1,1,163,138,0.668000," ","int((a+a*sec(d*x+c))*sin(d*x+c)^9,x)","-\frac{128 a \cos \left(d x +c \right)}{315 d}-\frac{\left(\sin^{8}\left(d x +c \right)\right) \cos \left(d x +c \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}-\frac{a \left(\sin^{8}\left(d x +c \right)\right)}{8 d}-\frac{a \left(\sin^{6}\left(d x +c \right)\right)}{6 d}-\frac{a \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-128/315*a*cos(d*x+c)/d-1/9/d*sin(d*x+c)^8*cos(d*x+c)*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)^2-1/8/d*a*sin(d*x+c)^8-1/6/d*a*sin(d*x+c)^6-1/4/d*a*sin(d*x+c)^4-1/2/d*a*sin(d*x+c)^2-a*ln(cos(d*x+c))/d","A"
2,1,129,109,0.614000," ","int((a+a*sec(d*x+c))*sin(d*x+c)^7,x)","-\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}-\frac{a \left(\sin^{6}\left(d x +c \right)\right)}{6 d}-\frac{a \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-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)^2-1/6/d*a*sin(d*x+c)^6-1/4/d*a*sin(d*x+c)^4-1/2/d*a*sin(d*x+c)^2-a*ln(cos(d*x+c))/d","A"
3,1,95,81,0.595000," ","int((a+a*sec(d*x+c))*sin(d*x+c)^5,x)","-\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}-\frac{a \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-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)^2-1/4/d*a*sin(d*x+c)^4-1/2/d*a*sin(d*x+c)^2-a*ln(cos(d*x+c))/d","A"
4,1,61,54,0.609000," ","int((a+a*sec(d*x+c))*sin(d*x+c)^3,x)","-\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}-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-1/3/d*a*cos(d*x+c)*sin(d*x+c)^2-2/3*a*cos(d*x+c)/d-1/2/d*a*sin(d*x+c)^2-a*ln(cos(d*x+c))/d","A"
5,1,28,26,0.204000," ","int((a+a*sec(d*x+c))*sin(d*x+c),x)","\frac{a \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a}{d \sec \left(d x +c \right)}"," ",0,"a/d*ln(sec(d*x+c))-a/d/sec(d*x+c)","A"
6,1,15,30,0.362000," ","int(csc(d*x+c)*(a+a*sec(d*x+c)),x)","\frac{a \ln \left(-1+\sec \left(d x +c \right)\right)}{d}"," ",0,"1/d*a*ln(-1+sec(d*x+c))","A"
7,1,48,67,0.590000," ","int(csc(d*x+c)^3*(a+a*sec(d*x+c)),x)","-\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,"-1/2/d*a/(-1+sec(d*x+c))+3/4/d*a*ln(-1+sec(d*x+c))+1/4/d*a*ln(1+sec(d*x+c))","A"
8,1,80,108,0.473000," ","int(csc(d*x+c)^5*(a+a*sec(d*x+c)),x)","-\frac{a}{8 d \left(-1+\sec \left(d x +c \right)\right)^{2}}-\frac{3 a}{4 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,"-1/8/d*a/(-1+sec(d*x+c))^2-3/4/d*a/(-1+sec(d*x+c))+11/16/d*a*ln(-1+sec(d*x+c))+1/8/d*a/(1+sec(d*x+c))+5/16/d*a*ln(1+sec(d*x+c))","A"
9,1,112,149,0.460000," ","int(csc(d*x+c)^7*(a+a*sec(d*x+c)),x)","-\frac{a}{24 d \left(-1+\sec \left(d x +c \right)\right)^{3}}-\frac{9 a}{32 d \left(-1+\sec \left(d x +c \right)\right)^{2}}-\frac{15 a}{16 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{a}{4 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,"-1/24/d*a/(-1+sec(d*x+c))^3-9/32/d*a/(-1+sec(d*x+c))^2-15/16/d*a/(-1+sec(d*x+c))+21/32/d*a*ln(-1+sec(d*x+c))-1/32/d*a/(1+sec(d*x+c))^2+1/4/d*a/(1+sec(d*x+c))+11/32/d*a*ln(1+sec(d*x+c))","A"
10,1,164,149,0.692000," ","int((a+a*sec(d*x+c))*sin(d*x+c)^8,x)","-\frac{a \cos \left(d x +c \right) \left(\sin^{7}\left(d x +c \right)\right)}{8 d}-\frac{7 a \cos \left(d x +c \right) \left(\sin^{5}\left(d x +c \right)\right)}{48 d}-\frac{35 a \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{192 d}-\frac{35 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{128 d}+\frac{35 a x}{128}+\frac{35 c a}{128 d}-\frac{a \left(\sin^{7}\left(d x +c \right)\right)}{7 d}-\frac{a \left(\sin^{5}\left(d x +c \right)\right)}{5 d}-\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \sin \left(d x +c \right)}{d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/8*a*cos(d*x+c)*sin(d*x+c)^7/d-7/48*a*cos(d*x+c)*sin(d*x+c)^5/d-35/192*a*cos(d*x+c)*sin(d*x+c)^3/d-35/128*a*cos(d*x+c)*sin(d*x+c)/d+35/128*a*x+35/128/d*c*a-1/7*a*sin(d*x+c)^7/d-1/5*a*sin(d*x+c)^5/d-1/3*a*sin(d*x+c)^3/d-a*sin(d*x+c)/d+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
11,1,130,115,0.684000," ","int((a+a*sec(d*x+c))*sin(d*x+c)^6,x)","-\frac{a \cos \left(d x +c \right) \left(\sin^{5}\left(d x +c \right)\right)}{6 d}-\frac{5 a \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{24 d}-\frac{5 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{16 d}+\frac{5 a x}{16}+\frac{5 c a}{16 d}-\frac{a \left(\sin^{5}\left(d x +c \right)\right)}{5 d}-\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \sin \left(d x +c \right)}{d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/6*a*cos(d*x+c)*sin(d*x+c)^5/d-5/24*a*cos(d*x+c)*sin(d*x+c)^3/d-5/16*a*cos(d*x+c)*sin(d*x+c)/d+5/16*a*x+5/16/d*c*a-1/5*a*sin(d*x+c)^5/d-1/3*a*sin(d*x+c)^3/d-a*sin(d*x+c)/d+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
12,1,96,81,0.606000," ","int((a+a*sec(d*x+c))*sin(d*x+c)^4,x)","-\frac{a \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{3 a x}{8}+\frac{3 c a}{8 d}-\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \sin \left(d x +c \right)}{d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/4*a*cos(d*x+c)*sin(d*x+c)^3/d-3/8*a*cos(d*x+c)*sin(d*x+c)/d+3/8*a*x+3/8/d*c*a-1/3*a*sin(d*x+c)^3/d-a*sin(d*x+c)/d+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
13,1,62,47,0.285000," ","int((a+a*sec(d*x+c))*sin(d*x+c)^2,x)","-\frac{a \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a x}{2}+\frac{c a}{2 d}-\frac{a \sin \left(d x +c \right)}{d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/2*a*cos(d*x+c)*sin(d*x+c)/d+1/2*a*x+1/2/d*c*a-a*sin(d*x+c)/d+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
14,1,47,37,0.602000," ","int(csc(d*x+c)^2*(a+a*sec(d*x+c)),x)","-\frac{a \cot \left(d x +c \right)}{d}-\frac{a}{d \sin \left(d x +c \right)}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-a*cot(d*x+c)/d-1/d*a/sin(d*x+c)+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
15,1,81,65,0.726000," ","int(csc(d*x+c)^4*(a+a*sec(d*x+c)),x)","-\frac{2 a \cot \left(d x +c \right)}{3 d}-\frac{a \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}-\frac{a}{3 d \sin \left(d x +c \right)^{3}}-\frac{a}{d \sin \left(d x +c \right)}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-2/3*a*cot(d*x+c)/d-1/3/d*a*cot(d*x+c)*csc(d*x+c)^2-1/3/d*a/sin(d*x+c)^3-1/d*a/sin(d*x+c)+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
16,1,115,93,0.727000," ","int(csc(d*x+c)^6*(a+a*sec(d*x+c)),x)","-\frac{8 a \cot \left(d x +c \right)}{15 d}-\frac{a \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 a \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{15 d}-\frac{a}{5 d \sin \left(d x +c \right)^{5}}-\frac{a}{3 d \sin \left(d x +c \right)^{3}}-\frac{a}{d \sin \left(d x +c \right)}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-8/15*a*cot(d*x+c)/d-1/5/d*a*cot(d*x+c)*csc(d*x+c)^4-4/15/d*a*cot(d*x+c)*csc(d*x+c)^2-1/5/d*a/sin(d*x+c)^5-1/3/d*a/sin(d*x+c)^3-1/d*a/sin(d*x+c)+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
17,1,149,121,0.813000," ","int(csc(d*x+c)^8*(a+a*sec(d*x+c)),x)","-\frac{16 a \cot \left(d x +c \right)}{35 d}-\frac{a \cot \left(d x +c \right) \left(\csc^{6}\left(d x +c \right)\right)}{7 d}-\frac{6 a \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{35 d}-\frac{8 a \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{35 d}-\frac{a}{7 d \sin \left(d x +c \right)^{7}}-\frac{a}{5 d \sin \left(d x +c \right)^{5}}-\frac{a}{3 d \sin \left(d x +c \right)^{3}}-\frac{a}{d \sin \left(d x +c \right)}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-16/35*a*cot(d*x+c)/d-1/7/d*a*cot(d*x+c)*csc(d*x+c)^6-6/35/d*a*cot(d*x+c)*csc(d*x+c)^4-8/35/d*a*cot(d*x+c)*csc(d*x+c)^2-1/7/d*a/sin(d*x+c)^7-1/5/d*a/sin(d*x+c)^5-1/3/d*a/sin(d*x+c)^3-1/d*a/sin(d*x+c)+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
18,1,183,149,0.813000," ","int(csc(d*x+c)^10*(a+a*sec(d*x+c)),x)","-\frac{128 a \cot \left(d x +c \right)}{315 d}-\frac{a \cot \left(d x +c \right) \left(\csc^{8}\left(d x +c \right)\right)}{9 d}-\frac{8 a \cot \left(d x +c \right) \left(\csc^{6}\left(d x +c \right)\right)}{63 d}-\frac{16 a \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{105 d}-\frac{64 a \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{315 d}-\frac{a}{9 d \sin \left(d x +c \right)^{9}}-\frac{a}{7 d \sin \left(d x +c \right)^{7}}-\frac{a}{5 d \sin \left(d x +c \right)^{5}}-\frac{a}{3 d \sin \left(d x +c \right)^{3}}-\frac{a}{d \sin \left(d x +c \right)}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-128/315*a*cot(d*x+c)/d-1/9/d*a*cot(d*x+c)*csc(d*x+c)^8-8/63/d*a*cot(d*x+c)*csc(d*x+c)^6-16/105/d*a*cot(d*x+c)*csc(d*x+c)^4-64/315/d*a*cot(d*x+c)*csc(d*x+c)^2-1/9/d*a/sin(d*x+c)^9-1/7/d*a/sin(d*x+c)^7-1/5/d*a/sin(d*x+c)^5-1/3/d*a/sin(d*x+c)^3-1/d*a/sin(d*x+c)+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
19,1,206,171,0.744000," ","int((a+a*sec(d*x+c))^2*sin(d*x+c)^9,x)","\frac{1024 a^{2} \cos \left(d x +c \right)}{315 d}+\frac{8 a^{2} \left(\sin^{8}\left(d x +c \right)\right) \cos \left(d x +c \right)}{9 d}+\frac{64 a^{2} \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{63 d}+\frac{128 a^{2} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{105 d}+\frac{512 a^{2} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{315 d}-\frac{a^{2} \left(\sin^{8}\left(d x +c \right)\right)}{4 d}-\frac{a^{2} \left(\sin^{6}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{2 a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} \left(\sin^{10}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}"," ",0,"1024/315*a^2*cos(d*x+c)/d+8/9/d*a^2*sin(d*x+c)^8*cos(d*x+c)+64/63/d*a^2*cos(d*x+c)*sin(d*x+c)^6+128/105/d*a^2*cos(d*x+c)*sin(d*x+c)^4+512/315/d*a^2*cos(d*x+c)*sin(d*x+c)^2-1/4/d*a^2*sin(d*x+c)^8-1/3/d*a^2*sin(d*x+c)^6-1/2/d*a^2*sin(d*x+c)^4-1/d*a^2*sin(d*x+c)^2-2*a^2*ln(cos(d*x+c))/d+1/d*a^2*sin(d*x+c)^10/cos(d*x+c)","A"
20,1,168,123,0.754000," ","int((a+a*sec(d*x+c))^2*sin(d*x+c)^7,x)","\frac{96 a^{2} \cos \left(d x +c \right)}{35 d}+\frac{6 a^{2} \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{7 d}+\frac{36 a^{2} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{35 d}+\frac{48 a^{2} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{35 d}-\frac{a^{2} \left(\sin^{6}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{2 a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}"," ",0,"96/35*a^2*cos(d*x+c)/d+6/7/d*a^2*cos(d*x+c)*sin(d*x+c)^6+36/35/d*a^2*cos(d*x+c)*sin(d*x+c)^4+48/35/d*a^2*cos(d*x+c)*sin(d*x+c)^2-1/3/d*a^2*sin(d*x+c)^6-1/2/d*a^2*sin(d*x+c)^4-1/d*a^2*sin(d*x+c)^2-2*a^2*ln(cos(d*x+c))/d+1/d*a^2*sin(d*x+c)^8/cos(d*x+c)","A"
21,1,130,106,0.740000," ","int((a+a*sec(d*x+c))^2*sin(d*x+c)^5,x)","\frac{32 a^{2} \cos \left(d x +c \right)}{15 d}+\frac{4 a^{2} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{5 d}+\frac{16 a^{2} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}-\frac{a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{2 a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}"," ",0,"32/15*a^2*cos(d*x+c)/d+4/5/d*a^2*cos(d*x+c)*sin(d*x+c)^4+16/15/d*a^2*cos(d*x+c)*sin(d*x+c)^2-1/2/d*a^2*sin(d*x+c)^4-1/d*a^2*sin(d*x+c)^2-2*a^2*ln(cos(d*x+c))/d+1/d*a^2*sin(d*x+c)^6/cos(d*x+c)","A"
22,1,92,60,0.734000," ","int((a+a*sec(d*x+c))^2*sin(d*x+c)^3,x)","\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^{2}\left(d x +c \right)\right)}{d}-\frac{2 a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}"," ",0,"2/3/d*a^2*cos(d*x+c)*sin(d*x+c)^2+4/3*a^2*cos(d*x+c)/d-1/d*a^2*sin(d*x+c)^2-2*a^2*ln(cos(d*x+c))/d+1/d*a^2*sin(d*x+c)^4/cos(d*x+c)","A"
23,1,46,43,0.250000," ","int((a+a*sec(d*x+c))^2*sin(d*x+c),x)","\frac{a^{2} \sec \left(d x +c \right)}{d}+\frac{2 a^{2} \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a^{2}}{d \sec \left(d x +c \right)}"," ",0,"a^2*sec(d*x+c)/d+2*a^2/d*ln(sec(d*x+c))-a^2/d/sec(d*x+c)","A"
24,1,32,48,0.408000," ","int(csc(d*x+c)*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \sec \left(d x +c \right)}{d}+\frac{2 a^{2} \ln \left(-1+\sec \left(d x +c \right)\right)}{d}"," ",0,"a^2*sec(d*x+c)/d+2/d*a^2*ln(-1+sec(d*x+c))","A"
25,1,50,69,0.587000," ","int(csc(d*x+c)^3*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \sec \left(d x +c \right)}{d}-\frac{a^{2}}{d \left(-1+\sec \left(d x +c \right)\right)}+\frac{2 a^{2} \ln \left(-1+\sec \left(d x +c \right)\right)}{d}"," ",0,"a^2*sec(d*x+c)/d-1/d*a^2/(-1+sec(d*x+c))+2/d*a^2*ln(-1+sec(d*x+c))","A"
26,1,85,107,0.494000," ","int(csc(d*x+c)^5*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \sec \left(d x +c \right)}{d}-\frac{a^{2}}{4 d \left(-1+\sec \left(d x +c \right)\right)^{2}}-\frac{7 a^{2}}{4 d \left(-1+\sec \left(d x +c \right)\right)}+\frac{17 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*sec(d*x+c)/d-1/4/d*a^2/(-1+sec(d*x+c))^2-7/4/d*a^2/(-1+sec(d*x+c))+17/8/d*a^2*ln(-1+sec(d*x+c))-1/8/d*a^2*ln(1+sec(d*x+c))","A"
27,1,121,148,0.503000," ","int(csc(d*x+c)^7*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \sec \left(d x +c \right)}{d}-\frac{a^{2}}{12 d \left(-1+\sec \left(d x +c \right)\right)^{3}}-\frac{5 a^{2}}{8 d \left(-1+\sec \left(d x +c \right)\right)^{2}}-\frac{39 a^{2}}{16 d \left(-1+\sec \left(d x +c \right)\right)}+\frac{9 a^{2} \ln \left(-1+\sec \left(d x +c \right)\right)}{4 d}-\frac{a^{2}}{16 d \left(1+\sec \left(d x +c \right)\right)}-\frac{a^{2} \ln \left(1+\sec \left(d x +c \right)\right)}{4 d}"," ",0,"a^2*sec(d*x+c)/d-1/12/d*a^2/(-1+sec(d*x+c))^3-5/8/d*a^2/(-1+sec(d*x+c))^2-39/16/d*a^2/(-1+sec(d*x+c))+9/4/d*a^2*ln(-1+sec(d*x+c))-1/16/d*a^2/(1+sec(d*x+c))-1/4/d*a^2*ln(1+sec(d*x+c))","A"
28,1,157,189,0.572000," ","int(csc(d*x+c)^9*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \sec \left(d x +c \right)}{d}-\frac{a^{2}}{32 d \left(-1+\sec \left(d x +c \right)\right)^{4}}-\frac{13 a^{2}}{48 d \left(-1+\sec \left(d x +c \right)\right)^{3}}-\frac{35 a^{2}}{32 d \left(-1+\sec \left(d x +c \right)\right)^{2}}-\frac{99 a^{2}}{32 d \left(-1+\sec \left(d x +c \right)\right)}+\frac{303 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{11 a^{2}}{64 d \left(1+\sec \left(d x +c \right)\right)}-\frac{47 a^{2} \ln \left(1+\sec \left(d x +c \right)\right)}{128 d}"," ",0,"a^2*sec(d*x+c)/d-1/32/d*a^2/(-1+sec(d*x+c))^4-13/48/d*a^2/(-1+sec(d*x+c))^3-35/32/d*a^2/(-1+sec(d*x+c))^2-99/32/d*a^2/(-1+sec(d*x+c))+303/128/d*a^2*ln(-1+sec(d*x+c))+1/64/d*a^2/(1+sec(d*x+c))^2-11/64/d*a^2/(1+sec(d*x+c))-47/128/d*a^2*ln(1+sec(d*x+c))","A"
29,1,210,183,0.704000," ","int((a+a*sec(d*x+c))^2*sin(d*x+c)^8,x)","\frac{7 a^{2} \left(\sin^{7}\left(d x +c \right)\right) \cos \left(d x +c \right)}{8 d}+\frac{49 a^{2} \cos \left(d x +c \right) \left(\sin^{5}\left(d x +c \right)\right)}{48 d}+\frac{245 a^{2} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{192 d}+\frac{245 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{128 d}-\frac{245 a^{2} x}{128}-\frac{245 a^{2} c}{128 d}-\frac{2 a^{2} \left(\sin^{7}\left(d x +c \right)\right)}{7 d}-\frac{2 a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{5 d}-\frac{2 a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a^{2} \sin \left(d x +c \right)}{d}+\frac{2 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2} \left(\sin^{9}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}"," ",0,"7/8/d*a^2*sin(d*x+c)^7*cos(d*x+c)+49/48/d*a^2*cos(d*x+c)*sin(d*x+c)^5+245/192/d*a^2*cos(d*x+c)*sin(d*x+c)^3+245/128*a^2*cos(d*x+c)*sin(d*x+c)/d-245/128*a^2*x-245/128/d*a^2*c-2/7*a^2*sin(d*x+c)^7/d-2/5*a^2*sin(d*x+c)^5/d-2/3*a^2*sin(d*x+c)^3/d-2*a^2*sin(d*x+c)/d+2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^2*sin(d*x+c)^9/cos(d*x+c)","A"
30,1,172,145,0.694000," ","int((a+a*sec(d*x+c))^2*sin(d*x+c)^6,x)","\frac{5 a^{2} \cos \left(d x +c \right) \left(\sin^{5}\left(d x +c \right)\right)}{6 d}+\frac{25 a^{2} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{24 d}+\frac{25 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{16 d}-\frac{25 a^{2} x}{16}-\frac{25 a^{2} c}{16 d}-\frac{2 a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{5 d}-\frac{2 a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a^{2} \sin \left(d x +c \right)}{d}+\frac{2 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2} \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}"," ",0,"5/6/d*a^2*cos(d*x+c)*sin(d*x+c)^5+25/24/d*a^2*cos(d*x+c)*sin(d*x+c)^3+25/16*a^2*cos(d*x+c)*sin(d*x+c)/d-25/16*a^2*x-25/16/d*a^2*c-2/5*a^2*sin(d*x+c)^5/d-2/3*a^2*sin(d*x+c)^3/d-2*a^2*sin(d*x+c)/d+2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^2*sin(d*x+c)^7/cos(d*x+c)","A"
31,1,134,107,0.696000," ","int((a+a*sec(d*x+c))^2*sin(d*x+c)^4,x)","\frac{3 a^{2} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{4 d}+\frac{9 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{9 a^{2} x}{8}-\frac{9 a^{2} c}{8 d}-\frac{2 a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a^{2} \sin \left(d x +c \right)}{d}+\frac{2 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}"," ",0,"3/4/d*a^2*cos(d*x+c)*sin(d*x+c)^3+9/8*a^2*cos(d*x+c)*sin(d*x+c)/d-9/8*a^2*x-9/8/d*a^2*c-2/3*a^2*sin(d*x+c)^3/d-2*a^2*sin(d*x+c)/d+2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^2*sin(d*x+c)^5/cos(d*x+c)","A"
32,1,86,69,0.400000," ","int((a+a*sec(d*x+c))^2*sin(d*x+c)^2,x)","-\frac{a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{a^{2} x}{2}-\frac{a^{2} c}{2 d}-\frac{2 a^{2} \sin \left(d x +c \right)}{d}+\frac{2 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2} \tan \left(d x +c \right)}{d}"," ",0,"-1/2*a^2*cos(d*x+c)*sin(d*x+c)/d-1/2*a^2*x-1/2/d*a^2*c-2*a^2*sin(d*x+c)/d+2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+a^2*tan(d*x+c)/d","A"
33,1,77,57,0.687000," ","int(csc(d*x+c)^2*(a+a*sec(d*x+c))^2,x)","-\frac{3 a^{2} \cot \left(d x +c \right)}{d}-\frac{2 a^{2}}{d \sin \left(d x +c \right)}+\frac{2 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}"," ",0,"-3*a^2*cot(d*x+c)/d-2/d*a^2/sin(d*x+c)+2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^2/sin(d*x+c)/cos(d*x+c)","A"
34,1,140,83,0.879000," ","int(csc(d*x+c)^4*(a+a*sec(d*x+c))^2,x)","-\frac{10 a^{2} \cot \left(d x +c \right)}{3 d}-\frac{a^{2} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}-\frac{2 a^{2}}{3 d \sin \left(d x +c \right)^{3}}-\frac{2 a^{2}}{d \sin \left(d x +c \right)}+\frac{2 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{a^{2}}{3 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{4 a^{2}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}"," ",0,"-10/3*a^2*cot(d*x+c)/d-1/3/d*a^2*cot(d*x+c)*csc(d*x+c)^2-2/3/d*a^2/sin(d*x+c)^3-2/d*a^2/sin(d*x+c)+2/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)+4/3/d*a^2/sin(d*x+c)/cos(d*x+c)","A"
35,1,202,121,0.900000," ","int(csc(d*x+c)^6*(a+a*sec(d*x+c))^2,x)","-\frac{56 a^{2} \cot \left(d x +c \right)}{15 d}-\frac{a^{2} \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 a^{2} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{15 d}-\frac{2 a^{2}}{5 d \sin \left(d x +c \right)^{5}}-\frac{2 a^{2}}{3 d \sin \left(d x +c \right)^{3}}-\frac{2 a^{2}}{d \sin \left(d x +c \right)}+\frac{2 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{a^{2}}{5 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}-\frac{2 a^{2}}{5 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{8 a^{2}}{5 d \sin \left(d x +c \right) \cos \left(d x +c \right)}"," ",0,"-56/15*a^2*cot(d*x+c)/d-1/5/d*a^2*cot(d*x+c)*csc(d*x+c)^4-4/15/d*a^2*cot(d*x+c)*csc(d*x+c)^2-2/5/d*a^2/sin(d*x+c)^5-2/3/d*a^2/sin(d*x+c)^3-2/d*a^2/sin(d*x+c)+2/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)-2/5/d*a^2/sin(d*x+c)^3/cos(d*x+c)+8/5/d*a^2/sin(d*x+c)/cos(d*x+c)","A"
36,1,264,153,1.021000," ","int(csc(d*x+c)^8*(a+a*sec(d*x+c))^2,x)","-\frac{144 a^{2} \cot \left(d x +c \right)}{35 d}-\frac{a^{2} \cot \left(d x +c \right) \left(\csc^{6}\left(d x +c \right)\right)}{7 d}-\frac{6 a^{2} \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{35 d}-\frac{8 a^{2} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{35 d}-\frac{2 a^{2}}{7 d \sin \left(d x +c \right)^{7}}-\frac{2 a^{2}}{5 d \sin \left(d x +c \right)^{5}}-\frac{2 a^{2}}{3 d \sin \left(d x +c \right)^{3}}-\frac{2 a^{2}}{d \sin \left(d x +c \right)}+\frac{2 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{a^{2}}{7 d \sin \left(d x +c \right)^{7} \cos \left(d x +c \right)}-\frac{8 a^{2}}{35 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}-\frac{16 a^{2}}{35 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{64 a^{2}}{35 d \sin \left(d x +c \right) \cos \left(d x +c \right)}"," ",0,"-144/35*a^2*cot(d*x+c)/d-1/7/d*a^2*cot(d*x+c)*csc(d*x+c)^6-6/35/d*a^2*cot(d*x+c)*csc(d*x+c)^4-8/35/d*a^2*cot(d*x+c)*csc(d*x+c)^2-2/7/d*a^2/sin(d*x+c)^7-2/5/d*a^2/sin(d*x+c)^5-2/3/d*a^2/sin(d*x+c)^3-2/d*a^2/sin(d*x+c)+2/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)-8/35/d*a^2/sin(d*x+c)^5/cos(d*x+c)-16/35/d*a^2/sin(d*x+c)^3/cos(d*x+c)+64/35/d*a^2/sin(d*x+c)/cos(d*x+c)","A"
37,1,326,185,1.026000," ","int(csc(d*x+c)^10*(a+a*sec(d*x+c))^2,x)","-\frac{1408 a^{2} \cot \left(d x +c \right)}{315 d}-\frac{a^{2} \cot \left(d x +c \right) \left(\csc^{8}\left(d x +c \right)\right)}{9 d}-\frac{8 a^{2} \cot \left(d x +c \right) \left(\csc^{6}\left(d x +c \right)\right)}{63 d}-\frac{16 a^{2} \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{105 d}-\frac{64 a^{2} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{315 d}-\frac{2 a^{2}}{9 d \sin \left(d x +c \right)^{9}}-\frac{2 a^{2}}{7 d \sin \left(d x +c \right)^{7}}-\frac{2 a^{2}}{5 d \sin \left(d x +c \right)^{5}}-\frac{2 a^{2}}{3 d \sin \left(d x +c \right)^{3}}-\frac{2 a^{2}}{d \sin \left(d x +c \right)}+\frac{2 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{a^{2}}{9 d \sin \left(d x +c \right)^{9} \cos \left(d x +c \right)}-\frac{10 a^{2}}{63 d \sin \left(d x +c \right)^{7} \cos \left(d x +c \right)}-\frac{16 a^{2}}{63 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}-\frac{32 a^{2}}{63 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{128 a^{2}}{63 d \sin \left(d x +c \right) \cos \left(d x +c \right)}"," ",0,"-1408/315*a^2*cot(d*x+c)/d-1/9/d*a^2*cot(d*x+c)*csc(d*x+c)^8-8/63/d*a^2*cot(d*x+c)*csc(d*x+c)^6-16/105/d*a^2*cot(d*x+c)*csc(d*x+c)^4-64/315/d*a^2*cot(d*x+c)*csc(d*x+c)^2-2/9/d*a^2/sin(d*x+c)^9-2/7/d*a^2/sin(d*x+c)^7-2/5/d*a^2/sin(d*x+c)^5-2/3/d*a^2/sin(d*x+c)^3-2/d*a^2/sin(d*x+c)+2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))-1/9/d*a^2/sin(d*x+c)^9/cos(d*x+c)-10/63/d*a^2/sin(d*x+c)^7/cos(d*x+c)-16/63/d*a^2/sin(d*x+c)^5/cos(d*x+c)-32/63/d*a^2/sin(d*x+c)^3/cos(d*x+c)+128/63/d*a^2/sin(d*x+c)/cos(d*x+c)","A"
38,1,230,187,0.772000," ","int((a+a*sec(d*x+c))^3*sin(d*x+c)^9,x)","\frac{3328 a^{3} \cos \left(d x +c \right)}{315 d}+\frac{26 a^{3} \left(\sin^{8}\left(d x +c \right)\right) \cos \left(d x +c \right)}{9 d}+\frac{208 a^{3} \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{63 d}+\frac{416 a^{3} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{105 d}+\frac{1664 a^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{315 d}+\frac{a^{3} \left(\sin^{8}\left(d x +c \right)\right)}{8 d}+\frac{a^{3} \left(\sin^{6}\left(d x +c \right)\right)}{6 d}+\frac{a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\sin^{10}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{a^{3} \left(\sin^{10}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"3328/315*a^3*cos(d*x+c)/d+26/9/d*a^3*sin(d*x+c)^8*cos(d*x+c)+208/63/d*a^3*cos(d*x+c)*sin(d*x+c)^6+416/105/d*a^3*cos(d*x+c)*sin(d*x+c)^4+1664/315/d*a^3*cos(d*x+c)*sin(d*x+c)^2+1/8/d*a^3*sin(d*x+c)^8+1/6/d*a^3*sin(d*x+c)^6+1/4/d*a^3*sin(d*x+c)^4+1/2/d*a^3*sin(d*x+c)^2+a^3*ln(cos(d*x+c))/d+3/d*a^3*sin(d*x+c)^10/cos(d*x+c)+1/2/d*a^3*sin(d*x+c)^10/cos(d*x+c)^2","A"
39,1,130,125,0.713000," ","int((a+a*sec(d*x+c))^3*sin(d*x+c)^7,x)","\frac{64 a^{3} \cos \left(d x +c \right)}{7 d}+\frac{20 a^{3} \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{7 d}+\frac{24 a^{3} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{7 d}+\frac{32 a^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{7 d}+\frac{3 a^{3} \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{a^{3} \left(\sin^{8}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"64/7*a^3*cos(d*x+c)/d+20/7/d*a^3*cos(d*x+c)*sin(d*x+c)^6+24/7/d*a^3*cos(d*x+c)*sin(d*x+c)^4+32/7/d*a^3*cos(d*x+c)*sin(d*x+c)^2+3/d*a^3*sin(d*x+c)^8/cos(d*x+c)+1/2/d*a^3*sin(d*x+c)^8/cos(d*x+c)^2","A"
40,1,155,124,0.778000," ","int((a+a*sec(d*x+c))^3*sin(d*x+c)^5,x)","\frac{112 a^{3} \cos \left(d x +c \right)}{15 d}+\frac{14 a^{3} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{5 d}+\frac{56 a^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}-\frac{a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{a^{3} \left(\sin^{6}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"112/15*a^3*cos(d*x+c)/d+14/5/d*a^3*cos(d*x+c)*sin(d*x+c)^4+56/15/d*a^3*cos(d*x+c)*sin(d*x+c)^2-1/4/d*a^3*sin(d*x+c)^4-1/2/d*a^3*sin(d*x+c)^2-a^3*ln(cos(d*x+c))/d+3/d*a^3*sin(d*x+c)^6/cos(d*x+c)+1/2/d*a^3*sin(d*x+c)^6/cos(d*x+c)^2","A"
41,1,109,92,0.803000," ","int((a+a*sec(d*x+c))^3*sin(d*x+c)^3,x)","\frac{8 a^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}+\frac{16 a^{3} \cos \left(d x +c \right)}{3 d}-\frac{3 a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{2 a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"8/3/d*a^3*cos(d*x+c)*sin(d*x+c)^2+16/3*a^3*cos(d*x+c)/d-3/2/d*a^3*sin(d*x+c)^2-2*a^3*ln(cos(d*x+c))/d+3/d*a^3*sin(d*x+c)^4/cos(d*x+c)+1/2*a^3*tan(d*x+c)^2/d","A"
42,1,63,60,0.250000," ","int((a+a*sec(d*x+c))^3*sin(d*x+c),x)","\frac{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{3 a^{3} \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a^{3}}{d \sec \left(d x +c \right)}"," ",0,"1/2*a^3*sec(d*x+c)^2/d+3*a^3*sec(d*x+c)/d+3*a^3/d*ln(sec(d*x+c))-a^3/d/sec(d*x+c)","A"
43,1,49,65,0.477000," ","int(csc(d*x+c)*(a+a*sec(d*x+c))^3,x)","\frac{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{4 a^{3} \ln \left(-1+\sec \left(d x +c \right)\right)}{d}"," ",0,"1/2*a^3*sec(d*x+c)^2/d+3*a^3*sec(d*x+c)/d+4/d*a^3*ln(-1+sec(d*x+c))","A"
44,1,67,86,0.727000," ","int(csc(d*x+c)^3*(a+a*sec(d*x+c))^3,x)","\frac{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{2 a^{3}}{d \left(-1+\sec \left(d x +c \right)\right)}+\frac{5 a^{3} \ln \left(-1+\sec \left(d x +c \right)\right)}{d}"," ",0,"1/2*a^3*sec(d*x+c)^2/d+3*a^3*sec(d*x+c)/d-2/d*a^3/(-1+sec(d*x+c))+5/d*a^3*ln(-1+sec(d*x+c))","A"
45,1,85,107,0.620000," ","int(csc(d*x+c)^5*(a+a*sec(d*x+c))^3,x)","\frac{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{4 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{6 a^{3} \ln \left(-1+\sec \left(d x +c \right)\right)}{d}"," ",0,"1/2*a^3*sec(d*x+c)^2/d+3*a^3*sec(d*x+c)/d-4/d*a^3/(-1+sec(d*x+c))-1/2/d*a^3/(-1+sec(d*x+c))^2+6/d*a^3*ln(-1+sec(d*x+c))","A"
46,1,120,145,0.609000," ","int(csc(d*x+c)^7*(a+a*sec(d*x+c))^3,x)","\frac{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}}{6 d \left(-1+\sec \left(d x +c \right)\right)^{3}}-\frac{11 a^{3}}{8 d \left(-1+\sec \left(d x +c \right)\right)^{2}}-\frac{49 a^{3}}{8 d \left(-1+\sec \left(d x +c \right)\right)}+\frac{111 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,"1/2*a^3*sec(d*x+c)^2/d+3*a^3*sec(d*x+c)/d-1/6/d*a^3/(-1+sec(d*x+c))^3-11/8/d*a^3/(-1+sec(d*x+c))^2-49/8/d*a^3/(-1+sec(d*x+c))+111/16/d*a^3*ln(-1+sec(d*x+c))+1/16/d*a^3*ln(1+sec(d*x+c))","A"
47,1,156,186,0.720000," ","int(csc(d*x+c)^9*(a+a*sec(d*x+c))^3,x)","\frac{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}}{16 d \left(-1+\sec \left(d x +c \right)\right)^{4}}-\frac{7 a^{3}}{12 d \left(-1+\sec \left(d x +c \right)\right)^{3}}-\frac{83 a^{3}}{32 d \left(-1+\sec \left(d x +c \right)\right)^{2}}-\frac{67 a^{3}}{8 d \left(-1+\sec \left(d x +c \right)\right)}+\frac{501 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{11 a^{3} \ln \left(1+\sec \left(d x +c \right)\right)}{64 d}"," ",0,"1/2*a^3*sec(d*x+c)^2/d+3*a^3*sec(d*x+c)/d-1/16/d*a^3/(-1+sec(d*x+c))^4-7/12/d*a^3/(-1+sec(d*x+c))^3-83/32/d*a^3/(-1+sec(d*x+c))^2-67/8/d*a^3/(-1+sec(d*x+c))+501/64/d*a^3*ln(-1+sec(d*x+c))+1/32/d*a^3/(1+sec(d*x+c))+11/64/d*a^3*ln(1+sec(d*x+c))","A"
48,1,235,190,0.929000," ","int((a+a*sec(d*x+c))^3*sin(d*x+c)^8,x)","\frac{23 a^{3} \left(\sin^{7}\left(d x +c \right)\right) \cos \left(d x +c \right)}{8 d}+\frac{161 a^{3} \cos \left(d x +c \right) \left(\sin^{5}\left(d x +c \right)\right)}{48 d}+\frac{805 a^{3} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{192 d}+\frac{805 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{128 d}-\frac{805 a^{3} x}{128}-\frac{805 a^{3} c}{128 d}+\frac{a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{14 d}+\frac{a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{10 d}+\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{6 d}+\frac{a^{3} \sin \left(d x +c \right)}{2 d}-\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 a^{3} \left(\sin^{9}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{a^{3} \left(\sin^{9}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"23/8/d*a^3*sin(d*x+c)^7*cos(d*x+c)+161/48*a^3*cos(d*x+c)*sin(d*x+c)^5/d+805/192*a^3*cos(d*x+c)*sin(d*x+c)^3/d+805/128*a^3*cos(d*x+c)*sin(d*x+c)/d-805/128*a^3*x-805/128/d*a^3*c+1/14*a^3*sin(d*x+c)^7/d+1/10*a^3*sin(d*x+c)^5/d+1/6*a^3*sin(d*x+c)^3/d+1/2*a^3*sin(d*x+c)/d-1/2/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/d*a^3*sin(d*x+c)^9/cos(d*x+c)+1/2/d*a^3*sin(d*x+c)^9/cos(d*x+c)^2","A"
49,1,197,166,0.844000," ","int((a+a*sec(d*x+c))^3*sin(d*x+c)^6,x)","\frac{17 a^{3} \cos \left(d x +c \right) \left(\sin^{5}\left(d x +c \right)\right)}{6 d}+\frac{85 a^{3} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{24 d}+\frac{85 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{16 d}-\frac{85 a^{3} x}{16}-\frac{85 a^{3} c}{16 d}-\frac{a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{10 d}-\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{6 d}-\frac{a^{3} \sin \left(d x +c \right)}{2 d}+\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"17/6*a^3*cos(d*x+c)*sin(d*x+c)^5/d+85/24*a^3*cos(d*x+c)*sin(d*x+c)^3/d+85/16*a^3*cos(d*x+c)*sin(d*x+c)/d-85/16*a^3*x-85/16/d*a^3*c-1/10*a^3*sin(d*x+c)^5/d-1/6*a^3*sin(d*x+c)^3/d-1/2*a^3*sin(d*x+c)/d+1/2/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/d*a^3*sin(d*x+c)^7/cos(d*x+c)+1/2/d*a^3*sin(d*x+c)^7/cos(d*x+c)^2","A"
50,1,159,128,0.755000," ","int((a+a*sec(d*x+c))^3*sin(d*x+c)^4,x)","\frac{11 a^{3} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{4 d}+\frac{33 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{33 a^{3} x}{8}-\frac{33 a^{3} c}{8 d}-\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{3} \sin \left(d x +c \right)}{2 d}+\frac{3 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"11/4*a^3*cos(d*x+c)*sin(d*x+c)^3/d+33/8*a^3*cos(d*x+c)*sin(d*x+c)/d-33/8*a^3*x-33/8/d*a^3*c-1/2*a^3*sin(d*x+c)^3/d-3/2*a^3*sin(d*x+c)/d+3/2/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/d*a^3*sin(d*x+c)^5/cos(d*x+c)+1/2/d*a^3*sin(d*x+c)^5/cos(d*x+c)^2","A"
51,1,111,90,0.455000," ","int((a+a*sec(d*x+c))^3*sin(d*x+c)^2,x)","-\frac{a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{5 a^{3} x}{2}-\frac{5 a^{3} c}{2 d}-\frac{5 a^{3} \sin \left(d x +c \right)}{2 d}+\frac{5 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 a^{3} \tan \left(d x +c \right)}{d}+\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"-1/2*a^3*cos(d*x+c)*sin(d*x+c)/d-5/2*a^3*x-5/2/d*a^3*c-5/2*a^3*sin(d*x+c)/d+5/2/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3*a^3*tan(d*x+c)/d+1/2/d*a^3*sin(d*x+c)^3/cos(d*x+c)^2","A"
52,1,102,76,0.746000," ","int(csc(d*x+c)^2*(a+a*sec(d*x+c))^3,x)","-\frac{7 a^{3} \cot \left(d x +c \right)}{d}-\frac{9 a^{3}}{2 d \sin \left(d x +c \right)}+\frac{9 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 a^{3}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}+\frac{a^{3}}{2 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}"," ",0,"-7*a^3*cot(d*x+c)/d-9/2/d*a^3/sin(d*x+c)+9/2/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/d*a^3/sin(d*x+c)/cos(d*x+c)+1/2/d*a^3/sin(d*x+c)/cos(d*x+c)^2","A"
53,1,188,102,1.026000," ","int(csc(d*x+c)^4*(a+a*sec(d*x+c))^3,x)","-\frac{26 a^{3} \cot \left(d x +c \right)}{3 d}-\frac{a^{3} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}-\frac{a^{3}}{d \sin \left(d x +c \right)^{3}}-\frac{11 a^{3}}{2 d \sin \left(d x +c \right)}+\frac{11 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}-\frac{a^{3}}{d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{4 a^{3}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{a^{3}}{3 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{2}}+\frac{5 a^{3}}{6 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}"," ",0,"-26/3*a^3*cot(d*x+c)/d-1/3/d*a^3*cot(d*x+c)*csc(d*x+c)^2-1/d*a^3/sin(d*x+c)^3-11/2/d*a^3/sin(d*x+c)+11/2/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)+4/d*a^3/sin(d*x+c)/cos(d*x+c)-1/3/d*a^3/sin(d*x+c)^3/cos(d*x+c)^2+5/6/d*a^3/sin(d*x+c)/cos(d*x+c)^2","A"
54,1,274,153,1.054000," ","int(csc(d*x+c)^6*(a+a*sec(d*x+c))^3,x)","-\frac{152 a^{3} \cot \left(d x +c \right)}{15 d}-\frac{a^{3} \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 a^{3} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{15 d}-\frac{3 a^{3}}{5 d \sin \left(d x +c \right)^{5}}-\frac{a^{3}}{d \sin \left(d x +c \right)^{3}}-\frac{13 a^{3}}{2 d \sin \left(d x +c \right)}+\frac{13 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}-\frac{3 a^{3}}{5 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}-\frac{6 a^{3}}{5 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{24 a^{3}}{5 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{a^{3}}{5 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)^{2}}-\frac{7 a^{3}}{15 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{2}}+\frac{7 a^{3}}{6 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}"," ",0,"-152/15*a^3*cot(d*x+c)/d-1/5/d*a^3*cot(d*x+c)*csc(d*x+c)^4-4/15/d*a^3*cot(d*x+c)*csc(d*x+c)^2-3/5/d*a^3/sin(d*x+c)^5-1/d*a^3/sin(d*x+c)^3-13/2/d*a^3/sin(d*x+c)+13/2/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)-6/5/d*a^3/sin(d*x+c)^3/cos(d*x+c)+24/5/d*a^3/sin(d*x+c)/cos(d*x+c)-1/5/d*a^3/sin(d*x+c)^5/cos(d*x+c)^2-7/15/d*a^3/sin(d*x+c)^3/cos(d*x+c)^2+7/6/d*a^3/sin(d*x+c)/cos(d*x+c)^2","A"
