*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-7680*cos(d*x+c)^3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+5642*cos(d*x+c)^5-4530*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-7680*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+556*cos(d*x+c)^4-4530*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2+3840*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-7928*cos(d*x+c)^3+2265*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+3840*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-460*cos(d*x+c)^2+2265*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+3150*cos(d*x+c))/sin(d*x+c)^10/a","B"
177,1,480,165,1.403000," ","int(tan(d*x+c)^6/(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(315 \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{9}{2}} \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)+1260 \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{9}{2}} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+1890 \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}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+1260 \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}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+315 \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{9}{2}} \sin \left(d x +c \right)-12256 \left(\cos^{5}\left(d x +c \right)\right)+11168 \left(\cos^{4}\left(d x +c \right)\right)+5312 \left(\cos^{3}\left(d x +c \right)\right)-4064 \left(\cos^{2}\left(d x +c \right)\right)-1280 \cos \left(d x +c \right)+1120\right)}{5040 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4} a}"," ",0,"1/5040/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(315*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)*cos(d*x+c)^4*sin(d*x+c)+1260*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)*cos(d*x+c)^3*sin(d*x+c)+1890*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)*cos(d*x+c)^2*sin(d*x+c)+1260*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)*cos(d*x+c)*sin(d*x+c)+315*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)-12256*cos(d*x+c)^5+11168*cos(d*x+c)^4+5312*cos(d*x+c)^3-4064*cos(d*x+c)^2-1280*cos(d*x+c)+1120)/sin(d*x+c)/cos(d*x+c)^4/a","B"
178,1,231,109,1.269000," ","int(tan(d*x+c)^4/(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(15 \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{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}+15 \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) \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)+68 \left(\cos^{3}\left(d x +c \right)\right)-64 \left(\cos^{2}\left(d x +c \right)\right)-16 \cos \left(d x +c \right)+12\right)}{30 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2} a}"," ",0,"1/30/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(15*sin(d*x+c)*cos(d*x+c)^2*(-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)+15*(-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))*cos(d*x+c)*2^(1/2)*sin(d*x+c)+68*cos(d*x+c)^3-64*cos(d*x+c)^2-16*cos(d*x+c)+12)/sin(d*x+c)/cos(d*x+c)^2/a","B"
179,1,116,55,0.934000," ","int(tan(d*x+c)^2/(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-2 \cos \left(d x +c \right)+2\right)}{d \sin \left(d x +c \right) a}"," ",0,"1/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(2^(1/2)*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)))^(1/2)-2*cos(d*x+c)+2)/sin(d*x+c)/a","B"
180,1,374,139,1.302000," ","int(cot(d*x+c)^2/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(8 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+7 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-8 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-6 \left(\cos^{3}\left(d x +c \right)\right)-7 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4 \left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{3} a}"," ",0,"-1/8/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(8*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)+7*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-8*2^(1/2)*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)))^(1/2)-6*cos(d*x+c)^3-7*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4*cos(d*x+c)^2+2*cos(d*x+c))/sin(d*x+c)^3/a","B"
181,1,722,216,1.508000," ","int(cot(d*x+c)^4/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2} \left(-384 \left(\cos^{3}\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)}}\, \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)-321 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-384 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-321 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+384 \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)}}\, \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)+410 \left(\cos^{4}\left(d x +c \right)\right)+321 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+384 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+142 \left(\cos^{3}\left(d x +c \right)\right)+321 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-298 \left(\cos^{2}\left(d x +c \right)\right)-126 \cos \left(d x +c \right)\right)}{384 d \sin \left(d x +c \right)^{7} a}"," ",0,"-1/384/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))*(-1+cos(d*x+c))^2*(-384*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-321*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-384*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)-321*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+384*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+410*cos(d*x+c)^4+321*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+384*2^(1/2)*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)))^(1/2)+142*cos(d*x+c)^3+321*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-298*cos(d*x+c)^2-126*cos(d*x+c))/sin(d*x+c)^7/a","B"
182,1,1068,291,1.500000," ","int(cot(d*x+c)^6/(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\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)^{3} \left(-15360 \sqrt{-\frac{2 \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) \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)-12525 \sqrt{-\frac{2 \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) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-15360 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \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)-12525 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+30720 \left(\cos^{3}\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)}}\, \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)+19474 \left(\cos^{6}\left(d x +c \right)\right)+25050 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+30720 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+6902 \left(\cos^{5}\left(d x +c \right)\right)+25050 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-15360 \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)}}\, \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)-28788 \left(\cos^{4}\left(d x +c \right)\right)-12525 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-15360 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-12316 \left(\cos^{3}\left(d x +c \right)\right)-12525 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+12130 \left(\cos^{2}\left(d x +c \right)\right)+5670 \cos \left(d x +c \right)\right)}{15360 d \sin \left(d x +c \right)^{11} a}"," ",0,"1/15360/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^3*(-15360*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*sin(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))-12525*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-15360*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(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))-12525*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+30720*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+19474*cos(d*x+c)^6+25050*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+30720*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)+6902*cos(d*x+c)^5+25050*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-15360*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-28788*cos(d*x+c)^4-12525*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-15360*2^(1/2)*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)))^(1/2)-12316*cos(d*x+c)^3-12525*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+12130*cos(d*x+c)^2+5670*cos(d*x+c))/sin(d*x+c)^11/a","B"
183,1,224,86,1.126000," ","int(tan(d*x+c)^5/(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(5 \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}\, \left(\cos^{2}\left(d x +c \right)\right)+10 \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}\, \cos \left(d x +c \right)+5 \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}}+8 \left(\cos^{2}\left(d x +c \right)\right)-24 \cos \left(d x +c \right)+8\right)}{20 d \cos \left(d x +c \right)^{2} a^{2}}"," ",0,"1/20/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(5*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)*cos(d*x+c)^2+10*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)*cos(d*x+c)+5*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)+8*cos(d*x+c)^2-24*cos(d*x+c)+8)/cos(d*x+c)^2/a^2","B"
184,1,81,46,1.046000," ","int(tan(d*x+c)^3/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-2\right)}{d \,a^{2}}"," ",0,"-1/d*(a*(1+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*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-2)/a^2","A"
185,1,45,46,0.135000," ","int(tan(d*x+c)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\frac{2}{a \sqrt{a +a \sec \left(d x +c \right)}}-\frac{2 \arctanh \left(\frac{\sqrt{a +a \sec \left(d x +c \right)}}{\sqrt{a}}\right)}{a^{\frac{3}{2}}}}{d}"," ",0,"1/d*(2/a/(a+a*sec(d*x+c))^(1/2)-2/a^(3/2)*arctanh((a+a*sec(d*x+c))^(1/2)/a^(1/2)))","A"
186,1,376,95,1.293000," ","int(cot(d*x+c)/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(12 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+3 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)+24 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+6 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+12 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+22 \left(\cos^{2}\left(d x +c \right)\right)+3 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+18 \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{12 d \sin \left(d x +c \right)^{4} a^{2}}"," ",0,"-1/12/d*(-1+cos(d*x+c))^2*(12*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2+24*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+6*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+12*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+22*cos(d*x+c)^2+3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+18*cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^4/a^2","B"
187,1,514,143,1.362000," ","int(cot(d*x+c)^3/(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{3} \left(480 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+165 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+960 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+330 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+898 \left(\cos^{4}\left(d x +c \right)\right)-960 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+702 \left(\cos^{3}\left(d x +c \right)\right)-330 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-480 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-730 \left(\cos^{2}\left(d x +c \right)\right)-165 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-630 \cos \left(d x +c \right)\right)}{480 d \sin \left(d x +c \right)^{8} a^{2}}"," ",0,"1/480/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))*(-1+cos(d*x+c))^3*(480*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+165*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+960*cos(d*x+c)^3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+330*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+898*cos(d*x+c)^4-960*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+702*cos(d*x+c)^3-330*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-480*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-730*cos(d*x+c)^2-165*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-630*cos(d*x+c))/sin(d*x+c)^8/a^2","B"
188,1,866,197,1.378000," ","int(cot(d*x+c)^5/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\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)^{4} \left(10752 \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) \left(\cos^{6}\left(d x +c \right)\right) \sqrt{2}+21504 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+4263 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{6}\left(d x +c \right)\right)-10752 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+8526 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-43008 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-4263 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+20726 \left(\cos^{6}\left(d x +c \right)\right)-10752 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-17052 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+16074 \left(\cos^{5}\left(d x +c \right)\right)+21504 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-4263 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)-33076 \left(\cos^{4}\left(d x +c \right)\right)+10752 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+8526 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-28476 \left(\cos^{3}\left(d x +c \right)\right)+4263 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+14462 \left(\cos^{2}\left(d x +c \right)\right)+12978 \cos \left(d x +c \right)\right)}{10752 d \sin \left(d x +c \right)^{12} a^{2}}"," ",0,"-1/10752/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^4*(10752*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^6*2^(1/2)+21504*cos(d*x+c)^5*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))+4263*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^6-10752*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+8526*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-43008*cos(d*x+c)^3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-4263*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+20726*cos(d*x+c)^6-10752*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2-17052*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+16074*cos(d*x+c)^5+21504*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-4263*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-33076*cos(d*x+c)^4+10752*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+8526*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-28476*cos(d*x+c)^3+4263*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+14462*cos(d*x+c)^2+12978*cos(d*x+c))/sin(d*x+c)^12/a^2","B"
189,1,391,137,1.372000," ","int(tan(d*x+c)^6/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(105 \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}} \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+315 \sqrt{2}\, \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{7}{2}}+315 \sqrt{2}\, \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{7}{2}}+105 \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)+2336 \left(\cos^{4}\left(d x +c \right)\right)-2848 \left(\cos^{3}\left(d x +c \right)\right)+128 \left(\cos^{2}\left(d x +c \right)\right)+624 \cos \left(d x +c \right)-240\right)}{840 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3} a^{2}}"," ",0,"-1/840/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(105*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)*2^(1/2)*sin(d*x+c)*cos(d*x+c)^3+315*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)))^(7/2)+315*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)))^(7/2)+105*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)+2336*cos(d*x+c)^4-2848*cos(d*x+c)^3+128*cos(d*x+c)^2+624*cos(d*x+c)-240)/sin(d*x+c)/cos(d*x+c)^3/a^2","B"
190,1,142,83,1.234000," ","int(tan(d*x+c)^4/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(3 \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)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-8 \left(\cos^{2}\left(d x +c \right)\right)+10 \cos \left(d x +c \right)-2\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right) a^{2}}"," ",0,"-1/3/d*(3*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-8*cos(d*x+c)^2+10*cos(d*x+c)-2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)/a^2","A"
191,1,142,70,0.903000," ","int(tan(d*x+c)^2/(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\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)+2 \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)\right)}{d \,a^{2}}"," ",0,"1/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+2*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)))/a^2","B"
192,1,542,184,1.330000," ","int(cot(d*x+c)^2/(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(64 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+128 \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)}}\, \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)+71 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+64 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+142 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+71 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-54 \left(\cos^{3}\left(d x +c \right)\right)-24 \left(\cos^{2}\left(d x +c \right)\right)+14 \cos \left(d x +c \right)\right)}{64 d \sin \left(d x +c \right)^{5} a^{2}}"," ",0,"1/64/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(64*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)+128*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+71*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+64*2^(1/2)*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)))^(1/2)+142*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+71*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-54*cos(d*x+c)^3-24*cos(d*x+c)^2+14*cos(d*x+c))/sin(d*x+c)^5/a^2","B"
193,1,732,263,1.472000," ","int(cot(d*x+c)^4/(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{3} \left(-1536 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \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)-1599 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-3072 \left(\cos^{3}\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)}}\, \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)-3198 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+1638 \left(\cos^{5}\left(d x +c \right)\right)+3072 \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)}}\, \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)+984 \left(\cos^{4}\left(d x +c \right)\right)+3198 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+1536 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-1380 \left(\cos^{3}\left(d x +c \right)\right)+1599 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-856 \left(\cos^{2}\left(d x +c \right)\right)+126 \cos \left(d x +c \right)\right)}{1536 d \sin \left(d x +c \right)^{9} a^{2}}"," ",0,"1/1536/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))*(-1+cos(d*x+c))^3*(-1536*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(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))-1599*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-3072*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-3198*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+1638*cos(d*x+c)^5+3072*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+984*cos(d*x+c)^4+3198*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+1536*2^(1/2)*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)))^(1/2)-1380*cos(d*x+c)^3+1599*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-856*cos(d*x+c)^2+126*cos(d*x+c))/sin(d*x+c)^9/a^2","B"
194,1,1240,338,1.545000," ","int(cot(d*x+c)^6/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\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)^{4} \left(-245760 \left(\cos^{6}\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)}}\, \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)-245445 \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-491520 \sqrt{-\frac{2 \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) \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)-490890 \sqrt{-\frac{2 \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) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+245760 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \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)+302082 \left(\cos^{7}\left(d x +c \right)\right)+245445 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+983040 \left(\cos^{3}\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)}}\, \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)+207048 \left(\cos^{6}\left(d x +c \right)\right)+981780 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+245760 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-457998 \left(\cos^{5}\left(d x +c \right)\right)+245445 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-491520 \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)}}\, \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)-362512 \left(\cos^{4}\left(d x +c \right)\right)-490890 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-245760 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+195222 \left(\cos^{3}\left(d x +c \right)\right)-245445 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+164680 \left(\cos^{2}\left(d x +c \right)\right)+630 \cos \left(d x +c \right)\right)}{245760 d \sin \left(d x +c \right)^{13} a^{2}}"," ",0,"-1/245760/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^4*(-245760*cos(d*x+c)^6*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-245445*cos(d*x+c)^6*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-491520*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*sin(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))-490890*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+245760*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(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))+302082*cos(d*x+c)^7+245445*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+983040*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+207048*cos(d*x+c)^6+981780*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+245760*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)-457998*cos(d*x+c)^5+245445*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-491520*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-362512*cos(d*x+c)^4-490890*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-245760*2^(1/2)*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)))^(1/2)+195222*cos(d*x+c)^3-245445*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+164680*cos(d*x+c)^2+630*cos(d*x+c))/sin(d*x+c)^13/a^2","B"
