1,1,55,0,0.102983,"\int \frac{\tan ^4(x)}{a+a \csc (x)} \, dx","Int[Tan[x]^4/(a + a*Csc[x]),x]","\frac{x}{a}-\frac{\tan ^5(x) (1-\csc (x))}{5 a}+\frac{\tan ^3(x) (5-4 \csc (x))}{15 a}-\frac{\tan (x) (15-8 \csc (x))}{15 a}","\frac{x}{a}-\frac{\tan ^5(x) (1-\csc (x))}{5 a}+\frac{\tan ^3(x) (5-4 \csc (x))}{15 a}-\frac{\tan (x) (15-8 \csc (x))}{15 a}",1,"x/a - ((15 - 8*Csc[x])*Tan[x])/(15*a) + ((5 - 4*Csc[x])*Tan[x]^3)/(15*a) - ((1 - Csc[x])*Tan[x]^5)/(5*a)","A",5,3,13,0.2308,1,"{3888, 3882, 8}"
2,1,68,0,0.0703221,"\int \frac{\tan ^3(x)}{a+a \csc (x)} \, dx","Int[Tan[x]^3/(a + a*Csc[x]),x]","\frac{1}{8 a (1-\sin (x))}+\frac{3}{4 a (\sin (x)+1)}-\frac{1}{8 a (\sin (x)+1)^2}+\frac{5 \log (1-\sin (x))}{16 a}+\frac{11 \log (\sin (x)+1)}{16 a}","\frac{1}{8 a (1-\sin (x))}+\frac{3}{4 a (\sin (x)+1)}-\frac{1}{8 a (\sin (x)+1)^2}+\frac{5 \log (1-\sin (x))}{16 a}+\frac{11 \log (\sin (x)+1)}{16 a}",1,"(5*Log[1 - Sin[x]])/(16*a) + (11*Log[1 + Sin[x]])/(16*a) + 1/(8*a*(1 - Sin[x])) - 1/(8*a*(1 + Sin[x])^2) + 3/(4*a*(1 + Sin[x]))","A",3,2,13,0.1538,1,"{3879, 88}"
3,1,39,0,0.0785335,"\int \frac{\tan ^2(x)}{a+a \csc (x)} \, dx","Int[Tan[x]^2/(a + a*Csc[x]),x]","-\frac{x}{a}-\frac{\tan ^3(x) (1-\csc (x))}{3 a}+\frac{\tan (x) (3-2 \csc (x))}{3 a}","-\frac{x}{a}-\frac{\tan ^3(x) (1-\csc (x))}{3 a}+\frac{\tan (x) (3-2 \csc (x))}{3 a}",1,"-(x/a) + ((3 - 2*Csc[x])*Tan[x])/(3*a) - ((1 - Csc[x])*Tan[x]^3)/(3*a)","A",4,3,13,0.2308,1,"{3888, 3882, 8}"
4,1,40,0,0.0486917,"\int \frac{\tan (x)}{a+a \csc (x)} \, dx","Int[Tan[x]/(a + a*Csc[x]),x]","-\frac{1}{2 a (\sin (x)+1)}-\frac{\log (1-\sin (x))}{4 a}-\frac{3 \log (\sin (x)+1)}{4 a}","-\frac{1}{2 a (\sin (x)+1)}-\frac{\log (1-\sin (x))}{4 a}-\frac{3 \log (\sin (x)+1)}{4 a}",1,"-Log[1 - Sin[x]]/(4*a) - (3*Log[1 + Sin[x]])/(4*a) - 1/(2*a*(1 + Sin[x]))","A",3,2,11,0.1818,1,"{3879, 88}"
5,1,9,0,0.0217797,"\int \frac{\cot (x)}{a+a \csc (x)} \, dx","Int[Cot[x]/(a + a*Csc[x]),x]","\frac{\log (\sin (x)+1)}{a}","\frac{\log (\sin (x)+1)}{a}",1,"Log[1 + Sin[x]]/a","A",2,2,11,0.1818,1,"{3879, 31}"
6,1,15,0,0.0397653,"\int \frac{\cot ^2(x)}{a+a \csc (x)} \, dx","Int[Cot[x]^2/(a + a*Csc[x]),x]","-\frac{x}{a}-\frac{\tanh ^{-1}(\cos (x))}{a}","-\frac{x}{a}-\frac{\tanh ^{-1}(\cos (x))}{a}",1,"-(x/a) - ArcTanh[Cos[x]]/a","A",3,2,13,0.1538,1,"{3888, 3770}"