55,1,360,178,1.115000," ","int(csc(d*x+c)^8*(a+a*sec(d*x+c))^3,x)","-\frac{80 a^{3} \cot \left(d x +c \right)}{7 d}-\frac{a^{3} \cot \left(d x +c \right) \left(\csc^{6}\left(d x +c \right)\right)}{7 d}-\frac{6 a^{3} \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{35 d}-\frac{8 a^{3} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{35 d}-\frac{3 a^{3}}{7 d \sin \left(d x +c \right)^{7}}-\frac{3 a^{3}}{5 d \sin \left(d x +c \right)^{5}}-\frac{a^{3}}{d \sin \left(d x +c \right)^{3}}-\frac{15 a^{3}}{2 d \sin \left(d x +c \right)}+\frac{15 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}-\frac{3 a^{3}}{7 d \sin \left(d x +c \right)^{7} \cos \left(d x +c \right)}-\frac{24 a^{3}}{35 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}-\frac{48 a^{3}}{35 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{192 a^{3}}{35 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{a^{3}}{7 d \sin \left(d x +c \right)^{7} \cos \left(d x +c \right)^{2}}-\frac{9 a^{3}}{35 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)^{2}}-\frac{3 a^{3}}{5 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{2}}+\frac{3 a^{3}}{2 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}"," ",0,"-80/7*a^3*cot(d*x+c)/d-1/7/d*a^3*cot(d*x+c)*csc(d*x+c)^6-6/35/d*a^3*cot(d*x+c)*csc(d*x+c)^4-8/35/d*a^3*cot(d*x+c)*csc(d*x+c)^2-3/7/d*a^3/sin(d*x+c)^7-3/5/d*a^3/sin(d*x+c)^5-1/d*a^3/sin(d*x+c)^3-15/2/d*a^3/sin(d*x+c)+15/2/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)-24/35/d*a^3/sin(d*x+c)^5/cos(d*x+c)-48/35/d*a^3/sin(d*x+c)^3/cos(d*x+c)+192/35/d*a^3/sin(d*x+c)/cos(d*x+c)-1/7/d*a^3/sin(d*x+c)^7/cos(d*x+c)^2-9/35/d*a^3/sin(d*x+c)^5/cos(d*x+c)^2-3/5/d*a^3/sin(d*x+c)^3/cos(d*x+c)^2+3/2/d*a^3/sin(d*x+c)/cos(d*x+c)^2","B"
56,1,446,210,1.126000," ","int(csc(d*x+c)^10*(a+a*sec(d*x+c))^3,x)","-\frac{3968 a^{3} \cot \left(d x +c \right)}{315 d}-\frac{a^{3} \cot \left(d x +c \right) \left(\csc^{8}\left(d x +c \right)\right)}{9 d}-\frac{8 a^{3} \cot \left(d x +c \right) \left(\csc^{6}\left(d x +c \right)\right)}{63 d}-\frac{16 a^{3} \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{105 d}-\frac{64 a^{3} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{315 d}-\frac{a^{3}}{3 d \sin \left(d x +c \right)^{9}}-\frac{3 a^{3}}{7 d \sin \left(d x +c \right)^{7}}-\frac{3 a^{3}}{5 d \sin \left(d x +c \right)^{5}}-\frac{a^{3}}{d \sin \left(d x +c \right)^{3}}-\frac{17 a^{3}}{2 d \sin \left(d x +c \right)}+\frac{17 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}-\frac{a^{3}}{3 d \sin \left(d x +c \right)^{9} \cos \left(d x +c \right)}-\frac{10 a^{3}}{21 d \sin \left(d x +c \right)^{7} \cos \left(d x +c \right)}-\frac{16 a^{3}}{21 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}-\frac{32 a^{3}}{21 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{128 a^{3}}{21 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{a^{3}}{9 d \sin \left(d x +c \right)^{9} \cos \left(d x +c \right)^{2}}-\frac{11 a^{3}}{63 d \sin \left(d x +c \right)^{7} \cos \left(d x +c \right)^{2}}-\frac{11 a^{3}}{35 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)^{2}}-\frac{11 a^{3}}{15 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{2}}+\frac{11 a^{3}}{6 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}"," ",0,"-3968/315*a^3*cot(d*x+c)/d-1/9/d*a^3*cot(d*x+c)*csc(d*x+c)^8-8/63/d*a^3*cot(d*x+c)*csc(d*x+c)^6-16/105/d*a^3*cot(d*x+c)*csc(d*x+c)^4-64/315/d*a^3*cot(d*x+c)*csc(d*x+c)^2-1/3/d*a^3/sin(d*x+c)^9-3/7/d*a^3/sin(d*x+c)^7-3/5/d*a^3/sin(d*x+c)^5-1/d*a^3/sin(d*x+c)^3-17/2/d*a^3/sin(d*x+c)+17/2/d*a^3*ln(sec(d*x+c)+tan(d*x+c))-1/3/d*a^3/sin(d*x+c)^9/cos(d*x+c)-10/21/d*a^3/sin(d*x+c)^7/cos(d*x+c)-16/21/d*a^3/sin(d*x+c)^5/cos(d*x+c)-32/21/d*a^3/sin(d*x+c)^3/cos(d*x+c)+128/21/d*a^3/sin(d*x+c)/cos(d*x+c)-1/9/d*a^3/sin(d*x+c)^9/cos(d*x+c)^2-11/63/d*a^3/sin(d*x+c)^7/cos(d*x+c)^2-11/35/d*a^3/sin(d*x+c)^5/cos(d*x+c)^2-11/15/d*a^3/sin(d*x+c)^3/cos(d*x+c)^2+11/6/d*a^3/sin(d*x+c)/cos(d*x+c)^2","B"
57,1,89,81,0.542000," ","int(sin(d*x+c)^9/(a+a*sec(d*x+c)),x)","\frac{-\frac{1}{2 \sec \left(d x +c \right)^{6}}-\frac{1}{2 \sec \left(d x +c \right)^{2}}+\frac{3}{7 \sec \left(d x +c \right)^{7}}-\frac{1}{9 \sec \left(d x +c \right)^{9}}+\frac{1}{3 \sec \left(d x +c \right)^{3}}+\frac{3}{4 \sec \left(d x +c \right)^{4}}+\frac{1}{8 \sec \left(d x +c \right)^{8}}-\frac{3}{5 \sec \left(d x +c \right)^{5}}}{d a}"," ",0,"1/d/a*(-1/2/sec(d*x+c)^6-1/2/sec(d*x+c)^2+3/7/sec(d*x+c)^7-1/9/sec(d*x+c)^9+1/3/sec(d*x+c)^3+3/4/sec(d*x+c)^4+1/8/sec(d*x+c)^8-3/5/sec(d*x+c)^5)","A"
58,1,70,65,0.457000," ","int(sin(d*x+c)^7/(a+a*sec(d*x+c)),x)","-\frac{\frac{1}{6 \sec \left(d x +c \right)^{6}}+\frac{1}{2 \sec \left(d x +c \right)^{2}}-\frac{1}{7 \sec \left(d x +c \right)^{7}}-\frac{1}{3 \sec \left(d x +c \right)^{3}}-\frac{1}{2 \sec \left(d x +c \right)^{4}}+\frac{2}{5 \sec \left(d x +c \right)^{5}}}{d a}"," ",0,"-1/d/a*(1/6/sec(d*x+c)^6+1/2/sec(d*x+c)^2-1/7/sec(d*x+c)^7-1/3/sec(d*x+c)^3-1/2/sec(d*x+c)^4+2/5/sec(d*x+c)^5)","A"
59,1,49,49,0.445000," ","int(sin(d*x+c)^5/(a+a*sec(d*x+c)),x)","\frac{-\frac{1}{2 \sec \left(d x +c \right)^{2}}+\frac{1}{3 \sec \left(d x +c \right)^{3}}+\frac{1}{4 \sec \left(d x +c \right)^{4}}-\frac{1}{5 \sec \left(d x +c \right)^{5}}}{d a}"," ",0,"1/d/a*(-1/2/sec(d*x+c)^2+1/3/sec(d*x+c)^3+1/4/sec(d*x+c)^4-1/5/sec(d*x+c)^5)","A"
60,1,30,33,0.428000," ","int(sin(d*x+c)^3/(a+a*sec(d*x+c)),x)","-\frac{\frac{1}{2 \sec \left(d x +c \right)^{2}}-\frac{1}{3 \sec \left(d x +c \right)^{3}}}{d a}"," ",0,"-1/d/a*(1/2/sec(d*x+c)^2-1/3/sec(d*x+c)^3)","A"
61,1,49,31,0.056000," ","int(sin(d*x+c)/(a+a*sec(d*x+c)),x)","-\frac{1}{d a \sec \left(d x +c \right)}-\frac{\ln \left(\sec \left(d x +c \right)\right)}{d a}+\frac{\ln \left(1+\sec \left(d x +c \right)\right)}{d a}"," ",0,"-1/d/a/sec(d*x+c)-1/d/a*ln(sec(d*x+c))+1/d/a*ln(1+sec(d*x+c))","A"
62,1,54,52,0.483000," ","int(csc(d*x+c)/(a+a*sec(d*x+c)),x)","\frac{\ln \left(-1+\cos \left(d x +c \right)\right)}{4 a d}-\frac{1}{2 a d \left(1+\cos \left(d x +c \right)\right)}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{4 d a}"," ",0,"1/4/a/d*ln(-1+cos(d*x+c))-1/2/a/d/(1+cos(d*x+c))-1/4*ln(1+cos(d*x+c))/d/a","A"
63,1,72,74,0.652000," ","int(csc(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{\ln \left(-1+\cos \left(d x +c \right)\right)}{16 a d}-\frac{1}{8 a d \left(1+\cos \left(d x +c \right)\right)^{2}}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{16 d a}"," ",0,"1/8/a/d/(-1+cos(d*x+c))+1/16/a/d*ln(-1+cos(d*x+c))-1/8/a/d/(1+cos(d*x+c))^2-1/16*ln(1+cos(d*x+c))/d/a","A"
64,1,108,96,0.563000," ","int(csc(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}{16 a d \left(-1+\cos \left(d x +c \right)\right)}+\frac{\ln \left(-1+\cos \left(d x +c \right)\right)}{32 a d}-\frac{1}{24 a d \left(1+\cos \left(d x +c \right)\right)^{3}}-\frac{1}{32 a d \left(1+\cos \left(d x +c \right)\right)^{2}}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{32 d a}"," ",0,"-1/32/a/d/(-1+cos(d*x+c))^2+1/16/a/d/(-1+cos(d*x+c))+1/32/a/d*ln(-1+cos(d*x+c))-1/24/a/d/(1+cos(d*x+c))^3-1/32/a/d/(1+cos(d*x+c))^2-1/32*ln(1+cos(d*x+c))/d/a","A"
65,1,290,113,0.444000," ","int(sin(d*x+c)^8/(a+a*sec(d*x+c)),x)","\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{115 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{383 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{5053 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{1344 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{44099 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{1344 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{383 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{115 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{5 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d}"," ",0,"5/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)+115/192/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^3+383/192/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^5+5053/1344/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^7+44099/1344/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^9-383/192/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^11-115/192/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^13-5/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^15-5/64/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
66,1,222,89,0.432000," ","int(sin(d*x+c)^6/(a+a*sec(d*x+c)),x)","-\frac{\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{17 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{223 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{33 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{17 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}"," ",0,"-1/8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11-17/24/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9+223/20/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7+33/20/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5+17/24/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3+1/8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)-1/8/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
67,1,154,65,0.416000," ","int(sin(d*x+c)^4/(a+a*sec(d*x+c)),x)","-\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{53 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{12 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{12 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d}"," ",0,"-1/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7+53/12/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5+11/12/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3+1/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)-1/4/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
68,1,85,40,0.330000," ","int(sin(d*x+c)^2/(a+a*sec(d*x+c)),x)","\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-1/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
69,1,36,33,0.468000," ","int(csc(d*x+c)^2/(a+a*sec(d*x+c)),x)","\frac{-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-\frac{1}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{4 d a}"," ",0,"1/4/d/a*(-1/3*tan(1/2*d*x+1/2*c)^3-1/tan(1/2*d*x+1/2*c))","A"
70,1,62,49,0.572000," ","int(csc(d*x+c)^4/(a+a*sec(d*x+c)),x)","\frac{-\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-\frac{1}{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{16 d a}"," ",0,"1/16/d/a*(-1/5*tan(1/2*d*x+1/2*c)^5-2/3*tan(1/2*d*x+1/2*c)^3-1/3/tan(1/2*d*x+1/2*c)^3-2/tan(1/2*d*x+1/2*c))","A"
71,1,88,65,0.546000," ","int(csc(d*x+c)^6/(a+a*sec(d*x+c)),x)","\frac{-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}-\frac{4 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-\frac{4}{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{1}{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{5}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{64 d a}"," ",0,"1/64/d/a*(-1/7*tan(1/2*d*x+1/2*c)^7-4/5*tan(1/2*d*x+1/2*c)^5-5/3*tan(1/2*d*x+1/2*c)^3-4/3/tan(1/2*d*x+1/2*c)^3-1/5/tan(1/2*d*x+1/2*c)^5-5/tan(1/2*d*x+1/2*c))","A"
72,1,114,81,0.605000," ","int(csc(d*x+c)^8/(a+a*sec(d*x+c)),x)","\frac{-\frac{\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9}-\frac{6 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}-\frac{14 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-\frac{14 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-\frac{1}{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}-\frac{14}{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{6}{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{14}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{256 d a}"," ",0,"1/256/d/a*(-1/9*tan(1/2*d*x+1/2*c)^9-6/7*tan(1/2*d*x+1/2*c)^7-14/5*tan(1/2*d*x+1/2*c)^5-14/3*tan(1/2*d*x+1/2*c)^3-1/7/tan(1/2*d*x+1/2*c)^7-14/3/tan(1/2*d*x+1/2*c)^3-6/5/tan(1/2*d*x+1/2*c)^5-14/tan(1/2*d*x+1/2*c))","A"
73,1,140,97,0.588000," ","int(csc(d*x+c)^10/(a+a*sec(d*x+c)),x)","\frac{-\frac{\left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{11}-\frac{8 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9}-\frac{27 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}-\frac{48 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-14 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\frac{8}{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}-\frac{1}{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{9}}-\frac{16}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{27}{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{42}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{1024 d a}"," ",0,"1/1024/d/a*(-1/11*tan(1/2*d*x+1/2*c)^11-8/9*tan(1/2*d*x+1/2*c)^9-27/7*tan(1/2*d*x+1/2*c)^7-48/5*tan(1/2*d*x+1/2*c)^5-14*tan(1/2*d*x+1/2*c)^3-8/7/tan(1/2*d*x+1/2*c)^7-1/9/tan(1/2*d*x+1/2*c)^9-16/tan(1/2*d*x+1/2*c)^3-27/5/tan(1/2*d*x+1/2*c)^5-42/tan(1/2*d*x+1/2*c))","A"
74,1,88,127,0.691000," ","int(sin(d*x+c)^11/(a+a*sec(d*x+c))^2,x)","-\frac{\frac{1}{\sec \left(d x +c \right)^{6}}-\frac{1}{11 \sec \left(d x +c \right)^{11}}+\frac{2}{9 \sec \left(d x +c \right)^{9}}+\frac{1}{3 \sec \left(d x +c \right)^{3}}-\frac{1}{2 \sec \left(d x +c \right)^{4}}-\frac{3}{4 \sec \left(d x +c \right)^{8}}+\frac{1}{5 \sec \left(d x +c \right)^{10}}-\frac{2}{5 \sec \left(d x +c \right)^{5}}}{d \,a^{2}}"," ",0,"-1/d/a^2*(1/sec(d*x+c)^6-1/11/sec(d*x+c)^11+2/9/sec(d*x+c)^9+1/3/sec(d*x+c)^3-1/2/sec(d*x+c)^4-3/4/sec(d*x+c)^8+1/5/sec(d*x+c)^10-2/5/sec(d*x+c)^5)","A"
75,1,79,106,0.628000," ","int(sin(d*x+c)^9/(a+a*sec(d*x+c))^2,x)","\frac{-\frac{2}{3 \sec \left(d x +c \right)^{6}}+\frac{1}{7 \sec \left(d x +c \right)^{7}}-\frac{1}{9 \sec \left(d x +c \right)^{9}}-\frac{1}{3 \sec \left(d x +c \right)^{3}}+\frac{1}{2 \sec \left(d x +c \right)^{4}}+\frac{1}{4 \sec \left(d x +c \right)^{8}}+\frac{1}{5 \sec \left(d x +c \right)^{5}}}{d \,a^{2}}"," ",0,"1/d/a^2*(-2/3/sec(d*x+c)^6+1/7/sec(d*x+c)^7-1/9/sec(d*x+c)^9-1/3/sec(d*x+c)^3+1/2/sec(d*x+c)^4+1/4/sec(d*x+c)^8+1/5/sec(d*x+c)^5)","A"
76,1,50,65,0.595000," ","int(sin(d*x+c)^7/(a+a*sec(d*x+c))^2,x)","-\frac{\frac{1}{3 \sec \left(d x +c \right)^{6}}-\frac{1}{7 \sec \left(d x +c \right)^{7}}+\frac{1}{3 \sec \left(d x +c \right)^{3}}-\frac{1}{2 \sec \left(d x +c \right)^{4}}}{d \,a^{2}}"," ",0,"-1/d/a^2*(1/3/sec(d*x+c)^6-1/7/sec(d*x+c)^7+1/3/sec(d*x+c)^3-1/2/sec(d*x+c)^4)","A"
77,1,39,49,0.611000," ","int(sin(d*x+c)^5/(a+a*sec(d*x+c))^2,x)","\frac{-\frac{1}{3 \sec \left(d x +c \right)^{3}}+\frac{1}{2 \sec \left(d x +c \right)^{4}}-\frac{1}{5 \sec \left(d x +c \right)^{5}}}{d \,a^{2}}"," ",0,"1/d/a^2*(-1/3/sec(d*x+c)^3+1/2/sec(d*x+c)^4-1/5/sec(d*x+c)^5)","A"
78,1,82,64,0.650000," ","int(sin(d*x+c)^3/(a+a*sec(d*x+c))^2,x)","\frac{1}{3 d \,a^{2} \sec \left(d x +c \right)^{3}}-\frac{1}{d \,a^{2} \sec \left(d x +c \right)^{2}}+\frac{2}{d \,a^{2} \sec \left(d x +c \right)}+\frac{2 \ln \left(\sec \left(d x +c \right)\right)}{d \,a^{2}}-\frac{2 \ln \left(1+\sec \left(d x +c \right)\right)}{d \,a^{2}}"," ",0,"1/3/d/a^2/sec(d*x+c)^3-1/d/a^2/sec(d*x+c)^2+2/d/a^2/sec(d*x+c)+2/d/a^2*ln(sec(d*x+c))-2/d/a^2*ln(1+sec(d*x+c))","A"
79,1,68,52,0.174000," ","int(sin(d*x+c)/(a+a*sec(d*x+c))^2,x)","-\frac{1}{d \,a^{2} \sec \left(d x +c \right)}-\frac{2 \ln \left(\sec \left(d x +c \right)\right)}{d \,a^{2}}-\frac{1}{a^{2} d \left(1+\sec \left(d x +c \right)\right)}+\frac{2 \ln \left(1+\sec \left(d x +c \right)\right)}{d \,a^{2}}"," ",0,"-1/d/a^2/sec(d*x+c)-2/d/a^2*ln(sec(d*x+c))-1/a^2/d/(1+sec(d*x+c))+2/d/a^2*ln(1+sec(d*x+c))","A"
80,1,72,54,0.570000," ","int(csc(d*x+c)/(a+a*sec(d*x+c))^2,x)","\frac{\ln \left(-1+\cos \left(d x +c \right)\right)}{8 d \,a^{2}}+\frac{1}{4 d \,a^{2} \left(1+\cos \left(d x +c \right)\right)^{2}}-\frac{3}{4 d \,a^{2} \left(1+\cos \left(d x +c \right)\right)}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{8 a^{2} d}"," ",0,"1/8/d/a^2*ln(-1+cos(d*x+c))+1/4/d/a^2/(1+cos(d*x+c))^2-3/4/d/a^2/(1+cos(d*x+c))-1/8*ln(1+cos(d*x+c))/a^2/d","A"
81,1,57,42,0.723000," ","int(csc(d*x+c)^3/(a+a*sec(d*x+c))^2,x)","\frac{\frac{1}{-16+16 \cos \left(d x +c \right)}+\frac{1}{12 \left(1+\cos \left(d x +c \right)\right)^{3}}-\frac{1}{8 \left(1+\cos \left(d x +c \right)\right)^{2}}-\frac{1}{16 \left(1+\cos \left(d x +c \right)\right)}}{d \,a^{2}}"," ",0,"1/d/a^2*(1/16/(-1+cos(d*x+c))+1/12/(1+cos(d*x+c))^3-1/8/(1+cos(d*x+c))^2-1/16/(1+cos(d*x+c)))","A"
82,1,144,132,0.697000," ","int(csc(d*x+c)^5/(a+a*sec(d*x+c))^2,x)","-\frac{1}{64 d \,a^{2} \left(-1+\cos \left(d x +c \right)\right)^{2}}+\frac{1}{64 d \,a^{2} \left(-1+\cos \left(d x +c \right)\right)}-\frac{\ln \left(-1+\cos \left(d x +c \right)\right)}{128 d \,a^{2}}+\frac{1}{32 d \,a^{2} \left(1+\cos \left(d x +c \right)\right)^{4}}-\frac{1}{48 d \,a^{2} \left(1+\cos \left(d x +c \right)\right)^{3}}-\frac{1}{32 d \,a^{2} \left(1+\cos \left(d x +c \right)\right)^{2}}-\frac{1}{32 d \,a^{2} \left(1+\cos \left(d x +c \right)\right)}+\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{128 a^{2} d}"," ",0,"-1/64/d/a^2/(-1+cos(d*x+c))^2+1/64/d/a^2/(-1+cos(d*x+c))-1/128/d/a^2*ln(-1+cos(d*x+c))+1/32/d/a^2/(1+cos(d*x+c))^4-1/48/d/a^2/(1+cos(d*x+c))^3-1/32/d/a^2/(1+cos(d*x+c))^2-1/32/d/a^2/(1+cos(d*x+c))+1/128*ln(1+cos(d*x+c))/a^2/d","A"
83,1,290,151,0.660000," ","int(sin(d*x+c)^8/(a+a*sec(d*x+c))^2,x)","-\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{253 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{4213 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{960 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{55583 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6720 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{31007 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6720 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{20363 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{960 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{253 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{11 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{11 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{2}}"," ",0,"-11/64/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)-253/192/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^3-4213/960/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^5-55583/6720/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^7+31007/6720/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^9-20363/960/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^11+253/192/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^13+11/64/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^15+11/64/d/a^2*arctan(tan(1/2*d*x+1/2*c))","A"
84,1,222,94,0.634000," ","int(sin(d*x+c)^6/(a+a*sec(d*x+c))^2,x)","\frac{3 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{205 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{29 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{99 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{17 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}"," ",0,"3/8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11-205/24/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9-29/20/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7-99/20/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5-17/8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3-3/8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)+3/8/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
85,1,154,79,0.671000," ","int(sin(d*x+c)^4/(a+a*sec(d*x+c))^2,x)","-\frac{25 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{83 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{12 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{77 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{12 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{7 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2}}"," ",0,"-25/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-83/12/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-77/12/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-7/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+7/4/d/a^2*arctan(tan(1/2*d*x+1/2*c))","A"
86,1,103,65,0.626000," ","int(sin(d*x+c)^2/(a+a*sec(d*x+c))^2,x)","\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2}}+\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"2/d/a^2*tan(1/2*d*x+1/2*c)+5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-5/d/a^2*arctan(tan(1/2*d*x+1/2*c))","A"
87,1,60,65,0.624000," ","int(csc(d*x+c)^2/(a+a*sec(d*x+c))^2,x)","\frac{\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{1}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{8 d \,a^{2}}"," ",0,"1/8/d/a^2*(1/5*tan(1/2*d*x+1/2*c)^5-1/3*tan(1/2*d*x+1/2*c)^3-tan(1/2*d*x+1/2*c)-1/tan(1/2*d*x+1/2*c))","A"
88,1,86,81,0.800000," ","int(csc(d*x+c)^4/(a+a*sec(d*x+c))^2,x)","\frac{\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{1}{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{1}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{32 d \,a^{2}}"," ",0,"1/32/d/a^2*(1/7*tan(1/2*d*x+1/2*c)^7+1/5*tan(1/2*d*x+1/2*c)^5-2/3*tan(1/2*d*x+1/2*c)^3-2*tan(1/2*d*x+1/2*c)-1/3/tan(1/2*d*x+1/2*c)^3-1/tan(1/2*d*x+1/2*c))","A"
89,1,112,97,0.719000," ","int(csc(d*x+c)^6/(a+a*sec(d*x+c))^2,x)","\frac{\frac{\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9}+\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{1}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{1}{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{1}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{128 d \,a^{2}}"," ",0,"1/128/d/a^2*(1/9*tan(1/2*d*x+1/2*c)^9+3/7*tan(1/2*d*x+1/2*c)^7+1/5*tan(1/2*d*x+1/2*c)^5-5/3*tan(1/2*d*x+1/2*c)^3-5*tan(1/2*d*x+1/2*c)-1/tan(1/2*d*x+1/2*c)^3-1/5/tan(1/2*d*x+1/2*c)^5-1/tan(1/2*d*x+1/2*c))","A"
90,1,112,113,0.840000," ","int(csc(d*x+c)^8/(a+a*sec(d*x+c))^2,x)","\frac{\frac{\left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{11}+\frac{5 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9}+\frac{8 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}-\frac{14 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-14 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{1}{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}-\frac{8}{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{1}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}}{512 d \,a^{2}}"," ",0,"1/512/d/a^2*(1/11*tan(1/2*d*x+1/2*c)^11+5/9*tan(1/2*d*x+1/2*c)^9+8/7*tan(1/2*d*x+1/2*c)^7-14/3*tan(1/2*d*x+1/2*c)^3-14*tan(1/2*d*x+1/2*c)-1/7/tan(1/2*d*x+1/2*c)^7-8/3/tan(1/2*d*x+1/2*c)^3-1/tan(1/2*d*x+1/2*c)^5)","A"
91,1,90,127,0.890000," ","int(sin(d*x+c)^11/(a+a*sec(d*x+c))^3,x)","-\frac{\frac{1}{6 \sec \left(d x +c \right)^{6}}+\frac{3}{10 \sec \left(d x +c \right)^{10}}-\frac{1}{11 \sec \left(d x +c \right)^{11}}+\frac{5}{7 \sec \left(d x +c \right)^{7}}-\frac{1}{9 \sec \left(d x +c \right)^{9}}+\frac{1}{4 \sec \left(d x +c \right)^{4}}-\frac{5}{8 \sec \left(d x +c \right)^{8}}-\frac{3}{5 \sec \left(d x +c \right)^{5}}}{d \,a^{3}}"," ",0,"-1/d/a^3*(1/6/sec(d*x+c)^6+3/10/sec(d*x+c)^10-1/11/sec(d*x+c)^11+5/7/sec(d*x+c)^7-1/9/sec(d*x+c)^9+1/4/sec(d*x+c)^4-5/8/sec(d*x+c)^8-3/5/sec(d*x+c)^5)","A"
92,1,69,97,0.721000," ","int(sin(d*x+c)^9/(a+a*sec(d*x+c))^3,x)","\frac{-\frac{1}{3 \sec \left(d x +c \right)^{6}}-\frac{2}{7 \sec \left(d x +c \right)^{7}}-\frac{1}{9 \sec \left(d x +c \right)^{9}}-\frac{1}{4 \sec \left(d x +c \right)^{4}}+\frac{3}{8 \sec \left(d x +c \right)^{8}}+\frac{3}{5 \sec \left(d x +c \right)^{5}}}{d \,a^{3}}"," ",0,"1/d/a^3*(-1/3/sec(d*x+c)^6-2/7/sec(d*x+c)^7-1/9/sec(d*x+c)^9-1/4/sec(d*x+c)^4+3/8/sec(d*x+c)^8+3/5/sec(d*x+c)^5)","A"
93,1,50,65,0.639000," ","int(sin(d*x+c)^7/(a+a*sec(d*x+c))^3,x)","-\frac{\frac{1}{2 \sec \left(d x +c \right)^{6}}-\frac{1}{7 \sec \left(d x +c \right)^{7}}+\frac{1}{4 \sec \left(d x +c \right)^{4}}-\frac{3}{5 \sec \left(d x +c \right)^{5}}}{d \,a^{3}}"," ",0,"-1/d/a^3*(1/2/sec(d*x+c)^6-1/7/sec(d*x+c)^7+1/4/sec(d*x+c)^4-3/5/sec(d*x+c)^5)","A"
94,1,114,96,0.716000," ","int(sin(d*x+c)^5/(a+a*sec(d*x+c))^3,x)","-\frac{1}{5 d \,a^{3} \sec \left(d x +c \right)^{5}}+\frac{3}{4 d \,a^{3} \sec \left(d x +c \right)^{4}}-\frac{4}{3 d \,a^{3} \sec \left(d x +c \right)^{3}}+\frac{2}{d \,a^{3} \sec \left(d x +c \right)^{2}}-\frac{4}{d \,a^{3} \sec \left(d x +c \right)}-\frac{4 \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,"-1/5/d/a^3/sec(d*x+c)^5+3/4/d/a^3/sec(d*x+c)^4-4/3/d/a^3/sec(d*x+c)^3+2/d/a^3/sec(d*x+c)^2-4/d/a^3/sec(d*x+c)-4/d/a^3*ln(sec(d*x+c))+4/d/a^3*ln(1+sec(d*x+c))","A"
95,1,100,85,0.726000," ","int(sin(d*x+c)^3/(a+a*sec(d*x+c))^3,x)","\frac{1}{3 d \,a^{3} \sec \left(d x +c \right)^{3}}-\frac{3}{2 d \,a^{3} \sec \left(d x +c \right)^{2}}+\frac{5}{d \,a^{3} \sec \left(d x +c \right)}+\frac{7 \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{7 \ln \left(1+\sec \left(d x +c \right)\right)}{d \,a^{3}}"," ",0,"1/3/d/a^3/sec(d*x+c)^3-3/2/d/a^3/sec(d*x+c)^2+5/d/a^3/sec(d*x+c)+7/d/a^3*ln(sec(d*x+c))+2/d/a^3/(1+sec(d*x+c))-7/d/a^3*ln(1+sec(d*x+c))","A"
96,1,86,73,0.258000," ","int(sin(d*x+c)/(a+a*sec(d*x+c))^3,x)","-\frac{1}{d \,a^{3} \sec \left(d x +c \right)}-\frac{3 \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{2}{d \,a^{3} \left(1+\sec \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\sec \left(d x +c \right)\right)}{d \,a^{3}}"," ",0,"-1/d/a^3/sec(d*x+c)-3/d/a^3*ln(sec(d*x+c))-1/2/a^3/d/(1+sec(d*x+c))^2-2/d/a^3/(1+sec(d*x+c))+3/d/a^3*ln(1+sec(d*x+c))","A"
97,1,90,74,0.687000," ","int(csc(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{5}{8 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)^{2}}-\frac{7}{8 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)}-\frac{\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+5/8/d/a^3/(1+cos(d*x+c))^2-7/8/d/a^3/(1+cos(d*x+c))-1/16*ln(1+cos(d*x+c))/a^3/d","A"
98,1,126,114,0.865000," ","int(csc(d*x+c)^3/(a+a*sec(d*x+c))^3,x)","\frac{1}{32 d \,a^{3} \left(-1+\cos \left(d x +c \right)\right)}-\frac{\ln \left(-1+\cos \left(d x +c \right)\right)}{64 d \,a^{3}}-\frac{1}{16 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)^{4}}+\frac{1}{6 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)^{3}}-\frac{3}{32 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)^{2}}-\frac{1}{16 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)}+\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{64 a^{3} d}"," ",0,"1/32/d/a^3/(-1+cos(d*x+c))-1/64/d/a^3*ln(-1+cos(d*x+c))-1/16/d/a^3/(1+cos(d*x+c))^4+1/6/d/a^3/(1+cos(d*x+c))^3-3/32/d/a^3/(1+cos(d*x+c))^2-1/16/d/a^3/(1+cos(d*x+c))+1/64*ln(1+cos(d*x+c))/a^3/d","A"
99,1,126,116,0.801000," ","int(csc(d*x+c)^5/(a+a*sec(d*x+c))^3,x)","-\frac{1}{128 d \,a^{3} \left(-1+\cos \left(d x +c \right)\right)^{2}}-\frac{3 \ln \left(-1+\cos \left(d x +c \right)\right)}{256 d \,a^{3}}-\frac{1}{40 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)^{5}}+\frac{3}{64 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)^{4}}-\frac{1}{64 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)^{2}}-\frac{3}{128 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\cos \left(d x +c \right)\right)}{256 a^{3} d}"," ",0,"-1/128/d/a^3/(-1+cos(d*x+c))^2-3/256/d/a^3*ln(-1+cos(d*x+c))-1/40/d/a^3/(1+cos(d*x+c))^5+3/64/d/a^3/(1+cos(d*x+c))^4-1/64/d/a^3/(1+cos(d*x+c))^2-3/128/d/a^3/(1+cos(d*x+c))+3/256*ln(1+cos(d*x+c))/a^3/d","A"
100,1,290,141,0.678000," ","int(sin(d*x+c)^8/(a+a*sec(d*x+c))^3,x)","\frac{29 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{667 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{11107 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{960 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{146537 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6720 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{72669 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2240 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{1759 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{320 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{1143 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{29 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{29 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{3}}"," ",0,"29/64/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)+667/192/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^3+11107/960/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^5+146537/6720/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^7+72669/2240/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^9+1759/320/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^11+1143/64/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^13-29/64/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^15-29/64/d/a^3*arctan(tan(1/2*d*x+1/2*c))","B"
101,1,222,117,0.733000," ","int(sin(d*x+c)^6/(a+a*sec(d*x+c))^3,x)","\frac{105 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{211 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{969 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{759 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{391 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{23 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{23 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3}}"," ",0,"105/8/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11+211/8/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9+969/20/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7+759/20/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5+391/24/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3+23/8/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)-23/8/d/a^3*arctan(tan(1/2*d*x+1/2*c))","A"
102,1,171,102,0.753000," ","int(sin(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{77 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{149 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{123 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{35 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{51 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3}}"," ",0,"-4/d/a^3*tan(1/2*d*x+1/2*c)-77/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-149/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-123/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-35/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+51/4/d/a^3*arctan(tan(1/2*d*x+1/2*c))","A"
103,1,122,89,0.565000," ","int(sin(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{6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3}}+\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{11 \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+6/d/a^3*tan(1/2*d*x+1/2*c)+7/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+5/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-11/d/a^3*arctan(tan(1/2*d*x+1/2*c))","A"
104,1,60,81,0.726000," ","int(csc(d*x+c)^2/(a+a*sec(d*x+c))^3,x)","\frac{-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{1}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{16 d \,a^{3}}"," ",0,"1/16/d/a^3*(-1/7*tan(1/2*d*x+1/2*c)^7+2/5*tan(1/2*d*x+1/2*c)^5-2*tan(1/2*d*x+1/2*c)-1/tan(1/2*d*x+1/2*c))","A"
105,1,60,95,0.806000," ","int(csc(d*x+c)^4/(a+a*sec(d*x+c))^3,x)","\frac{-\frac{\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{1}{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}}{64 d \,a^{3}}"," ",0,"1/64/d/a^3*(-1/9*tan(1/2*d*x+1/2*c)^9+3/5*tan(1/2*d*x+1/2*c)^5-3*tan(1/2*d*x+1/2*c)-1/3/tan(1/2*d*x+1/2*c)^3)","A"
106,1,112,113,0.796000," ","int(csc(d*x+c)^6/(a+a*sec(d*x+c))^3,x)","\frac{-\frac{\left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{11}-\frac{2 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9}+\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{6 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{2}{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{1}{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{256 d \,a^{3}}"," ",0,"1/256/d/a^3*(-1/11*tan(1/2*d*x+1/2*c)^11-2/9*tan(1/2*d*x+1/2*c)^9+2/7*tan(1/2*d*x+1/2*c)^7+6/5*tan(1/2*d*x+1/2*c)^5-6*tan(1/2*d*x+1/2*c)-2/3/tan(1/2*d*x+1/2*c)^3-1/5/tan(1/2*d*x+1/2*c)^5+2/tan(1/2*d*x+1/2*c))","A"
107,1,138,129,0.821000," ","int(csc(d*x+c)^8/(a+a*sec(d*x+c))^3,x)","\frac{-\frac{\left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{13}-\frac{4 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{11}-\frac{\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\frac{8 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{14 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-14 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{1}{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}-\frac{1}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{4}{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{8}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{1024 d \,a^{3}}"," ",0,"1/1024/d/a^3*(-1/13*tan(1/2*d*x+1/2*c)^13-4/11*tan(1/2*d*x+1/2*c)^11-1/3*tan(1/2*d*x+1/2*c)^9+8/7*tan(1/2*d*x+1/2*c)^7+14/5*tan(1/2*d*x+1/2*c)^5-14*tan(1/2*d*x+1/2*c)-1/7/tan(1/2*d*x+1/2*c)^7-1/tan(1/2*d*x+1/2*c)^3-4/5/tan(1/2*d*x+1/2*c)^5+8/tan(1/2*d*x+1/2*c))","A"
108,1,290,161,3.714000," ","int((a+a*sec(d*x+c))*(e*sin(d*x+c))^(5/2),x)","-\frac{2 a e \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}-\frac{a \,e^{\frac{5}{2}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)}{d}+\frac{a \,e^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)}{d}+\frac{2 a \,e^{3} \left(\sin^{4}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{6 a \,e^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{5 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{3 a \,e^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{5 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{2 a \,e^{3} \left(\sin^{2}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}"," ",0,"-2/3*a*e*(e*sin(d*x+c))^(3/2)/d-a*e^(5/2)*arctan((e*sin(d*x+c))^(1/2)/e^(1/2))/d+a*e^(5/2)*arctanh((e*sin(d*x+c))^(1/2)/e^(1/2))/d+2/5/d*a*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*sin(d*x+c)^4-6/5/d*a*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/5/d*a*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2/5/d*a*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*sin(d*x+c)^2","A"
109,1,210,160,3.633000," ","int((a+a*sec(d*x+c))*(e*sin(d*x+c))^(3/2),x)","\frac{a \,e^{\frac{3}{2}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)}{d}+\frac{a \,e^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)}{d}-\frac{2 a e \sqrt{e \sin \left(d x +c \right)}}{d}-\frac{a \,e^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{3 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{2 a \,e^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{2 a \,e^{2} \sin \left(d x +c \right)}{3 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}"," ",0,"a*e^(3/2)*arctan((e*sin(d*x+c))^(1/2)/e^(1/2))/d+a*e^(3/2)*arctanh((e*sin(d*x+c))^(1/2)/e^(1/2))/d-2*a*e*(e*sin(d*x+c))^(1/2)/d-1/3/d*a*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+2/3/d*a*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*sin(d*x+c)^3-2/3/d*a*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*sin(d*x+c)","A"
110,1,198,118,3.640000," ","int((a+a*sec(d*x+c))*(e*sin(d*x+c))^(1/2),x)","-\frac{a \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right) \sqrt{e}}{d}+\frac{a \arctanh \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right) \sqrt{e}}{d}-\frac{2 a e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{a e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}"," ",0,"-a*arctan((e*sin(d*x+c))^(1/2)/e^(1/2))*e^(1/2)/d+a*arctanh((e*sin(d*x+c))^(1/2)/e^(1/2))*e^(1/2)/d-2/d*a*e*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/d*a*e*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))","A"