195,1,155,66,1.190000," ","int(tan(d*x+c)^5/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 \cos \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}}+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}}+32 \cos \left(d x +c \right)-4\right)}{6 d \cos \left(d x +c \right) a^{3}}"," ",0,"-1/6/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*cos(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)+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)+32*cos(d*x+c)-4)/cos(d*x+c)/a^3","B"
196,1,154,46,1.136000," ","int(tan(d*x+c)^3/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+4 \cos \left(d x +c \right)\right)}{d \left(1+\cos \left(d x +c \right)\right) a^{3}}"," ",0,"-1/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+4*cos(d*x+c))/(1+cos(d*x+c))/a^3","B"
197,1,62,66,0.128000," ","int(tan(d*x+c)/(a+a*sec(d*x+c))^(5/2),x)","\frac{-\frac{2 \arctanh \left(\frac{\sqrt{a +a \sec \left(d x +c \right)}}{\sqrt{a}}\right)}{a^{\frac{5}{2}}}+\frac{2}{a^{2} \sqrt{a +a \sec \left(d x +c \right)}}+\frac{2}{3 a \left(a +a \sec \left(d x +c \right)\right)^{\frac{3}{2}}}}{d}"," ",0,"1/d*(-2/a^(5/2)*arctanh((a+a*sec(d*x+c))^(1/2)/a^(1/2))+2/a^2/(a+a*sec(d*x+c))^(1/2)+2/3/a/(a+a*sec(d*x+c))^(3/2))","A"
198,1,496,115,1.329000," ","int(cot(d*x+c)/(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{3} \left(40 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+5 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+120 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+15 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)+120 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+98 \left(\cos^{3}\left(d x +c \right)\right)+15 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+40 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}+160 \left(\cos^{2}\left(d x +c \right)\right)+5 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+70 \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{40 d \sin \left(d x +c \right)^{6} a^{3}}"," ",0,"1/40/d*(-1+cos(d*x+c))^3*(40*cos(d*x+c)^3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+5*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+120*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+15*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2+120*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+98*cos(d*x+c)^3+15*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+40*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)+160*cos(d*x+c)^2+5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+70*cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^6/a^3","B"
199,1,744,163,1.572000," ","int(cot(d*x+c)^3/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{4} \left(6720 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+1365 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+20160 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+4095 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+13440 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+16034 \left(\cos^{5}\left(d x +c \right)\right)+2730 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-13440 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+25280 \left(\cos^{4}\left(d x +c \right)\right)-2730 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)-20160 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-3164 \left(\cos^{3}\left(d x +c \right)\right)-4095 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-6720 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-24080 \left(\cos^{2}\left(d x +c \right)\right)-1365 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-10710 \cos \left(d x +c \right)\right)}{6720 d \sin \left(d x +c \right)^{10} a^{3}}"," ",0,"-1/6720/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))*(-1+cos(d*x+c))^4*(6720*cos(d*x+c)^5*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))+1365*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+20160*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+4095*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+13440*cos(d*x+c)^3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+16034*cos(d*x+c)^5+2730*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-13440*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+25280*cos(d*x+c)^4-2730*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-20160*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-3164*cos(d*x+c)^3-4095*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-6720*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-24080*cos(d*x+c)^2-1365*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-10710*cos(d*x+c))/sin(d*x+c)^10/a^3","B"
200,1,986,217,1.490000," ","int(cot(d*x+c)^5/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\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)^{5} \left(322560 \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) \left(\cos^{7}\left(d x +c \right)\right) \sqrt{2}+82845 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{7}\left(d x +c \right)\right)+967680 \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) \left(\cos^{6}\left(d x +c \right)\right) \sqrt{2}+248535 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{6}\left(d x +c \right)\right)+322560 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+82845 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-1612800 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+764402 \left(\cos^{7}\left(d x +c \right)\right)-414225 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-1612800 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+1183040 \left(\cos^{6}\left(d x +c \right)\right)-414225 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+322560 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-807214 \left(\cos^{5}\left(d x +c \right)\right)+82845 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right)+967680 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-2224080 \left(\cos^{4}\left(d x +c \right)\right)+248535 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+322560 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}-378378 \left(\cos^{3}\left(d x +c \right)\right)+82845 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+1063440 \left(\cos^{2}\left(d x +c \right)\right)+479430 \cos \left(d x +c \right)\right)}{322560 d \sin \left(d x +c \right)^{14} a^{3}}"," ",0,"1/322560/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^5*(322560*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^7*2^(1/2)+82845*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^7+967680*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^6*2^(1/2)+248535*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^6+322560*cos(d*x+c)^5*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))+82845*cos(d*x+c)^5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-1612800*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+764402*cos(d*x+c)^7-414225*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-1612800*cos(d*x+c)^3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+1183040*cos(d*x+c)^6-414225*cos(d*x+c)^3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+322560*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*cos(d*x+c)^2-807214*cos(d*x+c)^5+82845*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2+967680*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-2224080*cos(d*x+c)^4+248535*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+322560*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)-378378*cos(d*x+c)^3+82845*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+1063440*cos(d*x+c)^2+479430*cos(d*x+c))/sin(d*x+c)^14/a^3","B"
201,1,302,111,1.216000," ","int(tan(d*x+c)^6/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(15 \sqrt{2}\, \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{5}{2}}+30 \sqrt{2}\, \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{5}{2}}+15 \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)-184 \left(\cos^{3}\left(d x +c \right)\right)+272 \left(\cos^{2}\left(d x +c \right)\right)-112 \cos \left(d x +c \right)+24\right)}{60 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2} a^{3}}"," ",0,"1/60/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(15*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)))^(5/2)+30*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)))^(5/2)+15*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)-184*cos(d*x+c)^3+272*cos(d*x+c)^2-112*cos(d*x+c)+24)/sin(d*x+c)/cos(d*x+c)^2/a^3","B"
202,1,326,96,1.209000," ","int(tan(d*x+c)^4/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(\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) \cos \left(d x +c \right)+\sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+4 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right)+4 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-2 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \left(1+\cos \left(d x +c \right)\right) a^{3}}"," ",0,"-1/d*(2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)+2^(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))+4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)+4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-2*sin(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/(1+cos(d*x+c))/a^3","B"
203,1,370,107,0.925000," ","int(tan(d*x+c)^2/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\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) \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)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+2 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-2 \left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)\right)}{2 d \left(1+\cos \left(d x +c \right)\right) \sin \left(d x +c \right) a^{3}}"," ",0,"1/2/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(2*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+3*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+2*2^(1/2)*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)))^(1/2)+3*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-2*cos(d*x+c)^2+2*cos(d*x+c))/(1+cos(d*x+c))/sin(d*x+c)/a^3","B"
204,1,714,229,1.399000," ","int(cot(d*x+c)^2/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{3} \left(768 \left(\cos^{3}\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)}}\, \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)+2304 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+957 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+2304 \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)}}\, \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)+2871 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+768 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+2871 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-818 \left(\cos^{4}\left(d x +c \right)\right)+957 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-698 \left(\cos^{3}\left(d x +c \right)\right)+370 \left(\cos^{2}\left(d x +c \right)\right)+378 \cos \left(d x +c \right)\right)}{768 d \sin \left(d x +c \right)^{7} a^{3}}"," ",0,"-1/768/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^3*(768*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+2304*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)+957*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+2304*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+2871*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+768*2^(1/2)*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)))^(1/2)+2871*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-818*cos(d*x+c)^4+957*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-698*cos(d*x+c)^3+370*cos(d*x+c)^2+378*cos(d*x+c))/sin(d*x+c)^7/a^3","B"
205,1,1066,310,1.559000," ","int(cot(d*x+c)^4/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{4} \left(24576 \sqrt{-\frac{2 \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) \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)+73728 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \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)+29049 \sqrt{-\frac{2 \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) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+49152 \left(\cos^{3}\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)}}\, \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)+87147 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-49152 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+58098 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-29258 \left(\cos^{6}\left(d x +c \right)\right)-73728 \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)}}\, \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)-58098 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-28466 \left(\cos^{5}\left(d x +c \right)\right)-24576 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-87147 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+28116 \left(\cos^{4}\left(d x +c \right)\right)-29049 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+34852 \left(\cos^{3}\left(d x +c \right)\right)-4490 \left(\cos^{2}\left(d x +c \right)\right)-8946 \cos \left(d x +c \right)\right)}{24576 d \sin \left(d x +c \right)^{11} a^{3}}"," ",0,"1/24576/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))*(-1+cos(d*x+c))^4*(24576*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*sin(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))+73728*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(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))+29049*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+49152*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+87147*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-49152*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)+58098*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-29258*cos(d*x+c)^6-73728*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-58098*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-28466*cos(d*x+c)^5-24576*2^(1/2)*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)))^(1/2)-87147*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+28116*cos(d*x+c)^4-29049*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+34852*cos(d*x+c)^3-4490*cos(d*x+c)^2-8946*cos(d*x+c))/sin(d*x+c)^11/a^3","B"
206,1,1412,385,1.624000," ","int(cot(d*x+c)^6/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\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)^{5} \left(-983040 \left(\cos^{7}\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)}}\, \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)-1116915 \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-2949120 \left(\cos^{6}\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)}}\, \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)-3350745 \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-983040 \sqrt{-\frac{2 \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) \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)+1278126 \left(\cos^{8}\left(d x +c \right)\right)-1116915 \sqrt{-\frac{2 \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) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+4915200 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \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)+1363110 \left(\cos^{7}\left(d x +c \right)\right)+5584575 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+4915200 \left(\cos^{3}\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)}}\, \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)-1972170 \left(\cos^{6}\left(d x +c \right)\right)+5584575 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-983040 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-2720050 \left(\cos^{5}\left(d x +c \right)\right)-1116915 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-2949120 \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)}}\, \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)+810890 \left(\cos^{4}\left(d x +c \right)\right)-3350745 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-983040 \sqrt{2}\, \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) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+1673842 \left(\cos^{3}\left(d x +c \right)\right)-1116915 \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+30610 \left(\cos^{2}\left(d x +c \right)\right)-267750 \cos \left(d x +c \right)\right)}{983040 d \sin \left(d x +c \right)^{15} a^{3}}"," ",0,"1/983040/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^5*(-983040*cos(d*x+c)^7*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-1116915*cos(d*x+c)^7*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-2949120*cos(d*x+c)^6*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-3350745*cos(d*x+c)^6*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-983040*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*sin(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))+1278126*cos(d*x+c)^8-1116915*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+4915200*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(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))+1363110*cos(d*x+c)^7+5584575*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+4915200*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-1972170*cos(d*x+c)^6+5584575*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-983040*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)-2720050*cos(d*x+c)^5-1116915*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-2949120*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+810890*cos(d*x+c)^4-3350745*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-983040*2^(1/2)*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)))^(1/2)+1673842*cos(d*x+c)^3-1116915*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+30610*cos(d*x+c)^2-267750*cos(d*x+c))/sin(d*x+c)^15/a^3","B"
207,1,724,148,1.167000," ","int(tan(f*x+e)^2/(a+a*sec(f*x+e))^(9/2),x)","-\frac{\left(192 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+384 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+273 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right)+546 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right)-384 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-314 \left(\cos^{5}\left(f x +e \right)\right)-192 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-546 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right)+216 \left(\cos^{4}\left(f x +e \right)\right)-273 \sin \left(f x +e \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+348 \left(\cos^{3}\left(f x +e \right)\right)-88 \left(\cos^{2}\left(f x +e \right)\right)-162 \cos \left(f x +e \right)\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{192 f \sin \left(f x +e \right)^{3} \left(1+\cos \left(f x +e \right)\right)^{2} a^{5}}"," ",0,"-1/192/f*(192*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)^4*sin(f*x+e)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+384*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+273*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)^4*sin(f*x+e)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))+546*cos(f*x+e)^3*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))-384*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-314*cos(f*x+e)^5-192*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-546*cos(f*x+e)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))+216*cos(f*x+e)^4-273*sin(f*x+e)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+348*cos(f*x+e)^3-88*cos(f*x+e)^2-162*cos(f*x+e))*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^3/(1+cos(f*x+e))^2/a^5","B"
208,0,0,121,2.550000," ","int((a+a*sec(d*x+c))^n*(e*tan(d*x+c))^m,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(e \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+a*sec(d*x+c))^n*(e*tan(d*x+c))^m,x)","F"
209,0,0,229,1.901000," ","int((a+a*sec(d*x+c))^3*(e*tan(d*x+c))^m,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{3} \left(e \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+a*sec(d*x+c))^3*(e*tan(d*x+c))^m,x)","F"
210,0,0,153,2.372000," ","int((a+a*sec(d*x+c))^2*(e*tan(d*x+c))^m,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{2} \left(e \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+a*sec(d*x+c))^2*(e*tan(d*x+c))^m,x)","F"
211,0,0,121,2.452000," ","int((a+a*sec(d*x+c))*(e*tan(d*x+c))^m,x)","\int \left(a +a \sec \left(d x +c \right)\right) \left(e \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+a*sec(d*x+c))*(e*tan(d*x+c))^m,x)","F"
212,0,0,122,2.451000," ","int((e*tan(d*x+c))^m/(a+a*sec(d*x+c)),x)","\int \frac{\left(e \tan \left(d x +c \right)\right)^{m}}{a +a \sec \left(d x +c \right)}\, dx"," ",0,"int((e*tan(d*x+c))^m/(a+a*sec(d*x+c)),x)","F"
213,0,0,161,1.722000," ","int((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^2,x)","\int \frac{\left(e \tan \left(d x +c \right)\right)^{m}}{\left(a +a \sec \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^2,x)","F"
214,0,0,238,1.848000," ","int((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^3,x)","\int \frac{\left(e \tan \left(d x +c \right)\right)^{m}}{\left(a +a \sec \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^3,x)","F"
215,0,0,119,1.610000," ","int((a+a*sec(d*x+c))^(3/2)*(e*tan(d*x+c))^m,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{\frac{3}{2}} \left(e \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+a*sec(d*x+c))^(3/2)*(e*tan(d*x+c))^m,x)","F"
216,0,0,119,1.614000," ","int((a+a*sec(d*x+c))^(1/2)*(e*tan(d*x+c))^m,x)","\int \sqrt{a +a \sec \left(d x +c \right)}\, \left(e \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+a*sec(d*x+c))^(1/2)*(e*tan(d*x+c))^m,x)","F"