111,1,122,117,2.544000," ","int((a+a*sec(d*x+c))/(e*sin(d*x+c))^(1/2),x)","\frac{a \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)}{d \sqrt{e}}+\frac{a \arctanh \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)}{d \sqrt{e}}-\frac{a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}"," ",0,"a*arctan((e*sin(d*x+c))^(1/2)/e^(1/2))/d/e^(1/2)+a*arctanh((e*sin(d*x+c))^(1/2)/e^(1/2))/d/e^(1/2)-1/d*a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)","A"
112,1,247,165,3.246000," ","int((a+a*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x)","-\frac{a \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)}{d \,e^{\frac{3}{2}}}+\frac{a \arctanh \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)}{d \,e^{\frac{3}{2}}}-\frac{2 a}{d e \sqrt{e \sin \left(d x +c \right)}}+\frac{2 a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{2 a \cos \left(d x +c \right)}{d e \sqrt{e \sin \left(d x +c \right)}}"," ",0,"-a*arctan((e*sin(d*x+c))^(1/2)/e^(1/2))/d/e^(3/2)+a*arctanh((e*sin(d*x+c))^(1/2)/e^(1/2))/d/e^(3/2)-2*a/d/e/(e*sin(d*x+c))^(1/2)+2/d*a/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/d*a/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2*a*cos(d*x+c)/d/e/(e*sin(d*x+c))^(1/2)","A"
113,1,212,164,3.474000," ","int((a+a*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x)","\frac{a \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)}{d \,e^{\frac{5}{2}}}+\frac{a \arctanh \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)}{d \,e^{\frac{5}{2}}}-\frac{2 a}{3 d e \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{a \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{3 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{2 a \sin \left(d x +c \right)}{3 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{2 a}{3 d \,e^{2} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}"," ",0,"a*arctan((e*sin(d*x+c))^(1/2)/e^(1/2))/d/e^(5/2)+a*arctanh((e*sin(d*x+c))^(1/2)/e^(1/2))/d/e^(5/2)-2/3*a/d/e/(e*sin(d*x+c))^(3/2)-1/3/d*a/e^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+2/3/d*a/e^2*sin(d*x+c)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)-2/3/d*a/e^2/sin(d*x+c)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)","A"
114,1,265,196,6.135000," ","int((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^(5/2),x)","-\frac{a^{2} \left(60 \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right) \sqrt{e \sin \left(d x +c \right)}\, e^{\frac{5}{2}} \cos \left(d x +c \right)-60 \sqrt{e \sin \left(d x +c \right)}\, \arctanh \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right) e^{\frac{5}{2}} \cos \left(d x +c \right)-54 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) e^{3}+27 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) e^{3}-12 e^{3} \left(\cos^{4}\left(d x +c \right)\right)-40 e^{3} \left(\cos^{3}\left(d x +c \right)\right)+42 e^{3} \left(\cos^{2}\left(d x +c \right)\right)+40 e^{3} \cos \left(d x +c \right)-30 e^{3}\right)}{30 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"-1/30/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2*(60*arctan((e*sin(d*x+c))^(1/2)/e^(1/2))*(e*sin(d*x+c))^(1/2)*e^(5/2)*cos(d*x+c)-60*(e*sin(d*x+c))^(1/2)*arctanh((e*sin(d*x+c))^(1/2)/e^(1/2))*e^(5/2)*cos(d*x+c)-54*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*e^3+27*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*e^3-12*e^3*cos(d*x+c)^4-40*e^3*cos(d*x+c)^3+42*e^3*cos(d*x+c)^2+40*e^3*cos(d*x+c)-30*e^3)/d","A"
115,1,201,196,5.495000," ","int((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^(3/2),x)","\frac{a^{2} \left(12 \cos \left(d x +c \right) e^{\frac{3}{2}} \sqrt{e \sin \left(d x +c \right)}\, \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)+12 \cos \left(d x +c \right) e^{\frac{3}{2}} \sqrt{e \sin \left(d x +c \right)}\, \arctanh \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)+\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) e^{2}-4 e^{2} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-24 e^{2} \sin \left(d x +c \right) \cos \left(d x +c \right)+6 e^{2} \sin \left(d x +c \right)\right)}{6 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"1/6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2*(12*cos(d*x+c)*e^(3/2)*(e*sin(d*x+c))^(1/2)*arctan((e*sin(d*x+c))^(1/2)/e^(1/2))+12*cos(d*x+c)*e^(3/2)*(e*sin(d*x+c))^(1/2)*arctanh((e*sin(d*x+c))^(1/2)/e^(1/2))+(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*e^2-4*e^2*sin(d*x+c)*cos(d*x+c)^2-24*e^2*sin(d*x+c)*cos(d*x+c)+6*e^2*sin(d*x+c))/d","A"
116,1,220,151,6.158000," ","int((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^(1/2),x)","-\frac{a^{2} \left(2 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) e -\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) e +4 \cos \left(d x +c \right) \sqrt{e}\, \sqrt{e \sin \left(d x +c \right)}\, \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)-4 \cos \left(d x +c \right) \sqrt{e}\, \sqrt{e \sin \left(d x +c \right)}\, \arctanh \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)+2 e \left(\cos^{2}\left(d x +c \right)\right)-2 e \right)}{2 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"-1/2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2*(2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*e-(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*e+4*cos(d*x+c)*e^(1/2)*(e*sin(d*x+c))^(1/2)*arctan((e*sin(d*x+c))^(1/2)/e^(1/2))-4*cos(d*x+c)*e^(1/2)*(e*sin(d*x+c))^(1/2)*arctanh((e*sin(d*x+c))^(1/2)/e^(1/2))+2*e*cos(d*x+c)^2-2*e)/d","A"
117,1,163,151,5.248000," ","int((a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(1/2),x)","\frac{a^{2} \left(-3 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{e}+4 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \arctanh \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)+4 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right)+2 \sqrt{e}\, \sin \left(d x +c \right)\right)}{2 \sqrt{e}\, \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"1/2/e^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2*(-3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*e^(1/2)+4*cos(d*x+c)*(e*sin(d*x+c))^(1/2)*arctanh((e*sin(d*x+c))^(1/2)/e^(1/2))+4*cos(d*x+c)*(e*sin(d*x+c))^(1/2)*arctan((e*sin(d*x+c))^(1/2)/e^(1/2))+2*e^(1/2)*sin(d*x+c))/d","A"
118,1,238,230,5.682000," ","int((a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x)","-\frac{a^{2} \left(-10 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) e^{\frac{3}{2}}+5 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) e^{\frac{3}{2}}+10 e^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)+4 \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right) \sqrt{e \sin \left(d x +c \right)}\, e \cos \left(d x +c \right)-4 \sqrt{e \sin \left(d x +c \right)}\, \arctanh \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right) e \cos \left(d x +c \right)+8 e^{\frac{3}{2}} \cos \left(d x +c \right)-2 e^{\frac{3}{2}}\right)}{2 e^{\frac{5}{2}} \sqrt{e \sin \left(d x +c \right)}\, \cos \left(d x +c \right) d}"," ",0,"-1/2/e^(5/2)/(e*sin(d*x+c))^(1/2)/cos(d*x+c)*a^2*(-10*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*e^(3/2)+5*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*e^(3/2)+10*e^(3/2)*cos(d*x+c)^2+4*arctan((e*sin(d*x+c))^(1/2)/e^(1/2))*(e*sin(d*x+c))^(1/2)*e*cos(d*x+c)-4*(e*sin(d*x+c))^(1/2)*arctanh((e*sin(d*x+c))^(1/2)/e^(1/2))*e*cos(d*x+c)+8*e^(3/2)*cos(d*x+c)-2*e^(3/2))/d","A"
119,1,301,230,6.248000," ","int((a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x)","\frac{a^{2} \left(7 \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) e^{\frac{7}{2}}-14 e^{\frac{7}{2}} \left(\cos^{4}\left(d x +c \right)\right)-8 e^{\frac{7}{2}} \left(\cos^{3}\left(d x +c \right)\right)+12 \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right) \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}} e^{2} \left(\cos^{3}\left(d x +c \right)\right)+12 \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right) e^{2} \left(\cos^{3}\left(d x +c \right)\right)+20 e^{\frac{7}{2}} \left(\cos^{2}\left(d x +c \right)\right)+8 e^{\frac{7}{2}} \cos \left(d x +c \right)-12 \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right) \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}} e^{2} \cos \left(d x +c \right)-12 \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\sqrt{e}}\right) e^{2} \cos \left(d x +c \right)-6 e^{\frac{7}{2}}\right)}{6 e^{\frac{9}{2}} \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}} \cos \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)-1\right) d}"," ",0,"1/6/e^(9/2)/(e*sin(d*x+c))^(3/2)/cos(d*x+c)/(cos(d*x+c)^2-1)*a^2*(7*sin(d*x+c)^(7/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*e^(7/2)-14*e^(7/2)*cos(d*x+c)^4-8*e^(7/2)*cos(d*x+c)^3+12*arctan((e*sin(d*x+c))^(1/2)/e^(1/2))*(e*sin(d*x+c))^(3/2)*e^2*cos(d*x+c)^3+12*(e*sin(d*x+c))^(3/2)*arctanh((e*sin(d*x+c))^(1/2)/e^(1/2))*e^2*cos(d*x+c)^3+20*e^(7/2)*cos(d*x+c)^2+8*e^(7/2)*cos(d*x+c)-12*arctan((e*sin(d*x+c))^(1/2)/e^(1/2))*(e*sin(d*x+c))^(3/2)*e^2*cos(d*x+c)-12*(e*sin(d*x+c))^(3/2)*arctanh((e*sin(d*x+c))^(1/2)/e^(1/2))*e^2*cos(d*x+c)-6*e^(7/2))/d","A"
120,1,128,151,3.276000," ","int((e*sin(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x)","\frac{\frac{2 e \left(e \sin \left(d x +c \right)\right)^{\frac{5}{2}}}{5 a}+\frac{2 e^{4} \left(3 \left(\sin^{5}\left(d x +c \right)\right)+\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-5 \left(\sin^{3}\left(d x +c \right)\right)+2 \sin \left(d x +c \right)\right)}{21 a \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(2/5*e/a*(e*sin(d*x+c))^(5/2)+2/21*e^4*(3*sin(d*x+c)^5+(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-5*sin(d*x+c)^3+2*sin(d*x+c))/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
121,1,173,120,3.488000," ","int((e*sin(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x)","\frac{2 e^{3} \left(6 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)+3 \left(\cos^{4}\left(d x +c \right)\right)-5 \left(\cos^{3}\left(d x +c \right)\right)-3 \left(\cos^{2}\left(d x +c \right)\right)+5 \cos \left(d x +c \right)\right)}{15 a \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"2/15/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*e^3*(6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3*cos(d*x+c)^4-5*cos(d*x+c)^3-3*cos(d*x+c)^2+5*cos(d*x+c))/d","A"
122,1,112,120,3.281000," ","int((e*sin(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x)","\frac{2 e^{2} \left(\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{3 a \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"2/3/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*e^2*((-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-cos(d*x+c)^2*sin(d*x+c)+3*cos(d*x+c)*sin(d*x+c))/d","A"
123,1,149,117,3.894000," ","int((e*sin(d*x+c))^(1/2)/(a+a*sec(d*x+c)),x)","-\frac{2 e \left(2 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right)\right)}{a \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"-2/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*e*(2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-cos(d*x+c)^2+cos(d*x+c))/d","A"
124,1,121,117,3.339000," ","int(1/(a+a*sec(d*x+c))/(e*sin(d*x+c))^(1/2),x)","\frac{-\frac{2 e}{3 a \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{2 \left(\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{5}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)+\sin^{3}\left(d x +c \right)-\sin \left(d x +c \right)\right)}{3 a \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(-2/3/a*e/(e*sin(d*x+c))^(3/2)-2/3*((-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+sin(d*x+c)^3-sin(d*x+c))/a/sin(d*x+c)^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
125,1,187,147,3.703000," ","int(1/(a+a*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x)","\frac{-\frac{2 e}{5 a \left(e \sin \left(d x +c \right)\right)^{\frac{5}{2}}}+\frac{\frac{4 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{2 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{5}+\frac{4 \left(\sin^{5}\left(d x +c \right)\right)}{5}-\frac{6 \left(\sin^{3}\left(d x +c \right)\right)}{5}+\frac{2 \sin \left(d x +c \right)}{5}}{e a \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(-2/5/a*e/(e*sin(d*x+c))^(5/2)+2/5/e*(2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+2*sin(d*x+c)^5-3*sin(d*x+c)^3+sin(d*x+c))/a/sin(d*x+c)^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
126,1,136,147,3.284000," ","int(1/(a+a*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x)","\frac{-\frac{2 e}{7 a \left(e \sin \left(d x +c \right)\right)^{\frac{7}{2}}}-\frac{2 \left(\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{9}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-2 \left(\sin^{5}\left(d x +c \right)\right)+5 \left(\sin^{3}\left(d x +c \right)\right)-3 \sin \left(d x +c \right)\right)}{21 e^{2} a \sin \left(d x +c \right)^{4} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(-2/7/a*e/(e*sin(d*x+c))^(7/2)-2/21/e^2*((-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(9/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2*sin(d*x+c)^5+5*sin(d*x+c)^3-3*sin(d*x+c))/a/sin(d*x+c)^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
127,1,145,172,4.121000," ","int((e*sin(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x)","-\frac{2 e^{4} \left(-15 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+65 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)+42 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-65 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+168 \cos \left(d x +c \right) \sin \left(d x +c \right)\right)}{105 a^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"-2/105/a^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*e^4*(-15*sin(d*x+c)*cos(d*x+c)^4+65*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+42*cos(d*x+c)^3*sin(d*x+c)-65*cos(d*x+c)^2*sin(d*x+c)+168*cos(d*x+c)*sin(d*x+c))/d","A"
128,1,173,197,4.034000," ","int((e*sin(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x)","-\frac{2 e^{3} \left(33 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-66 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{4}\left(d x +c \right)\right)+10 \left(\cos^{3}\left(d x +c \right)\right)+33 \left(\cos^{2}\left(d x +c \right)\right)-40 \cos \left(d x +c \right)\right)}{15 a^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"-2/15/a^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*e^3*(33*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-66*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3*cos(d*x+c)^4+10*cos(d*x+c)^3+33*cos(d*x+c)^2-40*cos(d*x+c))/d","A"
129,1,153,197,4.299000," ","int((e*sin(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x)","-\frac{2 e^{3} \left(3 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{6}\left(d x +c \right)\right)+6 \left(\cos^{5}\left(d x +c \right)\right)+4 \left(\cos^{4}\left(d x +c \right)\right)-14 \left(\cos^{3}\left(d x +c \right)\right)-3 \left(\cos^{2}\left(d x +c \right)\right)+8 \cos \left(d x +c \right)\right)}{3 a^{2} \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}} \cos \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)-1\right) d}"," ",0,"-2/3/a^2/(e*sin(d*x+c))^(3/2)/cos(d*x+c)/(cos(d*x+c)^2-1)*e^3*(3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-cos(d*x+c)^6+6*cos(d*x+c)^5+4*cos(d*x+c)^4-14*cos(d*x+c)^3-3*cos(d*x+c)^2+8*cos(d*x+c))/d","A"
130,1,205,194,4.831000," ","int((e*sin(d*x+c))^(1/2)/(a+a*sec(d*x+c))^2,x)","\frac{-\frac{2 e \left(-\frac{2 e^{2}}{5 \left(e \sin \left(d x +c \right)\right)^{\frac{5}{2}}}+\frac{2}{\sqrt{e \sin \left(d x +c \right)}}\right)}{a^{2}}-\frac{2 e \left(14 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-7 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)+9 \left(\sin^{5}\left(d x +c \right)\right)-11 \left(\sin^{3}\left(d x +c \right)\right)+2 \sin \left(d x +c \right)\right)}{5 a^{2} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(-2*e/a^2*(-2/5*e^2/(e*sin(d*x+c))^(5/2)+2/(e*sin(d*x+c))^(1/2))-2/5*e*(14*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-7*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+9*sin(d*x+c)^5-11*sin(d*x+c)^3+2*sin(d*x+c))/a^2/sin(d*x+c)^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
131,1,148,194,4.179000," ","int(1/(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(1/2),x)","\frac{\frac{4 e^{3} \left(7 \left(\cos^{2}\left(d x +c \right)\right)-4\right)}{21 a^{2} \left(e \sin \left(d x +c \right)\right)^{\frac{7}{2}}}-\frac{2 \left(5 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{9}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)+11 \left(\sin^{5}\left(d x +c \right)\right)-17 \left(\sin^{3}\left(d x +c \right)\right)+6 \sin \left(d x +c \right)\right)}{21 a^{2} \sin \left(d x +c \right)^{4} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(4/21/a^2*e^3/(e*sin(d*x+c))^(7/2)*(7*cos(d*x+c)^2-4)-2/21*(5*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(9/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+11*sin(d*x+c)^5-17*sin(d*x+c)^3+6*sin(d*x+c))/a^2/sin(d*x+c)^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
132,1,213,224,4.425000," ","int(1/(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x)","\frac{\frac{4 e^{3} \left(9 \left(\cos^{2}\left(d x +c \right)\right)-4\right)}{45 a^{2} \left(e \sin \left(d x +c \right)\right)^{\frac{9}{2}}}+\frac{\frac{4 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{11}{2}}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{15}-\frac{2 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{11}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{15}+\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{15}-\frac{38 \left(\sin^{5}\left(d x +c \right)\right)}{45}+\frac{46 \left(\sin^{3}\left(d x +c \right)\right)}{45}-\frac{4 \sin \left(d x +c \right)}{9}}{e \,a^{2} \sin \left(d x +c \right)^{5} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(4/45*e^3/a^2/(e*sin(d*x+c))^(9/2)*(9*cos(d*x+c)^2-4)+2/45/e*(6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(11/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(11/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+6*sin(d*x+c)^7-19*sin(d*x+c)^5+23*sin(d*x+c)^3-10*sin(d*x+c))/a^2/sin(d*x+c)^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
133,1,160,224,4.840000," ","int(1/(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x)","\frac{\frac{4 e^{3} \left(11 \left(\cos^{2}\left(d x +c \right)\right)-4\right)}{77 a^{2} \left(e \sin \left(d x +c \right)\right)^{\frac{11}{2}}}-\frac{2 \left(\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{13}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-2 \left(\sin^{7}\left(d x +c \right)\right)+47 \left(\sin^{5}\left(d x +c \right)\right)-87 \left(\sin^{3}\left(d x +c \right)\right)+42 \sin \left(d x +c \right)\right)}{231 e^{2} a^{2} \sin \left(d x +c \right)^{6} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(4/77*e^3/a^2/(e*sin(d*x+c))^(11/2)*(11*cos(d*x+c)^2-4)-2/231/e^2*((-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(13/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2*sin(d*x+c)^7+47*sin(d*x+c)^5-87*sin(d*x+c)^3+42*sin(d*x+c))/a^2/sin(d*x+c)^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
134,0,0,231,3.495000," ","int((a+a*sec(d*x+c))^3*(e*sin(d*x+c))^m,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{3} \left(e \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+a*sec(d*x+c))^3*(e*sin(d*x+c))^m,x)","F"
135,0,0,181,3.005000," ","int((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^m,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{2} \left(e \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^m,x)","F"
136,0,0,111,2.495000," ","int((a+a*sec(d*x+c))*(e*sin(d*x+c))^m,x)","\int \left(a +a \sec \left(d x +c \right)\right) \left(e \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+a*sec(d*x+c))*(e*sin(d*x+c))^m,x)","F"
137,0,0,94,2.110000," ","int((e*sin(d*x+c))^m/(a+a*sec(d*x+c)),x)","\int \frac{\left(e \sin \left(d x +c \right)\right)^{m}}{a +a \sec \left(d x +c \right)}\, dx"," ",0,"int((e*sin(d*x+c))^m/(a+a*sec(d*x+c)),x)","F"
138,0,0,195,1.463000," ","int((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^2,x)","\int \frac{\left(e \sin \left(d x +c \right)\right)^{m}}{\left(a +a \sec \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^2,x)","F"
139,0,0,224,1.341000," ","int((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^3,x)","\int \frac{\left(e \sin \left(d x +c \right)\right)^{m}}{\left(a +a \sec \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^3,x)","F"
140,0,0,88,1.171000," ","int((a+a*sec(d*x+c))^(3/2)*(e*sin(d*x+c))^m,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{\frac{3}{2}} \left(e \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+a*sec(d*x+c))^(3/2)*(e*sin(d*x+c))^m,x)","F"
141,0,0,91,1.238000," ","int((a+a*sec(d*x+c))^(1/2)*(e*sin(d*x+c))^m,x)","\int \sqrt{a +a \sec \left(d x +c \right)}\, \left(e \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+a*sec(d*x+c))^(1/2)*(e*sin(d*x+c))^m,x)","F"
142,0,0,93,1.163000," ","int((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^(1/2),x)","\int \frac{\left(e \sin \left(d x +c \right)\right)^{m}}{\sqrt{a +a \sec \left(d x +c \right)}}\, dx"," ",0,"int((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^(1/2),x)","F"
143,0,0,98,1.128000," ","int((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^(3/2),x)","\int \frac{\left(e \sin \left(d x +c \right)\right)^{m}}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^(3/2),x)","F"
144,0,0,114,2.791000," ","int((a+a*sec(d*x+c))^n*(e*sin(d*x+c))^m,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(e \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+a*sec(d*x+c))^n*(e*sin(d*x+c))^m,x)","F"
145,0,0,175,3.007000," ","int((a+a*sec(d*x+c))^n*sin(d*x+c)^7,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(\sin^{7}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*sin(d*x+c)^7,x)","F"
146,0,0,119,2.788000," ","int((a+a*sec(d*x+c))^n*sin(d*x+c)^5,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(\sin^{5}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*sin(d*x+c)^5,x)","F"
147,0,0,81,3.020000," ","int((a+a*sec(d*x+c))^n*sin(d*x+c)^3,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(\sin^{3}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*sin(d*x+c)^3,x)","F"
148,0,0,44,1.208000," ","int((a+a*sec(d*x+c))^n*sin(d*x+c),x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \sin \left(d x +c \right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*sin(d*x+c),x)","F"
149,0,0,38,1.307000," ","int(csc(d*x+c)*(a+a*sec(d*x+c))^n,x)","\int \csc \left(d x +c \right) \left(a +a \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)*(a+a*sec(d*x+c))^n,x)","F"
150,0,0,106,1.396000," ","int(csc(d*x+c)^3*(a+a*sec(d*x+c))^n,x)","\int \left(\csc^{3}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)^3*(a+a*sec(d*x+c))^n,x)","F"
151,0,0,234,1.300000," ","int(csc(d*x+c)^5*(a+a*sec(d*x+c))^n,x)","\int \left(\csc^{5}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)^5*(a+a*sec(d*x+c))^n,x)","F"
152,0,0,208,3.554000," ","int((a+a*sec(d*x+c))^n*sin(d*x+c)^4,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(\sin^{4}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*sin(d*x+c)^4,x)","F"
153,0,0,87,2.789000," ","int((a+a*sec(d*x+c))^n*sin(d*x+c)^2,x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(\sin^{2}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*sin(d*x+c)^2,x)","F"
154,0,0,86,1.321000," ","int(csc(d*x+c)^2*(a+a*sec(d*x+c))^n,x)","\int \left(\csc^{2}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)^2*(a+a*sec(d*x+c))^n,x)","F"
155,0,0,341,1.391000," ","int(csc(d*x+c)^4*(a+a*sec(d*x+c))^n,x)","\int \left(\csc^{4}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)^4*(a+a*sec(d*x+c))^n,x)","F"
156,0,0,95,0.820000," ","int((a+a*sec(d*x+c))^n*sin(d*x+c)^(3/2),x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(\sin^{\frac{3}{2}}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*sin(d*x+c)^(3/2),x)","F"
157,0,0,95,0.794000," ","int((a+a*sec(d*x+c))^n*sin(d*x+c)^(1/2),x)","\int \left(a +a \sec \left(d x +c \right)\right)^{n} \left(\sqrt{\sin}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^n*sin(d*x+c)^(1/2),x)","F"
158,0,0,95,0.843000," ","int((a+a*sec(d*x+c))^n/sin(d*x+c)^(1/2),x)","\int \frac{\left(a +a \sec \left(d x +c \right)\right)^{n}}{\sqrt{\sin \left(d x +c \right)}}\, dx"," ",0,"int((a+a*sec(d*x+c))^n/sin(d*x+c)^(1/2),x)","F"
159,0,0,95,0.808000," ","int((a+a*sec(d*x+c))^n/sin(d*x+c)^(3/2),x)","\int \frac{\left(a +a \sec \left(d x +c \right)\right)^{n}}{\sin \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+a*sec(d*x+c))^n/sin(d*x+c)^(3/2),x)","F"
160,1,129,109,0.632000," ","int((a+b*sec(d*x+c))*sin(d*x+c)^7,x)","-\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}-\frac{b \left(\sin^{6}\left(d x +c \right)\right)}{6 d}-\frac{b \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{b \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{b \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-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)^2-1/6/d*b*sin(d*x+c)^6-1/4/d*b*sin(d*x+c)^4-1/2/d*b*sin(d*x+c)^2-b*ln(cos(d*x+c))/d","A"
161,1,95,81,0.589000," ","int((a+b*sec(d*x+c))*sin(d*x+c)^5,x)","-\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}-\frac{b \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{b \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{b \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-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)^2-1/4/d*b*sin(d*x+c)^4-1/2/d*b*sin(d*x+c)^2-b*ln(cos(d*x+c))/d","A"
162,1,61,54,0.601000," ","int((a+b*sec(d*x+c))*sin(d*x+c)^3,x)","-\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}-\frac{b \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{b \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-1/3/d*a*cos(d*x+c)*sin(d*x+c)^2-2/3*a*cos(d*x+c)/d-1/2/d*b*sin(d*x+c)^2-b*ln(cos(d*x+c))/d","A"
163,1,28,26,0.192000," ","int((a+b*sec(d*x+c))*sin(d*x+c),x)","\frac{b \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a}{d \sec \left(d x +c \right)}"," ",0,"1/d*b*ln(sec(d*x+c))-1/d*a/sec(d*x+c)","A"
164,1,35,26,0.344000," ","int(csc(d*x+c)*(a+b*sec(d*x+c)),x)","\frac{b \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"b*ln(tan(d*x+c))/d+1/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
165,1,68,58,0.778000," ","int(csc(d*x+c)^3*(a+b*sec(d*x+c)),x)","-\frac{a \cot \left(d x +c \right) \csc \left(d x +c \right)}{2 d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{b}{2 d \sin \left(d x +c \right)^{2}}+\frac{b \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/2*a*cot(d*x+c)*csc(d*x+c)/d+1/2/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/2/d*b/sin(d*x+c)^2+b*ln(tan(d*x+c))/d","A"
166,1,102,92,0.730000," ","int(csc(d*x+c)^5*(a+b*sec(d*x+c)),x)","-\frac{a \cot \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a \cot \left(d x +c \right) \csc \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{b}{4 d \sin \left(d x +c \right)^{4}}-\frac{b}{2 d \sin \left(d x +c \right)^{2}}+\frac{b \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/4*a*cot(d*x+c)*csc(d*x+c)^3/d-3/8*a*cot(d*x+c)*csc(d*x+c)/d+3/8/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/4/d*b/sin(d*x+c)^4-1/2/d*b/sin(d*x+c)^2+b*ln(tan(d*x+c))/d","A"
167,1,136,126,0.749000," ","int(csc(d*x+c)^7*(a+b*sec(d*x+c)),x)","-\frac{a \cot \left(d x +c \right) \left(\csc^{5}\left(d x +c \right)\right)}{6 d}-\frac{5 a \cot \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right)}{24 d}-\frac{5 a \cot \left(d x +c \right) \csc \left(d x +c \right)}{16 d}+\frac{5 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{b}{6 d \sin \left(d x +c \right)^{6}}-\frac{b}{4 d \sin \left(d x +c \right)^{4}}-\frac{b}{2 d \sin \left(d x +c \right)^{2}}+\frac{b \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/6*a*cot(d*x+c)*csc(d*x+c)^5/d-5/24*a*cot(d*x+c)*csc(d*x+c)^3/d-5/16*a*cot(d*x+c)*csc(d*x+c)/d+5/16/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/6/d*b/sin(d*x+c)^6-1/4/d*b/sin(d*x+c)^4-1/2/d*b/sin(d*x+c)^2+b*ln(tan(d*x+c))/d","A"
168,1,130,115,0.651000," ","int((a+b*sec(d*x+c))*sin(d*x+c)^6,x)","-\frac{a \cos \left(d x +c \right) \left(\sin^{5}\left(d x +c \right)\right)}{6 d}-\frac{5 a \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{24 d}-\frac{5 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{16 d}+\frac{5 a x}{16}+\frac{5 c a}{16 d}-\frac{b \left(\sin^{5}\left(d x +c \right)\right)}{5 d}-\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{b \sin \left(d x +c \right)}{d}+\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/6*a*cos(d*x+c)*sin(d*x+c)^5/d-5/24*a*cos(d*x+c)*sin(d*x+c)^3/d-5/16*a*cos(d*x+c)*sin(d*x+c)/d+5/16*a*x+5/16/d*c*a-1/5*b*sin(d*x+c)^5/d-1/3*b*sin(d*x+c)^3/d-b*sin(d*x+c)/d+1/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
169,1,96,81,0.649000," ","int((a+b*sec(d*x+c))*sin(d*x+c)^4,x)","-\frac{a \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{3 a x}{8}+\frac{3 c a}{8 d}-\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{b \sin \left(d x +c \right)}{d}+\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/4*a*cos(d*x+c)*sin(d*x+c)^3/d-3/8*a*cos(d*x+c)*sin(d*x+c)/d+3/8*a*x+3/8/d*c*a-1/3*b*sin(d*x+c)^3/d-b*sin(d*x+c)/d+1/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
170,1,62,47,0.312000," ","int((a+b*sec(d*x+c))*sin(d*x+c)^2,x)","-\frac{a \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a x}{2}+\frac{c a}{2 d}-\frac{b \sin \left(d x +c \right)}{d}+\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/2*a*cos(d*x+c)*sin(d*x+c)/d+1/2*a*x+1/2/d*c*a-b*sin(d*x+c)/d+1/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
171,1,47,37,0.729000," ","int(csc(d*x+c)^2*(a+b*sec(d*x+c)),x)","-\frac{a \cot \left(d x +c \right)}{d}-\frac{b}{d \sin \left(d x +c \right)}+\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-a*cot(d*x+c)/d-1/d*b/sin(d*x+c)+1/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
172,1,81,65,0.863000," ","int(csc(d*x+c)^4*(a+b*sec(d*x+c)),x)","-\frac{2 a \cot \left(d x +c \right)}{3 d}-\frac{a \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}-\frac{b}{3 d \sin \left(d x +c \right)^{3}}-\frac{b}{d \sin \left(d x +c \right)}+\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-2/3*a*cot(d*x+c)/d-1/3/d*a*cot(d*x+c)*csc(d*x+c)^2-1/3/d*b/sin(d*x+c)^3-1/d*b/sin(d*x+c)+1/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
173,1,115,93,0.866000," ","int(csc(d*x+c)^6*(a+b*sec(d*x+c)),x)","-\frac{8 a \cot \left(d x +c \right)}{15 d}-\frac{a \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 a \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{15 d}-\frac{b}{5 d \sin \left(d x +c \right)^{5}}-\frac{b}{3 d \sin \left(d x +c \right)^{3}}-\frac{b}{d \sin \left(d x +c \right)}+\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-8/15*a*cot(d*x+c)/d-1/5/d*a*cot(d*x+c)*csc(d*x+c)^4-4/15/d*a*cot(d*x+c)*csc(d*x+c)^2-1/5/d*b/sin(d*x+c)^5-1/3/d*b/sin(d*x+c)^3-1/d*b/sin(d*x+c)+1/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
174,1,184,118,0.631000," ","int((a+b*sec(d*x+c))^2*sin(d*x+c)^5,x)","-\frac{8 a^{2} \cos \left(d x +c \right)}{15 d}-\frac{\cos \left(d x +c \right) a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 \cos \left(d x +c \right) a^{2} \left(\sin^{2}\left(d x +c \right)\right)}{15 d}-\frac{a b \left(\sin^{4}\left(d x +c \right)\right)}{2 d}-\frac{a b \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{2 a b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{8 b^{2} \cos \left(d x +c \right)}{3 d}+\frac{b^{2} \left(\sin^{4}\left(d x +c \right)\right) \cos \left(d x +c \right)}{d}+\frac{4 b^{2} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"-8/15*a^2*cos(d*x+c)/d-1/5/d*cos(d*x+c)*a^2*sin(d*x+c)^4-4/15/d*cos(d*x+c)*a^2*sin(d*x+c)^2-1/2/d*a*b*sin(d*x+c)^4-1/d*a*b*sin(d*x+c)^2-2*a*b*ln(cos(d*x+c))/d+1/d*b^2*sin(d*x+c)^6/cos(d*x+c)+8/3*b^2*cos(d*x+c)/d+1/d*b^2*sin(d*x+c)^4*cos(d*x+c)+4/3/d*b^2*cos(d*x+c)*sin(d*x+c)^2","A"
175,1,125,78,0.626000," ","int((a+b*sec(d*x+c))^2*sin(d*x+c)^3,x)","-\frac{\cos \left(d x +c \right) a^{2} \left(\sin^{2}\left(d x +c \right)\right)}{3 d}-\frac{2 a^{2} \cos \left(d x +c \right)}{3 d}-\frac{a b \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{2 a b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{b^{2} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{2 b^{2} \cos \left(d x +c \right)}{d}"," ",0,"-1/3/d*cos(d*x+c)*a^2*sin(d*x+c)^2-2/3*a^2*cos(d*x+c)/d-1/d*a*b*sin(d*x+c)^2-2*a*b*ln(cos(d*x+c))/d+1/d*b^2*sin(d*x+c)^4/cos(d*x+c)+1/d*b^2*cos(d*x+c)*sin(d*x+c)^2+2*b^2*cos(d*x+c)/d","A"
176,1,45,42,0.194000," ","int((a+b*sec(d*x+c))^2*sin(d*x+c),x)","\frac{b^{2} \sec \left(d x +c \right)}{d}+\frac{2 a b \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a^{2}}{d \sec \left(d x +c \right)}"," ",0,"b^2*sec(d*x+c)/d+2/d*a*b*ln(sec(d*x+c))-1/d*a^2/sec(d*x+c)","A"
177,1,77,70,0.381000," ","int(csc(d*x+c)*(a+b*sec(d*x+c))^2,x)","\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{2 a b \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{b^{2}}{d \cos \left(d x +c \right)}+\frac{b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"1/d*a^2*ln(csc(d*x+c)-cot(d*x+c))+2*a*b*ln(tan(d*x+c))/d+1/d*b^2/cos(d*x+c)+1/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","A"
178,1,139,108,0.743000," ","int(csc(d*x+c)^3*(a+b*sec(d*x+c))^2,x)","-\frac{a^{2} \cot \left(d x +c \right) \csc \left(d x +c \right)}{2 d}+\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{a b}{d \sin \left(d x +c \right)^{2}}+\frac{2 a b \ln \left(\tan \left(d x +c \right)\right)}{d}-\frac{b^{2}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{3 b^{2}}{2 d \cos \left(d x +c \right)}+\frac{3 b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/2*a^2*cot(d*x+c)*csc(d*x+c)/d+1/2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-1/d*a*b/sin(d*x+c)^2+2*a*b*ln(tan(d*x+c))/d-1/2/d*b^2/sin(d*x+c)^2/cos(d*x+c)+3/2/d*b^2/cos(d*x+c)+3/2/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","A"
179,1,246,163,0.699000," ","int((a+b*sec(d*x+c))^2*sin(d*x+c)^6,x)","-\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right) \cos \left(d x +c \right)}{6 d}-\frac{5 a^{2} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{24 d}-\frac{5 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{16 d}+\frac{5 a^{2} x}{16}+\frac{5 a^{2} c}{16 d}-\frac{2 a b \left(\sin^{5}\left(d x +c \right)\right)}{5 d}-\frac{2 a b \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a b \sin \left(d x +c \right)}{d}+\frac{2 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right) \cos \left(d x +c \right)}{d}+\frac{5 b^{2} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{4 d}+\frac{15 b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{15 b^{2} x}{8}-\frac{15 c \,b^{2}}{8 d}"," ",0,"-1/6/d*a^2*sin(d*x+c)^5*cos(d*x+c)-5/24/d*a^2*cos(d*x+c)*sin(d*x+c)^3-5/16*a^2*cos(d*x+c)*sin(d*x+c)/d+5/16*a^2*x+5/16/d*a^2*c-2/5*a*b*sin(d*x+c)^5/d-2/3*a*b*sin(d*x+c)^3/d-2*a*b*sin(d*x+c)/d+2/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^2*sin(d*x+c)^7/cos(d*x+c)+1/d*b^2*sin(d*x+c)^5*cos(d*x+c)+5/4/d*b^2*cos(d*x+c)*sin(d*x+c)^3+15/8/d*b^2*cos(d*x+c)*sin(d*x+c)-15/8*b^2*x-15/8/d*c*b^2","A"
180,1,187,168,0.638000," ","int((a+b*sec(d*x+c))^2*sin(d*x+c)^4,x)","-\frac{a^{2} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{3 a^{2} x}{8}+\frac{3 a^{2} c}{8 d}-\frac{2 a b \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a b \sin \left(d x +c \right)}{d}+\frac{2 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{b^{2} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{d}+\frac{3 b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{3 b^{2} x}{2}-\frac{3 c \,b^{2}}{2 d}"," ",0,"-1/4/d*a^2*cos(d*x+c)*sin(d*x+c)^3-3/8*a^2*cos(d*x+c)*sin(d*x+c)/d+3/8*a^2*x+3/8/d*a^2*c-2/3*a*b*sin(d*x+c)^3/d-2*a*b*sin(d*x+c)/d+2/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^2*sin(d*x+c)^5/cos(d*x+c)+1/d*b^2*cos(d*x+c)*sin(d*x+c)^3+3/2/d*b^2*cos(d*x+c)*sin(d*x+c)-3/2*b^2*x-3/2/d*c*b^2","A"
181,1,99,73,0.388000," ","int((a+b*sec(d*x+c))^2*sin(d*x+c)^2,x)","-\frac{a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a^{2} x}{2}+\frac{a^{2} c}{2 d}-\frac{2 a b \sin \left(d x +c \right)}{d}+\frac{2 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-b^{2} x +\frac{b^{2} \tan \left(d x +c \right)}{d}-\frac{c \,b^{2}}{d}"," ",0,"-1/2*a^2*cos(d*x+c)*sin(d*x+c)/d+1/2*a^2*x+1/2/d*a^2*c-2*a*b*sin(d*x+c)/d+2/d*a*b*ln(sec(d*x+c)+tan(d*x+c))-b^2*x+b^2*tan(d*x+c)/d-1/d*c*b^2","A"
182,1,89,59,0.648000," ","int(csc(d*x+c)^2*(a+b*sec(d*x+c))^2,x)","-\frac{a^{2} \cot \left(d x +c \right)}{d}-\frac{2 a b}{d \sin \left(d x +c \right)}+\frac{2 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{2}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{2 b^{2} \cot \left(d x +c \right)}{d}"," ",0,"-a^2*cot(d*x+c)/d-2/d*a*b/sin(d*x+c)+2/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^2/sin(d*x+c)/cos(d*x+c)-2/d*b^2*cot(d*x+c)","A"
183,1,151,96,0.921000," ","int(csc(d*x+c)^4*(a+b*sec(d*x+c))^2,x)","-\frac{2 a^{2} \cot \left(d x +c \right)}{3 d}-\frac{a^{2} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}-\frac{2 a b}{3 d \sin \left(d x +c \right)^{3}}-\frac{2 a b}{d \sin \left(d x +c \right)}+\frac{2 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{b^{2}}{3 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{4 b^{2}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{8 b^{2} \cot \left(d x +c \right)}{3 d}"," ",0,"-2/3*a^2*cot(d*x+c)/d-1/3/d*a^2*cot(d*x+c)*csc(d*x+c)^2-2/3/d*a*b/sin(d*x+c)^3-2/d*a*b/sin(d*x+c)+2/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)+4/3/d*b^2/sin(d*x+c)/cos(d*x+c)-8/3/d*b^2*cot(d*x+c)","A"
184,1,212,135,0.980000," ","int(csc(d*x+c)^6*(a+b*sec(d*x+c))^2,x)","-\frac{8 a^{2} \cot \left(d x +c \right)}{15 d}-\frac{a^{2} \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 a^{2} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{15 d}-\frac{2 a b}{5 d \sin \left(d x +c \right)^{5}}-\frac{2 a b}{3 d \sin \left(d x +c \right)^{3}}-\frac{2 a b}{d \sin \left(d x +c \right)}+\frac{2 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{b^{2}}{5 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}-\frac{2 b^{2}}{5 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{8 b^{2}}{5 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{16 b^{2} \cot \left(d x +c \right)}{5 d}"," ",0,"-8/15*a^2*cot(d*x+c)/d-1/5/d*a^2*cot(d*x+c)*csc(d*x+c)^4-4/15/d*a^2*cot(d*x+c)*csc(d*x+c)^2-2/5/d*a*b/sin(d*x+c)^5-2/3/d*a*b/sin(d*x+c)^3-2/d*a*b/sin(d*x+c)+2/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)-2/5/d*b^2/sin(d*x+c)^3/cos(d*x+c)+8/5/d*b^2/sin(d*x+c)/cos(d*x+c)-16/5/d*b^2*cot(d*x+c)","A"
185,1,266,160,0.657000," ","int((a+b*sec(d*x+c))^3*sin(d*x+c)^5,x)","-\frac{8 a^{3} \cos \left(d x +c \right)}{15 d}-\frac{a^{3} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 a^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}-\frac{3 a^{2} b \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{2} b \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 b^{2} a \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{8 a \,b^{2} \cos \left(d x +c \right)}{d}+\frac{3 b^{2} a \left(\sin^{4}\left(d x +c \right)\right) \cos \left(d x +c \right)}{d}+\frac{4 b^{2} a \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{b^{3} \left(\sin^{6}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{2 d}+\frac{\left(\sin^{2}\left(d x +c \right)\right) b^{3}}{d}+\frac{2 b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-8/15*a^3*cos(d*x+c)/d-1/5/d*a^3*cos(d*x+c)*sin(d*x+c)^4-4/15/d*a^3*cos(d*x+c)*sin(d*x+c)^2-3/4/d*a^2*b*sin(d*x+c)^4-3/2/d*a^2*b*sin(d*x+c)^2-3*a^2*b*ln(cos(d*x+c))/d+3/d*b^2*a*sin(d*x+c)^6/cos(d*x+c)+8*a*b^2*cos(d*x+c)/d+3/d*b^2*a*sin(d*x+c)^4*cos(d*x+c)+4/d*b^2*a*cos(d*x+c)*sin(d*x+c)^2+1/2/d*b^3*sin(d*x+c)^6/cos(d*x+c)^2+1/2/d*b^3*sin(d*x+c)^4+1/d*sin(d*x+c)^2*b^3+2*b^3*ln(cos(d*x+c))/d","A"
186,1,164,110,0.651000," ","int((a+b*sec(d*x+c))^3*sin(d*x+c)^3,x)","-\frac{a^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}-\frac{2 a^{3} \cos \left(d x +c \right)}{3 d}-\frac{3 a^{2} b \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 b^{2} a \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{3 b^{2} a \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{6 a \,b^{2} \cos \left(d x +c \right)}{d}+\frac{b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-1/3/d*a^3*cos(d*x+c)*sin(d*x+c)^2-2/3*a^3*cos(d*x+c)/d-3/2/d*a^2*b*sin(d*x+c)^2-3*a^2*b*ln(cos(d*x+c))/d+3/d*b^2*a*sin(d*x+c)^4/cos(d*x+c)+3/d*b^2*a*cos(d*x+c)*sin(d*x+c)^2+6*a*b^2*cos(d*x+c)/d+1/2*b^3*tan(d*x+c)^2/d+b^3*ln(cos(d*x+c))/d","A"
187,1,65,62,0.192000," ","int((a+b*sec(d*x+c))^3*sin(d*x+c),x)","\frac{b^{3} \left(\sec^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a \,b^{2} \sec \left(d x +c \right)}{d}+\frac{3 a^{2} b \ln \left(\sec \left(d x +c \right)\right)}{d}-\frac{a^{3}}{d \sec \left(d x +c \right)}"," ",0,"1/2*b^3*sec(d*x+c)^2/d+3*a*b^2*sec(d*x+c)/d+3/d*a^2*b*ln(sec(d*x+c))-1/d*a^3/sec(d*x+c)","A"
188,1,113,96,0.388000," ","int(csc(d*x+c)*(a+b*sec(d*x+c))^3,x)","\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{3 b^{2} a}{d \cos \left(d x +c \right)}+\frac{3 b^{2} a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{b^{3}}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/d*a^3*ln(csc(d*x+c)-cot(d*x+c))+3*a^2*b*ln(tan(d*x+c))/d+3/d*b^2*a/cos(d*x+c)+3/d*b^2*a*ln(csc(d*x+c)-cot(d*x+c))+1/2/d*b^3/cos(d*x+c)^2+1/d*b^3*ln(tan(d*x+c))","A"
189,1,201,154,0.750000," ","int(csc(d*x+c)^3*(a+b*sec(d*x+c))^3,x)","-\frac{a^{3} \cot \left(d x +c \right) \csc \left(d x +c \right)}{2 d}+\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} b}{2 d \sin \left(d x +c \right)^{2}}+\frac{3 a^{2} b \ln \left(\tan \left(d x +c \right)\right)}{d}-\frac{3 b^{2} a}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{9 b^{2} a}{2 d \cos \left(d x +c \right)}+\frac{9 b^{2} a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}+\frac{b^{3}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{2}}-\frac{b^{3}}{d \sin \left(d x +c \right)^{2}}+\frac{2 b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/2*a^3*cot(d*x+c)*csc(d*x+c)/d+1/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/2/d*a^2*b/sin(d*x+c)^2+3*a^2*b*ln(tan(d*x+c))/d-3/2/d*b^2*a/sin(d*x+c)^2/cos(d*x+c)+9/2/d*b^2*a/cos(d*x+c)+9/2/d*b^2*a*ln(csc(d*x+c)-cot(d*x+c))+1/2/d*b^3/sin(d*x+c)^2/cos(d*x+c)^2-1/d*b^3/sin(d*x+c)^2+2/d*b^3*ln(tan(d*x+c))","A"
190,1,354,273,0.697000," ","int((a+b*sec(d*x+c))^3*sin(d*x+c)^6,x)","-\frac{a^{3} \cos \left(d x +c \right) \left(\sin^{5}\left(d x +c \right)\right)}{6 d}-\frac{5 a^{3} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{24 d}-\frac{5 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{16 d}+\frac{5 a^{3} x}{16}+\frac{5 a^{3} c}{16 d}-\frac{3 a^{2} b \left(\sin^{5}\left(d x +c \right)\right)}{5 d}-\frac{a^{2} b \left(\sin^{3}\left(d x +c \right)\right)}{d}-\frac{3 a^{2} b \sin \left(d x +c \right)}{d}+\frac{3 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 b^{2} a \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{3 b^{2} a \left(\sin^{5}\left(d x +c \right)\right) \cos \left(d x +c \right)}{d}+\frac{15 b^{2} a \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{4 d}+\frac{45 a \,b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{45 a \,b^{2} x}{8}-\frac{45 a \,b^{2} c}{8 d}+\frac{b^{3} \left(\sin^{7}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{3} \left(\sin^{5}\left(d x +c \right)\right)}{2 d}+\frac{5 b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{6 d}+\frac{5 b^{3} \sin \left(d x +c \right)}{2 d}-\frac{5 b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"-1/6*a^3*cos(d*x+c)*sin(d*x+c)^5/d-5/24*a^3*cos(d*x+c)*sin(d*x+c)^3/d-5/16*a^3*cos(d*x+c)*sin(d*x+c)/d+5/16*a^3*x+5/16/d*a^3*c-3/5*a^2*b*sin(d*x+c)^5/d-a^2*b*sin(d*x+c)^3/d-3*a^2*b*sin(d*x+c)/d+3/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/d*b^2*a*sin(d*x+c)^7/cos(d*x+c)+3/d*b^2*a*sin(d*x+c)^5*cos(d*x+c)+15/4/d*b^2*a*cos(d*x+c)*sin(d*x+c)^3+45/8*a*b^2*cos(d*x+c)*sin(d*x+c)/d-45/8*a*b^2*x-45/8/d*a*b^2*c+1/2/d*b^3*sin(d*x+c)^7/cos(d*x+c)^2+1/2/d*b^3*sin(d*x+c)^5+5/6*b^3*sin(d*x+c)^3/d+5/2*b^3*sin(d*x+c)/d-5/2/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
191,1,276,222,0.622000," ","int((a+b*sec(d*x+c))^3*sin(d*x+c)^4,x)","-\frac{a^{3} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{3 a^{3} x}{8}+\frac{3 a^{3} c}{8 d}-\frac{a^{2} b \left(\sin^{3}\left(d x +c \right)\right)}{d}-\frac{3 a^{2} b \sin \left(d x +c \right)}{d}+\frac{3 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 b^{2} a \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{3 b^{2} a \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{d}+\frac{9 a \,b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{9 a \,b^{2} x}{2}-\frac{9 a \,b^{2} c}{2 d}+\frac{b^{3} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{2 d}+\frac{3 b^{3} \sin \left(d x +c \right)}{2 d}-\frac{3 b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"-1/4*a^3*cos(d*x+c)*sin(d*x+c)^3/d-3/8*a^3*cos(d*x+c)*sin(d*x+c)/d+3/8*a^3*x+3/8/d*a^3*c-a^2*b*sin(d*x+c)^3/d-3*a^2*b*sin(d*x+c)/d+3/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/d*b^2*a*sin(d*x+c)^5/cos(d*x+c)+3/d*b^2*a*cos(d*x+c)*sin(d*x+c)^3+9/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d-9/2*a*b^2*x-9/2/d*a*b^2*c+1/2/d*b^3*sin(d*x+c)^5/cos(d*x+c)^2+1/2*b^3*sin(d*x+c)^3/d+3/2*b^3*sin(d*x+c)/d-3/2/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
192,1,167,126,0.415000," ","int((a+b*sec(d*x+c))^3*sin(d*x+c)^2,x)","-\frac{a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a^{3} x}{2}+\frac{a^{3} c}{2 d}-\frac{3 a^{2} b \sin \left(d x +c \right)}{d}+\frac{3 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-3 a \,b^{2} x +\frac{3 a \,b^{2} \tan \left(d x +c \right)}{d}-\frac{3 a \,b^{2} c}{d}+\frac{b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{3} \sin \left(d x +c \right)}{2 d}-\frac{b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"-1/2*a^3*cos(d*x+c)*sin(d*x+c)/d+1/2*a^3*x+1/2/d*a^3*c-3*a^2*b*sin(d*x+c)/d+3/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))-3*a*b^2*x+3*a*b^2*tan(d*x+c)/d-3/d*a*b^2*c+1/2/d*b^3*sin(d*x+c)^3/cos(d*x+c)^2+1/2*b^3*sin(d*x+c)/d-1/2/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
193,1,158,127,0.639000," ","int(csc(d*x+c)^2*(a+b*sec(d*x+c))^3,x)","-\frac{a^{3} \cot \left(d x +c \right)}{d}-\frac{3 a^{2} b}{d \sin \left(d x +c \right)}+\frac{3 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 b^{2} a}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{6 a \,b^{2} \cot \left(d x +c \right)}{d}+\frac{b^{3}}{2 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{3 b^{3}}{2 d \sin \left(d x +c \right)}+\frac{3 b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"-a^3*cot(d*x+c)/d-3/d*a^2*b/sin(d*x+c)+3/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/d*b^2*a/sin(d*x+c)/cos(d*x+c)-6*a*b^2*cot(d*x+c)/d+1/2/d*b^3/sin(d*x+c)/cos(d*x+c)^2-3/2/d*b^3/sin(d*x+c)+3/2/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
194,1,246,195,0.921000," ","int(csc(d*x+c)^4*(a+b*sec(d*x+c))^3,x)","-\frac{2 a^{3} \cot \left(d x +c \right)}{3 d}-\frac{a^{3} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} b}{d \sin \left(d x +c \right)^{3}}-\frac{3 a^{2} b}{d \sin \left(d x +c \right)}+\frac{3 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{b^{2} a}{d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{4 b^{2} a}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{8 a \,b^{2} \cot \left(d x +c \right)}{d}-\frac{b^{3}}{3 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{2}}+\frac{5 b^{3}}{6 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{5 b^{3}}{2 d \sin \left(d x +c \right)}+\frac{5 b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"-2/3*a^3*cot(d*x+c)/d-1/3/d*a^3*cot(d*x+c)*csc(d*x+c)^2-1/d*a^2*b/sin(d*x+c)^3-3/d*a^2*b/sin(d*x+c)+3/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))-1/d*b^2*a/sin(d*x+c)^3/cos(d*x+c)+4/d*b^2*a/sin(d*x+c)/cos(d*x+c)-8*a*b^2*cot(d*x+c)/d-1/3/d*b^3/sin(d*x+c)^3/cos(d*x+c)^2+5/6/d*b^3/sin(d*x+c)/cos(d*x+c)^2-5/2/d*b^3/sin(d*x+c)+5/2/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
195,1,334,261,0.971000," ","int(csc(d*x+c)^6*(a+b*sec(d*x+c))^3,x)","-\frac{8 a^{3} \cot \left(d x +c \right)}{15 d}-\frac{a^{3} \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 a^{3} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{15 d}-\frac{3 a^{2} b}{5 d \sin \left(d x +c \right)^{5}}-\frac{a^{2} b}{d \sin \left(d x +c \right)^{3}}-\frac{3 a^{2} b}{d \sin \left(d x +c \right)}+\frac{3 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{3 b^{2} a}{5 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}-\frac{6 b^{2} a}{5 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{24 b^{2} a}{5 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{48 a \,b^{2} \cot \left(d x +c \right)}{5 d}-\frac{b^{3}}{5 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)^{2}}-\frac{7 b^{3}}{15 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{2}}+\frac{7 b^{3}}{6 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{7 b^{3}}{2 d \sin \left(d x +c \right)}+\frac{7 b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"-8/15*a^3*cot(d*x+c)/d-1/5/d*a^3*cot(d*x+c)*csc(d*x+c)^4-4/15/d*a^3*cot(d*x+c)*csc(d*x+c)^2-3/5/d*a^2*b/sin(d*x+c)^5-1/d*a^2*b/sin(d*x+c)^3-3/d*a^2*b/sin(d*x+c)+3/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))-3/5/d*b^2*a/sin(d*x+c)^5/cos(d*x+c)-6/5/d*b^2*a/sin(d*x+c)^3/cos(d*x+c)+24/5/d*b^2*a/sin(d*x+c)/cos(d*x+c)-48/5*a*b^2*cot(d*x+c)/d-1/5/d*b^3/sin(d*x+c)^5/cos(d*x+c)^2-7/15/d*b^3/sin(d*x+c)^3/cos(d*x+c)^2+7/6/d*b^3/sin(d*x+c)/cos(d*x+c)^2-7/2/d*b^3/sin(d*x+c)+7/2/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
196,1,363,211,0.541000," ","int(sin(d*x+c)^7/(a+b*sec(d*x+c)),x)","\frac{\cos^{7}\left(d x +c \right)}{7 d a}-\frac{b \left(\cos^{6}\left(d x +c \right)\right)}{6 a^{2} d}-\frac{3 \left(\cos^{5}\left(d x +c \right)\right)}{5 d a}+\frac{\left(\cos^{5}\left(d x +c \right)\right) b^{2}}{5 d \,a^{3}}+\frac{3 b \left(\cos^{4}\left(d x +c \right)\right)}{4 a^{2} d}-\frac{\left(\cos^{4}\left(d x +c \right)\right) b^{3}}{4 d \,a^{4}}+\frac{\cos^{3}\left(d x +c \right)}{d a}-\frac{\left(\cos^{3}\left(d x +c \right)\right) b^{2}}{d \,a^{3}}+\frac{\left(\cos^{3}\left(d x +c \right)\right) b^{4}}{3 d \,a^{5}}-\frac{3 b \left(\cos^{2}\left(d x +c \right)\right)}{2 a^{2} d}+\frac{3 \left(\cos^{2}\left(d x +c \right)\right) b^{3}}{2 d \,a^{4}}-\frac{\left(\cos^{2}\left(d x +c \right)\right) b^{5}}{2 d \,a^{6}}-\frac{\cos \left(d x +c \right)}{d a}+\frac{3 \cos \left(d x +c \right) b^{2}}{d \,a^{3}}-\frac{3 \cos \left(d x +c \right) b^{4}}{d \,a^{5}}+\frac{\cos \left(d x +c \right) b^{6}}{d \,a^{7}}+\frac{b \ln \left(b +a \cos \left(d x +c \right)\right)}{a^{2} d}-\frac{3 b^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{4}}+\frac{3 b^{5} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{6}}-\frac{b^{7} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{8}}"," ",0,"1/7*cos(d*x+c)^7/d/a-1/6*b*cos(d*x+c)^6/a^2/d-3/5*cos(d*x+c)^5/d/a+1/5/d/a^3*cos(d*x+c)^5*b^2+3/4*b*cos(d*x+c)^4/a^2/d-1/4/d/a^4*cos(d*x+c)^4*b^3+cos(d*x+c)^3/d/a-1/d/a^3*cos(d*x+c)^3*b^2+1/3/d/a^5*cos(d*x+c)^3*b^4-3/2*b*cos(d*x+c)^2/a^2/d+3/2/d/a^4*cos(d*x+c)^2*b^3-1/2/d/a^6*cos(d*x+c)^2*b^5-cos(d*x+c)/d/a+3/d/a^3*cos(d*x+c)*b^2-3/d/a^5*cos(d*x+c)*b^4+1/d/a^7*cos(d*x+c)*b^6+b*ln(b+a*cos(d*x+c))/a^2/d-3/d*b^3/a^4*ln(b+a*cos(d*x+c))+3/d*b^5/a^6*ln(b+a*cos(d*x+c))-1/d*b^7/a^8*ln(b+a*cos(d*x+c))","A"
197,1,216,144,0.403000," ","int(sin(d*x+c)^5/(a+b*sec(d*x+c)),x)","-\frac{\cos^{5}\left(d x +c \right)}{5 d a}+\frac{b \left(\cos^{4}\left(d x +c \right)\right)}{4 a^{2} d}+\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{3 d a}-\frac{\left(\cos^{3}\left(d x +c \right)\right) b^{2}}{3 d \,a^{3}}-\frac{b \left(\cos^{2}\left(d x +c \right)\right)}{a^{2} d}+\frac{\left(\cos^{2}\left(d x +c \right)\right) b^{3}}{2 d \,a^{4}}-\frac{\cos \left(d x +c \right)}{d a}+\frac{2 \cos \left(d x +c \right) b^{2}}{d \,a^{3}}-\frac{\cos \left(d x +c \right) b^{4}}{d \,a^{5}}+\frac{b \ln \left(b +a \cos \left(d x +c \right)\right)}{a^{2} d}-\frac{2 b^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{4}}+\frac{b^{5} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{6}}"," ",0,"-1/5*cos(d*x+c)^5/d/a+1/4*b*cos(d*x+c)^4/a^2/d+2/3*cos(d*x+c)^3/d/a-1/3/d/a^3*cos(d*x+c)^3*b^2-b*cos(d*x+c)^2/a^2/d+1/2/d/a^4*cos(d*x+c)^2*b^3-cos(d*x+c)/d/a+2/d/a^3*cos(d*x+c)*b^2-1/d/a^5*cos(d*x+c)*b^4+b*ln(b+a*cos(d*x+c))/a^2/d-2/d*b^3/a^4*ln(b+a*cos(d*x+c))+1/d*b^5/a^6*ln(b+a*cos(d*x+c))","A"
198,1,106,85,0.397000," ","int(sin(d*x+c)^3/(a+b*sec(d*x+c)),x)","\frac{\cos^{3}\left(d x +c \right)}{3 d a}-\frac{b \left(\cos^{2}\left(d x +c \right)\right)}{2 a^{2} d}-\frac{\cos \left(d x +c \right)}{d a}+\frac{\cos \left(d x +c \right) b^{2}}{d \,a^{3}}+\frac{b \ln \left(b +a \cos \left(d x +c \right)\right)}{a^{2} d}-\frac{b^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{4}}"," ",0,"1/3*cos(d*x+c)^3/d/a-1/2*b*cos(d*x+c)^2/a^2/d-cos(d*x+c)/d/a+1/d/a^3*cos(d*x+c)*b^2+b*ln(b+a*cos(d*x+c))/a^2/d-1/d*b^3/a^4*ln(b+a*cos(d*x+c))","A"
199,1,53,34,0.062000," ","int(sin(d*x+c)/(a+b*sec(d*x+c)),x)","\frac{b \ln \left(a +b \sec \left(d x +c \right)\right)}{d \,a^{2}}-\frac{1}{d a \sec \left(d x +c \right)}-\frac{b \ln \left(\sec \left(d x +c \right)\right)}{d \,a^{2}}"," ",0,"1/d*b/a^2*ln(a+b*sec(d*x+c))-1/d/a/sec(d*x+c)-1/d*b/a^2*ln(sec(d*x+c))","A"
200,1,75,70,0.416000," ","int(csc(d*x+c)/(a+b*sec(d*x+c)),x)","\frac{b \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a -b \right) \left(a +b \right)}+\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/(a-b)/(a+b)*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"
201,1,121,110,0.550000," ","int(csc(d*x+c)^3/(a+b*sec(d*x+c)),x)","\frac{a^{2} b \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}+\frac{1}{d \left(4 a +4 b \right) \left(-1+\cos \left(d x +c \right)\right)}+\frac{a \ln \left(-1+\cos \left(d x +c \right)\right)}{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{a \ln \left(1+\cos \left(d x +c \right)\right)}{4 \left(a -b \right)^{2} d}"," ",0,"1/d*a^2*b/(a+b)^2/(a-b)^2*ln(b+a*cos(d*x+c))+1/d/(4*a+4*b)/(-1+cos(d*x+c))+1/4/d*a/(a+b)^2*ln(-1+cos(d*x+c))+1/d/(4*a-4*b)/(1+cos(d*x+c))-1/4*a*ln(1+cos(d*x+c))/(a-b)^2/d","A"
202,1,259,171,0.546000," ","int(csc(d*x+c)^5/(a+b*sec(d*x+c)),x)","\frac{a^{4} b \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \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{3 a}{16 d \left(a +b \right)^{2} \left(-1+\cos \left(d x +c \right)\right)}+\frac{b}{16 d \left(a +b \right)^{2} \left(-1+\cos \left(d x +c \right)\right)}+\frac{3 a^{2} \ln \left(-1+\cos \left(d x +c \right)\right)}{16 d \left(a +b \right)^{3}}+\frac{a \ln \left(-1+\cos \left(d x +c \right)\right) b}{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{3 a}{16 d \left(a -b \right)^{2} \left(1+\cos \left(d x +c \right)\right)}-\frac{b}{16 d \left(a -b \right)^{2} \left(1+\cos \left(d x +c \right)\right)}-\frac{3 a^{2} \ln \left(1+\cos \left(d x +c \right)\right)}{16 d \left(a -b \right)^{3}}+\frac{a \ln \left(1+\cos \left(d x +c \right)\right) b}{16 d \left(a -b \right)^{3}}"," ",0,"1/d*a^4*b/(a+b)^3/(a-b)^3*ln(b+a*cos(d*x+c))-1/2/d/(8*a+8*b)/(-1+cos(d*x+c))^2+3/16/d/(a+b)^2/(-1+cos(d*x+c))*a+1/16/d/(a+b)^2/(-1+cos(d*x+c))*b+3/16/d/(a+b)^3*a^2*ln(-1+cos(d*x+c))+1/16/d/(a+b)^3*a*ln(-1+cos(d*x+c))*b+1/2/d/(8*a-8*b)/(1+cos(d*x+c))^2+3/16/d/(a-b)^2/(1+cos(d*x+c))*a-1/16/d/(a-b)^2/(1+cos(d*x+c))*b-3/16/d*a^2/(a-b)^3*ln(1+cos(d*x+c))+1/16/d*a/(a-b)^3*ln(1+cos(d*x+c))*b","A"
203,1,1566,213,0.523000," ","int(sin(d*x+c)^6/(a+b*sec(d*x+c)),x)","\frac{172 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{5 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{11 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{2 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{6}}{d \,a^{7}}-\frac{15 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{4 d \,a^{3}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5}}-\frac{6 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 \,a^{5} \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 \,a^{7} \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{6 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 \,a^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{33 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{85 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{5 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{48 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{33 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{85 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{10 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{68 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{3 d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{\left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{20 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{5}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{38 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{29 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{4 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{3 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{2 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{38 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{11 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{2 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{48 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{10 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{68 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{3 d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{172 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{5 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{7 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{2 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}+\frac{20 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{29 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}"," ",0,"-1/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b^4-48/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b^3-6/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))+2/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b^5-2/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b^4-29/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b^2-2/d/a^7*arctan(tan(1/2*d*x+1/2*c))*b^6-15/4/d/a^3*arctan(tan(1/2*d*x+1/2*c))*b^2+5/d/a^5*arctan(tan(1/2*d*x+1/2*c))*b^4+5/8/d/a/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11+85/24/d/a/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9+33/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7-33/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5+11/2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b^2+172/5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b+20/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b^5-85/24/d/a/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3-5/8/d/a/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)+7/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b^2-68/3/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b^3+172/5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b-7/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b^2-4/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b^3+3/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b^4+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b+2/d*b^7/a^7/((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))-4/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b^3+5/8/a/d*arctan(tan(1/2*d*x+1/2*c))+38/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b-11/2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b^2-48/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b^3+10/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b^5+2/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b^5+38/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b+29/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b^2+2/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b^4+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b-68/3/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b^3-3/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b^4+1/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b^4+20/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b^5+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))+10/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b^5","B"
204,1,769,146,0.448000," ","int(sin(d*x+c)^4/(a+b*sec(d*x+c)),x)","-\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{4 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 \,a^{3} \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 \,a^{5} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{26 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{11 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{26 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d}"," ",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))+4/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))-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))+3/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*b-1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*b^2-2/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*b^3+26/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*b-1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*b^2-6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*b^3+11/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-11/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3+1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*b^2+26/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*b-6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*b^3+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*b-2/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*b^3-3/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*b^2-3/d/a^3*arctan(tan(1/2*d*x+1/2*c))*b^2+2/d/a^5*arctan(tan(1/2*d*x+1/2*c))*b^4+3/4/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
205,1,269,87,0.362000," ","int(sin(d*x+c)^2/(a+b*sec(d*x+c)),x)","-\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 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 \,a^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3}}"," ",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^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))+1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*b+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*b-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+1/a/d*arctan(tan(1/2*d*x+1/2*c))-2/d/a^3*arctan(tan(1/2*d*x+1/2*c))*b^2","B"
206,1,96,75,0.469000," ","int(csc(d*x+c)^2/(a+b*sec(d*x+c)),x)","\frac{\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a -2 b}-\frac{2 a 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)}{\left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{2 \left(a +b \right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{d}"," ",0,"1/d*(1/2/(a-b)*tan(1/2*d*x+1/2*c)-2/(a-b)/(a+b)*a*b/((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/(a+b)/tan(1/2*d*x+1/2*c))","A"
207,1,165,127,0.541000," ","int(csc(d*x+c)^4/(a+b*sec(d*x+c)),x)","\frac{\frac{\frac{a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{3}+3 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{8 \left(a -b \right)^{2}}-\frac{2 a^{3} 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)}{\left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{24 \left(a +b \right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{3 a +b}{8 \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{d}"," ",0,"1/d*(1/8/(a-b)^2*(1/3*a*tan(1/2*d*x+1/2*c)^3-1/3*tan(1/2*d*x+1/2*c)^3*b+3*a*tan(1/2*d*x+1/2*c)-tan(1/2*d*x+1/2*c)*b)-2/(a-b)^2/(a+b)^2*a^3*b/((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/(a+b)/tan(1/2*d*x+1/2*c)^3-1/8*(3*a+b)/(a+b)^2/tan(1/2*d*x+1/2*c))","A"
208,1,282,186,0.604000," ","int(csc(d*x+c)^6/(a+b*sec(d*x+c)),x)","\frac{\frac{\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{5}-\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a b}{5}+\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{5}+\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{3}-\frac{8 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a b}{3}+\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}+10 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-8 a b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{32 \left(a -b \right)^{3}}-\frac{2 a^{5} 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)}{\left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{160 \left(a +b \right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{5 a +3 b}{96 \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{10 a^{2}+8 a b +2 b^{2}}{32 \left(a +b \right)^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{d}"," ",0,"1/d*(1/32/(a-b)^3*(1/5*tan(1/2*d*x+1/2*c)^5*a^2-2/5*tan(1/2*d*x+1/2*c)^5*a*b+1/5*tan(1/2*d*x+1/2*c)^5*b^2+5/3*tan(1/2*d*x+1/2*c)^3*a^2-8/3*tan(1/2*d*x+1/2*c)^3*a*b+tan(1/2*d*x+1/2*c)^3*b^2+10*a^2*tan(1/2*d*x+1/2*c)-8*a*b*tan(1/2*d*x+1/2*c)+2*b^2*tan(1/2*d*x+1/2*c))-2/(a-b)^3/(a+b)^3*a^5*b/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/160/(a+b)/tan(1/2*d*x+1/2*c)^5-1/96*(5*a+3*b)/(a+b)^2/tan(1/2*d*x+1/2*c)^3-1/32/(a+b)^3*(10*a^2+8*a*b+2*b^2)/tan(1/2*d*x+1/2*c))","A"
209,1,456,257,0.588000," ","int(sin(d*x+c)^7/(a+b*sec(d*x+c))^2,x)","\frac{\cos^{7}\left(d x +c \right)}{7 a^{2} d}-\frac{b \left(\cos^{6}\left(d x +c \right)\right)}{3 a^{3} d}-\frac{3 \left(\cos^{5}\left(d x +c \right)\right)}{5 a^{2} d}+\frac{3 \left(\cos^{5}\left(d x +c \right)\right) b^{2}}{5 d \,a^{4}}+\frac{3 b \left(\cos^{4}\left(d x +c \right)\right)}{2 a^{3} d}-\frac{\left(\cos^{4}\left(d x +c \right)\right) b^{3}}{d \,a^{5}}+\frac{\cos^{3}\left(d x +c \right)}{a^{2} d}-\frac{3 \left(\cos^{3}\left(d x +c \right)\right) b^{2}}{d \,a^{4}}+\frac{5 \left(\cos^{3}\left(d x +c \right)\right) b^{4}}{3 d \,a^{6}}-\frac{3 b \left(\cos^{2}\left(d x +c \right)\right)}{a^{3} d}+\frac{6 \left(\cos^{2}\left(d x +c \right)\right) b^{3}}{d \,a^{5}}-\frac{3 \left(\cos^{2}\left(d x +c \right)\right) b^{5}}{d \,a^{7}}-\frac{\cos \left(d x +c \right)}{a^{2} d}+\frac{9 \cos \left(d x +c \right) b^{2}}{d \,a^{4}}-\frac{15 \cos \left(d x +c \right) b^{4}}{d \,a^{6}}+\frac{7 \cos \left(d x +c \right) b^{6}}{d \,a^{8}}+\frac{2 b \ln \left(b +a \cos \left(d x +c \right)\right)}{a^{3} d}-\frac{12 b^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{5}}+\frac{18 b^{5} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{7}}-\frac{8 b^{7} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{9}}+\frac{b^{2}}{a^{3} d \left(b +a \cos \left(d x +c \right)\right)}-\frac{3 b^{4}}{d \,a^{5} \left(b +a \cos \left(d x +c \right)\right)}+\frac{3 b^{6}}{d \,a^{7} \left(b +a \cos \left(d x +c \right)\right)}-\frac{b^{8}}{d \,a^{9} \left(b +a \cos \left(d x +c \right)\right)}"," ",0,"1/7*cos(d*x+c)^7/a^2/d-1/3*b*cos(d*x+c)^6/a^3/d-3/5*cos(d*x+c)^5/a^2/d+3/5/d/a^4*cos(d*x+c)^5*b^2+3/2*b*cos(d*x+c)^4/a^3/d-1/d/a^5*cos(d*x+c)^4*b^3+cos(d*x+c)^3/a^2/d-3/d/a^4*cos(d*x+c)^3*b^2+5/3/d/a^6*cos(d*x+c)^3*b^4-3*b*cos(d*x+c)^2/a^3/d+6/d/a^5*cos(d*x+c)^2*b^3-3/d/a^7*cos(d*x+c)^2*b^5-cos(d*x+c)/a^2/d+9/d/a^4*cos(d*x+c)*b^2-15/d/a^6*cos(d*x+c)*b^4+7/d/a^8*cos(d*x+c)*b^6+2*b*ln(b+a*cos(d*x+c))/a^3/d-12/d/a^5*b^3*ln(b+a*cos(d*x+c))+18/d/a^7*b^5*ln(b+a*cos(d*x+c))-8/d/a^9*b^7*ln(b+a*cos(d*x+c))+b^2/a^3/d/(b+a*cos(d*x+c))-3/d*b^4/a^5/(b+a*cos(d*x+c))+3/d*b^6/a^7/(b+a*cos(d*x+c))-1/d*b^8/a^9/(b+a*cos(d*x+c))","A"
210,1,285,188,0.515000," ","int(sin(d*x+c)^5/(a+b*sec(d*x+c))^2,x)","-\frac{\cos^{5}\left(d x +c \right)}{5 a^{2} d}+\frac{b \left(\cos^{4}\left(d x +c \right)\right)}{2 a^{3} d}+\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{3 a^{2} d}-\frac{\left(\cos^{3}\left(d x +c \right)\right) b^{2}}{d \,a^{4}}-\frac{2 b \left(\cos^{2}\left(d x +c \right)\right)}{a^{3} d}+\frac{2 \left(\cos^{2}\left(d x +c \right)\right) b^{3}}{d \,a^{5}}-\frac{\cos \left(d x +c \right)}{a^{2} d}+\frac{6 \cos \left(d x +c \right) b^{2}}{d \,a^{4}}-\frac{5 \cos \left(d x +c \right) b^{4}}{d \,a^{6}}+\frac{2 b \ln \left(b +a \cos \left(d x +c \right)\right)}{a^{3} d}-\frac{8 b^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{5}}+\frac{6 b^{5} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{7}}+\frac{b^{2}}{a^{3} d \left(b +a \cos \left(d x +c \right)\right)}-\frac{2 b^{4}}{d \,a^{5} \left(b +a \cos \left(d x +c \right)\right)}+\frac{b^{6}}{d \,a^{7} \left(b +a \cos \left(d x +c \right)\right)}"," ",0,"-1/5*cos(d*x+c)^5/a^2/d+1/2*b*cos(d*x+c)^4/a^3/d+2/3*cos(d*x+c)^3/a^2/d-1/d/a^4*cos(d*x+c)^3*b^2-2*b*cos(d*x+c)^2/a^3/d+2/d/a^5*cos(d*x+c)^2*b^3-cos(d*x+c)/a^2/d+6/d/a^4*cos(d*x+c)*b^2-5/d/a^6*cos(d*x+c)*b^4+2*b*ln(b+a*cos(d*x+c))/a^3/d-8/d/a^5*b^3*ln(b+a*cos(d*x+c))+6/d/a^7*b^5*ln(b+a*cos(d*x+c))+b^2/a^3/d/(b+a*cos(d*x+c))-2/d*b^4/a^5/(b+a*cos(d*x+c))+1/d*b^6/a^7/(b+a*cos(d*x+c))","A"