217,0,0,119,1.668000," ","int((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^(1/2),x)","\int \frac{\left(e \tan \left(d x +c \right)\right)^{m}}{\sqrt{a +a \sec \left(d x +c \right)}}\, dx"," ",0,"int((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^(1/2),x)","F"
218,0,0,119,1.548000," ","int((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^(3/2),x)","\int \frac{\left(e \tan \left(d x +c \right)\right)^{m}}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^(3/2),x)","F"
219,0,0,125,1.392000," ","int((a+a*sec(d*x+c))^n*tan(d*x+c)^7,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(\tan^{7}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*tan(d*x+c)^7,x)","F"
220,0,0,99,1.186000," ","int((a+a*sec(d*x+c))^n*tan(d*x+c)^5,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(\tan^{5}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*tan(d*x+c)^5,x)","F"
221,0,0,71,1.160000," ","int((a+a*sec(d*x+c))^n*tan(d*x+c)^3,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(\tan^{3}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*tan(d*x+c)^3,x)","F"
222,0,0,45,1.148000," ","int((a+a*sec(d*x+c))^n*tan(d*x+c),x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \tan \left(d x +c \right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*tan(d*x+c),x)","F"
223,0,0,74,1.438000," ","int(cot(d*x+c)*(a+a*sec(d*x+c))^n,x)","\int \cot \left(d x +c \right) \left(a +a \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cot(d*x+c)*(a+a*sec(d*x+c))^n,x)","F"
224,0,0,125,1.063000," ","int(cot(d*x+c)^3*(a+a*sec(d*x+c))^n,x)","\int \left(\cot^{3}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cot(d*x+c)^3*(a+a*sec(d*x+c))^n,x)","F"
225,0,0,100,1.035000," ","int((a+a*sec(d*x+c))^n*tan(d*x+c)^4,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(\tan^{4}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*tan(d*x+c)^4,x)","F"
226,0,0,100,0.761000," ","int((a+a*sec(d*x+c))^n*tan(d*x+c)^2,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(\tan^{2}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*tan(d*x+c)^2,x)","F"
227,0,0,98,1.029000," ","int(cot(d*x+c)^2*(a+a*sec(d*x+c))^n,x)","\int \left(\cot^{2}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cot(d*x+c)^2*(a+a*sec(d*x+c))^n,x)","F"
228,0,0,100,1.134000," ","int(cot(d*x+c)^4*(a+a*sec(d*x+c))^n,x)","\int \left(\cot^{4}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cot(d*x+c)^4*(a+a*sec(d*x+c))^n,x)","F"
229,0,0,100,1.756000," ","int((a+a*sec(d*x+c))^n*tan(d*x+c)^(3/2),x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*tan(d*x+c)^(3/2),x)","F"
230,0,0,100,1.733000," ","int((a+a*sec(d*x+c))^n*tan(d*x+c)^(1/2),x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(\sqrt{\tan}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*tan(d*x+c)^(1/2),x)","F"
231,0,0,99,1.536000," ","int((a+a*sec(d*x+c))^n/tan(d*x+c)^(1/2),x)","\int \frac{\left(a +a \sec \left(d x +c \right)\right)^{n}}{\sqrt{\tan \left(d x +c \right)}}\, dx"," ",0,"int((a+a*sec(d*x+c))^n/tan(d*x+c)^(1/2),x)","F"
232,0,0,100,1.443000," ","int((a+a*sec(d*x+c))^n/tan(d*x+c)^(3/2),x)","\int \frac{\left(a +a \sec \left(d x +c \right)\right)^{n}}{\tan \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+a*sec(d*x+c))^n/tan(d*x+c)^(3/2),x)","F"
233,1,648,291,2.483000," ","int((e*cot(d*x+c))^(5/2)*(a+a*sec(d*x+c)),x)","\frac{a \left(-1+\cos \left(d x +c \right)\right) \left(3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-4 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \cos \left(d x +c \right) \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}}{6 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)}"," ",0,"1/6*a/d*(-1+cos(d*x+c))*(3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-4*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+2*cos(d*x+c)*2^(1/2))*(1+cos(d*x+c))^2*(e*cos(d*x+c)/sin(d*x+c))^(5/2)/cos(d*x+c)^3/sin(d*x+c)*2^(1/2)","C"
234,1,1390,319,2.348000," ","int((e*cot(d*x+c))^(3/2)*(a+a*sec(d*x+c)),x)","-\frac{a \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-4 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-4 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+4 \cos \left(d x +c \right) \sqrt{2}\right) \sin \left(d x +c \right) \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"-1/2*a/d*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-4*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-4*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+4*cos(d*x+c)*2^(1/2))*sin(d*x+c)*(e*cos(d*x+c)/sin(d*x+c))^(3/2)/cos(d*x+c)^2*2^(1/2)","C"
235,1,284,252,2.365000," ","int((a+a*sec(d*x+c))*(e*cot(d*x+c))^(1/2),x)","-\frac{a \sqrt{\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}"," ",0,"-1/2*a/d*(e*cos(d*x+c)/sin(d*x+c))^(1/2)*(-1+cos(d*x+c))*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2)))/sin(d*x+c)^2/cos(d*x+c)*(1+cos(d*x+c))^2*2^(1/2)","C"
236,1,1409,274,2.362000," ","int((a+a*sec(d*x+c))/(e*cot(d*x+c))^(1/2),x)","\frac{a \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+4 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+4 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-2 \cos \left(d x +c \right) \sqrt{2}+2 \sqrt{2}\right) \sqrt{2}}{2 d \sin \left(d x +c \right)^{5} \sqrt{\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}}}"," ",0,"1/2*a/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+4*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+4*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-2*cos(d*x+c)*2^(1/2)+2*2^(1/2))/sin(d*x+c)^5/(e*cos(d*x+c)/sin(d*x+c))^(1/2)*2^(1/2)","C"
237,1,688,291,2.077000," ","int((a+a*sec(d*x+c))/(e*cot(d*x+c))^(3/2),x)","\frac{a \left(-1+\cos \left(d x +c \right)\right) \left(3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-4 \cos \left(d x +c \right) \sqrt{2}-2 \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{6 d \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{5}}"," ",0,"1/6*a/d*(-1+cos(d*x+c))*(3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-4*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+6*cos(d*x+c)^2*2^(1/2)-4*cos(d*x+c)*2^(1/2)-2*2^(1/2))*(1+cos(d*x+c))^2/(e*cos(d*x+c)/sin(d*x+c))^(3/2)/sin(d*x+c)^5*2^(1/2)","C"
238,1,650,324,2.681000," ","int((e*cot(d*x+c))^(5/2)*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 \cos \left(d x +c \right) \sqrt{2}\right) \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{6 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)}"," ",0,"1/6*a^2/d*(-1+cos(d*x+c))*(3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+4*cos(d*x+c)*2^(1/2))*(e*cos(d*x+c)/sin(d*x+c))^(5/2)*(1+cos(d*x+c))^2/cos(d*x+c)^3/sin(d*x+c)*2^(1/2)","C"
239,1,1392,316,2.542000," ","int((e*cot(d*x+c))^(3/2)*(a+a*sec(d*x+c))^2,x)","-\frac{a^{2} \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+4 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-8 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+4 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-8 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+8 \cos \left(d x +c \right) \sqrt{2}\right) \sin \left(d x +c \right) \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"-1/2*a^2/d*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+4*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-8*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+4*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-8*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+8*cos(d*x+c)*2^(1/2))*sin(d*x+c)*(e*cos(d*x+c)/sin(d*x+c))^(3/2)/cos(d*x+c)^2*2^(1/2)","C"
240,1,655,286,2.724000," ","int((a+a*sec(d*x+c))^2*(e*cot(d*x+c))^(1/2),x)","\frac{a^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \cos \left(d x +c \right) \sqrt{2}-2 \sqrt{2}\right) \sqrt{2}}{2 d \cos \left(d x +c \right) \sin \left(d x +c \right)^{3}}"," ",0,"1/2*a^2/d*(1+cos(d*x+c))^2*(e*cos(d*x+c)/sin(d*x+c))^(1/2)*(-1+cos(d*x+c))*(-I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+2*cos(d*x+c)*2^(1/2)-2*2^(1/2))/cos(d*x+c)/sin(d*x+c)^3*2^(1/2)","C"
241,1,1480,310,2.354000," ","int((a+a*sec(d*x+c))^2/(e*cot(d*x+c))^(1/2),x)","\frac{a^{2} \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+24 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-12 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+24 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-12 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-14 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+12 \cos \left(d x +c \right) \sqrt{2}+2 \sqrt{2}\right) \sqrt{2}}{6 d \cos \left(d x +c \right) \sin \left(d x +c \right)^{5} \sqrt{\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}}}"," ",0,"1/6*a^2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-3*I*cos(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+24*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-12*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+24*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-12*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-14*cos(d*x+c)^2*2^(1/2)+12*cos(d*x+c)*2^(1/2)+2*2^(1/2))/cos(d*x+c)/sin(d*x+c)^5/(e*cos(d*x+c)/sin(d*x+c))^(1/2)*2^(1/2)","C"
242,1,721,340,2.278000," ","int((a+a*sec(d*x+c))^2/(e*cot(d*x+c))^(3/2),x)","-\frac{a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(15 i \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-15 i \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-15 \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+10 \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-15 \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-24 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+14 \cos \left(d x +c \right) \sqrt{2}+6 \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{30 d \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}"," ",0,"-1/30*a^2/d*(-1+cos(d*x+c))*(15*I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+10*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-24*2^(1/2)*cos(d*x+c)^3+4*cos(d*x+c)^2*2^(1/2)+14*cos(d*x+c)*2^(1/2)+6*2^(1/2))*(1+cos(d*x+c))^2/(e*cos(d*x+c)/sin(d*x+c))^(3/2)/sin(d*x+c)^5/cos(d*x+c)*2^(1/2)","C"
243,1,2113,368,2.002000," ","int((e*cot(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-1/10/a/d*(-1+cos(d*x+c))*(10*I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+5*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+5*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+5*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-12*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+6*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-5*I*cos(d*x+c)^2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-5*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+10*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+10*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-24*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+12*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+5*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-10*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)+5*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+5*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-12*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+6*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-6*cos(d*x+c)^2*2^(1/2)-4*cos(d*x+c)*2^(1/2))*(e*cos(d*x+c)/sin(d*x+c))^(3/2)/cos(d*x+c)^2/sin(d*x+c)*2^(1/2)","C"
244,1,1269,296,2.119000," ","int((e*cot(d*x+c))^(1/2)/(a+a*sec(d*x+c)),x)","\frac{\sqrt{\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-2 \cos \left(d x +c \right) \sqrt{2}\right) \sqrt{2}}{6 a d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}"," ",0,"1/6/a/d*(e*cos(d*x+c)/sin(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-8*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-8*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+2*cos(d*x+c)^2*2^(1/2)-2*cos(d*x+c)*2^(1/2))/sin(d*x+c)^5/cos(d*x+c)*2^(1/2)","C"
245,1,352,320,2.069000," ","int(1/(a+a*sec(d*x+c))/(e*cot(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+4 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \left(-1+\cos \left(d x +c \right)\right) \sqrt{2}}{2 a d \sin \left(d x +c \right)^{3} \sqrt{\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}}}"," ",0,"-1/2/a/d*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+4*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*(-1+cos(d*x+c))/sin(d*x+c)^3/(e*cos(d*x+c)/sin(d*x+c))^(1/2)*2^(1/2)","C"
246,1,319,268,1.971000," ","int(1/(e*cot(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x)","\frac{\left(1+\cos \left(d x +c \right)\right)^{2} \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{2}}{2 a d \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{4}}"," ",0,"1/2/a/d*(1+cos(d*x+c))^2*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-4*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-1+cos(d*x+c))*cos(d*x+c)/(e*cos(d*x+c)/sin(d*x+c))^(3/2)/sin(d*x+c)^4*2^(1/2)","C"
247,1,1419,300,2.396000," ","int(1/(e*cot(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-4 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-4 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+2 \cos \left(d x +c \right) \sqrt{2}-2 \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{2 a d \sin \left(d x +c \right)^{7} \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/2/a/d*(-1+cos(d*x+c))^2*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-4*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-4*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+2*cos(d*x+c)*2^(1/2)-2*2^(1/2))*cos(d*x+c)^2*(1+cos(d*x+c))^2/sin(d*x+c)^7/(e*cos(d*x+c)/sin(d*x+c))^(5/2)*2^(1/2)","C"
248,1,698,306,2.385000," ","int(1/(e*cot(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-8 \cos \left(d x +c \right) \sqrt{2}+2 \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{6 a d \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)^{7}}"," ",0,"-1/6/a/d*(-1+cos(d*x+c))*(3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-8*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+6*cos(d*x+c)^2*2^(1/2)-8*cos(d*x+c)*2^(1/2)+2*2^(1/2))*cos(d*x+c)^2*(1+cos(d*x+c))^2/(e*cos(d*x+c)/sin(d*x+c))^(7/2)/sin(d*x+c)^7*2^(1/2)","C"
249,1,1505,338,2.086000," ","int(1/(e*cot(d*x+c))^(9/2)/(a+a*sec(d*x+c)),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(-15 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+15 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-36 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+18 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+15 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-15 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-15 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-36 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+18 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+28 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-24 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-10 \cos \left(d x +c \right) \sqrt{2}+6 \sqrt{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{30 a d \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{9}{2}} \sin \left(d x +c \right)^{9}}"," ",0,"1/30/a/d*(-1+cos(d*x+c))^2*(-15*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-15*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-15*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-15*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-36*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+18*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+15*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+15*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-15*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-15*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-36*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+18*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+28*2^(1/2)*cos(d*x+c)^3-24*cos(d*x+c)^2*2^(1/2)-10*cos(d*x+c)*2^(1/2)+6*2^(1/2))*cos(d*x+c)^2*(1+cos(d*x+c))^2/(e*cos(d*x+c)/sin(d*x+c))^(9/2)/sin(d*x+c)^9*2^(1/2)","C"
250,1,2117,374,2.317000," ","int(1/(a+a*sec(d*x+c))^2/(e*cot(d*x+c))^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/10/a^2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^3*(-10*I*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-5*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-5*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-5*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+24*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-12*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+5*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+5*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-10*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-10*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+48*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-24*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-5*I*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+10*I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)-5*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-5*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+24*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-12*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+2*cos(d*x+c)^2*2^(1/2)-2*cos(d*x+c)*2^(1/2))/sin(d*x+c)^7/(e*cos(d*x+c)/sin(d*x+c))^(1/2)*2^(1/2)","C"
251,1,1267,326,2.044000," ","int(1/(e*cot(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-10 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-10 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-4 \cos \left(d x +c \right) \sqrt{2}\right) \cos \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{6 a^{2} d \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{7}}"," ",0,"-1/6/a^2/d*(-1+cos(d*x+c))^2*(3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-10*cos(d*x+c)*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-10*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+4*cos(d*x+c)^2*2^(1/2)-4*cos(d*x+c)*2^(1/2))*cos(d*x+c)*(1+cos(d*x+c))^2/(e*cos(d*x+c)/sin(d*x+c))^(3/2)/sin(d*x+c)^7*2^(1/2)","C"
252,1,360,328,2.138000," ","int(1/(e*cot(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x)","\frac{\left(1+\cos \left(d x +c \right)\right)^{2} \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+8 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}}{2 a^{2} d \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{5}}"," ",0,"1/2/a^2/d*(1+cos(d*x+c))^2*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-4*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+8*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-1+cos(d*x+c))*cos(d*x+c)^2/(e*cos(d*x+c)/sin(d*x+c))^(5/2)/sin(d*x+c)^5*2^(1/2)","C"
253,1,653,296,2.233000," ","int(1/(e*cot(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-6 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \cos \left(d x +c \right) \sqrt{2}+2 \sqrt{2}\right) \left(-1+\cos \left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{2 a^{2} d \sin \left(d x +c \right)^{7} \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{7}{2}}}"," ",0,"-1/2/a^2/d*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-6*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)-2*cos(d*x+c)*2^(1/2)+2*2^(1/2))*(-1+cos(d*x+c))*cos(d*x+c)^3*(1+cos(d*x+c))^2/sin(d*x+c)^7/(e*cos(d*x+c)/sin(d*x+c))^(7/2)*2^(1/2)","C"
254,1,1480,328,2.086000," ","int(1/(e*cot(d*x+c))^(9/2)/(a+a*sec(d*x+c))^2,x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+12 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-24 \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+12 \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}-24 \EllipticE \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(d x +c \right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}+10 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-12 \cos \left(d x +c \right) \sqrt{2}+2 \sqrt{2}\right) \left(\cos^{3}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{6 a^{2} d \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{9}{2}} \sin \left(d x +c \right)^{9}}"," ",0,"1/6/a^2/d*(-1+cos(d*x+c))^2*(3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+3*I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-3*I*cos(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-24*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-3*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+12*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)-24*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)+10*cos(d*x+c)^2*2^(1/2)-12*cos(d*x+c)*2^(1/2)+2*2^(1/2))*cos(d*x+c)^3*(1+cos(d*x+c))^2/(e*cos(d*x+c)/sin(d*x+c))^(9/2)/sin(d*x+c)^9*2^(1/2)","C"
255,1,721,354,2.109000," ","int(1/(e*cot(d*x+c))^(11/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(15 i \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-15 i \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-15 \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-15 \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+50 \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-24 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+44 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-26 \cos \left(d x +c \right) \sqrt{2}+6 \sqrt{2}\right) \left(\cos^{3}\left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{30 a^{2} d \left(\frac{e \cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)^{\frac{11}{2}} \sin \left(d x +c \right)^{9}}"," ",0,"-1/30/a^2/d*(-1+cos(d*x+c))*(15*I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*I*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-15*sin(d*x+c)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2+50*sin(d*x+c)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2-24*2^(1/2)*cos(d*x+c)^3+44*cos(d*x+c)^2*2^(1/2)-26*cos(d*x+c)*2^(1/2)+6*2^(1/2))*cos(d*x+c)^3*(1+cos(d*x+c))^2/(e*cos(d*x+c)/sin(d*x+c))^(11/2)/sin(d*x+c)^9*2^(1/2)","C"