211,1,153,117,0.442000," ","int(sin(d*x+c)^3/(a+b*sec(d*x+c))^2,x)","\frac{\cos^{3}\left(d x +c \right)}{3 a^{2} d}-\frac{b \left(\cos^{2}\left(d x +c \right)\right)}{a^{3} d}-\frac{\cos \left(d x +c \right)}{a^{2} d}+\frac{3 \cos \left(d x +c \right) b^{2}}{d \,a^{4}}+\frac{2 b \ln \left(b +a \cos \left(d x +c \right)\right)}{a^{3} d}-\frac{4 b^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{5}}+\frac{b^{2}}{a^{3} d \left(b +a \cos \left(d x +c \right)\right)}-\frac{b^{4}}{d \,a^{5} \left(b +a \cos \left(d x +c \right)\right)}"," ",0,"1/3*cos(d*x+c)^3/a^2/d-b*cos(d*x+c)^2/a^3/d-cos(d*x+c)/a^2/d+3/d/a^4*cos(d*x+c)*b^2+2*b*ln(b+a*cos(d*x+c))/a^3/d-4/d/a^5*b^3*ln(b+a*cos(d*x+c))+b^2/a^3/d/(b+a*cos(d*x+c))-1/d*b^4/a^5/(b+a*cos(d*x+c))","A"
212,1,75,57,0.068000," ","int(sin(d*x+c)/(a+b*sec(d*x+c))^2,x)","-\frac{b}{d \,a^{2} \left(a +b \sec \left(d x +c \right)\right)}+\frac{2 b \ln \left(a +b \sec \left(d x +c \right)\right)}{d \,a^{3}}-\frac{1}{d \,a^{2} \sec \left(d x +c \right)}-\frac{2 b \ln \left(\sec \left(d x +c \right)\right)}{d \,a^{3}}"," ",0,"-1/d*b/a^2/(a+b*sec(d*x+c))+2/d/a^3*b*ln(a+b*sec(d*x+c))-1/d/a^2/sec(d*x+c)-2/d/a^3*b*ln(sec(d*x+c))","A"
213,1,106,105,0.438000," ","int(csc(d*x+c)/(a+b*sec(d*x+c))^2,x)","\frac{b^{2}}{d \left(a +b \right) \left(a -b \right) a \left(b +a \cos \left(d x +c \right)\right)}+\frac{2 a b \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{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*b^2/(a+b)/(a-b)/a/(b+a*cos(d*x+c))+2/d*a*b/(a-b)^2/(a+b)^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"
214,1,224,162,0.653000," ","int(csc(d*x+c)^3/(a+b*sec(d*x+c))^2,x)","\frac{b^{2} a}{d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(b +a \cos \left(d x +c \right)\right)}+\frac{2 a^{3} b \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}+\frac{2 a \,b^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \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}{4 d \left(a +b \right)^{3}}-\frac{\ln \left(-1+\cos \left(d x +c \right)\right) b}{4 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}{4 d \left(a -b \right)^{3}}-\frac{\ln \left(1+\cos \left(d x +c \right)\right) b}{4 d \left(a -b \right)^{3}}"," ",0,"1/d*b^2/(a+b)^2*a/(a-b)^2/(b+a*cos(d*x+c))+2/d*a^3*b/(a+b)^3/(a-b)^3*ln(b+a*cos(d*x+c))+2/d*a*b^3/(a+b)^3/(a-b)^3*ln(b+a*cos(d*x+c))+1/4/d/(a+b)^2/(-1+cos(d*x+c))+1/4/d/(a+b)^3*ln(-1+cos(d*x+c))*a-1/4/d/(a+b)^3*ln(-1+cos(d*x+c))*b+1/4/d/(a-b)^2/(1+cos(d*x+c))-1/4/d/(a-b)^3*ln(1+cos(d*x+c))*a-1/4/d/(a-b)^3*ln(1+cos(d*x+c))*b","A"
215,1,368,251,0.663000," ","int(csc(d*x+c)^5/(a+b*sec(d*x+c))^2,x)","\frac{b^{2} a^{3}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}+\frac{2 a^{5} b \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{4 a^{3} b^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \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{3 a}{16 d \left(a +b \right)^{3} \left(-1+\cos \left(d x +c \right)\right)}-\frac{b}{16 d \left(a +b \right)^{3} \left(-1+\cos \left(d x +c \right)\right)}+\frac{3 \ln \left(-1+\cos \left(d x +c \right)\right) a^{2}}{16 d \left(a +b \right)^{4}}-\frac{\ln \left(-1+\cos \left(d x +c \right)\right) a b}{4 d \left(a +b \right)^{4}}-\frac{\ln \left(-1+\cos \left(d x +c \right)\right) b^{2}}{16 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{3 a}{16 d \left(a -b \right)^{3} \left(1+\cos \left(d x +c \right)\right)}+\frac{b}{16 d \left(a -b \right)^{3} \left(1+\cos \left(d x +c \right)\right)}-\frac{3 \ln \left(1+\cos \left(d x +c \right)\right) a^{2}}{16 d \left(a -b \right)^{4}}-\frac{\ln \left(1+\cos \left(d x +c \right)\right) a b}{4 d \left(a -b \right)^{4}}+\frac{\ln \left(1+\cos \left(d x +c \right)\right) b^{2}}{16 d \left(a -b \right)^{4}}"," ",0,"1/d*b^2*a^3/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))+2/d*a^5*b/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))+4/d*a^3*b^3/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))-1/16/d/(a+b)^2/(-1+cos(d*x+c))^2+3/16/d/(a+b)^3/(-1+cos(d*x+c))*a-1/16/d/(a+b)^3/(-1+cos(d*x+c))*b+3/16/d/(a+b)^4*ln(-1+cos(d*x+c))*a^2-1/4/d/(a+b)^4*ln(-1+cos(d*x+c))*a*b-1/16/d/(a+b)^4*ln(-1+cos(d*x+c))*b^2+1/16/d/(a-b)^2/(1+cos(d*x+c))^2+3/16/d/(a-b)^3/(1+cos(d*x+c))*a+1/16/d/(a-b)^3/(1+cos(d*x+c))*b-3/16/d/(a-b)^4*ln(1+cos(d*x+c))*a^2-1/4/d/(a-b)^4*ln(1+cos(d*x+c))*a*b+1/16/d/(a-b)^4*ln(1+cos(d*x+c))*b^2","A"
216,1,1735,444,0.638000," ","int(sin(d*x+c)^6/(a+b*sec(d*x+c))^2,x)","\frac{10 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{120 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{25 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{6}}-\frac{14 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{6}}{d \,a^{8}}-\frac{45 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{4 d \,a^{4}}+\frac{76 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{3 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{60 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{272 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{3 d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{4 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{85 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{33 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{33 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{5 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{85 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{22 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 \,a^{4} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{32 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 \,a^{6} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{344 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{5 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{192 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{344 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{5 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{33 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{2 d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{7} \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{120 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{60 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{21 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{4 d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{76 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{3 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{87 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{4 d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{272 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{3 d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{192 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{87 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{4 d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{15 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{15 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{14 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 \,a^{8} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{4 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{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}+\frac{33 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{2 d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{10 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{16 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{12 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{5}}{d \,a^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \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 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5} \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{21 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{4 d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{5 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{12 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{16 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}"," ",0,"76/3/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b-87/4/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b^2+15/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b^4-15/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b^4+22/d*b^3/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))-32/d*b^5/a^6/((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^7/a^8/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+60/d/a^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b^5-272/3/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b^3+4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b-21/4/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b^2+76/3/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b+87/4/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b^2-272/3/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b^3-192/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b^3+10/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b^4+120/d/a^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b^5+33/2/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b^2-10/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b^4-16/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b^3-33/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5+25/d/a^6*arctan(tan(1/2*d*x+1/2*c))*b^4-14/d/a^8*arctan(tan(1/2*d*x+1/2*c))*b^6-45/4/d/a^4*arctan(tan(1/2*d*x+1/2*c))*b^2-5/8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)+33/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7+5/8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11+85/24/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9-85/24/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3+12/d/a^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b^5+5/8/d/a^2*arctan(tan(1/2*d*x+1/2*c))-2/d*b^2/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^4/a^5*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)+21/4/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b^2-5/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b^4+344/5/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b-192/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b^3+344/5/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b-33/2/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b^2-2/d*b^6/a^7*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/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))+120/d/a^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b^5+60/d/a^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b^5+4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b-16/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b^3+5/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b^4+12/d/a^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b^5","B"
217,1,883,242,0.457000," ","int(sin(d*x+c)^4/(a+b*sec(d*x+c))^2,x)","-\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \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^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5} \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 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{14 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 \,a^{4} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{10 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 \,a^{6} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{4 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{8 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{52 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{3 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{24 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{11 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{52 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{3 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{24 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{8 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{9 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{4}}+\frac{10 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{6}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2}}"," ",0,"-2/d*b^2/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)+2/d*b^4/a^5*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/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))+14/d*b^3/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))-10/d*b^5/a^6/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+3/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7+4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*b-3/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*b^2-8/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*b^3+52/3/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*b-3/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*b^2-24/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*b^3+11/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-11/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3+3/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*b^2+52/3/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*b-24/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*b^3+4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*b-8/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*b^3-3/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+3/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*b^2-9/d/a^4*arctan(tan(1/2*d*x+1/2*c))*b^2+10/d/a^6*arctan(tan(1/2*d*x+1/2*c))*b^4+3/4/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
218,1,325,139,0.440000," ","int(sin(d*x+c)^2/(a+b*sec(d*x+c))^2,x)","-\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \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 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{6 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 \,a^{4} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{4}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-2/d*b^2/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/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))+6/d*b^3/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))+1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*b+4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*b-1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-6/d/a^4*arctan(tan(1/2*d*x+1/2*c))*b^2+1/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
219,1,162,181,0.505000," ","int(csc(d*x+c)^2/(a+b*sec(d*x+c))^2,x)","\frac{\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{2}-4 a b +2 b^{2}}+\frac{2 b \left(-\frac{a b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{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}-\frac{\left(2 a^{2}+b^{2}\right) \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)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a -b \right)^{2} \left(a +b \right)^{2}}-\frac{1}{2 \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{d}"," ",0,"1/d*(1/2/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)+2*b/(a-b)^2/(a+b)^2*(-a*b*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*a^2+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)))-1/2/(a+b)^2/tan(1/2*d*x+1/2*c))","A"
220,1,242,313,0.560000," ","int(csc(d*x+c)^4/(a+b*sec(d*x+c))^2,x)","\frac{\frac{\frac{a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{3}+3 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{8 \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right)}+\frac{2 a^{2} b \left(-\frac{a b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{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}-\frac{\left(2 a^{2}+3 b^{2}\right) \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)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{1}{24 \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{3 a -b}{8 \left(a +b \right)^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{d}"," ",0,"1/d*(1/8/(a^2-2*a*b+b^2)/(a-b)*(1/3*a*tan(1/2*d*x+1/2*c)^3-1/3*tan(1/2*d*x+1/2*c)^3*b+3*a*tan(1/2*d*x+1/2*c)+tan(1/2*d*x+1/2*c)*b)+2*a^2*b/(a+b)^3/(a-b)^3*(-a*b*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*a^2+3*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)))-1/24/(a+b)^2/tan(1/2*d*x+1/2*c)^3-1/8*(3*a-b)/(a+b)^3/tan(1/2*d*x+1/2*c))","A"
221,1,549,317,0.588000," ","int(sin(d*x+c)^7/(a+b*sec(d*x+c))^3,x)","\frac{5 \left(\cos^{3}\left(d x +c \right)\right) b^{4}}{d \,a^{7}}+\frac{15 \left(\cos^{2}\left(d x +c \right)\right) b^{3}}{d \,a^{6}}-\frac{21 \left(\cos^{2}\left(d x +c \right)\right) b^{5}}{2 d \,a^{8}}+\frac{3 b^{5}}{2 d \,a^{6} \left(b +a \cos \left(d x +c \right)\right)^{2}}-\frac{3 b^{7}}{2 d \,a^{8} \left(b +a \cos \left(d x +c \right)\right)^{2}}+\frac{b^{9}}{2 d \,a^{10} \left(b +a \cos \left(d x +c \right)\right)^{2}}-\frac{30 b^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{6}}+\frac{63 b^{5} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{8}}-\frac{36 b^{7} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{10}}-\frac{15 b^{4}}{d \,a^{6} \left(b +a \cos \left(d x +c \right)\right)}+\frac{18 \cos \left(d x +c \right) b^{2}}{d \,a^{5}}-\frac{45 \cos \left(d x +c \right) b^{4}}{d \,a^{7}}+\frac{28 \cos \left(d x +c \right) b^{6}}{d \,a^{9}}-\frac{9 b^{8}}{d \,a^{10} \left(b +a \cos \left(d x +c \right)\right)}+\frac{21 b^{6}}{d \,a^{8} \left(b +a \cos \left(d x +c \right)\right)}-\frac{b \left(\cos^{6}\left(d x +c \right)\right)}{2 a^{4} d}+\frac{9 b \left(\cos^{4}\left(d x +c \right)\right)}{4 a^{4} d}-\frac{9 b \left(\cos^{2}\left(d x +c \right)\right)}{2 a^{4} d}-\frac{5 \left(\cos^{4}\left(d x +c \right)\right) b^{3}}{2 d \,a^{6}}-\frac{6 \left(\cos^{3}\left(d x +c \right)\right) b^{2}}{d \,a^{5}}+\frac{6 \left(\cos^{5}\left(d x +c \right)\right) b^{2}}{5 d \,a^{5}}+\frac{3 b \ln \left(b +a \cos \left(d x +c \right)\right)}{a^{4} d}+\frac{\cos^{3}\left(d x +c \right)}{a^{3} d}+\frac{\cos^{7}\left(d x +c \right)}{7 a^{3} d}-\frac{3 \left(\cos^{5}\left(d x +c \right)\right)}{5 a^{3} d}-\frac{b^{3}}{2 a^{4} d \left(b +a \cos \left(d x +c \right)\right)^{2}}+\frac{3 b^{2}}{a^{4} d \left(b +a \cos \left(d x +c \right)\right)}-\frac{\cos \left(d x +c \right)}{a^{3} d}"," ",0,"3/2/d*b^5/a^6/(b+a*cos(d*x+c))^2-3/2/d*b^7/a^8/(b+a*cos(d*x+c))^2+1/2/d*b^9/a^10/(b+a*cos(d*x+c))^2-30/d/a^6*b^3*ln(b+a*cos(d*x+c))+63/d/a^8*b^5*ln(b+a*cos(d*x+c))-36/d/a^10*b^7*ln(b+a*cos(d*x+c))+5/d/a^7*cos(d*x+c)^3*b^4+15/d/a^6*cos(d*x+c)^2*b^3-15/d*b^4/a^6/(b+a*cos(d*x+c))-21/2/d/a^8*cos(d*x+c)^2*b^5+18/d/a^5*cos(d*x+c)*b^2-45/d/a^7*cos(d*x+c)*b^4+28/d/a^9*cos(d*x+c)*b^6+6/5/d/a^5*cos(d*x+c)^5*b^2-5/2/d/a^6*cos(d*x+c)^4*b^3-6/d/a^5*cos(d*x+c)^3*b^2-9/d*b^8/a^10/(b+a*cos(d*x+c))+21/d*b^6/a^8/(b+a*cos(d*x+c))+3*b*ln(b+a*cos(d*x+c))/a^4/d-1/2*b*cos(d*x+c)^6/a^4/d+9/4*b*cos(d*x+c)^4/a^4/d-9/2*b*cos(d*x+c)^2/a^4/d-1/2*b^3/a^4/d/(b+a*cos(d*x+c))^2+3*b^2/a^4/d/(b+a*cos(d*x+c))-3/5*cos(d*x+c)^5/a^3/d+1/7*cos(d*x+c)^7/a^3/d-cos(d*x+c)/a^3/d+cos(d*x+c)^3/a^3/d","A"
222,1,355,231,0.523000," ","int(sin(d*x+c)^5/(a+b*sec(d*x+c))^3,x)","-\frac{\cos^{5}\left(d x +c \right)}{5 a^{3} d}+\frac{3 b \left(\cos^{4}\left(d x +c \right)\right)}{4 a^{4} d}+\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{3 a^{3} d}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right) b^{2}}{d \,a^{5}}-\frac{3 b \left(\cos^{2}\left(d x +c \right)\right)}{a^{4} d}+\frac{5 \left(\cos^{2}\left(d x +c \right)\right) b^{3}}{d \,a^{6}}-\frac{\cos \left(d x +c \right)}{a^{3} d}+\frac{12 \cos \left(d x +c \right) b^{2}}{d \,a^{5}}-\frac{15 \cos \left(d x +c \right) b^{4}}{d \,a^{7}}-\frac{b^{3}}{2 a^{4} d \left(b +a \cos \left(d x +c \right)\right)^{2}}+\frac{b^{5}}{d \,a^{6} \left(b +a \cos \left(d x +c \right)\right)^{2}}-\frac{b^{7}}{2 d \,a^{8} \left(b +a \cos \left(d x +c \right)\right)^{2}}+\frac{3 b \ln \left(b +a \cos \left(d x +c \right)\right)}{a^{4} d}-\frac{20 b^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{6}}+\frac{21 b^{5} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{8}}+\frac{3 b^{2}}{a^{4} d \left(b +a \cos \left(d x +c \right)\right)}-\frac{10 b^{4}}{d \,a^{6} \left(b +a \cos \left(d x +c \right)\right)}+\frac{7 b^{6}}{d \,a^{8} \left(b +a \cos \left(d x +c \right)\right)}"," ",0,"-1/5*cos(d*x+c)^5/a^3/d+3/4*b*cos(d*x+c)^4/a^4/d+2/3*cos(d*x+c)^3/a^3/d-2/d/a^5*cos(d*x+c)^3*b^2-3*b*cos(d*x+c)^2/a^4/d+5/d/a^6*cos(d*x+c)^2*b^3-cos(d*x+c)/a^3/d+12/d/a^5*cos(d*x+c)*b^2-15/d/a^7*cos(d*x+c)*b^4-1/2*b^3/a^4/d/(b+a*cos(d*x+c))^2+1/d*b^5/a^6/(b+a*cos(d*x+c))^2-1/2/d*b^7/a^8/(b+a*cos(d*x+c))^2+3*b*ln(b+a*cos(d*x+c))/a^4/d-20/d/a^6*b^3*ln(b+a*cos(d*x+c))+21/d/a^8*b^5*ln(b+a*cos(d*x+c))+3*b^2/a^4/d/(b+a*cos(d*x+c))-10/d*b^4/a^6/(b+a*cos(d*x+c))+7/d*b^6/a^8/(b+a*cos(d*x+c))","A"
223,1,200,152,0.517000," ","int(sin(d*x+c)^3/(a+b*sec(d*x+c))^3,x)","\frac{\cos^{3}\left(d x +c \right)}{3 a^{3} d}-\frac{3 b \left(\cos^{2}\left(d x +c \right)\right)}{2 a^{4} d}-\frac{\cos \left(d x +c \right)}{a^{3} d}+\frac{6 \cos \left(d x +c \right) b^{2}}{d \,a^{5}}-\frac{b^{3}}{2 a^{4} d \left(b +a \cos \left(d x +c \right)\right)^{2}}+\frac{b^{5}}{2 d \,a^{6} \left(b +a \cos \left(d x +c \right)\right)^{2}}+\frac{3 b \ln \left(b +a \cos \left(d x +c \right)\right)}{a^{4} d}-\frac{10 b^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{6}}+\frac{3 b^{2}}{a^{4} d \left(b +a \cos \left(d x +c \right)\right)}-\frac{5 b^{4}}{d \,a^{6} \left(b +a \cos \left(d x +c \right)\right)}"," ",0,"1/3*cos(d*x+c)^3/a^3/d-3/2*b*cos(d*x+c)^2/a^4/d-cos(d*x+c)/a^3/d+6/d/a^5*cos(d*x+c)*b^2-1/2*b^3/a^4/d/(b+a*cos(d*x+c))^2+1/2/d*b^5/a^6/(b+a*cos(d*x+c))^2+3*b*ln(b+a*cos(d*x+c))/a^4/d-10/d/a^6*b^3*ln(b+a*cos(d*x+c))+3*b^2/a^4/d/(b+a*cos(d*x+c))-5/d*b^4/a^6/(b+a*cos(d*x+c))","A"
224,1,96,81,0.145000," ","int(sin(d*x+c)/(a+b*sec(d*x+c))^3,x)","-\frac{b}{2 d \,a^{2} \left(a +b \sec \left(d x +c \right)\right)^{2}}+\frac{3 b \ln \left(a +b \sec \left(d x +c \right)\right)}{d \,a^{4}}-\frac{2 b}{d \,a^{3} \left(a +b \sec \left(d x +c \right)\right)}-\frac{1}{d \,a^{3} \sec \left(d x +c \right)}-\frac{3 b \ln \left(\sec \left(d x +c \right)\right)}{d \,a^{4}}"," ",0,"-1/2/d*b/a^2/(a+b*sec(d*x+c))^2+3/d/a^4*b*ln(a+b*sec(d*x+c))-2/d/a^3*b/(a+b*sec(d*x+c))-1/d/a^3/sec(d*x+c)-3/d/a^4*b*ln(sec(d*x+c))","A"
225,1,206,157,0.510000," ","int(csc(d*x+c)/(a+b*sec(d*x+c))^3,x)","-\frac{b^{3}}{2 d \,a^{2} \left(a +b \right) \left(a -b \right) \left(b +a \cos \left(d x +c \right)\right)^{2}}+\frac{3 b \ln \left(b +a \cos \left(d x +c \right)\right) a^{2}}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}+\frac{b^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}+\frac{3 b^{2}}{d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(b +a \cos \left(d x +c \right)\right)}-\frac{b^{4}}{d \left(a +b \right)^{2} \left(a -b \right)^{2} a^{2} \left(b +a \cos \left(d x +c \right)\right)}+\frac{\ln \left(-1+\cos \left(d x +c \right)\right)}{2 d \left(a +b \right)^{3}}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{2 \left(a -b \right)^{3} d}"," ",0,"-1/2/d/a^2*b^3/(a+b)/(a-b)/(b+a*cos(d*x+c))^2+3/d*b/(a+b)^3/(a-b)^3*ln(b+a*cos(d*x+c))*a^2+1/d*b^3/(a+b)^3/(a-b)^3*ln(b+a*cos(d*x+c))+3/d*b^2/(a+b)^2/(a-b)^2/(b+a*cos(d*x+c))-1/d*b^4/(a+b)^2/(a-b)^2/a^2/(b+a*cos(d*x+c))+1/2/d/(a+b)^3*ln(-1+cos(d*x+c))-1/2*ln(1+cos(d*x+c))/(a-b)^3/d","A"
226,1,322,221,0.680000," ","int(csc(d*x+c)^3/(a+b*sec(d*x+c))^3,x)","-\frac{b^{3}}{2 d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(b +a \cos \left(d x +c \right)\right)^{2}}+\frac{3 b \ln \left(b +a \cos \left(d x +c \right)\right) a^{4}}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{8 b^{3} \ln \left(b +a \cos \left(d x +c \right)\right) a^{2}}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{b^{5} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{3 b^{2} a^{2}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}+\frac{b^{4}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}+\frac{1}{4 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}{4 d \left(a +b \right)^{4}}-\frac{\ln \left(-1+\cos \left(d x +c \right)\right) b}{2 d \left(a +b \right)^{4}}+\frac{1}{4 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}{4 d \left(a -b \right)^{4}}-\frac{\ln \left(1+\cos \left(d x +c \right)\right) b}{2 d \left(a -b \right)^{4}}"," ",0,"-1/2/d*b^3/(a+b)^2/(a-b)^2/(b+a*cos(d*x+c))^2+3/d*b/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))*a^4+8/d*b^3/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))*a^2+1/d*b^5/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))+3/d*b^2/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))*a^2+1/d*b^4/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))+1/4/d/(a+b)^3/(-1+cos(d*x+c))+1/4/d/(a+b)^4*ln(-1+cos(d*x+c))*a-1/2/d/(a+b)^4*ln(-1+cos(d*x+c))*b+1/4/d/(a-b)^3/(1+cos(d*x+c))-1/4/d/(a-b)^4*ln(1+cos(d*x+c))*a-1/2/d/(a-b)^4*ln(1+cos(d*x+c))*b","A"
227,1,427,303,0.640000," ","int(csc(d*x+c)^5/(a+b*sec(d*x+c))^3,x)","-\frac{b^{3} a^{2}}{2 d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)^{2}}+\frac{3 a^{6} b \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{5} \left(a -b \right)^{5}}+\frac{15 a^{4} b^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{5} \left(a -b \right)^{5}}+\frac{6 a^{2} b^{5} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{5} \left(a -b \right)^{5}}+\frac{3 a^{4} b^{2}}{d \left(a +b \right)^{4} \left(a -b \right)^{4} \left(b +a \cos \left(d x +c \right)\right)}+\frac{3 a^{2} b^{4}}{d \left(a +b \right)^{4} \left(a -b \right)^{4} \left(b +a \cos \left(d x +c \right)\right)}-\frac{1}{16 d \left(a +b \right)^{3} \left(-1+\cos \left(d x +c \right)\right)^{2}}+\frac{3 a}{16 d \left(a +b \right)^{4} \left(-1+\cos \left(d x +c \right)\right)}-\frac{3 b}{16 d \left(a +b \right)^{4} \left(-1+\cos \left(d x +c \right)\right)}+\frac{3 a^{2} \ln \left(-1+\cos \left(d x +c \right)\right)}{16 d \left(a +b \right)^{5}}-\frac{9 a \ln \left(-1+\cos \left(d x +c \right)\right) b}{16 d \left(a +b \right)^{5}}+\frac{1}{16 d \left(a -b \right)^{3} \left(1+\cos \left(d x +c \right)\right)^{2}}+\frac{3 a}{16 d \left(a -b \right)^{4} \left(1+\cos \left(d x +c \right)\right)}+\frac{3 b}{16 d \left(a -b \right)^{4} \left(1+\cos \left(d x +c \right)\right)}-\frac{3 a^{2} \ln \left(1+\cos \left(d x +c \right)\right)}{16 d \left(a -b \right)^{5}}-\frac{9 a \ln \left(1+\cos \left(d x +c \right)\right) b}{16 d \left(a -b \right)^{5}}"," ",0,"-1/2/d*b^3/(a+b)^3*a^2/(a-b)^3/(b+a*cos(d*x+c))^2+3/d*a^6*b/(a+b)^5/(a-b)^5*ln(b+a*cos(d*x+c))+15/d*a^4*b^3/(a+b)^5/(a-b)^5*ln(b+a*cos(d*x+c))+6/d*a^2*b^5/(a+b)^5/(a-b)^5*ln(b+a*cos(d*x+c))+3/d*a^4*b^2/(a+b)^4/(a-b)^4/(b+a*cos(d*x+c))+3/d*a^2*b^4/(a+b)^4/(a-b)^4/(b+a*cos(d*x+c))-1/16/d/(a+b)^3/(-1+cos(d*x+c))^2+3/16/d/(a+b)^4/(-1+cos(d*x+c))*a-3/16/d/(a+b)^4/(-1+cos(d*x+c))*b+3/16/d*a^2/(a+b)^5*ln(-1+cos(d*x+c))-9/16/d*a/(a+b)^5*ln(-1+cos(d*x+c))*b+1/16/d/(a-b)^3/(1+cos(d*x+c))^2+3/16/d/(a-b)^4/(1+cos(d*x+c))*a+3/16/d/(a-b)^4/(1+cos(d*x+c))*b-3/16/d*a^2/(a-b)^5*ln(1+cos(d*x+c))-9/16/d*a/(a-b)^5*ln(1+cos(d*x+c))*b","A"
228,1,2251,508,0.594000," ","int(sin(d*x+c)^6/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-45/2/d/a^5*arctan(tan(1/2*d*x+1/2*c))*b^2+75/d/a^7*arctan(tan(1/2*d*x+1/2*c))*b^4-56/d/a^9*arctan(tan(1/2*d*x+1/2*c))*b^6+5/8/d/a^3*arctan(tan(1/2*d*x+1/2*c))-5/8/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)-480/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b^3+30/d/a^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b^4+420/d/a^8/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b^5-30/d/a^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b^4+516/5/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b-480/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b^3+420/d/a^8/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b^5+38/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b+14/d*b^7/a^8/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)^3+33/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*b^2-40/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b^3+15/d/a^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b^4+87/2/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b^2+5/d*b^3/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)-19/d*b^5/a^6/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)+14/d*b^7/a^8/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)+85/24/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9+33/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7-33/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5-85/24/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3+5/8/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11+56/d*b^7/a^9/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+21/d*b^4/a^5/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)^3-6/d*b/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))+53/d*b^3/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))+5/d*b^3/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)^3-21/d*b^4/a^5/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)-19/d*b^5/a^6/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)^3+42/d/a^8/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b^5+21/2/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b^2-680/3/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b^3-45/d/a^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b^4+210/d/a^8/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*b^5-680/3/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b^3+516/5/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b-33/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*b^2-15/d/a^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b^4+6/d*b^2/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)-15/d*b^6/a^7/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)^3-6/d*b^2/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)^3+6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b+42/d/a^8/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b^5-21/2/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*b^2-40/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b^3+6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*b+38/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b-87/2/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b^2+45/d/a^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b^4+210/d/a^8/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*b^5-103/d*b^5/a^7/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+15/d*b^6/a^7/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)","B"
229,1,1227,310,0.532000," ","int(sin(d*x+c)^4/(a+b*sec(d*x+c))^3,x)","\frac{6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{18 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{5}}+\frac{30 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{7}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{11 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{60 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{6 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{26 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{6 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{5 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{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)^{2}}-\frac{10 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{6} \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)^{2}}-\frac{6 b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \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)^{2}}-\frac{20 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{26 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{6 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \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)^{2}}-\frac{20 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{60 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{11 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5} \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)^{2}}+\frac{5 b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{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)^{2}}-\frac{11 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5} \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)^{2}}-\frac{10 b^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{6} \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)^{2}}-\frac{6 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^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{33 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 \,a^{5} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{30 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 \,a^{7} \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"-18/d/a^5*arctan(tan(1/2*d*x+1/2*c))*b^2+30/d/a^7*arctan(tan(1/2*d*x+1/2*c))*b^4+3/4/d/a^3*arctan(tan(1/2*d*x+1/2*c))+5/d*b^3/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)-10/d*b^5/a^6/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)+3/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7+11/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-11/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-3/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)-60/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*b^3+6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*b-20/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*b^3+6/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*b^2+11/d*b^4/a^5/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)^3-6/d*b/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))+33/d*b^3/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))+5/d*b^3/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)^3-11/d*b^4/a^5/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)-10/d*b^5/a^6/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)^3-20/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*b^3+26/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*b-6/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*b^2-60/d/a^6/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*b^3+6/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*b^2+26/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*b-6/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*b^2+6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*b+6/d*b^2/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)-6/d*b^2/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*tan(1/2*d*x+1/2*c)^3-30/d*b^5/a^7/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))","B"