256,1,216,103,0.625000," ","int((a+b*sec(d*x+c))*tan(d*x+c)^7,x)","\frac{\left(\tan^{6}\left(d x +c \right)\right) a}{6 d}-\frac{a \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b \left(\sin^{8}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{7}}-\frac{b \left(\sin^{8}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{5}}+\frac{b \left(\sin^{8}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{3}}-\frac{b \left(\sin^{8}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)}-\frac{16 b \cos \left(d x +c \right)}{35 d}-\frac{b \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{7 d}-\frac{6 b \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{35 d}-\frac{8 b \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{35 d}"," ",0,"1/6/d*tan(d*x+c)^6*a-1/4*a*tan(d*x+c)^4/d+1/2*a*tan(d*x+c)^2/d+a*ln(cos(d*x+c))/d+1/7/d*b*sin(d*x+c)^8/cos(d*x+c)^7-1/35/d*b*sin(d*x+c)^8/cos(d*x+c)^5+1/35/d*b*sin(d*x+c)^8/cos(d*x+c)^3-1/7/d*b*sin(d*x+c)^8/cos(d*x+c)-16/35*b*cos(d*x+c)/d-1/7/d*b*cos(d*x+c)*sin(d*x+c)^6-6/35/d*b*cos(d*x+c)*sin(d*x+c)^4-8/35/d*b*cos(d*x+c)*sin(d*x+c)^2","B"
257,1,161,78,0.641000," ","int((a+b*sec(d*x+c))*tan(d*x+c)^5,x)","\frac{a \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b \left(\sin^{6}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}-\frac{b \left(\sin^{6}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{3}}+\frac{b \left(\sin^{6}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)}+\frac{8 b \cos \left(d x +c \right)}{15 d}+\frac{b \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 b \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}"," ",0,"1/4*a*tan(d*x+c)^4/d-1/2*a*tan(d*x+c)^2/d-a*ln(cos(d*x+c))/d+1/5/d*b*sin(d*x+c)^6/cos(d*x+c)^5-1/15/d*b*sin(d*x+c)^6/cos(d*x+c)^3+1/5/d*b*sin(d*x+c)^6/cos(d*x+c)+8/15*b*cos(d*x+c)/d+1/5/d*b*cos(d*x+c)*sin(d*x+c)^4+4/15/d*b*cos(d*x+c)*sin(d*x+c)^2","B"
258,1,104,51,0.643000," ","int((a+b*sec(d*x+c))*tan(d*x+c)^3,x)","\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{b \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}-\frac{b \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}-\frac{2 b \cos \left(d x +c \right)}{3 d}"," ",0,"1/2*a*tan(d*x+c)^2/d+a*ln(cos(d*x+c))/d+1/3/d*b*sin(d*x+c)^4/cos(d*x+c)^3-1/3/d*b*sin(d*x+c)^4/cos(d*x+c)-1/3/d*b*cos(d*x+c)*sin(d*x+c)^2-2/3*b*cos(d*x+c)/d","B"
259,1,25,25,0.176000," ","int((a+b*sec(d*x+c))*tan(d*x+c),x)","\frac{b \sec \left(d x +c \right)}{d}+\frac{a \ln \left(\sec \left(d x +c \right)\right)}{d}"," ",0,"b*sec(d*x+c)/d+a/d*ln(sec(d*x+c))","A"
260,1,35,39,0.459000," ","int(cot(d*x+c)*(a+b*sec(d*x+c)),x)","\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"a*ln(sin(d*x+c))/d+1/d*b*ln(csc(d*x+c)-cot(d*x+c))","A"
261,1,85,66,0.648000," ","int(cot(d*x+c)^3*(a+b*sec(d*x+c)),x)","-\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{b \cos \left(d x +c \right)}{2 d}-\frac{b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/2*a*cot(d*x+c)^2/d-a*ln(sin(d*x+c))/d-1/2/d*b/sin(d*x+c)^2*cos(d*x+c)^3-1/2*b*cos(d*x+c)/d-1/2/d*b*ln(csc(d*x+c)-cot(d*x+c))","A"
262,1,134,94,0.536000," ","int(cot(d*x+c)^5*(a+b*sec(d*x+c)),x)","-\frac{a \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{3 b \cos \left(d x +c \right)}{8 d}+\frac{3 b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}"," ",0,"-1/4*a*cot(d*x+c)^4/d+1/2*a*cot(d*x+c)^2/d+a*ln(sin(d*x+c))/d-1/4/d*b/sin(d*x+c)^4*cos(d*x+c)^5+1/8/d*b/sin(d*x+c)^2*cos(d*x+c)^5+1/8*b*cos(d*x+c)^3/d+3/8*b*cos(d*x+c)/d+3/8/d*b*ln(csc(d*x+c)-cot(d*x+c))","A"
263,1,185,120,0.619000," ","int(cot(d*x+c)^7*(a+b*sec(d*x+c)),x)","-\frac{a \left(\cot^{6}\left(d x +c \right)\right)}{6 d}+\frac{a \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b \left(\cos^{7}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}+\frac{b \left(\cos^{7}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}-\frac{b \left(\cos^{7}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}-\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{16 d}-\frac{5 b \left(\cos^{3}\left(d x +c \right)\right)}{48 d}-\frac{5 b \cos \left(d x +c \right)}{16 d}-\frac{5 b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}"," ",0,"-1/6/d*a*cot(d*x+c)^6+1/4*a*cot(d*x+c)^4/d-1/2*a*cot(d*x+c)^2/d-a*ln(sin(d*x+c))/d-1/6/d*b/sin(d*x+c)^6*cos(d*x+c)^7+1/24/d*b/sin(d*x+c)^4*cos(d*x+c)^7-1/16/d*b/sin(d*x+c)^2*cos(d*x+c)^7-1/16/d*b*cos(d*x+c)^5-5/48*b*cos(d*x+c)^3/d-5/16*b*cos(d*x+c)/d-5/16/d*b*ln(csc(d*x+c)-cot(d*x+c))","A"
264,1,178,94,0.428000," ","int((a+b*sec(d*x+c))*tan(d*x+c)^6,x)","\frac{a \left(\tan^{5}\left(d x +c \right)\right)}{5 d}-\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \tan \left(d x +c \right)}{d}-a x -\frac{c a}{d}+\frac{b \left(\sin^{7}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}-\frac{b \left(\sin^{7}\left(d x +c \right)\right)}{24 d \cos \left(d x +c \right)^{4}}+\frac{b \left(\sin^{7}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{b \left(\sin^{5}\left(d x +c \right)\right)}{16 d}+\frac{5 b \left(\sin^{3}\left(d x +c \right)\right)}{48 d}+\frac{5 b \sin \left(d x +c \right)}{16 d}-\frac{5 b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}"," ",0,"1/5*a*tan(d*x+c)^5/d-1/3*a*tan(d*x+c)^3/d+a*tan(d*x+c)/d-a*x-1/d*c*a+1/6/d*b*sin(d*x+c)^7/cos(d*x+c)^6-1/24/d*b*sin(d*x+c)^7/cos(d*x+c)^4+1/16/d*b*sin(d*x+c)^7/cos(d*x+c)^2+1/16*b*sin(d*x+c)^5/d+5/48*b*sin(d*x+c)^3/d+5/16*b*sin(d*x+c)/d-5/16/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
265,1,127,67,0.430000," ","int((a+b*sec(d*x+c))*tan(d*x+c)^4,x)","\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \tan \left(d x +c \right)}{d}+a x +\frac{c a}{d}+\frac{b \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{b \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{3 b \sin \left(d x +c \right)}{8 d}+\frac{3 b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/3*a*tan(d*x+c)^3/d-a*tan(d*x+c)/d+a*x+1/d*c*a+1/4/d*b*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*b*sin(d*x+c)^5/cos(d*x+c)^2-1/8*b*sin(d*x+c)^3/d-3/8*b*sin(d*x+c)/d+3/8/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
266,1,78,41,0.412000," ","int((a+b*sec(d*x+c))*tan(d*x+c)^2,x)","-a x +\frac{a \tan \left(d x +c \right)}{d}-\frac{c a}{d}+\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b \sin \left(d x +c \right)}{2 d}-\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"-a*x+a*tan(d*x+c)/d-1/d*c*a+1/2/d*b*sin(d*x+c)^3/cos(d*x+c)^2+1/2*b*sin(d*x+c)/d-1/2/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
267,1,35,26,0.454000," ","int(cot(d*x+c)^2*(a+b*sec(d*x+c)),x)","\frac{a \left(-\cot \left(d x +c \right)-d x -c \right)-\frac{b}{\sin \left(d x +c \right)}}{d}"," ",0,"1/d*(a*(-cot(d*x+c)-d*x-c)-b/sin(d*x+c))","A"
268,1,86,51,0.812000," ","int(cot(d*x+c)^4*(a+b*sec(d*x+c)),x)","\frac{a \left(-\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}+\cot \left(d x +c \right)+d x +c \right)+b \left(-\frac{\cos^{4}\left(d x +c \right)}{3 \sin \left(d x +c \right)^{3}}+\frac{\cos^{4}\left(d x +c \right)}{3 \sin \left(d x +c \right)}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}\right)}{d}"," ",0,"1/d*(a*(-1/3*cot(d*x+c)^3+cot(d*x+c)+d*x+c)+b*(-1/3/sin(d*x+c)^3*cos(d*x+c)^4+1/3/sin(d*x+c)*cos(d*x+c)^4+1/3*(2+cos(d*x+c)^2)*sin(d*x+c)))","A"
269,1,129,78,0.815000," ","int(cot(d*x+c)^6*(a+b*sec(d*x+c)),x)","\frac{a \left(-\frac{\left(\cot^{5}\left(d x +c \right)\right)}{5}+\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}-\cot \left(d x +c \right)-d x -c \right)+b \left(-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{15 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)}-\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)}{5}\right)}{d}"," ",0,"1/d*(a*(-1/5*cot(d*x+c)^5+1/3*cot(d*x+c)^3-cot(d*x+c)-d*x-c)+b*(-1/5/sin(d*x+c)^5*cos(d*x+c)^6+1/15/sin(d*x+c)^3*cos(d*x+c)^6-1/5/sin(d*x+c)*cos(d*x+c)^6-1/5*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","A"
270,1,162,103,0.911000," ","int(cot(d*x+c)^8*(a+b*sec(d*x+c)),x)","\frac{a \left(-\frac{\left(\cot^{7}\left(d x +c \right)\right)}{7}+\frac{\left(\cot^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}+\cot \left(d x +c \right)+d x +c \right)+b \left(-\frac{\cos^{8}\left(d x +c \right)}{7 \sin \left(d x +c \right)^{7}}+\frac{\cos^{8}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{5}}-\frac{\cos^{8}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{3}}+\frac{\cos^{8}\left(d x +c \right)}{7 \sin \left(d x +c \right)}+\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)}{7}\right)}{d}"," ",0,"1/d*(a*(-1/7*cot(d*x+c)^7+1/5*cot(d*x+c)^5-1/3*cot(d*x+c)^3+cot(d*x+c)+d*x+c)+b*(-1/7/sin(d*x+c)^7*cos(d*x+c)^8+1/35/sin(d*x+c)^5*cos(d*x+c)^8-1/35/sin(d*x+c)^3*cos(d*x+c)^8+1/7/sin(d*x+c)*cos(d*x+c)^8+1/7*(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"
271,1,317,169,0.769000," ","int((a+b*sec(d*x+c))^2*tan(d*x+c)^9,x)","\frac{\left(\tan^{8}\left(d x +c \right)\right) a^{2}}{8 d}-\frac{a^{2} \left(\tan^{6}\left(d x +c \right)\right)}{6 d}+\frac{a^{2} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{2 a b \left(\sin^{10}\left(d x +c \right)\right)}{9 d \cos \left(d x +c \right)^{9}}-\frac{2 a b \left(\sin^{10}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)^{7}}+\frac{2 a b \left(\sin^{10}\left(d x +c \right)\right)}{105 d \cos \left(d x +c \right)^{5}}-\frac{2 a b \left(\sin^{10}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)^{3}}+\frac{2 a b \left(\sin^{10}\left(d x +c \right)\right)}{9 d \cos \left(d x +c \right)}+\frac{256 a b \cos \left(d x +c \right)}{315 d}+\frac{2 a b \cos \left(d x +c \right) \left(\sin^{8}\left(d x +c \right)\right)}{9 d}+\frac{16 a b \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{63 d}+\frac{32 a b \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{105 d}+\frac{128 a b \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{315 d}+\frac{b^{2} \left(\sin^{10}\left(d x +c \right)\right)}{10 d \cos \left(d x +c \right)^{10}}"," ",0,"1/8/d*tan(d*x+c)^8*a^2-1/6/d*a^2*tan(d*x+c)^6+1/4*a^2*tan(d*x+c)^4/d-1/2*a^2*tan(d*x+c)^2/d-a^2*ln(cos(d*x+c))/d+2/9/d*a*b*sin(d*x+c)^10/cos(d*x+c)^9-2/63/d*a*b*sin(d*x+c)^10/cos(d*x+c)^7+2/105/d*a*b*sin(d*x+c)^10/cos(d*x+c)^5-2/63/d*a*b*sin(d*x+c)^10/cos(d*x+c)^3+2/9/d*a*b*sin(d*x+c)^10/cos(d*x+c)+256/315*a*b*cos(d*x+c)/d+2/9/d*a*b*cos(d*x+c)*sin(d*x+c)^8+16/63/d*a*b*cos(d*x+c)*sin(d*x+c)^6+32/105/d*a*b*cos(d*x+c)*sin(d*x+c)^4+128/315/d*a*b*cos(d*x+c)*sin(d*x+c)^2+1/10/d*b^2*sin(d*x+c)^10/cos(d*x+c)^10","A"
272,1,256,137,0.644000," ","int((a+b*sec(d*x+c))^2*tan(d*x+c)^7,x)","\frac{a^{2} \left(\tan^{6}\left(d x +c \right)\right)}{6 d}-\frac{a^{2} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{2 a b \left(\sin^{8}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{7}}-\frac{2 a b \left(\sin^{8}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{5}}+\frac{2 a b \left(\sin^{8}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{3}}-\frac{2 a b \left(\sin^{8}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)}-\frac{32 a b \cos \left(d x +c \right)}{35 d}-\frac{2 a b \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{7 d}-\frac{12 a b \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{35 d}-\frac{16 a b \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{35 d}+\frac{b^{2} \left(\sin^{8}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{8}}"," ",0,"1/6/d*a^2*tan(d*x+c)^6-1/4*a^2*tan(d*x+c)^4/d+1/2*a^2*tan(d*x+c)^2/d+a^2*ln(cos(d*x+c))/d+2/7/d*a*b*sin(d*x+c)^8/cos(d*x+c)^7-2/35/d*a*b*sin(d*x+c)^8/cos(d*x+c)^5+2/35/d*a*b*sin(d*x+c)^8/cos(d*x+c)^3-2/7/d*a*b*sin(d*x+c)^8/cos(d*x+c)-32/35*a*b*cos(d*x+c)/d-2/7/d*a*b*cos(d*x+c)*sin(d*x+c)^6-12/35/d*a*b*cos(d*x+c)*sin(d*x+c)^4-16/35/d*a*b*cos(d*x+c)*sin(d*x+c)^2+1/8/d*b^2*sin(d*x+c)^8/cos(d*x+c)^8","A"
273,1,197,107,0.661000," ","int((a+b*sec(d*x+c))^2*tan(d*x+c)^5,x)","\frac{a^{2} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{2 a b \left(\sin^{6}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}-\frac{2 a b \left(\sin^{6}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{3}}+\frac{2 a b \left(\sin^{6}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)}+\frac{16 a b \cos \left(d x +c \right)}{15 d}+\frac{2 a b \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{5 d}+\frac{8 a b \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}+\frac{b^{2} \left(\sin^{6}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}"," ",0,"1/4*a^2*tan(d*x+c)^4/d-1/2*a^2*tan(d*x+c)^2/d-a^2*ln(cos(d*x+c))/d+2/5/d*a*b*sin(d*x+c)^6/cos(d*x+c)^5-2/15/d*a*b*sin(d*x+c)^6/cos(d*x+c)^3+2/5/d*a*b*sin(d*x+c)^6/cos(d*x+c)+16/15*a*b*cos(d*x+c)/d+2/5/d*a*b*cos(d*x+c)*sin(d*x+c)^4+8/15/d*a*b*cos(d*x+c)*sin(d*x+c)^2+1/6/d*b^2*sin(d*x+c)^6/cos(d*x+c)^6","A"
274,1,136,81,0.665000," ","int((a+b*sec(d*x+c))^2*tan(d*x+c)^3,x)","\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{2 a b \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{2 a b \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}-\frac{2 a b \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}-\frac{4 a b \cos \left(d x +c \right)}{3 d}+\frac{b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/2*a^2*tan(d*x+c)^2/d+a^2*ln(cos(d*x+c))/d+2/3/d*a*b*sin(d*x+c)^4/cos(d*x+c)^3-2/3/d*a*b*sin(d*x+c)^4/cos(d*x+c)-2/3/d*a*b*cos(d*x+c)*sin(d*x+c)^2-4/3*a*b*cos(d*x+c)/d+1/4/d*b^2*sin(d*x+c)^4/cos(d*x+c)^4","A"
275,1,45,45,0.192000," ","int((a+b*sec(d*x+c))^2*tan(d*x+c),x)","\frac{b^{2} \left(\sec^{2}\left(d x +c \right)\right)}{2 d}+\frac{2 a b \sec \left(d x +c \right)}{d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)\right)}{d}"," ",0,"1/2*b^2*sec(d*x+c)^2/d+2*a*b*sec(d*x+c)/d+1/d*a^2*ln(sec(d*x+c))","A"
276,1,53,57,0.547000," ","int(cot(d*x+c)*(a+b*sec(d*x+c))^2,x)","\frac{b^{2} \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{2 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"1/d*b^2*ln(tan(d*x+c))+2/d*a*b*ln(csc(d*x+c)-cot(d*x+c))+a^2*ln(sin(d*x+c))/d","A"
277,1,108,86,0.693000," ","int(cot(d*x+c)^3*(a+b*sec(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a b \left(\cos^{3}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{a b \cos \left(d x +c \right)}{d}-\frac{a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{b^{2}}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"-1/2*a^2*cot(d*x+c)^2/d-a^2*ln(sin(d*x+c))/d-1/d*a*b/sin(d*x+c)^2*cos(d*x+c)^3-a*b*cos(d*x+c)/d-1/d*a*b*ln(csc(d*x+c)-cot(d*x+c))-1/2/d*b^2/sin(d*x+c)^2","A"
278,1,169,118,0.582000," ","int(cot(d*x+c)^5*(a+b*sec(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a b \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{4}}+\frac{a b \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{2}}+\frac{a b \left(\cos^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a b \cos \left(d x +c \right)}{4 d}+\frac{3 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{4 d}-\frac{b^{2} \left(\cos^{4}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}"," ",0,"-1/4*a^2*cot(d*x+c)^4/d+1/2*a^2*cot(d*x+c)^2/d+a^2*ln(sin(d*x+c))/d-1/2/d*a*b/sin(d*x+c)^4*cos(d*x+c)^5+1/4/d*a*b/sin(d*x+c)^2*cos(d*x+c)^5+1/4*a*b*cos(d*x+c)^3/d+3/4*a*b*cos(d*x+c)/d+3/4/d*a*b*ln(csc(d*x+c)-cot(d*x+c))-1/4/d*b^2/sin(d*x+c)^4*cos(d*x+c)^4","A"
279,1,219,143,0.409000," ","int((a+b*sec(d*x+c))^2*tan(d*x+c)^6,x)","\frac{a^{2} \left(\tan^{5}\left(d x +c \right)\right)}{5 d}-\frac{a^{2} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \tan \left(d x +c \right)}{d}-a^{2} x -\frac{a^{2} c}{d}+\frac{a b \left(\sin^{7}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{6}}-\frac{a b \left(\sin^{7}\left(d x +c \right)\right)}{12 d \cos \left(d x +c \right)^{4}}+\frac{a b \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a b \left(\sin^{5}\left(d x +c \right)\right)}{8 d}+\frac{5 a b \left(\sin^{3}\left(d x +c \right)\right)}{24 d}+\frac{5 a b \sin \left(d x +c \right)}{8 d}-\frac{5 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b^{2} \left(\sin^{7}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{7}}"," ",0,"1/5*a^2*tan(d*x+c)^5/d-1/3*a^2*tan(d*x+c)^3/d+a^2*tan(d*x+c)/d-a^2*x-1/d*a^2*c+1/3/d*a*b*sin(d*x+c)^7/cos(d*x+c)^6-1/12/d*a*b*sin(d*x+c)^7/cos(d*x+c)^4+1/8/d*a*b*sin(d*x+c)^7/cos(d*x+c)^2+1/8*a*b*sin(d*x+c)^5/d+5/24*a*b*sin(d*x+c)^3/d+5/8*a*b*sin(d*x+c)/d-5/8/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/7/d*b^2*sin(d*x+c)^7/cos(d*x+c)^7","A"
280,1,164,106,0.391000," ","int((a+b*sec(d*x+c))^2*tan(d*x+c)^4,x)","\frac{a^{2} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} \tan \left(d x +c \right)}{d}+a^{2} x +\frac{a^{2} c}{d}+\frac{a b \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}-\frac{a b \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}-\frac{a b \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a b \sin \left(d x +c \right)}{4 d}+\frac{3 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}"," ",0,"1/3*a^2*tan(d*x+c)^3/d-a^2*tan(d*x+c)/d+a^2*x+1/d*a^2*c+1/2/d*a*b*sin(d*x+c)^5/cos(d*x+c)^4-1/4/d*a*b*sin(d*x+c)^5/cos(d*x+c)^2-1/4*a*b*sin(d*x+c)^3/d-3/4*a*b*sin(d*x+c)/d+3/4/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/5/d*b^2*sin(d*x+c)^5/cos(d*x+c)^5","A"
281,1,109,68,0.393000," ","int((a+b*sec(d*x+c))^2*tan(d*x+c)^2,x)","-a^{2} x +\frac{a^{2} \tan \left(d x +c \right)}{d}-\frac{a^{2} c}{d}+\frac{a b \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{a b \sin \left(d x +c \right)}{d}-\frac{a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}"," ",0,"-a^2*x+a^2*tan(d*x+c)/d-1/d*a^2*c+1/d*a*b*sin(d*x+c)^3/cos(d*x+c)^2+a*b*sin(d*x+c)/d-1/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/3/d*b^2*sin(d*x+c)^3/cos(d*x+c)^3","A"
282,1,49,48,0.684000," ","int(cot(d*x+c)^2*(a+b*sec(d*x+c))^2,x)","\frac{a^{2} \left(-\cot \left(d x +c \right)-d x -c \right)-\frac{2 a b}{\sin \left(d x +c \right)}-b^{2} \cot \left(d x +c \right)}{d}"," ",0,"1/d*(a^2*(-cot(d*x+c)-d*x-c)-2*a*b/sin(d*x+c)-b^2*cot(d*x+c))","A"
283,1,111,79,0.818000," ","int(cot(d*x+c)^4*(a+b*sec(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}+\cot \left(d x +c \right)+d x +c \right)+2 a b \left(-\frac{\cos^{4}\left(d x +c \right)}{3 \sin \left(d x +c \right)^{3}}+\frac{\cos^{4}\left(d x +c \right)}{3 \sin \left(d x +c \right)}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}\right)-\frac{b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 \sin \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(a^2*(-1/3*cot(d*x+c)^3+cot(d*x+c)+d*x+c)+2*a*b*(-1/3/sin(d*x+c)^3*cos(d*x+c)^4+1/3/sin(d*x+c)*cos(d*x+c)^4+1/3*(2+cos(d*x+c)^2)*sin(d*x+c))-1/3*b^2/sin(d*x+c)^3*cos(d*x+c)^3)","A"
284,1,154,112,0.806000," ","int(cot(d*x+c)^6*(a+b*sec(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\cot^{5}\left(d x +c \right)\right)}{5}+\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}-\cot \left(d x +c \right)-d x -c \right)+2 a b \left(-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{15 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)}-\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)}{5}\right)-\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5 \sin \left(d x +c \right)^{5}}}{d}"," ",0,"1/d*(a^2*(-1/5*cot(d*x+c)^5+1/3*cot(d*x+c)^3-cot(d*x+c)-d*x-c)+2*a*b*(-1/5/sin(d*x+c)^5*cos(d*x+c)^6+1/15/sin(d*x+c)^3*cos(d*x+c)^6-1/5/sin(d*x+c)*cos(d*x+c)^6-1/5*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/5*b^2/sin(d*x+c)^5*cos(d*x+c)^5)","A"
285,1,187,141,0.952000," ","int(cot(d*x+c)^8*(a+b*sec(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\cot^{7}\left(d x +c \right)\right)}{7}+\frac{\left(\cot^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\cot^{3}\left(d x +c \right)\right)}{3}+\cot \left(d x +c \right)+d x +c \right)+2 a b \left(-\frac{\cos^{8}\left(d x +c \right)}{7 \sin \left(d x +c \right)^{7}}+\frac{\cos^{8}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{5}}-\frac{\cos^{8}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{3}}+\frac{\cos^{8}\left(d x +c \right)}{7 \sin \left(d x +c \right)}+\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)}{7}\right)-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{7 \sin \left(d x +c \right)^{7}}}{d}"," ",0,"1/d*(a^2*(-1/7*cot(d*x+c)^7+1/5*cot(d*x+c)^5-1/3*cot(d*x+c)^3+cot(d*x+c)+d*x+c)+2*a*b*(-1/7/sin(d*x+c)^7*cos(d*x+c)^8+1/35/sin(d*x+c)^5*cos(d*x+c)^8-1/35/sin(d*x+c)^3*cos(d*x+c)^8+1/7/sin(d*x+c)*cos(d*x+c)^8+1/7*(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))-1/7*b^2/sin(d*x+c)^7*cos(d*x+c)^7)","A"
286,1,460,238,0.551000," ","int(tan(d*x+c)^9/(a+b*sec(d*x+c)),x)","-\frac{\ln \left(b +a \cos \left(d x +c \right)\right)}{d a}-\frac{4}{5 d b \cos \left(d x +c \right)^{5}}+\frac{2}{d b \cos \left(d x +c \right)^{3}}-\frac{4}{d b \cos \left(d x +c \right)}+\frac{1}{7 d b \cos \left(d x +c \right)^{7}}-\frac{a}{6 d \,b^{2} \cos \left(d x +c \right)^{6}}+\frac{a^{2}}{5 d \,b^{3} \cos \left(d x +c \right)^{5}}+\frac{a^{4}}{3 d \,b^{5} \cos \left(d x +c \right)^{3}}-\frac{4 a^{2}}{3 d \,b^{3} \cos \left(d x +c \right)^{3}}+\frac{a^{6}}{d \,b^{7} \cos \left(d x +c \right)}-\frac{4 a^{4}}{d \,b^{5} \cos \left(d x +c \right)}-\frac{3 a}{d \,b^{2} \cos \left(d x +c \right)^{2}}+\frac{a^{7} \ln \left(\cos \left(d x +c \right)\right)}{d \,b^{8}}-\frac{4 a^{5} \ln \left(\cos \left(d x +c \right)\right)}{d \,b^{6}}+\frac{6 a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d \,b^{4}}-\frac{4 a \ln \left(\cos \left(d x +c \right)\right)}{d \,b^{2}}-\frac{a^{7} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{8}}+\frac{4 a^{5} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{6}}-\frac{6 a^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{4}}+\frac{4 a \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{2}}-\frac{a^{5}}{2 d \,b^{6} \cos \left(d x +c \right)^{2}}+\frac{2 a^{3}}{d \,b^{4} \cos \left(d x +c \right)^{2}}+\frac{6 a^{2}}{d \,b^{3} \cos \left(d x +c \right)}-\frac{a^{3}}{4 d \,b^{4} \cos \left(d x +c \right)^{4}}+\frac{a}{d \,b^{2} \cos \left(d x +c \right)^{4}}"," ",0,"-1/d/a*ln(b+a*cos(d*x+c))-4/5/d/b/cos(d*x+c)^5+2/d/b/cos(d*x+c)^3-4/d/b/cos(d*x+c)+1/7/d/b/cos(d*x+c)^7-1/6/d*a/b^2/cos(d*x+c)^6+1/5/d/b^3/cos(d*x+c)^5*a^2+1/3/d/b^5/cos(d*x+c)^3*a^4-4/3/d/b^3/cos(d*x+c)^3*a^2+1/d/b^7/cos(d*x+c)*a^6-4/d/b^5/cos(d*x+c)*a^4-3/d/b^2*a/cos(d*x+c)^2+1/d/b^8*a^7*ln(cos(d*x+c))-4/d/b^6*a^5*ln(cos(d*x+c))+6/d/b^4*a^3*ln(cos(d*x+c))-4/d/b^2*a*ln(cos(d*x+c))-1/d/b^8*a^7*ln(b+a*cos(d*x+c))+4/d/b^6*a^5*ln(b+a*cos(d*x+c))-6/d/b^4*a^3*ln(b+a*cos(d*x+c))+4/d/b^2*a*ln(b+a*cos(d*x+c))-1/2/d/b^6*a^5/cos(d*x+c)^2+2/d/b^4*a^3/cos(d*x+c)^2+6/d/b^3/cos(d*x+c)*a^2-1/4/d/b^4*a^3/cos(d*x+c)^4+1/d/b^2*a/cos(d*x+c)^4","A"