230,1,729,248,0.464000," ","int(sin(d*x+c)^2/(a+b*sec(d*x+c))^3,x)","-\frac{6 b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{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)^{2} \left(a +b \right)}-\frac{b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \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)^{2} \left(a +b \right)}+\frac{6 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{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)^{2} \left(a +b \right)}+\frac{6 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{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)^{2} \left(a -b \right)}-\frac{b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \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)^{2} \left(a -b \right)}-\frac{6 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{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)^{2} \left(a -b \right)}-\frac{6 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 \left(a^{2}-b^{2}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{19 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 \,a^{3} \left(a^{2}-b^{2}\right) \sqrt{\left(a -b \right) \left(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 \,a^{5} \left(a^{2}-b^{2}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{6 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{12 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{5}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"-6/d*b^2/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)*tan(1/2*d*x+1/2*c)^3-1/d*b^3/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)*tan(1/2*d*x+1/2*c)^3+6/d*b^4/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)*tan(1/2*d*x+1/2*c)^3+6/d*b^2/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)*tan(1/2*d*x+1/2*c)-1/d*b^3/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)*tan(1/2*d*x+1/2*c)-6/d*b^4/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)*tan(1/2*d*x+1/2*c)-6/d*b/a/(a^2-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))+19/d*b^3/a^3/(a^2-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))-12/d*b^5/a^5/(a^2-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))+1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*b+6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*b-1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-12/d/a^5*arctan(tan(1/2*d*x+1/2*c))*b^2+1/d/a^3*arctan(tan(1/2*d*x+1/2*c))","B"
231,1,234,341,0.579000," ","int(csc(d*x+c)^2/(a+b*sec(d*x+c))^3,x)","\frac{\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{3}-6 a^{2} b +6 b^{2} a -2 b^{3}}+\frac{2 b \left(\frac{\left(-3 a^{3} b +\frac{5}{2} a^{2} b^{2}-\frac{1}{2} a \,b^{3}+b^{4}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(3 a^{3} b +\frac{5}{2} a^{2} b^{2}+\frac{1}{2} a \,b^{3}+b^{4}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\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)^{2}}-\frac{3 \left(2 a^{2}+3 b^{2}\right) 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)}{2 \sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a -b \right)^{3} \left(a +b \right)^{3}}-\frac{1}{2 \left(a +b \right)^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{d}"," ",0,"1/d*(1/2/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)+2*b/(a-b)^3/(a+b)^3*(((-3*a^3*b+5/2*a^2*b^2-1/2*a*b^3+b^4)*tan(1/2*d*x+1/2*c)^3+(3*a^3*b+5/2*a^2*b^2+1/2*a*b^3+b^4)*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)^2-3/2*(2*a^2+3*b^2)*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/(a+b)^3/tan(1/2*d*x+1/2*c))","A"
232,1,328,472,0.620000," ","int(csc(d*x+c)^4/(a+b*sec(d*x+c))^3,x)","\frac{\frac{\frac{a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{3}+3 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{8 \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right) \left(a -b \right)}+\frac{2 a b \left(\frac{\left(\frac{5}{2} b^{2} a^{3}+3 a \,b^{4}-3 b \,a^{4}-\frac{5}{2} a^{2} b^{3}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(\frac{5}{2} b^{2} a^{3}+3 a \,b^{4}+3 b \,a^{4}+\frac{5}{2} a^{2} b^{3}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\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)^{2}}-\frac{\left(6 a^{4}+23 a^{2} b^{2}+6 b^{4}\right) \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)}{2 \sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a -b \right)^{4} \left(a +b \right)^{4}}-\frac{1}{24 \left(a +b \right)^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{3 a -3 b}{8 \left(a +b \right)^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{d}"," ",0,"1/d*(1/8/(a^3-3*a^2*b+3*a*b^2-b^3)/(a-b)*(1/3*a*tan(1/2*d*x+1/2*c)^3-1/3*tan(1/2*d*x+1/2*c)^3*b+3*a*tan(1/2*d*x+1/2*c)+3*tan(1/2*d*x+1/2*c)*b)+2*a*b/(a-b)^4/(a+b)^4*(((5/2*b^2*a^3+3*a*b^4-3*b*a^4-5/2*a^2*b^3)*tan(1/2*d*x+1/2*c)^3+(5/2*b^2*a^3+3*a*b^4+3*b*a^4+5/2*a^2*b^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)^2-1/2*(6*a^4+23*a^2*b^2+6*b^4)/((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/(a+b)^3/tan(1/2*d*x+1/2*c)^3-1/8/(a+b)^4*(3*a-3*b)/tan(1/2*d*x+1/2*c))","A"
233,1,1776,550,12.588000," ","int((e*sin(d*x+c))^(7/2)/(a+b*sec(d*x+c)),x)","\frac{2 b e \left(e \sin \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d \,a^{2}}+\frac{2 b \,e^{3} \sqrt{e \sin \left(d x +c \right)}}{d \,a^{2}}-\frac{2 b^{3} e^{3} \sqrt{e \sin \left(d x +c \right)}}{d \,a^{4}}+\frac{b \,e^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d \left(-a^{2} e^{2}+b^{2} e^{2}\right)}-\frac{2 b^{3} e^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d \,a^{2} \left(-a^{2} e^{2}+b^{2} e^{2}\right)}+\frac{b^{5} e^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d \,a^{4} \left(-a^{2} e^{2}+b^{2} e^{2}\right)}+\frac{b \,e^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d \left(-a^{2} e^{2}+b^{2} e^{2}\right)}-\frac{b^{3} e^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d \,a^{2} \left(-a^{2} e^{2}+b^{2} e^{2}\right)}+\frac{b^{5} e^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d \,a^{4} \left(-a^{2} e^{2}+b^{2} e^{2}\right)}+\frac{2 e^{4} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{7 d a \sqrt{e \sin \left(d x +c \right)}}-\frac{5 e^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{21 d a \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{4 e^{4} b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{3 d \,a^{3} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{e^{4} b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \,a^{5} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{16 e^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{21 d a \sqrt{e \sin \left(d x +c \right)}}+\frac{2 e^{4} \cos \left(d x +c \right) b^{2} \sin \left(d x +c \right)}{3 d \,a^{3} \sqrt{e \sin \left(d x +c \right)}}+\frac{e^{4} b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,a^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{a^{2}-b^{2}}\, \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{e^{4} b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{d \,a^{4} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{a^{2}-b^{2}}\, \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{e^{4} b^{6} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,a^{6} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{a^{2}-b^{2}}\, \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{e^{4} b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,a^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{a^{2}-b^{2}}\, \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{e^{4} b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{d \,a^{4} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{a^{2}-b^{2}}\, \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{e^{4} b^{6} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,a^{6} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{a^{2}-b^{2}}\, \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}"," ",0,"2/5/d*b*e/a^2*(e*sin(d*x+c))^(5/2)+2/d*b*e^3/a^2*(e*sin(d*x+c))^(1/2)-2/d*b^3*e^3/a^4*(e*sin(d*x+c))^(1/2)+1/d*b*e^5*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-2/d*b^3*e^5/a^2*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))+1/d*b^5*e^5/a^4*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))+1/2/d*b*e^5*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))-1/d*b^3*e^5/a^2*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+1/2/d*b^5*e^5/a^4*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+2/7/d*e^4/a*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)*sin(d*x+c)-5/21/d*e^4/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+4/3/d*e^4/a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/d*e^4/a^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-16/21/d*e^4/a*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*sin(d*x+c)+2/3/d*e^4/a^3*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2*sin(d*x+c)+1/2/d*e^4/a^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/d*e^4/a^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+1/2/d*e^4/a^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d*e^4/a^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+1/d*e^4/a^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d*e^4/a^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))","B"
234,1,1195,464,10.726000," ","int((e*sin(d*x+c))^(5/2)/(a+b*sec(d*x+c)),x)","\frac{2 b e \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d \,a^{2}}-\frac{b \,e^{3} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d \,a^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}+\frac{b^{3} e^{3} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d \,a^{4} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}+\frac{b \,e^{3} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d \,a^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}-\frac{b^{3} e^{3} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d \,a^{4} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}+\frac{2 e^{3} \left(\cos^{3}\left(d x +c \right)\right)}{5 d a \sqrt{e \sin \left(d x +c \right)}}-\frac{6 e^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{5 d a \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{3 e^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{5 d a \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{2 e^{3} \cos \left(d x +c \right)}{5 d a \sqrt{e \sin \left(d x +c \right)}}+\frac{2 e^{3} b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \,a^{3} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{e^{3} b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \,a^{3} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{e^{3} b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,a^{3} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{e^{3} b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,a^{5} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{e^{3} b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,a^{3} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{e^{3} b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,a^{5} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}"," ",0,"2/3/d*b*e/a^2*(e*sin(d*x+c))^(3/2)-1/2/d*b*e^3/a^2/(e^2*(a^2-b^2)/a^2)^(1/4)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+1/2/d*b^3*e^3/a^4/(e^2*(a^2-b^2)/a^2)^(1/4)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+1/d*b*e^3/a^2/(e^2*(a^2-b^2)/a^2)^(1/4)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-1/d*b^3*e^3/a^4/(e^2*(a^2-b^2)/a^2)^(1/4)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))+2/5/d/a*e^3*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)-6/5/d/a*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/5/d/a*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2/5/d/a*e^3*cos(d*x+c)/(e*sin(d*x+c))^(1/2)+2/d/a^3*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/d/a^3*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/2/d/a^3*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d/a^5*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+1/2/d/a^3*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d/a^5*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))","B"
235,1,1120,482,10.484000," ","int((e*sin(d*x+c))^(3/2)/(a+b*sec(d*x+c)),x)","\frac{2 e b \sqrt{e \sin \left(d x +c \right)}}{d \,a^{2}}+\frac{e^{3} b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d \left(-a^{2} e^{2}+b^{2} e^{2}\right)}-\frac{e^{3} b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d \,a^{2} \left(-a^{2} e^{2}+b^{2} e^{2}\right)}+\frac{e^{3} b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d \left(-a^{2} e^{2}+b^{2} e^{2}\right)}-\frac{e^{3} b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d \,a^{2} \left(-a^{2} e^{2}+b^{2} e^{2}\right)}-\frac{e^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{3 d a \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{2 e^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{3 d a \sqrt{e \sin \left(d x +c \right)}}+\frac{e^{2} b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \,a^{3} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{e^{2} b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,a^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{a^{2}-b^{2}}\, \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{e^{2} b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,a^{4} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{a^{2}-b^{2}}\, \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{e^{2} b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,a^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{a^{2}-b^{2}}\, \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{e^{2} b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,a^{4} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{a^{2}-b^{2}}\, \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}"," ",0,"2/d*e*b/a^2*(e*sin(d*x+c))^(1/2)+1/d*e^3*b*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-1/d*e^3*b^3/a^2*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))+1/2/d*e^3*b*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))-1/2/d*e^3*b^3/a^2*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))-1/3/d/a*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2/3/d/a*e^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*sin(d*x+c)+1/d/a^3*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/2/d/a^2*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d/a^4*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d/a^2*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+1/2/d/a^4*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))","B"
236,1,919,396,6.692000," ","int((e*sin(d*x+c))^(1/2)/(a+b*sec(d*x+c)),x)","\frac{e b \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d \,a^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}-\frac{e b \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d \,a^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}-\frac{e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) b^{2} \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{a}{-a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{a^{2}-b^{2}}}{2 d \,a^{2} \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) b^{2} \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{a}{a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{a^{2}-b^{2}}}{2 d \,a^{2} \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{2 e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) b^{2} \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d a \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) b^{2} \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d a \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) b^{2} \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{a}{-a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right)}{2 d a \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) b^{2} \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{a}{a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right)}{2 d a \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}"," ",0,"1/d*e*b/a^2/(e^2*(a^2-b^2)/a^2)^(1/4)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-1/2/d*e*b/a^2/(e^2*(a^2-b^2)/a^2)^(1/4)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))-1/2/d*e*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*b^2/a^2/(-a+(a^2-b^2)^(1/2))/(a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-a/(-a+(a^2-b^2)^(1/2)),1/2*2^(1/2))*(a^2-b^2)^(1/2)+1/2/d*e*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*b^2/a^2/(-a+(a^2-b^2)^(1/2))/(a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),a/(a+(a^2-b^2)^(1/2)),1/2*2^(1/2))*(a^2-b^2)^(1/2)+2/d*e*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*b^2/a/(-a+(a^2-b^2)^(1/2))/(a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/d*e*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*b^2/a/(-a+(a^2-b^2)^(1/2))/(a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/2/d*e*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*b^2/a/(-a+(a^2-b^2)^(1/2))/(a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-a/(-a+(a^2-b^2)^(1/2)),1/2*2^(1/2))-1/2/d*e*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*b^2/a/(-a+(a^2-b^2)^(1/2))/(a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),a/(a+(a^2-b^2)^(1/2)),1/2*2^(1/2))","B"
237,1,937,414,7.104000," ","int(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(1/2),x)","\frac{b e \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d \left(-a^{2} e^{2}+b^{2} e^{2}\right)}+\frac{b e \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d \left(-a^{2} e^{2}+b^{2} e^{2}\right)}-\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \left(a^{2}-b^{2}\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d a \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{a}{-a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right) b^{2}}{2 d a \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{a}{-a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right) b^{2}}{2 d \sqrt{a^{2}-b^{2}}\, \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{a}{a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right) b^{2}}{2 d a \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{a}{a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right) b^{2}}{2 d \sqrt{a^{2}-b^{2}}\, \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}"," ",0,"1/2/d*b*e*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+1/d*b*e*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-1/d/a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*(a^2-b^2)/(-a+(a^2-b^2)^(1/2))/(a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/d*a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(-a+(a^2-b^2)^(1/2))/(a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/2/d/a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(-a+(a^2-b^2)^(1/2))/(a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-a/(-a+(a^2-b^2)^(1/2)),1/2*2^(1/2))*b^2-1/2/d*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(a^2-b^2)^(1/2)/(-a+(a^2-b^2)^(1/2))/(a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-a/(-a+(a^2-b^2)^(1/2)),1/2*2^(1/2))*b^2-1/2/d/a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(-a+(a^2-b^2)^(1/2))/(a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),a/(a+(a^2-b^2)^(1/2)),1/2*2^(1/2))*b^2+1/2/d*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(a^2-b^2)^(1/2)/(-a+(a^2-b^2)^(1/2))/(a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),a/(a+(a^2-b^2)^(1/2)),1/2*2^(1/2))*b^2","B"
238,1,1083,468,7.710000," ","int(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x)","\frac{b \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d e \left(a -b \right) \left(a +b \right) \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}-\frac{b \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d e \left(a -b \right) \left(a +b \right) \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}+\frac{2 b}{d e \left(a^{2}-b^{2}\right) \sqrt{e \sin \left(d x +c \right)}}+\frac{b^{2} \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{a}{a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right)}{2 d e \sqrt{a^{2}-b^{2}}\, \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) a \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{a}{a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right)}{2 d e \left(a^{2}-b^{2}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{2 b^{2} \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) a}{d e \left(a^{2}-b^{2}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{b^{2} \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) a}{d e \left(a^{2}-b^{2}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{a}{-a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right)}{2 d e \sqrt{a^{2}-b^{2}}\, \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) a \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{a}{-a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right)}{2 d e \left(a^{2}-b^{2}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{2 b^{2} \cos \left(d x +c \right) a}{d e \left(a^{2}-b^{2}\right) \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \sqrt{e \sin \left(d x +c \right)}}"," ",0,"1/d/e*b/(a-b)/(a+b)/(e^2*(a^2-b^2)/a^2)^(1/4)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-1/2/d/e*b/(a-b)/(a+b)/(e^2*(a^2-b^2)/a^2)^(1/4)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+2/d/e*b/(a^2-b^2)/(e*sin(d*x+c))^(1/2)+1/2/d*b^2/e/(a^2-b^2)^(1/2)/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),a/(a+(a^2-b^2)^(1/2)),1/2*2^(1/2))*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)-1/2/d*b^2/e/(a^2-b^2)/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*a*EllipticPi((-sin(d*x+c)+1)^(1/2),a/(a+(a^2-b^2)^(1/2)),1/2*2^(1/2))-2/d*b^2/e/(a^2-b^2)/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*a+1/d*b^2/e/(a^2-b^2)/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*a-1/2/d*b^2/e/(a^2-b^2)^(1/2)/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-a/(-a+(a^2-b^2)^(1/2)),1/2*2^(1/2))-1/2/d*b^2/e/(a^2-b^2)/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*a*EllipticPi((-sin(d*x+c)+1)^(1/2),-a/(-a+(a^2-b^2)^(1/2)),1/2*2^(1/2))+2/d*b^2/e/(a^2-b^2)/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a","B"
239,1,681,490,11.400000," ","int(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x)","\frac{2 b}{3 d e \left(a^{2}-b^{2}\right) \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{b \,a^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d e \left(a -b \right) \left(a +b \right) \left(-a^{2} e^{2}+b^{2} e^{2}\right)}+\frac{b \,a^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d e \left(a -b \right) \left(a +b \right) \left(-a^{2} e^{2}+b^{2} e^{2}\right)}+\frac{b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \sqrt{a^{2}-b^{2}}\, \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \sqrt{a^{2}-b^{2}}\, \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{5}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{3 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \left(\cos^{2}\left(d x +c \right)-1\right)}+\frac{2 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{3 d \,e^{2} \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \left(\cos^{2}\left(d x +c \right)-1\right)}"," ",0,"2/3/d*b/e/(a^2-b^2)/(e*sin(d*x+c))^(3/2)+1/2/d*b/e/(a-b)/(a+b)*a^2*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+1/d*b/e/(a-b)/(a+b)*a^2*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))+1/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a-b)/(a+b)*b^2/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a-b)/(a+b)*b^2/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+1/3/d*a/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(cos(d*x+c)^2-1)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+2/3/d*a/e^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(cos(d*x+c)^2-1)*sin(d*x+c)","A"
240,1,1672,541,8.486000," ","int(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(7/2),x)","\frac{2 b}{5 d e \left(a +b \right) \left(a -b \right) \left(e \sin \left(d x +c \right)\right)^{\frac{5}{2}}}+\frac{2 b \,a^{2}}{d \,e^{3} \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{e \sin \left(d x +c \right)}}+\frac{b \,a^{2} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d \,e^{3} \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}-\frac{b \,a^{2} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d \,e^{3} \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}-\frac{b^{2} a^{2} \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{a}{-a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{a^{2}-b^{2}}}{2 d \,e^{3} \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{b^{2} a^{2} \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{a}{a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{a^{2}-b^{2}}}{2 d \,e^{3} \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{b^{2} a^{3} \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{a}{-a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{3} \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{b^{2} a^{3} \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{a}{a +\sqrt{a^{2}-b^{2}}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{3} \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{6 b^{2} a^{3} \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{5 d \,e^{3} \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{4 b^{4} a \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{5 d \,e^{3} \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{3 b^{2} a^{3} \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{5 d \,e^{3} \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{2 b^{4} a \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{5 d \,e^{3} \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{6 b^{2} a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{5 d \,e^{3} \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +b \right)^{2} \left(a -b \right)^{2} \sin \left(d x +c \right)^{2} \sqrt{e \sin \left(d x +c \right)}}-\frac{4 b^{4} a \left(\cos^{3}\left(d x +c \right)\right)}{5 d \,e^{3} \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +b \right)^{2} \left(a -b \right)^{2} \sin \left(d x +c \right)^{2} \sqrt{e \sin \left(d x +c \right)}}+\frac{8 b^{2} a^{3} \cos \left(d x +c \right)}{5 d \,e^{3} \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +b \right)^{2} \left(a -b \right)^{2} \sin \left(d x +c \right)^{2} \sqrt{e \sin \left(d x +c \right)}}+\frac{2 b^{4} a \cos \left(d x +c \right)}{5 d \,e^{3} \left(a +\sqrt{a^{2}-b^{2}}\right) \left(-a +\sqrt{a^{2}-b^{2}}\right) \left(a +b \right)^{2} \left(a -b \right)^{2} \sin \left(d x +c \right)^{2} \sqrt{e \sin \left(d x +c \right)}}"," ",0,"2/5/d*b/e/(a+b)/(a-b)/(e*sin(d*x+c))^(5/2)+2/d*b/e^3/(a-b)^2/(a+b)^2*a^2/(e*sin(d*x+c))^(1/2)+1/d*b/e^3*a^2/(a-b)^2/(a+b)^2/(e^2*(a^2-b^2)/a^2)^(1/4)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-1/2/d*b/e^3*a^2/(a-b)^2/(a+b)^2/(e^2*(a^2-b^2)/a^2)^(1/4)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))-1/2/d/e^3*b^2*a^2/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-a/(-a+(a^2-b^2)^(1/2)),1/2*2^(1/2))*(a^2-b^2)^(1/2)+1/2/d/e^3*b^2*a^2/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),a/(a+(a^2-b^2)^(1/2)),1/2*2^(1/2))*(a^2-b^2)^(1/2)-1/2/d/e^3*b^2*a^3/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-a/(-a+(a^2-b^2)^(1/2)),1/2*2^(1/2))-1/2/d/e^3*b^2*a^3/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),a/(a+(a^2-b^2)^(1/2)),1/2*2^(1/2))-6/5/d/e^3*b^2*a^3/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-4/5/d/e^3*b^4*a/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/5/d/e^3*b^2*a^3/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+2/5/d/e^3*b^4*a/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-6/5/d/e^3*b^2*a^3/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/(a+b)^2/(a-b)^2/sin(d*x+c)^2*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)-4/5/d/e^3*b^4*a/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/(a+b)^2/(a-b)^2/sin(d*x+c)^2*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)+8/5/d/e^3*b^2*a^3/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/(a+b)^2/(a-b)^2/sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)+2/5/d/e^3*b^4*a/(a+(a^2-b^2)^(1/2))/(-a+(a^2-b^2)^(1/2))/(a+b)^2/(a-b)^2/sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)","B"
241,1,3808,1143,21.443000," ","int((e*sin(d*x+c))^(9/2)/(a+b*sec(d*x+c))^2,x)","\text{output too large to display}"," ",0,"-1/d*e^5*sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*a^2+b^2)-5/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+7/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/a^8*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+1/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/a^6/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/a^6/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-5/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+7/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/a^8*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+34/45/d*e^5*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)/a^2-8/15/d*e^5*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2-8/3/d/a^5*e^3*b^3*(e*sin(d*x+c))^(3/2)+4/3/d/a^3*e^3*b*(e*sin(d*x+c))^(3/2)-2/9/d*e^5*cos(d*x+c)^5/(e*sin(d*x+c))^(1/2)/a^2+4/7*b*e*(e*sin(d*x+c))^(7/2)/a^3/d-1/d/a^5*e^5*b^5*(e*sin(d*x+c))^(3/2)/(-a^2*cos(d*x+c)^2*e^2+b^2*e^2)+2/d/a^3*e^5*b/(e^2*(a^2-b^2)/a^2)^(1/4)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-1/d/a^3*e^5*b/(e^2*(a^2-b^2)/a^2)^(1/4)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))-15/2/d/a^5*e^5*b^3/(e^2*(a^2-b^2)/a^2)^(1/4)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))+15/4/d/a^5*e^5*b^3/(e^2*(a^2-b^2)/a^2)^(1/4)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+11/2/d/a^7*e^5*b^5/(e^2*(a^2-b^2)/a^2)^(1/4)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-11/4/d/a^7*e^5*b^5/(e^2*(a^2-b^2)/a^2)^(1/4)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))-6/5/d*e^5*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)/a^4*b^2+6/5/d*e^5*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^4*b^2+1/d/a^3*e^5*b^3*(e*sin(d*x+c))^(3/2)/(-a^2*cos(d*x+c)^2*e^2+b^2*e^2)-1/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+7/4/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/a^6/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/4/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^8/a^8/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+7/4/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/a^6/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/4/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^8/a^8/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+48/5/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-10/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^4-24/5/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^4*b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+5/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^6*b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/d*e^5*sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/a^4/(a^2-b^2)/(-cos(d*x+c)^2*a^2+b^2)-14/15/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+7/15/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+2/d*e^5*sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^2/(a^2-b^2)/(-cos(d*x+c)^2*a^2+b^2)","B"
242,1,3412,1174,21.386000," ","int((e*sin(d*x+c))^(7/2)/(a+b*sec(d*x+c))^2,x)","\text{output too large to display}"," ",0,"-1/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/a^6/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/d*e^4*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*a^2+b^2)+4/5*b*e*(e*sin(d*x+c))^(5/2)/a^3/d+1/d/a^3*e^5*b^3*(e*sin(d*x+c))^(1/2)/(-a^2*cos(d*x+c)^2*e^2+b^2*e^2)-1/d/a^5*e^5*b^5*(e*sin(d*x+c))^(1/2)/(-a^2*cos(d*x+c)^2*e^2+b^2*e^2)+2/7/d*e^4*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)/a^2*sin(d*x+c)-16/21/d*e^4*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*sin(d*x+c)+2/d*e^4*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^4*b^2*sin(d*x+c)+1/d/a*e^5*b*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+9/4/d/a^5*e^5*b^5*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+2/d/a*e^5*b*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-13/2/d/a^3*e^5*b^3*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))+9/2/d/a^5*e^5*b^5*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-13/4/d/a^3*e^5*b^3*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+3/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/a^5/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-5/4/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^8/a^7/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-3/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/a^5/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-9/4/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^3/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+5/4/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^8/a^7/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+1/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+4/d/a^3*e^3*b*(e*sin(d*x+c))^(1/2)-8/d/a^5*e^3*b^3*(e*sin(d*x+c))^(1/2)+9/4/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^3/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-5/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^5/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+4/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^4*b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-5/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^6*b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+2/d*e^4*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^2/(a^2-b^2)/(-cos(d*x+c)^2*a^2+b^2)-1/d*e^4*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/a^4/(a^2-b^2)/(-cos(d*x+c)^2*a^2+b^2)-5/21/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+7/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/a^7/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-3/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^3/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+5/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^5/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-7/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/a^7/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^3/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))","B"
243,1,2540,914,16.079000," ","int((e*sin(d*x+c))^(5/2)/(a+b*sec(d*x+c))^2,x)","\text{Expression too large to display}"," ",0,"-1/d*e^3*sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*a^2+b^2)+6/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2/5*e^3*cos(d*x+c)/a^2/d/(e*sin(d*x+c))^(1/2)+2/5*e^3*cos(d*x+c)^3/a^2/d/(e*sin(d*x+c))^(1/2)+4/3*b*e*(e*sin(d*x+c))^(3/2)/a^3/d+1/d/a^3*e^3*b^3*(e*sin(d*x+c))^(3/2)/(-a^2*cos(d*x+c)^2*e^2+b^2*e^2)+2/d/a^3*e^3*b/(e^2*(a^2-b^2)/a^2)^(1/4)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-1/d/a^3*e^3*b/(e^2*(a^2-b^2)/a^2)^(1/4)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))-7/2/d/a^5*e^3*b^3/(e^2*(a^2-b^2)/a^2)^(1/4)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))+7/4/d/a^5*e^3*b^3/(e^2*(a^2-b^2)/a^2)^(1/4)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))-1/2/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*b^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/2/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^4*b^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/2/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-5/2/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/2/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^4*b^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*b^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-5/2/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))*b^2+5/4/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^4*b^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-3/4/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^6*b^6/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))*b^2+5/4/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^4*b^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-3/4/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^6*b^6/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+1/d*e^3*sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*b^4/(a^2-b^2)/(-cos(d*x+c)^2*a^2+b^2)-6/5/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/5/d*e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))","B"
244,1,2282,948,16.851000," ","int((e*sin(d*x+c))^(3/2)/(a+b*sec(d*x+c))^2,x)","\frac{4 b e \sqrt{e \sin \left(d x +c \right)}}{a^{3} d}+\frac{e^{3} b^{3} \sqrt{e \sin \left(d x +c \right)}}{d \,a^{3} \left(-a^{2} \left(\cos^{2}\left(d x +c \right)\right) e^{2}+b^{2} e^{2}\right)}+\frac{e^{3} b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d a \left(-a^{2} e^{2}+b^{2} e^{2}\right)}-\frac{5 e^{3} b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{4 d \,a^{3} \left(-a^{2} e^{2}+b^{2} e^{2}\right)}+\frac{2 e^{3} b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d a \left(-a^{2} e^{2}+b^{2} e^{2}\right)}-\frac{5 e^{3} b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d \,a^{3} \left(-a^{2} e^{2}+b^{2} e^{2}\right)}-\frac{e^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{3 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{2}}-\frac{2 e^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{3 d \sqrt{e \sin \left(d x +c \right)}\, a^{2}}+\frac{3 e^{2} b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{4}}-\frac{e^{2} \sin \left(d x +c \right) \cos \left(d x +c \right) b^{2}}{d \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \left(-\left(\cos^{2}\left(d x +c \right)\right) a^{2}+b^{2}\right)}+\frac{e^{2} \sin \left(d x +c \right) \cos \left(d x +c \right) b^{4}}{d \sqrt{e \sin \left(d x +c \right)}\, a^{2} \left(a^{2}-b^{2}\right) \left(-\left(\cos^{2}\left(d x +c \right)\right) a^{2}+b^{2}\right)}-\frac{e^{2} b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{2} \left(a^{2}-b^{2}\right)}+\frac{e^{2} b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{4} \left(a^{2}-b^{2}\right)}-\frac{e^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right) b^{2}}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{\frac{3}{2}} a \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{7 e^{2} b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}} \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{5 e^{2} b^{6} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{5} \left(a^{2}-b^{2}\right)^{\frac{3}{2}} \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{e^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right) b^{2}}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{\frac{3}{2}} a \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{7 e^{2} b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}} \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{5 e^{2} b^{6} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{5} \left(a^{2}-b^{2}\right)^{\frac{3}{2}} \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{3 e^{2} b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{3} \sqrt{a^{2}-b^{2}}\, \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{5 e^{2} b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{5} \sqrt{a^{2}-b^{2}}\, \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{3 e^{2} b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{3} \sqrt{a^{2}-b^{2}}\, \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{5 e^{2} b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{5} \sqrt{a^{2}-b^{2}}\, \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}"," ",0,"4*b*e*(e*sin(d*x+c))^(1/2)/a^3/d+1/d/a^3*e^3*b^3*(e*sin(d*x+c))^(1/2)/(-a^2*cos(d*x+c)^2*e^2+b^2*e^2)+1/d/a*e^3*b*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))-5/4/d/a^3*e^3*b^3*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+2/d/a*e^3*b*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-5/2/d/a^3*e^3*b^3*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-1/3/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2/3/d*e^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*sin(d*x+c)+3/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/d*e^2*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*a^2+b^2)+1/d*e^2*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*b^4/(a^2-b^2)/(-cos(d*x+c)^2*a^2+b^2)-1/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*b^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^4*b^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^(3/2)/a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))*b^2+7/4/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^3*b^4/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-5/4/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^5*b^6/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+1/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^(3/2)/a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))*b^2-7/4/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^3*b^4/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+5/4/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^5*b^6/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^3/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-5/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^5/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-3/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^3/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+5/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^5/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))","B"
245,1,1563,882,13.396000," ","int((e*sin(d*x+c))^(1/2)/(a+b*sec(d*x+c))^2,x)","\frac{e \,b^{3} \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{d a \left(a^{2}-b^{2}\right) \left(-a^{2} \left(\cos^{2}\left(d x +c \right)\right) e^{2}+b^{2} e^{2}\right)}+\frac{2 e b \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d a \left(a^{2}-b^{2}\right) \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}-\frac{3 e \,b^{3} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d \,a^{3} \left(a^{2}-b^{2}\right) \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}-\frac{e b \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d a \left(a^{2}-b^{2}\right) \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}+\frac{3 e \,b^{3} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{4 d \,a^{3} \left(a^{2}-b^{2}\right) \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}-\frac{2 e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{2}}+\frac{e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{2}}-\frac{e \left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right) b^{2}}{d \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \left(-\left(\cos^{2}\left(d x +c \right)\right) a^{2}+b^{2}\right)}+\frac{e \,b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{2} \left(a^{2}-b^{2}\right)}-\frac{e \,b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{2} \left(a^{2}-b^{2}\right)}-\frac{e \,b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{2} \left(a^{2}-b^{2}\right) \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{3 e \,b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{4} \left(a^{2}-b^{2}\right) \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{e \,b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{2} \left(a^{2}-b^{2}\right) \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{3 e \,b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{4} \left(a^{2}-b^{2}\right) \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{3 e \,b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{4} \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{3 e \,b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{4} \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}"," ",0,"1/d/a*e*b^3/(a^2-b^2)*(e*sin(d*x+c))^(3/2)/(-a^2*cos(d*x+c)^2*e^2+b^2*e^2)+2/d/a*e*b/(a^2-b^2)/(e^2*(a^2-b^2)/a^2)^(1/4)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-3/2/d/a^3*e*b^3/(a^2-b^2)/(e^2*(a^2-b^2)/a^2)^(1/4)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-1/d/a*e*b/(a^2-b^2)/(e^2*(a^2-b^2)/a^2)^(1/4)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+3/4/d/a^3*e*b^3/(a^2-b^2)/(e^2*(a^2-b^2)/a^2)^(1/4)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))-2/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/d*e*sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*a^2+b^2)+1/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/2/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/2/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/4/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/4/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/a^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/2/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/2/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))","A"
246,1,1475,913,15.314000," ","int(1/(a+b*sec(d*x+c))^2/(e*sin(d*x+c))^(1/2),x)","\frac{e \,b^{3} \sqrt{e \sin \left(d x +c \right)}}{d a \left(a^{2}-b^{2}\right) \left(-a^{2} \left(\cos^{2}\left(d x +c \right)\right) e^{2}+b^{2} e^{2}\right)}+\frac{2 a e b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d \left(a^{2}-b^{2}\right) \left(-a^{2} e^{2}+b^{2} e^{2}\right)}-\frac{e \,b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d a \left(a^{2}-b^{2}\right) \left(-a^{2} e^{2}+b^{2} e^{2}\right)}+\frac{a e b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d \left(a^{2}-b^{2}\right) \left(-a^{2} e^{2}+b^{2} e^{2}\right)}-\frac{e \,b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{4 d a \left(a^{2}-b^{2}\right) \left(-a^{2} e^{2}+b^{2} e^{2}\right)}-\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{2}}-\frac{\sin \left(d x +c \right) \cos \left(d x +c \right) b^{2}}{d \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \left(-\left(\cos^{2}\left(d x +c \right)\right) a^{2}+b^{2}\right)}-\frac{b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{2} \left(a^{2}-b^{2}\right)}-\frac{b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a \left(a^{2}-b^{2}\right)^{\frac{3}{2}} \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{5 b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}} \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a \left(a^{2}-b^{2}\right)^{\frac{3}{2}} \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{5 b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}} \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{3 b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{3} \sqrt{a^{2}-b^{2}}\, \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{3 b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, a^{3} \sqrt{a^{2}-b^{2}}\, \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}"," ",0,"1/d/a*e*b^3/(a^2-b^2)*(e*sin(d*x+c))^(1/2)/(-a^2*cos(d*x+c)^2*e^2+b^2*e^2)+2/d*a*e*b/(a^2-b^2)*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-1/2/d/a*e*b^3/(a^2-b^2)*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))+1/d*a*e*b/(a^2-b^2)*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))-1/4/d/a*e*b^3/(a^2-b^2)*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))-1/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/d*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*a^2+b^2)-1/2/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^2*b^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/2/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a*b^2/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+5/4/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^3*b^4/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+1/2/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a*b^2/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-5/4/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/a^3*b^4/(a^2-b^2)^(3/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/2/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^3/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-3/2/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/a^3/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))","A"
247,1,2263,1147,17.212000," ","int(1/(a+b*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x)","\frac{4 a b}{d e \left(a^{2}-b^{2}\right)^{2} \sqrt{e \sin \left(d x +c \right)}}+\frac{a \,b^{3} \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{d e \left(a -b \right)^{2} \left(a +b \right)^{2} \left(-a^{2} \left(\cos^{2}\left(d x +c \right)\right) e^{2}+b^{2} e^{2}\right)}+\frac{2 a b \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d e \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}-\frac{a b \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d e \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}+\frac{b^{3} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d a e \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}-\frac{b^{3} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{4 d a e \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right) b^{2} a^{2}}{d e \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(-\left(\cos^{2}\left(d x +c \right)\right) a^{2}+b^{2}\right)}+\frac{b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right)}-\frac{b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{2 d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right)}-\frac{b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{3 b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{4 d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) a^{2} \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{3 b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{4 d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) a^{2} \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{3 b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right)^{2} \left(a +b \right)^{2} \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right)^{2} \left(a +b \right)^{2} a^{2} \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{3 b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right)^{2} \left(a +b \right)^{2} \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right)^{2} \left(a +b \right)^{2} a^{2} \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{2 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}}{d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{2}}+\frac{2 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}}{d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{2}}-\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}}{d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{2}}-\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}}{d e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{2}}-\frac{2 \cos \left(d x +c \right) a^{2}}{d e \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{2}}-\frac{2 \cos \left(d x +c \right) b^{2}}{d e \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{2}}"," ",0,"4/d/e*a*b/(a^2-b^2)^2/(e*sin(d*x+c))^(1/2)+1/d*a/e*b^3/(a-b)^2/(a+b)^2*(e*sin(d*x+c))^(3/2)/(-a^2*cos(d*x+c)^2*e^2+b^2*e^2)+2/d*a/e*b/(a-b)^2/(a+b)^2/(e^2*(a^2-b^2)/a^2)^(1/4)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-1/d*a/e*b/(a-b)^2/(a+b)^2/(e^2*(a^2-b^2)/a^2)^(1/4)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+1/2/d/a/e*b^3/(a-b)^2/(a+b)^2/(e^2*(a^2-b^2)/a^2)^(1/4)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-1/4/d/a/e*b^3/(a-b)^2/(a+b)^2/(e^2*(a^2-b^2)/a^2)^(1/4)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))-1/d/e*sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)/(a+b)*a^2/(a^2-b^2)/(-cos(d*x+c)^2*a^2+b^2)+1/d/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)/(a+b)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/2/d/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)/(a+b)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/2/d/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)/(a+b)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/4/d/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)/(a+b)/(a^2-b^2)/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)/(a+b)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/4/d/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)/(a+b)/(a^2-b^2)/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/2/d/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)^2/(a+b)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)^2/(a+b)^2/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/2/d/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)^2/(a+b)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)^2/(a+b)^2/a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+2/d/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+2/d/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-1/d/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2-1/d/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-2/d/e*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*a^2-2/d/e*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*b^2","A"
248,1,2159,1171,18.902000," ","int(1/(a+b*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x)","\frac{4 a b}{3 d e \left(a^{2}-b^{2}\right)^{2} \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{a \,b^{3} \sqrt{e \sin \left(d x +c \right)}}{d e \left(a -b \right)^{2} \left(a +b \right)^{2} \left(-a^{2} \left(\cos^{2}\left(d x +c \right)\right) e^{2}+b^{2} e^{2}\right)}+\frac{a^{3} b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d e \left(a -b \right)^{2} \left(a +b \right)^{2} \left(-a^{2} e^{2}+b^{2} e^{2}\right)}+\frac{3 a \,b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \ln \left(\frac{\sqrt{e \sin \left(d x +c \right)}+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}{\sqrt{e \sin \left(d x +c \right)}-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{4 d e \left(a -b \right)^{2} \left(a +b \right)^{2} \left(-a^{2} e^{2}+b^{2} e^{2}\right)}+\frac{2 a^{3} b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{d e \left(a -b \right)^{2} \left(a +b \right)^{2} \left(-a^{2} e^{2}+b^{2} e^{2}\right)}+\frac{3 a \,b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{a^{2}}\right)^{\frac{1}{4}}}\right)}{2 d e \left(a -b \right)^{2} \left(a +b \right)^{2} \left(-a^{2} e^{2}+b^{2} e^{2}\right)}-\frac{\sin \left(d x +c \right) \cos \left(d x +c \right) b^{2} a^{2}}{d \,e^{2} \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(-\left(\cos^{2}\left(d x +c \right)\right) a^{2}+b^{2}\right)}-\frac{b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right)}-\frac{b^{2} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right)^{\frac{3}{2}} \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{5 b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{4 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right)^{\frac{3}{2}} a \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{b^{2} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right)^{\frac{3}{2}} \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{5 b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{4 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right)^{\frac{3}{2}} a \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{3 b^{2} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}\, \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right)^{2} \left(a +b \right)^{2} a \sqrt{a^{2}-b^{2}}\, \left(1-\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}-\frac{3 b^{2} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}\, \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{b^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{a^{2}-b^{2}}}{a}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right)^{2} \left(a +b \right)^{2} a \sqrt{a^{2}-b^{2}}\, \left(1+\frac{\sqrt{a^{2}-b^{2}}}{a}\right)}+\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{5}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}}{3 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{2} \left(\cos^{2}\left(d x +c \right)-1\right)}+\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{5}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}}{3 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{2} \left(\cos^{2}\left(d x +c \right)-1\right)}+\frac{2 \cos \left(d x +c \right) \sin \left(d x +c \right) a^{2}}{3 d \,e^{2} \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{2} \left(\cos^{2}\left(d x +c \right)-1\right)}+\frac{2 \cos \left(d x +c \right) \sin \left(d x +c \right) b^{2}}{3 d \,e^{2} \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{2} \left(\cos^{2}\left(d x +c \right)-1\right)}"," ",0,"4/3/d/e*a*b/(a^2-b^2)^2/(e*sin(d*x+c))^(3/2)+1/d*a/e*b^3/(a-b)^2/(a+b)^2*(e*sin(d*x+c))^(1/2)/(-a^2*cos(d*x+c)^2*e^2+b^2*e^2)+1/d*a^3/e*b/(a-b)^2/(a+b)^2*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+3/4/d*a/e*b^3/(a-b)^2/(a+b)^2*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*ln(((e*sin(d*x+c))^(1/2)+(e^2*(a^2-b^2)/a^2)^(1/4))/((e*sin(d*x+c))^(1/2)-(e^2*(a^2-b^2)/a^2)^(1/4)))+2/d*a^3/e*b/(a-b)^2/(a+b)^2*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))+3/2/d*a/e*b^3/(a-b)^2/(a+b)^2*(e^2*(a^2-b^2)/a^2)^(1/4)/(-a^2*e^2+b^2*e^2)*arctan((e*sin(d*x+c))^(1/2)/(e^2*(a^2-b^2)/a^2)^(1/4))-1/d/e^2*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)/(a+b)*a^2/(a^2-b^2)/(-cos(d*x+c)^2*a^2+b^2)-1/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)/(a+b)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)/(a+b)/(a^2-b^2)^(3/2)*a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+5/4/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)/(a+b)/(a^2-b^2)^(3/2)/a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+1/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)/(a+b)/(a^2-b^2)^(3/2)*a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-5/4/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)/(a+b)/(a^2-b^2)^(3/2)/a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+3/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)^2/(a+b)^2*a/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-1/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)^2/(a+b)^2/a/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(a^2-b^2)^(1/2)/a),1/2*2^(1/2))-3/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)^2/(a+b)^2*a/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+1/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)^2/(a+b)^2/a/(a^2-b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(a^2-b^2)^(1/2)/a)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(a^2-b^2)^(1/2)/a),1/2*2^(1/2))+1/3/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(cos(d*x+c)^2-1)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+1/3/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(cos(d*x+c)^2-1)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2+2/3/d/e^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(cos(d*x+c)^2-1)*sin(d*x+c)*a^2+2/3/d/e^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(cos(d*x+c)^2-1)*sin(d*x+c)*b^2","A"
249,1,215,116,1.335000," ","int((a+b*sec(f*x+e))^(1/2),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -2 a \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right)\right) \left(-1+\cos \left(f x +e \right)\right)}{f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2}}"," ",0,"-2/f*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*(1+cos(f*x+e))^2*(EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a-EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b-2*a*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2)))*(-1+cos(f*x+e))/(b+a*cos(f*x+e))/sin(f*x+e)^2","A"
250,1,264,110,1.341000," ","int(csc(f*x+e)^2*(a+b*sec(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(\sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(f x +e \right) \cos \left(f x +e \right)+\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) b +a \left(\cos^{2}\left(f x +e \right)\right)+b \cos \left(f x +e \right)\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}}{f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{5}}"," ",0,"-1/f*(-1+cos(f*x+e))^2*((cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b*sin(f*x+e)*cos(f*x+e)+EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*b+a*cos(f*x+e)^2+b*cos(f*x+e))*(1+cos(f*x+e))^2*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)/(b+a*cos(f*x+e))/sin(f*x+e)^5","B"
251,1,1199,282,1.366000," ","int((a+b*sec(f*x+e))^(3/2),x)","\frac{2 \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(\cos \left(f x +e \right) a^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)-2 \cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -\cos \left(f x +e \right) b^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)+\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +\cos \left(f x +e \right) b^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)-2 \cos \left(f x +e \right) a^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right)+\sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(f x +e \right)-2 \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -b^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)+\sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +b^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)-2 a^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right)-\left(\cos^{2}\left(f x +e \right)\right) a b +a b \cos \left(f x +e \right)-\cos \left(f x +e \right) b^{2}+b^{2}\right)}{f \sin \left(f x +e \right)^{5} \left(b +a \cos \left(f x +e \right)\right)}"," ",0,"2/f*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(cos(f*x+e)*a^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))-2*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b-cos(f*x+e)*b^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))+cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b+cos(f*x+e)*b^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))-2*cos(f*x+e)*a^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))+(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*sin(f*x+e)-2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b-b^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))+(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b+b^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))-2*a^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))-cos(f*x+e)^2*a*b+a*b*cos(f*x+e)-cos(f*x+e)*b^2+b^2)/sin(f*x+e)^5/(b+a*cos(f*x+e))","B"
252,1,849,208,1.388000," ","int(csc(f*x+e)^2*(a+b*sec(f*x+e))^(3/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(3 \cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +3 \cos \left(f x +e \right) b^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)-3 \cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -3 \cos \left(f x +e \right) b^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)+3 \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +3 b^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)-3 \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -3 b^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)-a^{2} \left(\cos^{2}\left(f x +e \right)\right)-3 \left(\cos^{2}\left(f x +e \right)\right) a b +a b \cos \left(f x +e \right)-3 \cos \left(f x +e \right) b^{2}+2 b^{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}}{f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{5}}"," ",0,"1/f*(-1+cos(f*x+e))^2*(3*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b+3*cos(f*x+e)*b^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))-3*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b-3*cos(f*x+e)*b^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))+3*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b+3*b^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))-3*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b-3*b^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))-a^2*cos(f*x+e)^2-3*cos(f*x+e)^2*a*b+a*b*cos(f*x+e)-3*cos(f*x+e)*b^2+2*b^2)*(1+cos(f*x+e))^2*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)/(b+a*cos(f*x+e))/sin(f*x+e)^5","B"
253,1,178,97,1.357000," ","int(1/(a+b*sec(f*x+e))^(1/2),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)-2 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right)\right) \left(-1+\cos \left(f x +e \right)\right)}{f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2}}"," ",0,"-2/f*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*(1+cos(f*x+e))^2*(EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))-2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2)))*(-1+cos(f*x+e))/(b+a*cos(f*x+e))/sin(f*x+e)^2","A"
254,1,852,233,1.490000," ","int(csc(f*x+e)^2/(a+b*sec(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +\cos \left(f x +e \right) b^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)-\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -\cos \left(f x +e \right) b^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)+\sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +b^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)-\sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -b^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)+a^{2} \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) a b +a b \cos \left(f x +e \right)-\cos \left(f x +e \right) b^{2}\right) \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}}{f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{5} \left(a -b \right) \left(a +b \right)}"," ",0,"-1/f*(-1+cos(f*x+e))^2*(cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b+cos(f*x+e)*b^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))-cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b-cos(f*x+e)*b^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))+(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b+b^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))-(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b-b^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))+a^2*cos(f*x+e)^2-cos(f*x+e)^2*a*b+a*b*cos(f*x+e)-cos(f*x+e)*b^2)*(1+cos(f*x+e))^2*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)/(b+a*cos(f*x+e))/sin(f*x+e)^5/(a-b)/(a+b)","B"
255,1,1209,318,1.450000," ","int(1/(a+b*sec(f*x+e))^(3/2),x)","\frac{\sqrt{4}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(\cos \left(f x +e \right) a^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)+\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -\cos \left(f x +e \right) b^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)-2 \cos \left(f x +e \right) a^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right)+2 \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+\sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(f x +e \right)+\sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -\sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -b^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)-2 a^{2} \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right)+2 \sin \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+\left(\cos^{2}\left(f x +e \right)\right) a b -b^{2} \left(\cos^{2}\left(f x +e \right)\right)-a b \cos \left(f x +e \right)+\cos \left(f x +e \right) b^{2}\right)}{f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right) a \left(a +b \right) \left(a -b \right)}"," ",0,"1/f*4^(1/2)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)*a^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))+cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b-cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b-cos(f*x+e)*b^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))-2*cos(f*x+e)*a^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))+2*sin(f*x+e)*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*b^2+(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*sin(f*x+e)+(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b-(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b-b^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))-2*a^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))+2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*b^2+cos(f*x+e)^2*a*b-b^2*cos(f*x+e)^2-a*b*cos(f*x+e)+cos(f*x+e)*b^2)/(b+a*cos(f*x+e))/sin(f*x+e)/a/(a+b)/(a-b)","B"