287,1,292,162,0.480000," ","int(tan(d*x+c)^7/(a+b*sec(d*x+c)),x)","-\frac{a^{5} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{6}}+\frac{3 a^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{4}}-\frac{3 a \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{2}}+\frac{\ln \left(b +a \cos \left(d x +c \right)\right)}{d a}-\frac{a}{4 d \,b^{2} \cos \left(d x +c \right)^{4}}+\frac{a^{2}}{3 d \,b^{3} \cos \left(d x +c \right)^{3}}-\frac{1}{d b \cos \left(d x +c \right)^{3}}+\frac{a^{4}}{d \,b^{5} \cos \left(d x +c \right)}-\frac{3 a^{2}}{d \,b^{3} \cos \left(d x +c \right)}+\frac{3}{d b \cos \left(d x +c \right)}-\frac{a^{3}}{2 d \,b^{4} \cos \left(d x +c \right)^{2}}+\frac{3 a}{2 d \,b^{2} \cos \left(d x +c \right)^{2}}+\frac{a^{5} \ln \left(\cos \left(d x +c \right)\right)}{d \,b^{6}}-\frac{3 a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d \,b^{4}}+\frac{3 a \ln \left(\cos \left(d x +c \right)\right)}{d \,b^{2}}+\frac{1}{5 d b \cos \left(d x +c \right)^{5}}"," ",0,"-1/d/b^6*a^5*ln(b+a*cos(d*x+c))+3/d/b^4*a^3*ln(b+a*cos(d*x+c))-3/d/b^2*a*ln(b+a*cos(d*x+c))+1/d/a*ln(b+a*cos(d*x+c))-1/4/d/b^2*a/cos(d*x+c)^4+1/3/d/b^3/cos(d*x+c)^3*a^2-1/d/b/cos(d*x+c)^3+1/d/b^5/cos(d*x+c)*a^4-3/d/b^3/cos(d*x+c)*a^2+3/d/b/cos(d*x+c)-1/2/d/b^4*a^3/cos(d*x+c)^2+3/2/d/b^2*a/cos(d*x+c)^2+1/d/b^6*a^5*ln(cos(d*x+c))-3/d/b^4*a^3*ln(cos(d*x+c))+3/d/b^2*a*ln(cos(d*x+c))+1/5/d/b/cos(d*x+c)^5","A"
288,1,163,104,0.437000," ","int(tan(d*x+c)^5/(a+b*sec(d*x+c)),x)","-\frac{a^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{4}}+\frac{2 a \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{2}}-\frac{\ln \left(b +a \cos \left(d x +c \right)\right)}{d a}-\frac{a}{2 d \,b^{2} \cos \left(d x +c \right)^{2}}+\frac{a^{2}}{d \,b^{3} \cos \left(d x +c \right)}-\frac{2}{d b \cos \left(d x +c \right)}+\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d \,b^{4}}-\frac{2 a \ln \left(\cos \left(d x +c \right)\right)}{d \,b^{2}}+\frac{1}{3 d b \cos \left(d x +c \right)^{3}}"," ",0,"-1/d/b^4*a^3*ln(b+a*cos(d*x+c))+2/d/b^2*a*ln(b+a*cos(d*x+c))-1/d/a*ln(b+a*cos(d*x+c))-1/2/d/b^2*a/cos(d*x+c)^2+1/d/b^3/cos(d*x+c)*a^2-2/d/b/cos(d*x+c)+1/d/b^4*a^3*ln(cos(d*x+c))-2/d/b^2*a*ln(cos(d*x+c))+1/3/d/b/cos(d*x+c)^3","A"
289,1,70,59,0.388000," ","int(tan(d*x+c)^3/(a+b*sec(d*x+c)),x)","-\frac{a \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{2}}+\frac{\ln \left(b +a \cos \left(d x +c \right)\right)}{d a}+\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d \,b^{2}}+\frac{1}{d b \cos \left(d x +c \right)}"," ",0,"-1/d/b^2*a*ln(b+a*cos(d*x+c))+1/d/a*ln(b+a*cos(d*x+c))+1/d/b^2*a*ln(cos(d*x+c))+1/d/b/cos(d*x+c)","A"
290,1,35,35,0.128000," ","int(tan(d*x+c)/(a+b*sec(d*x+c)),x)","-\frac{\ln \left(a +b \sec \left(d x +c \right)\right)}{d a}+\frac{\ln \left(\sec \left(d x +c \right)\right)}{d a}"," ",0,"-ln(a+b*sec(d*x+c))/d/a+1/d/a*ln(sec(d*x+c))","A"
291,1,80,90,0.709000," ","int(cot(d*x+c)/(a+b*sec(d*x+c)),x)","-\frac{b^{2} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right) \left(a -b \right) a}+\frac{\ln \left(-1+\cos \left(d x +c \right)\right)}{d \left(2 a +2 b \right)}+\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"-1/d*b^2/(a+b)/(a-b)/a*ln(b+a*cos(d*x+c))+1/d/(2*a+2*b)*ln(-1+cos(d*x+c))+1/d/(2*a-2*b)*ln(1+cos(d*x+c))","A"
292,1,167,149,0.876000," ","int(cot(d*x+c)^3/(a+b*sec(d*x+c)),x)","-\frac{b^{4} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2} a}+\frac{1}{d \left(4 a +4 b \right) \left(-1+\cos \left(d x +c \right)\right)}-\frac{\ln \left(-1+\cos \left(d x +c \right)\right) a}{2 d \left(a +b \right)^{2}}-\frac{3 \ln \left(-1+\cos \left(d x +c \right)\right) b}{4 d \left(a +b \right)^{2}}-\frac{1}{d \left(4 a -4 b \right) \left(1+\cos \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\cos \left(d x +c \right)\right) b}{4 d \left(a -b \right)^{2}}-\frac{a \ln \left(1+\cos \left(d x +c \right)\right)}{2 \left(a -b \right)^{2} d}"," ",0,"-1/d*b^4/(a+b)^2/(a-b)^2/a*ln(b+a*cos(d*x+c))+1/d/(4*a+4*b)/(-1+cos(d*x+c))-1/2/d/(a+b)^2*ln(-1+cos(d*x+c))*a-3/4/d/(a+b)^2*ln(-1+cos(d*x+c))*b-1/d/(4*a-4*b)/(1+cos(d*x+c))+3/4/d/(a-b)^2*ln(1+cos(d*x+c))*b-1/2*a*ln(1+cos(d*x+c))/(a-b)^2/d","A"
293,1,308,222,0.684000," ","int(cot(d*x+c)^5/(a+b*sec(d*x+c)),x)","-\frac{b^{6} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3} a}-\frac{1}{2 d \left(8 a +8 b \right) \left(-1+\cos \left(d x +c \right)\right)^{2}}-\frac{7 a}{16 d \left(a +b \right)^{2} \left(-1+\cos \left(d x +c \right)\right)}-\frac{9 b}{16 d \left(a +b \right)^{2} \left(-1+\cos \left(d x +c \right)\right)}+\frac{\ln \left(-1+\cos \left(d x +c \right)\right) a^{2}}{2 d \left(a +b \right)^{3}}+\frac{21 \ln \left(-1+\cos \left(d x +c \right)\right) a b}{16 d \left(a +b \right)^{3}}+\frac{15 \ln \left(-1+\cos \left(d x +c \right)\right) b^{2}}{16 d \left(a +b \right)^{3}}-\frac{1}{2 d \left(8 a -8 b \right) \left(1+\cos \left(d x +c \right)\right)^{2}}+\frac{7 a}{16 d \left(a -b \right)^{2} \left(1+\cos \left(d x +c \right)\right)}-\frac{9 b}{16 d \left(a -b \right)^{2} \left(1+\cos \left(d x +c \right)\right)}+\frac{\ln \left(1+\cos \left(d x +c \right)\right) a^{2}}{2 d \left(a -b \right)^{3}}-\frac{21 \ln \left(1+\cos \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{3}}+\frac{15 \ln \left(1+\cos \left(d x +c \right)\right) b^{2}}{16 d \left(a -b \right)^{3}}"," ",0,"-1/d*b^6/(a+b)^3/(a-b)^3/a*ln(b+a*cos(d*x+c))-1/2/d/(8*a+8*b)/(-1+cos(d*x+c))^2-7/16/d/(a+b)^2/(-1+cos(d*x+c))*a-9/16/d/(a+b)^2/(-1+cos(d*x+c))*b+1/2/d/(a+b)^3*ln(-1+cos(d*x+c))*a^2+21/16/d/(a+b)^3*ln(-1+cos(d*x+c))*a*b+15/16/d/(a+b)^3*ln(-1+cos(d*x+c))*b^2-1/2/d/(8*a-8*b)/(1+cos(d*x+c))^2+7/16/d/(a-b)^2/(1+cos(d*x+c))*a-9/16/d/(a-b)^2/(1+cos(d*x+c))*b+1/2/d/(a-b)^3*ln(1+cos(d*x+c))*a^2-21/16/d/(a-b)^3*ln(1+cos(d*x+c))*a*b+15/16/d/(a-b)^3*ln(1+cos(d*x+c))*b^2","A"
294,1,785,181,0.460000," ","int(tan(d*x+c)^6/(a+b*sec(d*x+c)),x)","\frac{a^{2}}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 a}{d \,b^{2} \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)^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{4}}{d \,b^{5}}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{2}}{2 d \,b^{3}}+\frac{a^{2}}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2 a}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{a}{3 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{a^{2}}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{a}{3 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{a^{2}}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{a}{2 d \,b^{2} \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) a^{4}}{d \,b^{5}}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a^{2}}{2 d \,b^{3}}+\frac{a^{3}}{d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{a^{3}}{d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{6 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 a \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d b \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d a \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 a^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{5} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{8 d b}-\frac{7}{8 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{1}{4 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{5}{8 d b \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}-\frac{7}{8 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{4 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}+\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{5}{8 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}"," ",0,"1/2/d/b^3/(tan(1/2*d*x+1/2*c)+1)*a^2-2/d/b^2/(tan(1/2*d*x+1/2*c)+1)*a-1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)^2*a+1/d/b^5*ln(tan(1/2*d*x+1/2*c)+1)*a^4-5/2/d/b^3*ln(tan(1/2*d*x+1/2*c)+1)*a^2+1/2/d/b^3/(tan(1/2*d*x+1/2*c)-1)*a^2-2/d/b^2/(tan(1/2*d*x+1/2*c)-1)*a+1/3/d/b^2/(tan(1/2*d*x+1/2*c)+1)^3*a-1/2/d/b^3/(tan(1/2*d*x+1/2*c)+1)^2*a^2+1/3/d/b^2/(tan(1/2*d*x+1/2*c)-1)^3*a+1/2/d/b^3/(tan(1/2*d*x+1/2*c)-1)^2*a^2+1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)^2*a-1/d/b^5*ln(tan(1/2*d*x+1/2*c)-1)*a^4+5/2/d/b^3*ln(tan(1/2*d*x+1/2*c)-1)*a^2+1/d/b^4/(tan(1/2*d*x+1/2*c)-1)*a^3+1/d/b^4/(tan(1/2*d*x+1/2*c)+1)*a^3-6/d/b*a/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d*b/a/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+15/8/d/b*ln(tan(1/2*d*x+1/2*c)+1)-7/8/d/b/(tan(1/2*d*x+1/2*c)+1)+1/4/d/b/(tan(1/2*d*x+1/2*c)-1)^4+1/2/d/b/(tan(1/2*d*x+1/2*c)-1)^3-5/8/d/b/(tan(1/2*d*x+1/2*c)-1)^2-15/8/d/b*ln(tan(1/2*d*x+1/2*c)-1)-7/8/d/b/(tan(1/2*d*x+1/2*c)-1)-1/4/d/b/(tan(1/2*d*x+1/2*c)+1)^4-2/d/a*arctan(tan(1/2*d*x+1/2*c))+1/2/d/b/(tan(1/2*d*x+1/2*c)+1)^3+5/8/d/b/(tan(1/2*d*x+1/2*c)+1)^2-2/d/b^5*a^5/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+6/d/b^3*a^3/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))","B"
295,1,374,113,0.442000," ","int(tan(d*x+c)^4/(a+b*sec(d*x+c)),x)","-\frac{2 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{4 a \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d b \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d a \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{a}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{2 d b \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^{2}}{d \,b^{3}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d b}-\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{a}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{1}{2 d b \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^{2}}{d \,b^{3}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d b}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"-2/d/b^3*a^3/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+4/d/b*a/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-2/d*b/a/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+1/2/d/b/(tan(1/2*d*x+1/2*c)-1)^2+1/d/b^2/(tan(1/2*d*x+1/2*c)-1)*a+1/2/d/b/(tan(1/2*d*x+1/2*c)-1)-1/d/b^3*ln(tan(1/2*d*x+1/2*c)-1)*a^2+3/2/d/b*ln(tan(1/2*d*x+1/2*c)-1)-1/2/d/b/(tan(1/2*d*x+1/2*c)+1)^2+1/d/b^2/(tan(1/2*d*x+1/2*c)+1)*a+1/2/d/b/(tan(1/2*d*x+1/2*c)+1)+1/d/b^3*ln(tan(1/2*d*x+1/2*c)+1)*a^2-3/2/d/b*ln(tan(1/2*d*x+1/2*c)+1)+2/d/a*arctan(tan(1/2*d*x+1/2*c))","B"
296,1,153,67,0.422000," ","int(tan(d*x+c)^2/(a+b*sec(d*x+c)),x)","-\frac{2 a \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d b \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d a \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d b}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d b}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"-2/d/b*a/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d*b/a/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/b*ln(tan(1/2*d*x+1/2*c)-1)+1/d/b*ln(tan(1/2*d*x+1/2*c)+1)-2/d/a*arctan(tan(1/2*d*x+1/2*c))","B"
297,1,123,101,0.625000," ","int(cot(d*x+c)^2/(a+b*sec(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \left(a -b \right)}-\frac{2 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a -b \right) \left(a +b \right) a \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{2 d \left(a +b \right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"1/2/d/(a-b)*tan(1/2*d*x+1/2*c)-2/d/(a-b)/(a+b)*b^3/a/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/2/d/(a+b)/tan(1/2*d*x+1/2*c)-2/d/a*arctan(tan(1/2*d*x+1/2*c))","A"
298,1,238,168,0.698000," ","int(cot(d*x+c)^4/(a+b*sec(d*x+c)),x)","\frac{a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \left(a -b \right)^{2}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{24 d \left(a -b \right)^{2}}-\frac{5 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \left(a -b \right)^{2}}+\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{8 d \left(a -b \right)^{2}}-\frac{2 b^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2} a \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{24 d \left(a +b \right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{5 a}{8 d \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{7 b}{8 d \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"1/24/d/(a-b)^2*a*tan(1/2*d*x+1/2*c)^3-1/24/d/(a-b)^2*tan(1/2*d*x+1/2*c)^3*b-5/8/d/(a-b)^2*a*tan(1/2*d*x+1/2*c)+7/8/d/(a-b)^2*tan(1/2*d*x+1/2*c)*b-2/d/(a+b)^2/(a-b)^2*b^5/a/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/24/d/(a+b)/tan(1/2*d*x+1/2*c)^3+5/8/d/(a+b)^2/tan(1/2*d*x+1/2*c)*a+7/8/d/(a+b)^2/tan(1/2*d*x+1/2*c)*b+2/d/a*arctan(tan(1/2*d*x+1/2*c))","A"
299,1,498,245,0.560000," ","int(tan(d*x+c)^9/(a+b*sec(d*x+c))^2,x)","\frac{3 a^{2}}{4 d \,b^{4} \cos \left(d x +c \right)^{4}}-\frac{6 a^{2}}{d \,b^{4} \cos \left(d x +c \right)^{2}}-\frac{a^{6}}{d \,b^{7} \left(b +a \cos \left(d x +c \right)\right)}+\frac{4 a^{4}}{d \,b^{5} \left(b +a \cos \left(d x +c \right)\right)}-\frac{6 a^{2}}{d \,b^{3} \left(b +a \cos \left(d x +c \right)\right)}-\frac{b}{d \,a^{2} \left(b +a \cos \left(d x +c \right)\right)}+\frac{7 a^{6} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{8}}-\frac{20 a^{4} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{6}}+\frac{18 a^{2} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{4}}-\frac{7 \ln \left(\cos \left(d x +c \right)\right) a^{6}}{d \,b^{8}}-\frac{4 a^{3}}{3 d \,b^{5} \cos \left(d x +c \right)^{3}}+\frac{8 a}{3 d \,b^{3} \cos \left(d x +c \right)^{3}}-\frac{6 a^{5}}{d \,b^{7} \cos \left(d x +c \right)}+\frac{16 a^{3}}{d \,b^{5} \cos \left(d x +c \right)}+\frac{20 \ln \left(\cos \left(d x +c \right)\right) a^{4}}{d \,b^{6}}-\frac{18 \ln \left(\cos \left(d x +c \right)\right) a^{2}}{d \,b^{4}}-\frac{2 a}{5 d \,b^{3} \cos \left(d x +c \right)^{5}}+\frac{5 a^{4}}{2 d \,b^{6} \cos \left(d x +c \right)^{2}}-\frac{4 \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{2}}-\frac{\ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{2}}-\frac{1}{d \,b^{2} \cos \left(d x +c \right)^{4}}+\frac{3}{d \,b^{2} \cos \left(d x +c \right)^{2}}+\frac{4 \ln \left(\cos \left(d x +c \right)\right)}{d \,b^{2}}+\frac{1}{6 d \,b^{2} \cos \left(d x +c \right)^{6}}+\frac{4}{d b \left(b +a \cos \left(d x +c \right)\right)}-\frac{12 a}{d \,b^{3} \cos \left(d x +c \right)}"," ",0,"3/4/d/b^4/cos(d*x+c)^4*a^2-6/d/b^4/cos(d*x+c)^2*a^2-1/d*a^6/b^7/(b+a*cos(d*x+c))+4/d*a^4/b^5/(b+a*cos(d*x+c))-6/d*a^2/b^3/(b+a*cos(d*x+c))-1/d/a^2*b/(b+a*cos(d*x+c))+7/d/b^8*a^6*ln(b+a*cos(d*x+c))-20/d/b^6*a^4*ln(b+a*cos(d*x+c))+18/d/b^4*a^2*ln(b+a*cos(d*x+c))-7/d/b^8*ln(cos(d*x+c))*a^6-4/3/d*a^3/b^5/cos(d*x+c)^3+8/3/d*a/b^3/cos(d*x+c)^3-6/d*a^5/b^7/cos(d*x+c)+16/d*a^3/b^5/cos(d*x+c)+20/d/b^6*ln(cos(d*x+c))*a^4-18/d/b^4*ln(cos(d*x+c))*a^2-2/5/d/b^3*a/cos(d*x+c)^5+5/2/d/b^6/cos(d*x+c)^2*a^4-4/d/b^2*ln(b+a*cos(d*x+c))-1/d/a^2*ln(b+a*cos(d*x+c))-1/d/b^2/cos(d*x+c)^4+3/d/b^2/cos(d*x+c)^2+4/d/b^2*ln(cos(d*x+c))+1/6/d/b^2/cos(d*x+c)^6+4/d/b/(b+a*cos(d*x+c))-12/d*a/b^3/cos(d*x+c)","B"
300,1,324,173,0.492000," ","int(tan(d*x+c)^7/(a+b*sec(d*x+c))^2,x)","-\frac{a^{4}}{d \,b^{5} \left(b +a \cos \left(d x +c \right)\right)}+\frac{3 a^{2}}{d \,b^{3} \left(b +a \cos \left(d x +c \right)\right)}-\frac{3}{d b \left(b +a \cos \left(d x +c \right)\right)}+\frac{b}{d \,a^{2} \left(b +a \cos \left(d x +c \right)\right)}+\frac{5 a^{4} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{6}}-\frac{9 a^{2} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{4}}+\frac{3 \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{2}}+\frac{\ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{2}}+\frac{3 a^{2}}{2 d \,b^{4} \cos \left(d x +c \right)^{2}}-\frac{3}{2 d \,b^{2} \cos \left(d x +c \right)^{2}}-\frac{5 \ln \left(\cos \left(d x +c \right)\right) a^{4}}{d \,b^{6}}+\frac{9 \ln \left(\cos \left(d x +c \right)\right) a^{2}}{d \,b^{4}}-\frac{3 \ln \left(\cos \left(d x +c \right)\right)}{d \,b^{2}}+\frac{1}{4 d \,b^{2} \cos \left(d x +c \right)^{4}}-\frac{2 a}{3 d \,b^{3} \cos \left(d x +c \right)^{3}}-\frac{4 a^{3}}{d \,b^{5} \cos \left(d x +c \right)}+\frac{6 a}{d \,b^{3} \cos \left(d x +c \right)}"," ",0,"-1/d*a^4/b^5/(b+a*cos(d*x+c))+3/d*a^2/b^3/(b+a*cos(d*x+c))-3/d/b/(b+a*cos(d*x+c))+1/d/a^2*b/(b+a*cos(d*x+c))+5/d/b^6*a^4*ln(b+a*cos(d*x+c))-9/d/b^4*a^2*ln(b+a*cos(d*x+c))+3/d/b^2*ln(b+a*cos(d*x+c))+1/d/a^2*ln(b+a*cos(d*x+c))+3/2/d/b^4/cos(d*x+c)^2*a^2-3/2/d/b^2/cos(d*x+c)^2-5/d/b^6*ln(cos(d*x+c))*a^4+9/d/b^4*ln(cos(d*x+c))*a^2-3/d/b^2*ln(cos(d*x+c))+1/4/d/b^2/cos(d*x+c)^4-2/3/d*a/b^3/cos(d*x+c)^3-4/d*a^3/b^5/cos(d*x+c)+6/d*a/b^3/cos(d*x+c)","A"
301,1,192,119,0.477000," ","int(tan(d*x+c)^5/(a+b*sec(d*x+c))^2,x)","-\frac{a^{2}}{d \,b^{3} \left(b +a \cos \left(d x +c \right)\right)}+\frac{2}{d b \left(b +a \cos \left(d x +c \right)\right)}-\frac{b}{d \,a^{2} \left(b +a \cos \left(d x +c \right)\right)}+\frac{3 a^{2} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{4}}-\frac{2 \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{2}}-\frac{\ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{2}}-\frac{3 \ln \left(\cos \left(d x +c \right)\right) a^{2}}{d \,b^{4}}+\frac{2 \ln \left(\cos \left(d x +c \right)\right)}{d \,b^{2}}+\frac{1}{2 d \,b^{2} \cos \left(d x +c \right)^{2}}-\frac{2 a}{d \,b^{3} \cos \left(d x +c \right)}"," ",0,"-1/d*a^2/b^3/(b+a*cos(d*x+c))+2/d/b/(b+a*cos(d*x+c))-1/d/a^2*b/(b+a*cos(d*x+c))+3/d/b^4*a^2*ln(b+a*cos(d*x+c))-2/d/b^2*ln(b+a*cos(d*x+c))-1/d/a^2*ln(b+a*cos(d*x+c))-3/d/b^4*ln(cos(d*x+c))*a^2+2/d/b^2*ln(cos(d*x+c))+1/2/d/b^2/cos(d*x+c)^2-2/d*a/b^3/cos(d*x+c)","A"
302,1,93,74,0.528000," ","int(tan(d*x+c)^3/(a+b*sec(d*x+c))^2,x)","-\frac{1}{d b \left(b +a \cos \left(d x +c \right)\right)}+\frac{b}{d \,a^{2} \left(b +a \cos \left(d x +c \right)\right)}+\frac{\ln \left(b +a \cos \left(d x +c \right)\right)}{d \,b^{2}}+\frac{\ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{2}}-\frac{\ln \left(\cos \left(d x +c \right)\right)}{d \,b^{2}}"," ",0,"-1/d/b/(b+a*cos(d*x+c))+1/d/a^2*b/(b+a*cos(d*x+c))+1/d/b^2*ln(b+a*cos(d*x+c))+1/d/a^2*ln(b+a*cos(d*x+c))-1/d/b^2*ln(cos(d*x+c))","A"
303,1,54,54,0.130000," ","int(tan(d*x+c)/(a+b*sec(d*x+c))^2,x)","\frac{1}{a d \left(a +b \sec \left(d x +c \right)\right)}-\frac{\ln \left(a +b \sec \left(d x +c \right)\right)}{a^{2} d}+\frac{\ln \left(\sec \left(d x +c \right)\right)}{d \,a^{2}}"," ",0,"1/a/d/(a+b*sec(d*x+c))-ln(a+b*sec(d*x+c))/a^2/d+1/d/a^2*ln(sec(d*x+c))","A"
304,1,141,134,0.606000," ","int(cot(d*x+c)/(a+b*sec(d*x+c))^2,x)","-\frac{b^{3}}{d \,a^{2} \left(a +b \right) \left(a -b \right) \left(b +a \cos \left(d x +c \right)\right)}-\frac{3 b^{2} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}+\frac{b^{4} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2} a^{2}}+\frac{\ln \left(-1+\cos \left(d x +c \right)\right)}{2 d \left(a +b \right)^{2}}+\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{2 \left(a -b \right)^{2} d}"," ",0,"-1/d/a^2*b^3/(a+b)/(a-b)/(b+a*cos(d*x+c))-3/d*b^2/(a+b)^2/(a-b)^2*ln(b+a*cos(d*x+c))+1/d*b^4/(a+b)^2/(a-b)^2/a^2*ln(b+a*cos(d*x+c))+1/2/d/(a+b)^2*ln(-1+cos(d*x+c))+1/2*ln(1+cos(d*x+c))/(a-b)^2/d","A"
305,1,226,189,0.719000," ","int(cot(d*x+c)^3/(a+b*sec(d*x+c))^2,x)","-\frac{b^{5}}{d \,a^{2} \left(a +b \right)^{2} \left(a -b \right)^{2} \left(b +a \cos \left(d x +c \right)\right)}-\frac{5 b^{4} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}+\frac{b^{6} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3} a^{2}}+\frac{1}{4 d \left(a +b \right)^{2} \left(-1+\cos \left(d x +c \right)\right)}-\frac{\ln \left(-1+\cos \left(d x +c \right)\right) a}{2 d \left(a +b \right)^{3}}-\frac{\ln \left(-1+\cos \left(d x +c \right)\right) b}{d \left(a +b \right)^{3}}-\frac{1}{4 d \left(a -b \right)^{2} \left(1+\cos \left(d x +c \right)\right)}-\frac{\ln \left(1+\cos \left(d x +c \right)\right) a}{2 d \left(a -b \right)^{3}}+\frac{\ln \left(1+\cos \left(d x +c \right)\right) b}{d \left(a -b \right)^{3}}"," ",0,"-1/d/a^2*b^5/(a+b)^2/(a-b)^2/(b+a*cos(d*x+c))-5/d*b^4/(a+b)^3/(a-b)^3*ln(b+a*cos(d*x+c))+1/d*b^6/(a+b)^3/(a-b)^3/a^2*ln(b+a*cos(d*x+c))+1/4/d/(a+b)^2/(-1+cos(d*x+c))-1/2/d/(a+b)^3*ln(-1+cos(d*x+c))*a-1/d/(a+b)^3*ln(-1+cos(d*x+c))*b-1/4/d/(a-b)^2/(1+cos(d*x+c))-1/2/d/(a-b)^3*ln(1+cos(d*x+c))*a+1/d/(a-b)^3*ln(1+cos(d*x+c))*b","A"
306,1,367,266,0.743000," ","int(cot(d*x+c)^5/(a+b*sec(d*x+c))^2,x)","-\frac{b^{7}}{d \,a^{2} \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}-\frac{7 b^{6} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{b^{8} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4} a^{2}}-\frac{1}{16 d \left(a +b \right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2}}-\frac{7 a}{16 d \left(a +b \right)^{3} \left(-1+\cos \left(d x +c \right)\right)}-\frac{11 b}{16 d \left(a +b \right)^{3} \left(-1+\cos \left(d x +c \right)\right)}+\frac{\ln \left(-1+\cos \left(d x +c \right)\right) a^{2}}{2 d \left(a +b \right)^{4}}+\frac{13 \ln \left(-1+\cos \left(d x +c \right)\right) a b}{8 d \left(a +b \right)^{4}}+\frac{3 \ln \left(-1+\cos \left(d x +c \right)\right) b^{2}}{2 d \left(a +b \right)^{4}}-\frac{1}{16 d \left(a -b \right)^{2} \left(1+\cos \left(d x +c \right)\right)^{2}}+\frac{7 a}{16 d \left(a -b \right)^{3} \left(1+\cos \left(d x +c \right)\right)}-\frac{11 b}{16 d \left(a -b \right)^{3} \left(1+\cos \left(d x +c \right)\right)}+\frac{\ln \left(1+\cos \left(d x +c \right)\right) a^{2}}{2 d \left(a -b \right)^{4}}-\frac{13 \ln \left(1+\cos \left(d x +c \right)\right) a b}{8 d \left(a -b \right)^{4}}+\frac{3 \ln \left(1+\cos \left(d x +c \right)\right) b^{2}}{2 d \left(a -b \right)^{4}}"," ",0,"-1/d/a^2*b^7/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))-7/d*b^6/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))+1/d*b^8/(a+b)^4/(a-b)^4/a^2*ln(b+a*cos(d*x+c))-1/16/d/(a+b)^2/(-1+cos(d*x+c))^2-7/16/d/(a+b)^3/(-1+cos(d*x+c))*a-11/16/d/(a+b)^3/(-1+cos(d*x+c))*b+1/2/d/(a+b)^4*ln(-1+cos(d*x+c))*a^2+13/8/d/(a+b)^4*ln(-1+cos(d*x+c))*a*b+3/2/d/(a+b)^4*ln(-1+cos(d*x+c))*b^2-1/16/d/(a-b)^2/(1+cos(d*x+c))^2+7/16/d/(a-b)^3/(1+cos(d*x+c))*a-11/16/d/(a-b)^3/(1+cos(d*x+c))*b+1/2/d/(a-b)^4*ln(1+cos(d*x+c))*a^2-13/8/d/(a-b)^4*ln(1+cos(d*x+c))*a*b+3/2/d/(a-b)^4*ln(1+cos(d*x+c))*b^2","A"