256,1,1065,294,1.318000," ","int(csc(f*x+e)^2/(a+b*sec(f*x+e))^(3/2),x)","\frac{\left(3 \sin \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \cos \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +4 \sin \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \cos \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+\sin \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \cos \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-4 \sin \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \cos \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -4 \sin \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \cos \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+3 \sin \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +4 \sin \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+\sin \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-4 \sin \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -4 \sin \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-\left(\cos^{2}\left(f x +e \right)\right) a^{3}+4 a^{2} \left(\cos^{2}\left(f x +e \right)\right) b -3 \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}-3 \cos \left(f x +e \right) a^{2} b +4 \cos \left(f x +e \right) a \,b^{2}-\cos \left(f x +e \right) b^{3}\right) \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{4}}{2 f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right) \left(a -b \right)^{2} \left(a +b \right)^{2}}"," ",0,"1/2/f*(3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*b+4*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b^2+sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b^3-4*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*b-4*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*cos(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b^2+3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*b+4*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b^2+sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b^3-4*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*b-4*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b^2-cos(f*x+e)^2*a^3+4*a^2*cos(f*x+e)^2*b-3*cos(f*x+e)^2*a*b^2-3*cos(f*x+e)*a^2*b+4*cos(f*x+e)*a*b^2-cos(f*x+e)*b^3)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*4^(1/2)/(b+a*cos(f*x+e))/sin(f*x+e)/(a-b)^2/(a+b)^2","B"
257,0,0,233,4.120000," ","int((a+b*sec(d*x+c))^3*(e*sin(d*x+c))^m,x)","\int \left(a +b \sec \left(d x +c \right)\right)^{3} \left(e \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+b*sec(d*x+c))^3*(e*sin(d*x+c))^m,x)","F"
258,0,0,176,4.091000," ","int((a+b*sec(d*x+c))^2*(e*sin(d*x+c))^m,x)","\int \left(a +b \sec \left(d x +c \right)\right)^{2} \left(e \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+b*sec(d*x+c))^2*(e*sin(d*x+c))^m,x)","F"
259,0,0,111,2.644000," ","int((a+b*sec(d*x+c))*(e*sin(d*x+c))^m,x)","\int \left(a +b \sec \left(d x +c \right)\right) \left(e \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+b*sec(d*x+c))*(e*sin(d*x+c))^m,x)","F"
260,0,0,209,1.976000," ","int((e*sin(d*x+c))^m/(a+b*sec(d*x+c)),x)","\int \frac{\left(e \sin \left(d x +c \right)\right)^{m}}{a +b \sec \left(d x +c \right)}\, dx"," ",0,"int((e*sin(d*x+c))^m/(a+b*sec(d*x+c)),x)","F"
261,0,0,365,1.135000," ","int((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^2,x)","\int \frac{\left(e \sin \left(d x +c \right)\right)^{m}}{\left(a +b \sec \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^2,x)","F"
262,0,0,523,1.220000," ","int((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^3,x)","\int \frac{\left(e \sin \left(d x +c \right)\right)^{m}}{\left(a +b \sec \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^3,x)","F"
263,0,0,25,1.134000," ","int((a+b*sec(d*x+c))^(3/2)*(e*sin(d*x+c))^m,x)","\int \left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}} \left(e \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+b*sec(d*x+c))^(3/2)*(e*sin(d*x+c))^m,x)","F"
264,0,0,25,1.083000," ","int((e*sin(d*x+c))^m*(a+b*sec(d*x+c))^(1/2),x)","\int \left(e \sin \left(d x +c \right)\right)^{m} \sqrt{a +b \sec \left(d x +c \right)}\, dx"," ",0,"int((e*sin(d*x+c))^m*(a+b*sec(d*x+c))^(1/2),x)","F"
265,0,0,25,1.022000," ","int((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^(1/2),x)","\int \frac{\left(e \sin \left(d x +c \right)\right)^{m}}{\sqrt{a +b \sec \left(d x +c \right)}}\, dx"," ",0,"int((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^(1/2),x)","F"
266,0,0,25,0.991000," ","int((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^(3/2),x)","\int \frac{\left(e \sin \left(d x +c \right)\right)^{m}}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^(3/2),x)","F"
267,0,0,25,2.441000," ","int((a+b*sec(d*x+c))^n*(e*sin(d*x+c))^m,x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \left(e \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((a+b*sec(d*x+c))^n*(e*sin(d*x+c))^m,x)","F"
268,0,0,156,2.723000," ","int((a+b*sec(d*x+c))^n*sin(d*x+c)^5,x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \left(\sin^{5}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sec(d*x+c))^n*sin(d*x+c)^5,x)","F"
269,0,0,119,2.710000," ","int((a+b*sec(d*x+c))^n*sin(d*x+c)^3,x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \left(\sin^{3}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sec(d*x+c))^n*sin(d*x+c)^3,x)","F"
270,0,0,50,0.987000," ","int((a+b*sec(d*x+c))^n*sin(d*x+c),x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \sin \left(d x +c \right)\, dx"," ",0,"int((a+b*sec(d*x+c))^n*sin(d*x+c),x)","F"
271,0,0,115,1.066000," ","int(csc(d*x+c)*(a+b*sec(d*x+c))^n,x)","\int \csc \left(d x +c \right) \left(a +b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)*(a+b*sec(d*x+c))^n,x)","F"
272,0,0,231,1.141000," ","int(csc(d*x+c)^3*(a+b*sec(d*x+c))^n,x)","\int \left(\csc^{3}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)^3*(a+b*sec(d*x+c))^n,x)","F"
273,0,0,23,3.605000," ","int((a+b*sec(d*x+c))^n*sin(d*x+c)^4,x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \left(\sin^{4}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sec(d*x+c))^n*sin(d*x+c)^4,x)","F"
274,0,0,23,2.834000," ","int((a+b*sec(d*x+c))^n*sin(d*x+c)^2,x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \left(\sin^{2}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sec(d*x+c))^n*sin(d*x+c)^2,x)","F"
275,0,0,122,1.135000," ","int(csc(d*x+c)^2*(a+b*sec(d*x+c))^n,x)","\int \left(\csc^{2}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)^2*(a+b*sec(d*x+c))^n,x)","F"
276,0,0,363,1.260000," ","int(csc(d*x+c)^4*(a+b*sec(d*x+c))^n,x)","\int \left(\csc^{4}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)^4*(a+b*sec(d*x+c))^n,x)","F"
277,0,0,23,0.895000," ","int((a+b*sec(d*x+c))^n*sin(d*x+c)^(3/2),x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \left(\sin^{\frac{3}{2}}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sec(d*x+c))^n*sin(d*x+c)^(3/2),x)","F"
278,0,0,23,0.805000," ","int((a+b*sec(d*x+c))^n*sin(d*x+c)^(1/2),x)","\int \left(a +b \sec \left(d x +c \right)\right)^{n} \left(\sqrt{\sin}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sec(d*x+c))^n*sin(d*x+c)^(1/2),x)","F"
279,0,0,23,0.822000," ","int((a+b*sec(d*x+c))^n/sin(d*x+c)^(1/2),x)","\int \frac{\left(a +b \sec \left(d x +c \right)\right)^{n}}{\sqrt{\sin \left(d x +c \right)}}\, dx"," ",0,"int((a+b*sec(d*x+c))^n/sin(d*x+c)^(1/2),x)","F"
280,0,0,23,0.828000," ","int((a+b*sec(d*x+c))^n/sin(d*x+c)^(3/2),x)","\int \frac{\left(a +b \sec \left(d x +c \right)\right)^{n}}{\sin \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^n/sin(d*x+c)^(3/2),x)","F"
281,1,679,194,2.098000," ","int((e*csc(d*x+c))^(5/2)*(a+a*sec(d*x+c)),x)","\frac{a \left(-1+\cos \left(d x +c \right)\right) \left(4 i \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right) \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-3 i \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right) \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-3 i \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right) \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-3 \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right) \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+3 \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right) \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+2 \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}}{6 d \sin \left(d x +c \right)}"," ",0,"1/6*a/d*(-1+cos(d*x+c))*(4*I*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*I*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*I*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-3*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*2^(1/2))*(1+cos(d*x+c))^2*(e/sin(d*x+c))^(5/2)/sin(d*x+c)*2^(1/2)","C"
282,1,1522,179,1.664000," ","int((e*csc(d*x+c))^(3/2)*(a+a*sec(d*x+c)),x)","\frac{a \left(i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+\cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+\cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+4 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-2 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+i \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-i \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+4 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-2 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-4 \sqrt{2}\right) \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}}{2 d}"," ",0,"1/2*a/d*(I*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)-I*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+4*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)-I*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+4*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-4*2^(1/2))*(e/sin(d*x+c))^(3/2)*sin(d*x+c)*2^(1/2)","C"
283,1,291,135,1.629000," ","int((a+a*sec(d*x+c))*(e*csc(d*x+c))^(1/2),x)","-\frac{a \sqrt{2}\, \sqrt{\frac{e}{\sin \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \left(i \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \cos \left(d x +c \right)-i+\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{i \cos \left(d x +c \right)-i+\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{i \cos \left(d x +c \right)-i+\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}}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"-1/2*a/d*2^(1/2)*(e/sin(d*x+c))^(1/2)*(-1+cos(d*x+c))*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(I*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+I*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-EllipticPi(((I*cos(d*x+c)-I+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*(1+cos(d*x+c))^2","C"
284,1,1535,136,1.443000," ","int((a+a*sec(d*x+c))/(e*csc(d*x+c))^(1/2),x)","\frac{a \left(i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+\cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+\cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-4 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+2 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+i \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-i \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-4 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+2 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-2 \cos \left(d x +c \right) \sqrt{2}+2 \sqrt{2}\right) \sqrt{2}}{2 d \sqrt{\frac{e}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)}"," ",0,"1/2*a/d*(I*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)-I*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)-4*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+I*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)-I*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)-4*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*cos(d*x+c)*2^(1/2)+2*2^(1/2))/(e/sin(d*x+c))^(1/2)/sin(d*x+c)*2^(1/2)","C"
285,1,710,188,1.324000," ","int((a+a*sec(d*x+c))/(e*csc(d*x+c))^(3/2),x)","-\frac{a \left(3 i \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-4 i \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+3 i \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+4 \cos \left(d x +c \right) \sqrt{2}-6 \sqrt{2}\right) \sqrt{2}}{6 d \left(-1+\cos \left(d x +c \right)\right) \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"-1/6*a/d*(3*I*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-4*I*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+3*I*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(d*x+c)^2*2^(1/2)+4*cos(d*x+c)*2^(1/2)-6*2^(1/2))/(-1+cos(d*x+c))/(e/sin(d*x+c))^(3/2)/sin(d*x+c)*2^(1/2)","C"
286,1,1529,201,1.316000," ","int((a+a*sec(d*x+c))/(e*csc(d*x+c))^(5/2),x)","\frac{a \left(-15 i \cos \left(d x +c \right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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 \cos \left(d x +c \right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+18 \cos \left(d x +c \right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+15 \cos \left(d x +c \right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+15 \cos \left(d x +c \right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-36 \cos \left(d x +c \right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-15 i \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{2}\, \left(\cos^{3}\left(d x +c \right)\right)+18 \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+15 \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+10 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-24 \cos \left(d x +c \right) \sqrt{2}+8 \sqrt{2}\right) \sqrt{2}}{30 d \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{3}}"," ",0,"1/30*a/d*(15*I*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-15*I*cos(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+18*cos(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+15*cos(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+15*cos(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-36*cos(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+15*I*cos(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-15*I*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+6*2^(1/2)*cos(d*x+c)^3+18*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+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)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-36*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+10*cos(d*x+c)^2*2^(1/2)-24*cos(d*x+c)*2^(1/2)+8*2^(1/2))/(e/sin(d*x+c))^(5/2)/sin(d*x+c)^3*2^(1/2)","C"
287,1,745,266,1.814000," ","int((e*csc(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(6 i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+6 i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-6 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+6 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-7 \cos \left(d x +c \right) \sqrt{2}+3 \sqrt{2}\right) \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{2}}{6 d \sin \left(d x +c \right) \cos \left(d x +c \right)}"," ",0,"-1/6*a^2/d*(-1+cos(d*x+c))*(6*I*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((I*cos(d*x+c)-I+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)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+6*I*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((I*cos(d*x+c)-I+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)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((I*cos(d*x+c)-I+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)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-7*cos(d*x+c)*2^(1/2)+3*2^(1/2))*(e/sin(d*x+c))^(5/2)*(1+cos(d*x+c))^2/sin(d*x+c)/cos(d*x+c)*2^(1/2)","C"
288,1,1593,246,1.663000," ","int((e*csc(d*x+c))^(3/2)*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \left(2 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-5 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+10 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+2 i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-2 i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+2 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+2 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-5 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+10 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-9 \cos \left(d x +c \right) \sqrt{2}+\sqrt{2}\right) \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}}{2 d \cos \left(d x +c \right)}"," ",0,"1/2*a^2/d*(2*I*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*I*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+2*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-5*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+10*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+2*I*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)-2*I*cos(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+2*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+2*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)-5*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+10*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-9*cos(d*x+c)*2^(1/2)+2^(1/2))*(e/sin(d*x+c))^(3/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2)","C"
289,1,744,166,1.899000," ","int((a+a*sec(d*x+c))^2*(e*csc(d*x+c))^(1/2),x)","\frac{a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-2 i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{2}-\sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{e}{\sin \left(d x +c \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))*(I*cos(d*x+c)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)-2*I*cos(d*x+c)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)-2*I*cos(d*x+c)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)-2*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((I*cos(d*x+c)-I+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^(1/2)-2^(1/2))*(1+cos(d*x+c))^2*(e/sin(d*x+c))^(1/2)/cos(d*x+c)/sin(d*x+c)^3*2^(1/2)","C"
290,1,1605,166,1.435000," ","int((a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(1/2),x)","\frac{a^{2} \left(2 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-2 i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+2 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-2 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+\cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+\cos \left(d x +c \right) \sqrt{2}+\sqrt{2}\right) \sqrt{2}}{2 d \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{e}{\sin \left(d x +c \right)}}}"," ",0,"1/2*a^2/d*(2*I*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*I*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+2*I*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)-2*I*cos(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+2*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-2*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+2*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+2*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)-2*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*cos(d*x+c)^2*2^(1/2)+cos(d*x+c)*2^(1/2)+2^(1/2))/sin(d*x+c)/cos(d*x+c)/(e/sin(d*x+c))^(1/2)*2^(1/2)","C"
291,1,763,226,1.334000," ","int((a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(3/2),x)","-\frac{a^{2} \left(6 i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+6 i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-13 i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-6 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+6 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+10 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-15 \cos \left(d x +c \right) \sqrt{2}+3 \sqrt{2}\right) \sqrt{2}}{6 d \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right) \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"-1/6*a^2/d*(6*I*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))+6*I*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))-13*I*cos(d*x+c)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)-6*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((I*cos(d*x+c)-I+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)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*2^(1/2)*cos(d*x+c)^3+10*cos(d*x+c)^2*2^(1/2)-15*cos(d*x+c)*2^(1/2)+3*2^(1/2))/(-1+cos(d*x+c))/cos(d*x+c)/(e/sin(d*x+c))^(3/2)/sin(d*x+c)*2^(1/2)","C"
292,1,1636,238,1.321000," ","int((a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(5/2),x)","-\frac{a^{2} \left(-30 i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+30 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+30 i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-30 i \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+27 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-54 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-30 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-30 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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^{4}\left(d x +c \right)\right) \sqrt{2}+27 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-54 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-30 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-30 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticPi \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-20 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+47 \cos \left(d x +c \right) \sqrt{2}-15 \sqrt{2}\right) \sqrt{2}}{30 d \cos \left(d x +c \right) \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{3}}"," ",0,"-1/30*a^2/d*(-30*I*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)-30*I*cos(d*x+c)^2*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+30*I*cos(d*x+c)^2*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+30*I*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)+27*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-54*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-30*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2-1/2*I,1/2*2^(1/2))-30*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)^4*2^(1/2)+27*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-54*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-30*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)-30*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticPi(((I*cos(d*x+c)-I+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)-20*2^(1/2)*cos(d*x+c)^3-6*cos(d*x+c)^2*2^(1/2)+47*cos(d*x+c)*2^(1/2)-15*2^(1/2))/cos(d*x+c)/(e/sin(d*x+c))^(5/2)/sin(d*x+c)^3*2^(1/2)","C"
293,1,465,167,1.331000," ","int((e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{3} \left(2 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+4 i \cos \left(d x +c \right) \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+2 i \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right) \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\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}-3 \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}}{21 a d \sin \left(d x +c \right)^{5}}"," ",0,"-1/21/a/d*(-1+cos(d*x+c))^3*(2*I*sin(d*x+c)*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+4*I*cos(d*x+c)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+2*I*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-2*cos(d*x+c)^2*2^(1/2)-2*cos(d*x+c)*2^(1/2)-3*2^(1/2))*(1+cos(d*x+c))^2*(e/sin(d*x+c))^(5/2)/sin(d*x+c)^5*2^(1/2)","C"
294,1,799,157,1.294000," ","int((e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+8 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-4 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+4 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-2 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-2 \cos \left(d x +c \right) \sqrt{2}-3 \sqrt{2}\right) \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}}{5 a d \sin \left(d x +c \right)}"," ",0,"-1/5/a/d*(-1+cos(d*x+c))*(4*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-2*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+8*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-4*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+4*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*cos(d*x+c)*2^(1/2)-3*2^(1/2))*(e/sin(d*x+c))^(3/2)/sin(d*x+c)*2^(1/2)","C"
295,1,326,121,1.344000," ","int((e*csc(d*x+c))^(1/2)/(a+a*sec(d*x+c)),x)","\frac{\sqrt{\frac{e}{\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(2 i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+2 i \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+\cos \left(d x +c \right) \sqrt{2}-\sqrt{2}\right) \sqrt{2}}{3 a d \sin \left(d x +c \right)^{5}}"," ",0,"1/3/a/d*(e/sin(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(2*I*cos(d*x+c)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)+2*I*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+cos(d*x+c)*2^(1/2)-2^(1/2))/sin(d*x+c)^5*2^(1/2)","C"
296,1,536,121,1.171000," ","int(1/(a+a*sec(d*x+c))/(e*csc(d*x+c))^(1/2),x)","-\frac{\left(4 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-2 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+4 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-2 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+\cos \left(d x +c \right) \sqrt{2}-\sqrt{2}\right) \sqrt{2}}{a d \sqrt{\frac{e}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)}"," ",0,"-1/a/d*(4*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+4*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-2*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+cos(d*x+c)*2^(1/2)-2^(1/2))/(e/sin(d*x+c))^(1/2)/sin(d*x+c)*2^(1/2)","C"
297,1,195,124,1.146000," ","int(1/(e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x)","\frac{\left(2 i \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right) \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+4 \cos \left(d x +c \right) \sqrt{2}-3 \sqrt{2}\right) \sqrt{2}}{3 a d \left(-1+\cos \left(d x +c \right)\right) \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"1/3/a/d*(2*I*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-cos(d*x+c)^2*2^(1/2)+4*cos(d*x+c)*2^(1/2)-3*2^(1/2))/(-1+cos(d*x+c))/(e/sin(d*x+c))^(3/2)/sin(d*x+c)*2^(1/2)","C"
298,1,551,136,1.398000," ","int(1/(e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x)","\frac{\left(12 \cos \left(d x +c \right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-6 \cos \left(d x +c \right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+12 \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-5 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+3 \cos \left(d x +c \right) \sqrt{2}-\sqrt{2}\right) \sqrt{2}}{15 a d \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{3}}"," ",0,"1/15/a/d*(12*cos(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-6*cos(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+3*2^(1/2)*cos(d*x+c)^3+12*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-6*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-5*cos(d*x+c)^2*2^(1/2)+3*cos(d*x+c)*2^(1/2)-2^(1/2))/(e/sin(d*x+c))^(5/2)/sin(d*x+c)^3*2^(1/2)","C"
299,1,221,161,1.228000," ","int(1/(e*csc(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x)","\frac{\left(10 i \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right) \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+15 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-36 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+16 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+26 \cos \left(d x +c \right) \sqrt{2}-21 \sqrt{2}\right) \sqrt{2}}{105 a d \left(-1+\cos \left(d x +c \right)\right) \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)^{3}}"," ",0,"1/105/a/d*(10*I*sin(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+15*cos(d*x+c)^4*2^(1/2)-36*2^(1/2)*cos(d*x+c)^3+16*cos(d*x+c)^2*2^(1/2)+26*cos(d*x+c)*2^(1/2)-21*2^(1/2))/(-1+cos(d*x+c))/(e/sin(d*x+c))^(7/2)/sin(d*x+c)^3*2^(1/2)","C"
300,1,609,268,1.402000," ","int((e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{4} \left(2 i \sin \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+6 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+6 i \cos \left(d x +c \right) \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+2 i \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(d x +c \right) \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-2 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-47 \cos \left(d x +c \right) \sqrt{2}-24 \sqrt{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}}{231 a^{2} d \sin \left(d x +c \right)^{7}}"," ",0,"1/231/a^2/d*(-1+cos(d*x+c))^4*(2*I*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^3*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+6*I*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+6*I*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)+2*I*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-2*2^(1/2)*cos(d*x+c)^3-4*cos(d*x+c)^2*2^(1/2)-47*cos(d*x+c)*2^(1/2)-24*2^(1/2))*(1+cos(d*x+c))^2*(e/sin(d*x+c))^(5/2)/sin(d*x+c)^7*2^(1/2)","C"
301,1,1044,250,1.343000," ","int((e*csc(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(12 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-6 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+36 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-18 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+36 \cos \left(d x +c \right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-18 \cos \left(d x +c \right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+12 \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{-i \cos \left(d x +c \right)+\sin \left(d x +c \right)+i}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\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}-25 \cos \left(d x +c \right) \sqrt{2}-14 \sqrt{2}\right) \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}}{45 a^{2} d \sin \left(d x +c \right)^{3}}"," ",0,"1/45/a^2/d*(-1+cos(d*x+c))^2*(12*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^3*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-6*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^3*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+36*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-18*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+36*cos(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-18*cos(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+12*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-6*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*((-I*cos(d*x+c)+sin(d*x+c)+I)/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-6*cos(d*x+c)^2*2^(1/2)-25*cos(d*x+c)*2^(1/2)-14*2^(1/2))*(e/sin(d*x+c))^(3/2)/sin(d*x+c)^3*2^(1/2)","C"
302,1,474,205,1.555000," ","int((e*csc(d*x+c))^(1/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\frac{e}{\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)^{3} \left(10 i \sin \left(d x +c \right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+20 i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+10 i \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+11 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-3 \cos \left(d x +c \right) \sqrt{2}-8 \sqrt{2}\right) \sqrt{2}}{21 a^{2} d \sin \left(d x +c \right)^{7}}"," ",0,"-1/21/a^2/d*(e/sin(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^3*(10*I*sin(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*cos(d*x+c)^2*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+20*I*cos(d*x+c)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)+10*I*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*sin(d*x+c)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+11*cos(d*x+c)^2*2^(1/2)-3*cos(d*x+c)*2^(1/2)-8*2^(1/2))/sin(d*x+c)^7*2^(1/2)","C"
303,1,811,205,1.303000," ","int(1/(a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(28 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-14 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+56 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-28 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+28 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-14 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+5 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+\cos \left(d x +c \right) \sqrt{2}-6 \sqrt{2}\right) \sqrt{2}}{5 a^{2} d \sqrt{\frac{e}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3}}"," ",0,"1/5/a^2/d*(-1+cos(d*x+c))*(28*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))-14*cos(d*x+c)^2*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+56*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-28*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+28*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-14*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+5*cos(d*x+c)^2*2^(1/2)+cos(d*x+c)*2^(1/2)-6*2^(1/2))/(e/sin(d*x+c))^(1/2)/sin(d*x+c)^3*2^(1/2)","C"
304,1,332,221,1.230000," ","int(1/(e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x)","\frac{\left(-6 i \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)-6 i \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+\sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-3 \cos \left(d x +c \right) \sqrt{2}+8 \sqrt{2}\right) \sqrt{2}}{3 a^{2} d \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{3}}"," ",0,"1/3/a^2/d*(-6*I*cos(d*x+c)*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-6*I*sin(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+2^(1/2)*cos(d*x+c)^3-6*cos(d*x+c)^2*2^(1/2)-3*cos(d*x+c)*2^(1/2)+8*2^(1/2))/(e/sin(d*x+c))^(3/2)/sin(d*x+c)^3*2^(1/2)","C"
305,1,563,225,1.304000," ","int(1/(e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x)","\frac{\left(-66 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+132 \cos \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+3 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-66 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}+132 \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}-10 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+33 \cos \left(d x +c \right) \sqrt{2}-26 \sqrt{2}\right) \sqrt{2}}{15 a^{2} d \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{3}}"," ",0,"1/15/a^2/d*(-66*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+132*cos(d*x+c)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+3*2^(1/2)*cos(d*x+c)^3-66*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)+132*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticE(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)-10*cos(d*x+c)^2*2^(1/2)+33*cos(d*x+c)*2^(1/2)-26*2^(1/2))/(e/sin(d*x+c))^(5/2)/sin(d*x+c)^3*2^(1/2)","C"
306,1,224,182,1.236000," ","int(1/(e*csc(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x)","\frac{\left(-130 i \sqrt{-\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \sqrt{-\frac{i \cos \left(d x +c \right)-i-\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(d x +c \right)-i+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}}, \frac{\sqrt{2}}{2}\right)+15 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-57 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+107 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-233 \cos \left(d x +c \right) \sqrt{2}+168 \sqrt{2}\right) \sqrt{2}}{105 a^{2} d \left(-1+\cos \left(d x +c \right)\right) \left(\frac{e}{\sin \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)^{3}}"," ",0,"1/105/a^2/d*(-130*I*sin(d*x+c)*(-I*(-1+cos(d*x+c))/sin(d*x+c))^(1/2)*((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2)*(-(I*cos(d*x+c)-I-sin(d*x+c))/sin(d*x+c))^(1/2)*EllipticF(((I*cos(d*x+c)-I+sin(d*x+c))/sin(d*x+c))^(1/2),1/2*2^(1/2))+15*cos(d*x+c)^4*2^(1/2)-57*2^(1/2)*cos(d*x+c)^3+107*cos(d*x+c)^2*2^(1/2)-233*cos(d*x+c)*2^(1/2)+168*2^(1/2))/(-1+cos(d*x+c))/(e/sin(d*x+c))^(7/2)/sin(d*x+c)^3*2^(1/2)","C"