307,1,723,189,0.506000," ","int(tan(d*x+c)^6/(a+b*sec(d*x+c))^2,x)","-\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)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \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)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{8 a^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{5} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{14 a^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{4 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d b \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{3 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{a}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3 a^{2}}{d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{a}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{4 a^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{5}}-\frac{5 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{3}}-\frac{1}{3 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{a}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3 a^{2}}{d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{a}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{4 a^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{5}}+\frac{5 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{3}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-2/d/b^4*a^3*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)+4/d/b^2*a*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)-2/d/a*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)+8/d/b^5*a^4/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-14/d/b^3*a^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+4/d/b/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d*b/a^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/3/d/b^2/(tan(1/2*d*x+1/2*c)-1)^3-1/d/b^3/(tan(1/2*d*x+1/2*c)-1)^2*a-1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)^2-3/d/b^4/(tan(1/2*d*x+1/2*c)-1)*a^2-1/d/b^3/(tan(1/2*d*x+1/2*c)-1)*a+2/d/b^2/(tan(1/2*d*x+1/2*c)-1)+4/d*a^3/b^5*ln(tan(1/2*d*x+1/2*c)-1)-5/d*a/b^3*ln(tan(1/2*d*x+1/2*c)-1)-1/3/d/b^2/(tan(1/2*d*x+1/2*c)+1)^3+1/d/b^3/(tan(1/2*d*x+1/2*c)+1)^2*a+1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)^2-3/d/b^4/(tan(1/2*d*x+1/2*c)+1)*a^2-1/d/b^3/(tan(1/2*d*x+1/2*c)+1)*a+2/d/b^2/(tan(1/2*d*x+1/2*c)+1)-4/d*a^3/b^5*ln(tan(1/2*d*x+1/2*c)+1)+5/d*a/b^3*ln(tan(1/2*d*x+1/2*c)+1)-2/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
308,1,353,141,0.398000," ","int(tan(d*x+c)^4/(a+b*sec(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)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{4 a^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d b \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{3}}-\frac{1}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{3}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-2/d/b^2*a*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)+2/d/a*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)+4/d/b^3*a^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-2/d/b/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-2/d*b/a^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/b^2/(tan(1/2*d*x+1/2*c)-1)+2/d*a/b^3*ln(tan(1/2*d*x+1/2*c)-1)-1/d/b^2/(tan(1/2*d*x+1/2*c)+1)-2/d*a/b^3*ln(tan(1/2*d*x+1/2*c)+1)+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
309,1,120,76,0.432000," ","int(tan(d*x+c)^2/(a+b*sec(d*x+c))^2,x)","-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{2 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-2/d/a*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)+2/d*b/a^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-2/d/a^2*arctan(tan(1/2*d*x+1/2*c))","A"
310,1,255,205,0.623000," ","int(cot(d*x+c)^2/(a+b*sec(d*x+c))^2,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \left(a^{2}-2 a b +b^{2}\right)}-\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2} a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{8 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 b^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2} a^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{2 d \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"1/2/d/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)-2/d*b^4/(a+b)^2/(a-b)^2/a*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)-8/d*b^3/(a+b)^2/(a-b)^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d*b^5/(a+b)^2/(a-b)^2/a^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/2/d/(a+b)^2/tan(1/2*d*x+1/2*c)-2/d/a^2*arctan(tan(1/2*d*x+1/2*c))","A"
311,1,416,330,0.694000," ","int(cot(d*x+c)^4/(a+b*sec(d*x+c))^2,x)","\frac{a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \left(a -b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{24 d \left(a -b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{5 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \left(a -b \right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{8 d \left(a -b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{2 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3} a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{12 b^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 b^{7} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3} a^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{24 d \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{5 a}{8 d \left(a +b \right)^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{9 b}{8 d \left(a +b \right)^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"1/24/d/(a-b)/(a^2-2*a*b+b^2)*a*tan(1/2*d*x+1/2*c)^3-1/24/d/(a-b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*b-5/8/d/(a-b)/(a^2-2*a*b+b^2)*a*tan(1/2*d*x+1/2*c)+9/8/d/(a-b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)*b-2/d*b^6/(a+b)^3/(a-b)^3/a*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)-12/d*b^5/(a+b)^3/(a-b)^3/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d*b^7/(a+b)^3/(a-b)^3/a^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/24/d/(a+b)^2/tan(1/2*d*x+1/2*c)^3+5/8/d/(a+b)^3/tan(1/2*d*x+1/2*c)*a+9/8/d/(a+b)^3/tan(1/2*d*x+1/2*c)*b+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))","A"
312,1,3747,646,1.765000," ","int((e*tan(d*x+c))^(5/2)/(a+b*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/d*(a-b)*(-1+cos(d*x+c))^2*(-I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2+2*cos(d*x+c)*2^(1/2)*a*b-(a^2-b^2)^(1/2)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b+2*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a*b-4*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a*b-I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2-cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a^2+cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b^2-cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a^2+cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b^2-cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2+I*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2-cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2+(a^2-b^2)^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a+(a^2-b^2)^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b-(a^2-b^2)^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a-(a^2-b^2)^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b+2*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a*b-4*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*a*b+I*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2+(a^2-b^2)^(1/2)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a+(a^2-b^2)^(1/2)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b-(a^2-b^2)^(1/2)*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a-2*2^(1/2)*a*b-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a^2+((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b^2-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a^2+((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b^2-((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2)*cos(d*x+c)^2*(1+cos(d*x+c))^2*(e*sin(d*x+c)/cos(d*x+c))^(5/2)/sin(d*x+c)^7*2^(1/2)/b/((a^2-b^2)^(1/2)-a+b)/((a^2-b^2)^(1/2)+a-b)/a","B"
313,1,1801,636,1.637000," ","int((e*tan(d*x+c))^(3/2)/(a+b*sec(d*x+c)),x)","\frac{\left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e \sin \left(d x +c \right)}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \left(i \left(a^{2}-b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \left(a^{2}-b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{2}-\sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b^{2}-\sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{2}-\sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b^{2}-i \sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b^{2}+i \sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{2}+i \sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b^{2}-i \sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a^{2}+2 \sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a b +2 \sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a b -2 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a -b}{a -b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) a^{2} b -2 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a -b}{a -b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) a \,b^{2}+2 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a -b}{-a +b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) a \,b^{2}-2 \sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a -b}{a -b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) a^{2}+2 \sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a -b}{a -b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) b^{2}-2 \sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a -b}{-a +b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) a^{2}+2 \sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a -b}{-a +b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) b^{2}+2 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a -b}{-a +b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) a^{2} b -2 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a -b}{-a +b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) a^{3}-2 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a -b}{-a +b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) b^{3}+\left(a^{2}-b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\left(a^{2}-b^{2}\right)^{\frac{3}{2}} \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 i \sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a b -2 i \sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a b +2 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a -b}{a -b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) a^{3}+2 \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a -b}{a -b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) b^{3}\right) \sqrt{2}}{2 d \sin \left(d x +c \right)^{4} \left(\sqrt{a^{2}-b^{2}}-a +b \right) \left(\sqrt{a^{2}-b^{2}}+a -b \right) \sqrt{a^{2}-b^{2}}\, a}"," ",0,"1/2/d*(1+cos(d*x+c))^2*(e*sin(d*x+c)/cos(d*x+c))^(3/2)*(-1+cos(d*x+c))*cos(d*x+c)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-I*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2+I*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2+I*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2-I*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2+2*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b+2*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b+I*(a^2-b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*(a^2-b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2-(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2-2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a^2*b-2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a*b^2+2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a*b^2-2*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a^2+2*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b^2-2*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a^2+2*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b^2-(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2-(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2+2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a^2*b+2*I*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b-2*I*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b+(a^2-b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+(a^2-b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a^3+2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b^3-2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a^3-2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b^3)/sin(d*x+c)^4*2^(1/2)/((a^2-b^2)^(1/2)-a+b)/((a^2-b^2)^(1/2)+a-b)/(a^2-b^2)^(1/2)/a","B"
314,1,859,328,1.748000," ","int((e*tan(d*x+c))^(1/2)/(a+b*sec(d*x+c)),x)","-\frac{\sqrt{\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{e \sin \left(d x +c \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) \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a -i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +i \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -\sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a -b}{a -b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right)+\sqrt{a^{2}-b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a -b}{-a +b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a -b}{a -b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) a -b \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{a -b}{a -b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a -b}{-a +b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) a -b \EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, -\frac{a -b}{-a +b +\sqrt{\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b -\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +\EllipticPi \left(\sqrt{\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b \right) \sqrt{2}\, b}{d \sin \left(d x +c \right)^{3} \left(\sqrt{a^{2}-b^{2}}-a +b \right) \left(\sqrt{a^{2}-b^{2}}+a -b \right) a}"," ",0,"-1/d*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(e*sin(d*x+c)/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+I*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))+(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a-b*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a-b*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b)/sin(d*x+c)^3*2^(1/2)*b/((a^2-b^2)^(1/2)-a+b)/((a^2-b^2)^(1/2)+a-b)/a","B"
315,1,2313,343,1.727000," ","int(1/(a+b*sec(d*x+c))/(e*tan(d*x+c))^(1/2),x)","\text{Expression too large to display}"," ",0,"1/2/d*(2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2-b^2)^(3/2)*a-(a^2-b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+(a^2-b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b-(a^2-b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+(a^2-b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b+2*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b^3+2*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b^3+(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3-(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^3+(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3+2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a^2*b^2-4*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a*b^3-2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a^2*b^2+4*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a*b^3-2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2-b^2)^(1/2)*a^3-(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^3+4*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2-b^2)^(1/2)*a^2*b-2*EllipticF(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(a^2-b^2)^(1/2)*a*b^2-2*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a*b^2-I*(a^2-b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b-I*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^3-I*(a^2-b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a+I*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^3-I*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^3-2*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a*b^2-3*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b+3*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^2-3*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b+3*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^2+I*(a^2-b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+I*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^3+I*(a^2-b^2)^(3/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b+3*I*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2*b-3*I*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*b^2-3*I*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2*b+3*I*(a^2-b^2)^(1/2)*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*b^2+2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),(a-b)/(a-b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b^4-2*EllipticPi(((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2),-(a-b)/(-a+b+((a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b^4)*((-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))^(1/2)*(-1+cos(d*x+c))/sin(d*x+c)^2/cos(d*x+c)*(1+cos(d*x+c))^2/(e*sin(d*x+c)/cos(d*x+c))^(1/2)*2^(1/2)/((a^2-b^2)^(1/2)-a+b)/((a^2-b^2)^(1/2)+a-b)/(a^2-b^2)^(1/2)/(a-b)/a","B"
316,1,6426,746,1.709000," ","int(1/(a+b*sec(d*x+c))/(e*tan(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
317,1,16178,725,1.934000," ","int(1/(a+b*sec(d*x+c))/(e*tan(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
318,1,3268,145,2.049000," ","int((a+b*sec(d*x+c))^(1/2)*tan(d*x+c)^5,x)","\text{output too large to display}"," ",0,"-1/2520/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))*(-1+cos(d*x+c))^4*(630*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*cos(d*x+c)^6*b^6-280*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*b^4-630*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*cos(d*x+c)^6*b^6+630*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*cos(d*x+c)^7*a*b^5-1197*cos(d*x+c)^6*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*b^4+1260*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*cos(d*x+c)^6*a*b^5-1260*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*cos(d*x+c)^6*a*b^5+2625*cos(d*x+c)^4*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*b^4+168*cos(d*x+c)^2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*b^4-2121*cos(d*x+c)^6*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)*b^5-2121*cos(d*x+c)^5*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)*b^5-189*cos(d*x+c)^5*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*b^4+2744*cos(d*x+c)^3*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*b^4-840*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*b^4-399*cos(d*x+c)^7*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*b^4+128*cos(d*x+c)^6*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)*a^5+128*cos(d*x+c)^7*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)*a^5+1260*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*cos(d*x+c)^7*a^2*b^4-630*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*cos(d*x+c)^7*a*b^5-1260*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*cos(d*x+c)^7*a^2*b^4-648*cos(d*x+c)^6*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)*a^2*b^3+128*cos(d*x+c)^6*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)*a^4*b-648*cos(d*x+c)^6*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)*a^3*b^2-2121*cos(d*x+c)^6*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)*a*b^4-2121*cos(d*x+c)^7*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)*a*b^4-648*cos(d*x+c)^7*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)*a^3*b^2+128*cos(d*x+c)^5*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)*a^4*b-648*cos(d*x+c)^5*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)*a^2*b^3+1260*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*a^(3/2)*cos(d*x+c)^7*(a-b)^(1/2)*b^4+1260*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*a^(1/2)*cos(d*x+c)^6*(a-b)^(1/2)*b^5-72*cos(d*x+c)^6*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*a^2*b^2-192*cos(d*x+c)^5*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*a^3*b+1008*cos(d*x+c)^5*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*a*b^3+120*cos(d*x+c)^4*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*a^2*b^2-64*cos(d*x+c)^3*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*a^3*b+216*cos(d*x+c)^3*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*a*b^3+48*cos(d*x+c)^2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*a^2*b^2-40*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a*b^3-24*cos(d*x+c)^7*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*a^2*b^2-64*cos(d*x+c)^6*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*a^3*b+336*cos(d*x+c)^6*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*a*b^3-24*cos(d*x+c)^5*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a^2*b^2-192*cos(d*x+c)^4*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*a^3*b+968*cos(d*x+c)^4*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*a*b^3+144*cos(d*x+c)^3*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*a^2*b^2-120*cos(d*x+c)^2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*a*b^3)/sin(d*x+c)^8/cos(d*x+c)^4/((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)/(a-b)^(1/2)/b^4","B"
319,1,2342,84,1.720000," ","int((a+b*sec(d*x+c))^(1/2)*tan(d*x+c)^3,x)","\text{Expression too large to display}"," ",0,"-1/60/d*(1+cos(d*x+c))*(-1+cos(d*x+c))^4*(-36*(a-b)^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*b^2+6*(a-b)^(1/2)*cos(d*x+c)^5*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*b^2+6*(a-b)^(1/2)*cos(d*x+c)^3*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*b^2+54*(a-b)^(1/2)*cos(d*x+c)^4*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*b^3+8*(a-b)^(1/2)*cos(d*x+c)^5*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^3+8*(a-b)^(1/2)*cos(d*x+c)^4*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^3+54*(a-b)^(1/2)*cos(d*x+c)^3*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*b^3+18*(a-b)^(1/2)*cos(d*x+c)^4*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*b^2+30*cos(d*x+c)^5*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b^2-15*cos(d*x+c)^5*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a*b^3-30*cos(d*x+c)^5*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b^2+15*cos(d*x+c)^5*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a*b^3+30*cos(d*x+c)^4*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a*b^3-30*cos(d*x+c)^4*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a*b^3-30*(a-b)^(1/2)*cos(d*x+c)^2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*b^2-15*cos(d*x+c)^4*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*b^4+15*cos(d*x+c)^4*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*b^4-12*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(1/2)*b^2+54*(a-b)^(1/2)*cos(d*x+c)^5*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a*b^2+8*(a-b)^(1/2)*cos(d*x+c)^3*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^2*b+8*(a-b)^(1/2)*cos(d*x+c)^4*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^2*b+54*(a-b)^(1/2)*cos(d*x+c)^4*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a*b^2-30*(a-b)^(1/2)*a^(3/2)*cos(d*x+c)^5*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b^2-30*(a-b)^(1/2)*a^(1/2)*cos(d*x+c)^4*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b^3-12*(a-b)^(1/2)*cos(d*x+c)^3*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a*b-4*(a-b)^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a*b-4*(a-b)^(1/2)*cos(d*x+c)^4*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a*b-12*(a-b)^(1/2)*cos(d*x+c)^2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a*b)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*4^(1/2)/((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)/sin(d*x+c)^8/cos(d*x+c)^2/b^2/(a-b)^(1/2)","B"
320,1,42,43,0.243000," ","int((a+b*sec(d*x+c))^(1/2)*tan(d*x+c),x)","\frac{2 \sqrt{a +b \sec \left(d x +c \right)}-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{a +b \sec \left(d x +c \right)}}{\sqrt{a}}\right)}{d}"," ",0,"1/d*(2*(a+b*sec(d*x+c))^(1/2)-2*a^(1/2)*arctanh((a+b*sec(d*x+c))^(1/2)/a^(1/2)))","A"
321,1,575,88,1.517000," ","int(cot(d*x+c)*(a+b*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{4}\, \cos \left(d x +c \right) \left(-1+\cos \left(d x +c \right)\right) \left(\sqrt{a +b}\, \ln \left(-\frac{2 \left(2 \cos \left(d x +c \right) \sqrt{a +b}\, \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+2 a \cos \left(d x +c \right)+b \cos \left(d x +c \right)+2 \sqrt{a +b}\, \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+b \right)}{-1+\cos \left(d x +c \right)}\right) \sqrt{a -b}-2 \sqrt{a}\, \ln \left(4 \sqrt{a}\, \cos \left(d x +c \right) \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 \sqrt{a}\, \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 a \cos \left(d x +c \right)+2 b \right) \sqrt{a -b}-a \ln \left(-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(2 \cos \left(d x +c \right) \sqrt{a -b}\, \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-2 a \cos \left(d x +c \right)+b \cos \left(d x +c \right)+2 \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{a -b}-b \right)}{\sin \left(d x +c \right)^{2} \sqrt{a -b}}\right)+\ln \left(-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(2 \cos \left(d x +c \right) \sqrt{a -b}\, \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-2 a \cos \left(d x +c \right)+b \cos \left(d x +c \right)+2 \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{a -b}-b \right)}{\sin \left(d x +c \right)^{2} \sqrt{a -b}}\right) b \right)}{4 d \sin \left(d x +c \right)^{2} \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{a -b}}"," ",0,"1/4/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*4^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))*((a+b)^(1/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*(a-b)^(1/2)-2*a^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*(a-b)^(1/2)-a*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))+ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*b)/sin(d*x+c)^2/((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)/(a-b)^(1/2)","B"
322,1,2844,177,1.479000," ","int(cot(d*x+c)^3*(a+b*sec(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"-1/16/d*(-1+cos(d*x+c))*(-4*(a-b)^(3/2)*(a+b)^(1/2)*cos(d*x+c)*4^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a-16*(a-b)^(3/2)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+4*(a+b)^(1/2)*cos(d*x+c)^2*4^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3+3*(a+b)^(1/2)*cos(d*x+c)^2*4^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*b^3+7*(a-b)^(3/2)*4^(1/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*a*b+3*(a+b)^(1/2)*4^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b-16*(a-b)^(3/2)*(a+b)^(1/2)*cos(d*x+c)^2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)-32*(a-b)^(3/2)*(a+b)^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)+4*(a-b)^(3/2)*4^(1/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*a^2+3*(a-b)^(3/2)*4^(1/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*b^2-4*(a+b)^(1/2)*4^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3-3*(a+b)^(1/2)*4^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*b^3+4*(a-b)^(3/2)*(a+b)^(1/2)*cos(d*x+c)*4^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*b+8*(a-b)^(3/2)*(a+b)^(1/2)*a^(1/2)*cos(d*x+c)^2*4^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b+4*(a-b)^(3/2)*(a+b)^(1/2)*cos(d*x+c)^2*4^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a-4*(a-b)^(3/2)*(a+b)^(1/2)*cos(d*x+c)^2*4^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*b+8*(a-b)^(3/2)*(a+b)^(1/2)*a^(3/2)*cos(d*x+c)^2*4^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)+4*(a+b)^(1/2)*4^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a*b^2-8*(a-b)^(3/2)*(a+b)^(1/2)*a^(3/2)*4^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)-4*(a-b)^(3/2)*cos(d*x+c)^2*4^(1/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*a^2-3*(a-b)^(3/2)*cos(d*x+c)^2*4^(1/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*b^2-7*(a-b)^(3/2)*cos(d*x+c)^2*4^(1/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*a*b-8*(a-b)^(3/2)*(a+b)^(1/2)*a^(1/2)*4^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b-3*(a+b)^(1/2)*cos(d*x+c)^2*4^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b-4*(a+b)^(1/2)*cos(d*x+c)^2*4^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)/sin(d*x+c)^4/((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)/(a+b)^(3/2)/(a-b)^(3/2)","B"
323,1,1106,309,1.404000," ","int((a+b*sec(d*x+c))^(1/2)*tan(d*x+c)^2,x)","\frac{2 \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2}+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a b +6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a b -4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a b +2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{2}+\cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2}+\cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a b +6 \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a b -4 \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a b +2 \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{2}-\left(\cos^{3}\left(d x +c \right)\right) a^{2}-\left(\cos^{3}\left(d x +c \right)\right) a b +\left(\cos^{2}\left(d x +c \right)\right) a^{2}-\left(\cos^{2}\left(d x +c \right)\right) a b -\left(\cos^{2}\left(d x +c \right)\right) b^{2}+2 a b \cos \left(d x +c \right)+b^{2}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2}}{3 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right) \sin \left(d x +c \right)^{5} b}"," ",0,"2/3/d*(-1+cos(d*x+c))^2*(cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2+cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b+6*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b-4*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b+2*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^2+cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2+cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b+6*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b-4*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b+2*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^2-cos(d*x+c)^3*a^2-cos(d*x+c)^3*a*b+cos(d*x+c)^2*a^2-cos(d*x+c)^2*a*b-cos(d*x+c)^2*b^2+2*a*b*cos(d*x+c)+b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2/(b+a*cos(d*x+c))/cos(d*x+c)/sin(d*x+c)^5/b","B"
324,1,215,116,1.143000," ","int((a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -2 a \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right)\right) \left(-1+\cos \left(d x +c \right)\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{2}}"," ",0,"-2/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1+cos(d*x+c))^2*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-2*a*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2)))*(-1+cos(d*x+c))/(b+a*cos(d*x+c))/sin(d*x+c)^2","A"
325,1,628,226,1.320000," ","int(cot(d*x+c)^2*(a+b*sec(d*x+c))^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(2 a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right) \cos \left(d x +c \right)-4 a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+2 a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right)-\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) b -4 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a +a \left(\cos^{2}\left(d x +c \right)\right)+b \cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{5}}"," ",0,"-1/d*(-1+cos(d*x+c))^2*(2*a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)*cos(d*x+c)-4*a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)+2*a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)-EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-4*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a+a*cos(d*x+c)^2+b*cos(d*x+c))*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5","B"
326,1,4997,128,1.752000," ","int(tan(d*x+c)^5/(a+b*sec(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"-1/420/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))*(-1+cos(d*x+c))^4*(192*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)^6*a^5+192*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)^5*a^5-210*cos(d*x+c)^6*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^6*b-105*cos(d*x+c)^6*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^5*b^2+420*cos(d*x+c)^6*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^4*b^3-315*cos(d*x+c)^6*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3*b^4+105*cos(d*x+c)^6*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b^5+210*cos(d*x+c)^6*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^6*b+105*cos(d*x+c)^6*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^5*b^2-420*cos(d*x+c)^6*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^4*b^3+315*cos(d*x+c)^6*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3*b^4-105*cos(d*x+c)^6*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b^5+105*cos(d*x+c)^5*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^6*b-210*cos(d*x+c)^5*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^5*b^2-105*cos(d*x+c)^5*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^4*b^3+420*cos(d*x+c)^5*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3*b^4-315*cos(d*x+c)^5*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b^5+105*cos(d*x+c)^5*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a*b^6-105*cos(d*x+c)^5*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^6*b+210*cos(d*x+c)^5*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^5*b^2+105*cos(d*x+c)^5*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^4*b^3-420*cos(d*x+c)^5*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3*b^4+315*cos(d*x+c)^5*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b^5-105*cos(d*x+c)^5*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a*b^6-60*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(3/2)*a*b^3+105*cos(d*x+c)^6*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^7-105*cos(d*x+c)^6*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^7-524*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)^5*a^3*b^2-524*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)^6*a^3*b^2+192*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)^4*a^4*b-524*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)^4*a^2*b^3+210*(a-b)^(3/2)*a^(3/2)*cos(d*x+c)^6*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b^4+210*(a-b)^(3/2)*a^(1/2)*cos(d*x+c)^5*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b^5-108*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^5*a^2*b^2-288*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^4*a^3*b+840*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^4*a*b^3+180*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^3*a^2*b^2-96*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^2*a^3*b+100*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^2*a*b^3+72*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)*a^2*b^2+192*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)^5*a^4*b-524*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*cos(d*x+c)^5*a^2*b^3-36*(a-b)^(3/2)*cos(d*x+c)^6*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a^2*b^2-96*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^5*a^3*b+280*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^5*a*b^3-36*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^4*a^2*b^2-288*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^3*a^3*b+780*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^3*a*b^3+216*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)^2*a^2*b^2-180*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*cos(d*x+c)*a*b^3)/cos(d*x+c)^3/sin(d*x+c)^8/((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)/b^4/a/(a-b)^(3/2)","B"
327,1,3003,67,1.683000," ","int(tan(d*x+c)^3/(a+b*sec(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"-1/12/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^3*(3*cos(d*x+c)^4*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^5-3*cos(d*x+c)^4*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^5+6*cos(d*x+c)^3*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b^3-3*cos(d*x+c)^3*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a*b^4-3*cos(d*x+c)^3*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^4*b+6*cos(d*x+c)^3*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3*b^2-6*cos(d*x+c)^3*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b^3+3*cos(d*x+c)^3*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a*b^4+4*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(3/2)*a*b-8*cos(d*x+c)^3*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^3-8*cos(d*x+c)^4*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^3-6*cos(d*x+c)^4*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^4*b+6*cos(d*x+c)^4*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3*b^2-3*cos(d*x+c)^4*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b^3+6*cos(d*x+c)^4*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^4*b-6*cos(d*x+c)^4*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3*b^2+3*cos(d*x+c)^4*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b^3+3*cos(d*x+c)^3*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^4*b-6*cos(d*x+c)^3*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3*b^2-8*cos(d*x+c)^2*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^2*b+6*cos(d*x+c)^4*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*(a-b)^(3/2)*a^(3/2)*b^2+6*cos(d*x+c)^3*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*(a-b)^(3/2)*a^(1/2)*b^3+12*cos(d*x+c)^2*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a*b+4*cos(d*x+c)^3*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a*b+12*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(3/2)*a*b-8*cos(d*x+c)^3*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^2*b)/sin(d*x+c)^6/cos(d*x+c)/((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)/b^2/a/(a-b)^(3/2)","B"
328,1,26,25,0.145000," ","int(tan(d*x+c)/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{a +b \sec \left(d x +c \right)}}{\sqrt{a}}\right)}{d \sqrt{a}}"," ",0,"-2*arctanh((a+b*sec(d*x+c))^(1/2)/a^(1/2))/d/a^(1/2)","A"
329,1,690,88,1.539000," ","int(cot(d*x+c)/(a+b*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{4}\, \cos \left(d x +c \right) \left(-2 \left(a -b \right)^{\frac{3}{2}} a^{\frac{3}{2}} \ln \left(4 \sqrt{a}\, \cos \left(d x +c \right) \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 \sqrt{a}\, \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 a \cos \left(d x +c \right)+2 b \right)+\left(a -b \right)^{\frac{3}{2}} \sqrt{a +b}\, \ln \left(-\frac{2 \left(2 \cos \left(d x +c \right) \sqrt{a +b}\, \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+2 a \cos \left(d x +c \right)+b \cos \left(d x +c \right)+2 \sqrt{a +b}\, \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+b \right)}{-1+\cos \left(d x +c \right)}\right) a -2 \left(a -b \right)^{\frac{3}{2}} \sqrt{a}\, \ln \left(4 \sqrt{a}\, \cos \left(d x +c \right) \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 \sqrt{a}\, \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}+4 a \cos \left(d x +c \right)+2 b \right) b -a^{3} \ln \left(-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(2 \cos \left(d x +c \right) \sqrt{a -b}\, \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-2 a \cos \left(d x +c \right)+b \cos \left(d x +c \right)+2 \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{a -b}-b \right)}{\sin \left(d x +c \right)^{2} \sqrt{a -b}}\right)+\ln \left(-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(2 \cos \left(d x +c \right) \sqrt{a -b}\, \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}-2 a \cos \left(d x +c \right)+b \cos \left(d x +c \right)+2 \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \sqrt{a -b}-b \right)}{\sin \left(d x +c \right)^{2} \sqrt{a -b}}\right) a \,b^{2}\right) \left(-1+\cos \left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{2} \sqrt{\frac{\left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right)^{2}}}\, \left(a -b \right)^{\frac{3}{2}} a \left(a +b \right)}"," ",0,"1/4/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*4^(1/2)*cos(d*x+c)*(-2*(a-b)^(3/2)*a^(3/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)+(a-b)^(3/2)*(a+b)^(1/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*a-2*(a-b)^(3/2)*a^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b-a^3*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))+ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a*b^2)*(-1+cos(d*x+c))/sin(d*x+c)^2/((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)/(a-b)^(3/2)/a/(a+b)","B"
330,1,4203,218,1.733000," ","int(cot(d*x+c)^3/(a+b*sec(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"-1/16/d*(-1+cos(d*x+c))*(8*cos(d*x+c)^2*(a-b)^(3/2)*(a+b)^(1/2)*a^(7/2)*4^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)-5*(a-b)^(3/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*4^(1/2)*a*b^3+(a+b)^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*4^(1/2)*a^4*b+9*(a+b)^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*4^(1/2)*a^3*b^2-(a+b)^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*4^(1/2)*a^2*b^3-5*(a+b)^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*4^(1/2)*a*b^4-8*(a-b)^(3/2)*(a+b)^(1/2)*a^(7/2)*4^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)-16*cos(d*x+c)^2*(a-b)^(3/2)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a^2-4*cos(d*x+c)^2*(a-b)^(3/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*4^(1/2)*a^4+4*cos(d*x+c)^2*(a+b)^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*4^(1/2)*a^5-32*cos(d*x+c)*(a-b)^(3/2)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a^2+16*(a-b)^(3/2)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a*b+5*(a-b)^(3/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*4^(1/2)*a^3*b-4*(a-b)^(3/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*4^(1/2)*a^2*b^2-16*(a-b)^(3/2)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a^2+4*(a-b)^(3/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*4^(1/2)*a^4-4*(a+b)^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*4^(1/2)*a^5+4*cos(d*x+c)^2*(a-b)^(3/2)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*4^(1/2)*a^3-12*cos(d*x+c)^2*(a-b)^(3/2)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*4^(1/2)*a^2*b+8*cos(d*x+c)^2*(a-b)^(3/2)*(a+b)^(1/2)*a^(5/2)*4^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b-8*cos(d*x+c)^2*(a-b)^(3/2)*(a+b)^(1/2)*a^(3/2)*4^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b^2+8*cos(d*x+c)*(a-b)^(3/2)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*4^(1/2)*a^2*b-8*cos(d*x+c)^2*(a-b)^(3/2)*(a+b)^(1/2)*a^(1/2)*4^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b^3-4*cos(d*x+c)*(a-b)^(3/2)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*4^(1/2)*a*b^2-4*cos(d*x+c)*(a-b)^(3/2)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*4^(1/2)*a^3+4*(a-b)^(3/2)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*4^(1/2)*a^2*b+4*(a-b)^(3/2)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*4^(1/2)*a*b^2-8*(a-b)^(3/2)*(a+b)^(1/2)*a^(5/2)*4^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b+16*cos(d*x+c)^2*(a-b)^(3/2)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a*b-5*cos(d*x+c)^2*(a-b)^(3/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*4^(1/2)*a^3*b+4*cos(d*x+c)^2*(a-b)^(3/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*4^(1/2)*a^2*b^2+5*cos(d*x+c)^2*(a-b)^(3/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*4^(1/2)*a*b^3+8*(a-b)^(3/2)*(a+b)^(1/2)*a^(3/2)*4^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b^2-cos(d*x+c)^2*(a+b)^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*4^(1/2)*a^4*b-9*cos(d*x+c)^2*(a+b)^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*4^(1/2)*a^3*b^2+cos(d*x+c)^2*(a+b)^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*4^(1/2)*a^2*b^3+5*cos(d*x+c)^2*(a+b)^(1/2)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*4^(1/2)*a*b^4+32*cos(d*x+c)*(a-b)^(3/2)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a*b+8*(a-b)^(3/2)*(a+b)^(1/2)*a^(1/2)*4^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)/((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)/sin(d*x+c)^4/(a+b)^(5/2)/(a-b)^(5/2)/a","B"
331,1,1780,365,1.804000," ","int(tan(d*x+c)^4/(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 b^{3}-30 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{3}+36 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}+8 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}+8 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -21 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-8 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -2 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+8 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -21 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-8 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -2 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+4 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b -8 a^{2} \left(\cos^{3}\left(d x +c \right)\right) b -\cos \left(d x +c \right) a \,b^{2}-20 a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)+21 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}-24 \left(\cos^{2}\left(d x +c \right)\right) b^{3}+21 \left(\cos^{3}\left(d x +c \right)\right) b^{3}-8 \left(\cos^{4}\left(d x +c \right)\right) a^{3}+4 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -21 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-30 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{3}+36 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}+8 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}-21 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}+8 \left(\cos^{3}\left(d x +c \right)\right) a^{3}\right)}{15 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{5} b^{3}}"," ",0,"2/15/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-21*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+4*cos(d*x+c)^2*a^2*b+3*b^3-30*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^3-20*a*b^2*cos(d*x+c)^3+36*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+8*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-21*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3-30*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^3+36*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+8*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-cos(d*x+c)*a*b^2+4*cos(d*x+c)^4*a^2*b+21*cos(d*x+c)^4*a*b^2-8*a^2*cos(d*x+c)^3*b+8*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-21*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-8*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-2*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+8*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-21*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-8*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-2*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+8*cos(d*x+c)^3*a^3-24*cos(d*x+c)^2*b^3+21*cos(d*x+c)^3*b^3-8*cos(d*x+c)^4*a^3)/(b+a*cos(d*x+c))/cos(d*x+c)^2/sin(d*x+c)^5/b^3","B"
332,1,823,283,1.394000," ","int(tan(d*x+c)^2/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \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(2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right) \cos \left(d x +c \right)-\cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -\cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -2 \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b +2 \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) b -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b +a \left(\cos^{2}\left(d x +c \right)\right)-a \cos \left(d x +c \right)+b \cos \left(d x +c \right)-b \right)}{d \sin \left(d x +c \right)^{5} \left(b +a \cos \left(d x +c \right)\right) b}"," ",0,"-2/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)*cos(d*x+c)-cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-2*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b+2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b+a*cos(d*x+c)^2-a*cos(d*x+c)+b*cos(d*x+c)-b)/sin(d*x+c)^5/(b+a*cos(d*x+c))/b","B"
333,1,180,97,1.247000," ","int(1/(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(-\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right)+2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right)\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{2}}"," ",0,"2/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(-EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))+2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2)))/(b+a*cos(d*x+c))/sin(d*x+c)^2","A"
334,1,1409,330,1.709000," ","int(cot(d*x+c)^2/(a+b*sec(d*x+c))^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right) \cos \left(d x +c \right)-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right) \cos \left(d x +c \right)-2 \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) a^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a b +3 \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{2}-\cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a b -\EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)+4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)+\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a b +3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)-\EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a b -\EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)-\left(\cos^{2}\left(d x +c \right)\right) a^{2}+\left(\cos^{2}\left(d x +c \right)\right) a b -a b \cos \left(d x +c \right)+\cos \left(d x +c \right) b^{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{5} \left(a -b \right) \left(a +b \right)}"," ",0,"1/d*(-1+cos(d*x+c))^2*(4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)*cos(d*x+c)-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)*cos(d*x+c)-2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b+3*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^2-cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b-EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)-EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b-EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-cos(d*x+c)^2*a^2+cos(d*x+c)^2*a*b-a*b*cos(d*x+c)+cos(d*x+c)*b^2)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5/(a-b)/(a+b)","B"
335,1,6612,132,2.393000," ","int(tan(d*x+c)^5/(a+b*sec(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
336,1,2830,78,1.662000," ","int(tan(d*x+c)^3/(a+b*sec(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"-1/4/d*(-1+cos(d*x+c))^3*(2*cos(d*x+c)^2*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^4*b^2+4*(a-b)^(3/2)*cos(d*x+c)^3*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a^3+12*(a-b)^(3/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a^3+4*(a-b)^(3/2)*cos(d*x+c)^3*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^4-2*cos(d*x+c)^2*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3*b^3-2*cos(d*x+c)^2*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^4*b^2+2*cos(d*x+c)^2*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3*b^3+cos(d*x+c)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3*b^3-cos(d*x+c)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b^4-cos(d*x+c)*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3*b^3+cos(d*x+c)*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b^4+12*(a-b)^(3/2)*cos(d*x+c)^2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a^3+cos(d*x+c)^3*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^5*b-cos(d*x+c)^3*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^4*b^2-cos(d*x+c)^3*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^5*b+cos(d*x+c)^3*ln(-2*(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^4*b^2+8*(a-b)^(3/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^3*b+2*(a-b)^(3/2)*a^(5/2)*cos(d*x+c)^3*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b^2+4*(a-b)^(3/2)*a^(3/2)*cos(d*x+c)^2*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b^3-12*(a-b)^(3/2)*cos(d*x+c)^2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a*b^2+2*(a-b)^(3/2)*a^(1/2)*cos(d*x+c)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b^4-4*(a-b)^(3/2)*cos(d*x+c)^3*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a*b^2-12*(a-b)^(3/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*a*b^2+8*(a-b)^(3/2)*cos(d*x+c)^2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^3*b+4*(a-b)^(3/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^2*b^2+4*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^2*b^2+4*(a-b)^(3/2)*cos(d*x+c)^2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^4-4*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(3/2)*a*b^2+4*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)*(a-b)^(3/2)*a^3)*cos(d*x+c)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*4^(1/2)/(b+a*cos(d*x+c))/((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(3/2)/sin(d*x+c)^6/b^2/(a-b)^(3/2)/a^2","B"
337,1,45,46,0.139000," ","int(tan(d*x+c)/(a+b*sec(d*x+c))^(3/2),x)","\frac{-\frac{2 \arctanh \left(\frac{\sqrt{a +b \sec \left(d x +c \right)}}{\sqrt{a}}\right)}{a^{\frac{3}{2}}}+\frac{2}{a \sqrt{a +b \sec \left(d x +c \right)}}}{d}"," ",0,"1/d*(-2/a^(3/2)*arctanh((a+b*sec(d*x+c))^(1/2)/a^(1/2))+2/a/(a+b*sec(d*x+c))^(1/2))","A"
338,1,2766,122,1.315000," ","int(cot(d*x+c)/(a+b*sec(d*x+c))^(3/2),x)","\text{Expression too large to display}"," ",0,"1/4/d*(-1+cos(d*x+c))*(-2*a^(9/2)*cos(d*x+c)*(a-b)^(3/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)-2*a^(7/2)*cos(d*x+c)*(a-b)^(3/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b-2*a^(7/2)*(a-b)^(3/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b+2*a^(5/2)*cos(d*x+c)*(a-b)^(3/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b^2-2*a^(5/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*(a-b)^(3/2)*b^2+2*a^(3/2)*cos(d*x+c)*(a-b)^(3/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b^3+(a+b)^(1/2)*cos(d*x+c)*(a-b)^(3/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*a^4-(a+b)^(1/2)*cos(d*x+c)*(a-b)^(3/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*a^3*b+2*a^(3/2)*(a-b)^(3/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*b^3+(a+b)^(1/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*(a-b)^(3/2)*a^3*b-(a+b)^(1/2)*ln(-2*(2*cos(d*x+c)*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+2*a*cos(d*x+c)+b*cos(d*x+c)+2*(a+b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+b)/(-1+cos(d*x+c)))*(a-b)^(3/2)*a^2*b^2+2*a^(1/2)*ln(4*a^(1/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)+4*a*cos(d*x+c)+2*b)*(a-b)^(3/2)*b^4-4*(a-b)^(3/2)*cos(d*x+c)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^2*b^2-4*cos(d*x+c)*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a*b^3-cos(d*x+c)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^6-cos(d*x+c)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^5*b+cos(d*x+c)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^4*b^2+cos(d*x+c)*ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3*b^3-4*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a^2*b^2-4*(a-b)^(3/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*a*b^3-ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^5*b-ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^4*b^2+ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^3*b^3+ln(-(-1+cos(d*x+c))*(2*cos(d*x+c)*(a-b)^(1/2)*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)-2*a*cos(d*x+c)+b*cos(d*x+c)+2*((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)*(a-b)^(1/2)-b)/sin(d*x+c)^2/(a-b)^(1/2))*a^2*b^4)*cos(d*x+c)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*4^(1/2)/((b+a*cos(d*x+c))*cos(d*x+c)/(1+cos(d*x+c))^2)^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^2/(a-b)^(5/2)/(a+b)^2/a^2","B"
339,1,10977,204,1.962000," ","int(cot(d*x+c)^3/(a+b*sec(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
340,1,1544,489,1.579000," ","int(tan(d*x+c)^4/(a+b*sec(d*x+c))^(3/2),x)","\frac{\sqrt{4}\, \left(8 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +2 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-8 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}-8 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +3 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+3 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-6 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{3}+8 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-8 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}-8 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +3 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+3 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-6 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{3}+8 \left(\cos^{3}\left(d x +c \right)\right) a^{3}-4 a^{2} \left(\cos^{3}\left(d x +c \right)\right) b -3 a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)+3 \left(\cos^{3}\left(d x +c \right)\right) b^{3}-8 \left(\cos^{2}\left(d x +c \right)\right) a^{3}+8 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b +2 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-3 \left(\cos^{2}\left(d x +c \right)\right) b^{3}-4 \cos \left(d x +c \right) a^{2} b +b^{2} a \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{3 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a \,b^{3}}"," ",0,"1/3/d*4^(1/2)*(8*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+2*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-8*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-8*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+3*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+3*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3-6*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^3+8*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-8*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-8*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+3*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+3*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3-6*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^3+8*cos(d*x+c)^3*a^3-4*a^2*cos(d*x+c)^3*b-3*a*b^2*cos(d*x+c)^3+3*cos(d*x+c)^3*b^3-8*cos(d*x+c)^2*a^3+8*cos(d*x+c)^2*a^2*b+2*cos(d*x+c)^2*a*b^2-3*cos(d*x+c)^2*b^3-4*cos(d*x+c)*a^2*b+b^2*a)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)/a/b^3","B"
341,1,633,315,1.188000," ","int(tan(d*x+c)^2/(a+b*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{4}\, \left(\cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +\cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -2 \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b -a \left(\cos^{2}\left(d x +c \right)\right)+\left(\cos^{2}\left(d x +c \right)\right) b +a \cos \left(d x +c \right)-b \cos \left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a b}"," ",0,"-1/d*4^(1/2)*(cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-2*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b-a*cos(d*x+c)^2+cos(d*x+c)^2*b+a*cos(d*x+c)-b*cos(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/a/b","B"
342,1,1209,318,1.253000," ","int(1/(a+b*sec(d*x+c))^(3/2),x)","\frac{\sqrt{4}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) a^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a b -\cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a b -\EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right) \cos \left(d x +c \right)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right) \cos \left(d x +c \right)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)+\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a b -\EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a b -\EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)+\left(\cos^{2}\left(d x +c \right)\right) a b -\left(\cos^{2}\left(d x +c \right)\right) b^{2}-a b \cos \left(d x +c \right)+\cos \left(d x +c \right) b^{2}\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a \left(a +b \right) \left(a -b \right)}"," ",0,"1/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b-cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b-EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)*cos(d*x+c)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)*cos(d*x+c)+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b-EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b-EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)+cos(d*x+c)^2*a*b-cos(d*x+c)^2*b^2-a*b*cos(d*x+c)+cos(d*x+c)*b^2)/(b+a*cos(d*x+c))/sin(d*x+c)/a/(a+b)/(a-b)","B"
343,1,2238,416,1.324000," ","int(cot(d*x+c)^2/(a+b*sec(d*x+c))^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/2/d*(2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b+cos(d*x+c)*a^3*b+3*cos(d*x+c)*a*b^3+2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^3-EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b-6*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^2-3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^3+8*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^2+2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^2+2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^4+2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4-4*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4-4*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^4-4*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4-4*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^4+2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^4+2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4+2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b+2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^2+2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^3-EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b-6*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^2-3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^3+8*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^2-2*cos(d*x+c)^2*a^3*b-2*cos(d*x+c)^2*a*b^3-2*cos(d*x+c)*a^2*b^2+cos(d*x+c)^2*a^2*b^2-2*cos(d*x+c)*b^4+cos(d*x+c)^2*a^4+2*cos(d*x+c)^2*b^4)*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/a/(a-b)^2/(a+b)^2","B"
344,0,0,231,1.803000," ","int((a+b*sec(f*x+e))^3*(d*tan(f*x+e))^n,x)","\int \left(a +b \sec \left(f x +e \right)\right)^{3} \left(d \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+b*sec(f*x+e))^3*(d*tan(f*x+e))^n,x)","F"
345,0,0,152,2.770000," ","int((a+b*sec(f*x+e))^2*(d*tan(f*x+e))^n,x)","\int \left(a +b \sec \left(f x +e \right)\right)^{2} \left(d \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+b*sec(f*x+e))^2*(d*tan(f*x+e))^n,x)","F"
346,0,0,121,2.539000," ","int((a+b*sec(f*x+e))*(d*tan(f*x+e))^n,x)","\int \left(a +b \sec \left(f x +e \right)\right) \left(d \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+b*sec(f*x+e))*(d*tan(f*x+e))^n,x)","F"
347,0,0,199,2.485000," ","int((d*tan(f*x+e))^n/(a+b*sec(f*x+e)),x)","\int \frac{\left(d \tan \left(f x +e \right)\right)^{n}}{a +b \sec \left(f x +e \right)}\, dx"," ",0,"int((d*tan(f*x+e))^n/(a+b*sec(f*x+e)),x)","F"
348,0,0,25,1.531000," ","int((a+b*sec(d*x+c))^(3/2)*(e*tan(d*x+c))^m,x)","\int \left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}} \left(e \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+b*sec(d*x+c))^(3/2)*(e*tan(d*x+c))^m,x)","F"
349,0,0,25,1.648000," ","int((a+b*sec(d*x+c))^(1/2)*(e*tan(d*x+c))^m,x)","\int \sqrt{a +b \sec \left(d x +c \right)}\, \left(e \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+b*sec(d*x+c))^(1/2)*(e*tan(d*x+c))^m,x)","F"
350,0,0,25,1.780000," ","int((e*tan(d*x+c))^m/(a+b*sec(d*x+c))^(1/2),x)","\int \frac{\left(e \tan \left(d x +c \right)\right)^{m}}{\sqrt{a +b \sec \left(d x +c \right)}}\, dx"," ",0,"int((e*tan(d*x+c))^m/(a+b*sec(d*x+c))^(1/2),x)","F"
351,0,0,25,1.566000," ","int((e*tan(d*x+c))^m/(a+b*sec(d*x+c))^(3/2),x)","\int \frac{\left(e \tan \left(d x +c \right)\right)^{m}}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*tan(d*x+c))^m/(a+b*sec(d*x+c))^(3/2),x)","F"
352,0,0,25,2.120000," ","int((a+b*sec(d*x+c))^n*(e*tan(d*x+c))^m,x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \left(e \tan \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+b*sec(d*x+c))^n*(e*tan(d*x+c))^m,x)","F"
353,0,0,179,1.244000," ","int((a+b*sec(d*x+c))^n*tan(d*x+c)^5,x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \left(\tan^{5}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sec(d*x+c))^n*tan(d*x+c)^5,x)","F"
354,0,0,104,1.142000," ","int((a+b*sec(d*x+c))^n*tan(d*x+c)^3,x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \left(\tan^{3}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sec(d*x+c))^n*tan(d*x+c)^3,x)","F"
355,0,0,50,1.001000," ","int((a+b*sec(d*x+c))^n*tan(d*x+c),x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \tan \left(d x +c \right)\, dx"," ",0,"int((a+b*sec(d*x+c))^n*tan(d*x+c),x)","F"
356,0,0,164,1.357000," ","int(cot(d*x+c)*(a+b*sec(d*x+c))^n,x)","\int \cot \left(d x +c \right) \left(a +b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cot(d*x+c)*(a+b*sec(d*x+c))^n,x)","F"
357,0,0,281,1.134000," ","int(cot(d*x+c)^3*(a+b*sec(d*x+c))^n,x)","\int \left(\cot^{3}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cot(d*x+c)^3*(a+b*sec(d*x+c))^n,x)","F"
358,0,0,23,1.103000," ","int((a+b*sec(d*x+c))^n*tan(d*x+c)^4,x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \left(\tan^{4}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sec(d*x+c))^n*tan(d*x+c)^4,x)","F"
359,0,0,208,0.839000," ","int((a+b*sec(d*x+c))^n*tan(d*x+c)^2,x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \left(\tan^{2}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sec(d*x+c))^n*tan(d*x+c)^2,x)","F"
360,0,0,23,1.048000," ","int(cot(d*x+c)^2*(a+b*sec(d*x+c))^n,x)","\int \left(\cot^{2}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cot(d*x+c)^2*(a+b*sec(d*x+c))^n,x)","F"
361,0,0,23,1.199000," ","int(cot(d*x+c)^4*(a+b*sec(d*x+c))^n,x)","\int \left(\cot^{4}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cot(d*x+c)^4*(a+b*sec(d*x+c))^n,x)","F"
362,0,0,23,1.894000," ","int((a+b*sec(d*x+c))^n*tan(d*x+c)^(3/2),x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \left(\tan^{\frac{3}{2}}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sec(d*x+c))^n*tan(d*x+c)^(3/2),x)","F"
363,0,0,23,1.653000," ","int((a+b*sec(d*x+c))^n*tan(d*x+c)^(1/2),x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \left(\sqrt{\tan}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sec(d*x+c))^n*tan(d*x+c)^(1/2),x)","F"
364,0,0,23,1.581000," ","int((a+b*sec(d*x+c))^n/tan(d*x+c)^(1/2),x)","\int \frac{\left(a +b \sec \left(d x +c \right)\right)^{n}}{\sqrt{\tan \left(d x +c \right)}}\, dx"," ",0,"int((a+b*sec(d*x+c))^n/tan(d*x+c)^(1/2),x)","F"
365,0,0,23,1.448000," ","int((a+b*sec(d*x+c))^n/tan(d*x+c)^(3/2),x)","\int \frac{\left(a +b \sec \left(d x +c \right)\right)^{n}}{\tan \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^n/tan(d*x+c)^(3/2),x)","F"