7,1,16,0,0.0415825,"\int \frac{\cot ^3(x)}{a+a \csc (x)} \, dx","Int[Cot[x]^3/(a + a*Csc[x]),x]","-\frac{\csc (x)}{a}-\frac{\log (\sin (x))}{a}","-\frac{\csc (x)}{a}-\frac{\log (\sin (x))}{a}",1,"-(Csc[x]/a) - Log[Sin[x]]/a","A",3,2,13,0.1538,1,"{3879, 43}"
8,1,31,0,0.0598691,"\int \frac{\cot ^4(x)}{a+a \csc (x)} \, dx","Int[Cot[x]^4/(a + a*Csc[x]),x]","\frac{x}{a}+\frac{\tanh ^{-1}(\cos (x))}{2 a}+\frac{\cot (x) (2-\csc (x))}{2 a}","\frac{x}{a}+\frac{\tanh ^{-1}(\cos (x))}{2 a}+\frac{\cot (x) (2-\csc (x))}{2 a}",1,"x/a + ArcTanh[Cos[x]]/(2*a) + (Cot[x]*(2 - Csc[x]))/(2*a)","A",4,3,13,0.2308,1,"{3888, 3881, 3770}"
9,1,36,0,0.0489153,"\int \frac{\cot ^5(x)}{a+a \csc (x)} \, dx","Int[Cot[x]^5/(a + a*Csc[x]),x]","-\frac{\csc ^3(x)}{3 a}+\frac{\csc ^2(x)}{2 a}+\frac{\csc (x)}{a}+\frac{\log (\sin (x))}{a}","-\frac{\csc ^3(x)}{3 a}+\frac{\csc ^2(x)}{2 a}+\frac{\csc (x)}{a}+\frac{\log (\sin (x))}{a}",1,"Csc[x]/a + Csc[x]^2/(2*a) - Csc[x]^3/(3*a) + Log[Sin[x]]/a","A",3,2,13,0.1538,1,"{3879, 75}"
10,1,49,0,0.0807971,"\int \frac{\cot ^6(x)}{a+a \csc (x)} \, dx","Int[Cot[x]^6/(a + a*Csc[x]),x]","-\frac{x}{a}-\frac{3 \tanh ^{-1}(\cos (x))}{8 a}+\frac{\cot ^3(x) (4-3 \csc (x))}{12 a}-\frac{\cot (x) (8-3 \csc (x))}{8 a}","-\frac{x}{a}-\frac{3 \tanh ^{-1}(\cos (x))}{8 a}+\frac{\cot ^3(x) (4-3 \csc (x))}{12 a}-\frac{\cot (x) (8-3 \csc (x))}{8 a}",1,"-(x/a) - (3*ArcTanh[Cos[x]])/(8*a) + (Cot[x]^3*(4 - 3*Csc[x]))/(12*a) - (Cot[x]*(8 - 3*Csc[x]))/(8*a)","A",5,3,13,0.2308,1,"{3888, 3881, 3770}"
11,1,58,0,0.0581809,"\int \frac{\cot ^7(x)}{a+a \csc (x)} \, dx","Int[Cot[x]^7/(a + a*Csc[x]),x]","-\frac{\csc ^5(x)}{5 a}+\frac{\csc ^4(x)}{4 a}+\frac{2 \csc ^3(x)}{3 a}-\frac{\csc ^2(x)}{a}-\frac{\csc (x)}{a}-\frac{\log (\sin (x))}{a}","-\frac{\csc ^5(x)}{5 a}+\frac{\csc ^4(x)}{4 a}+\frac{2 \csc ^3(x)}{3 a}-\frac{\csc ^2(x)}{a}-\frac{\csc (x)}{a}-\frac{\log (\sin (x))}{a}",1,"-(Csc[x]/a) - Csc[x]^2/a + (2*Csc[x]^3)/(3*a) + Csc[x]^4/(4*a) - Csc[x]^5/(5*a) - Log[Sin[x]]/a","A",3,2,13,0.1538,1,"{3879, 88}"
12,1,178,0,0.2719794,"\int \frac{\tan ^5(x)}{a+b \csc (x)} \, dx","Int[Tan[x]^5/(a + b*Csc[x]),x]","\frac{b^6 \log (a+b \csc (x))}{a \left(a^2-b^2\right)^3}-\frac{\left(8 a^2+21 a b+15 b^2\right) \log (1-\csc (x))}{16 (a+b)^3}-\frac{\left(8 a^2-21 a b+15 b^2\right) \log (\csc (x)+1)}{16 (a-b)^3}+\frac{5 a+7 b}{16 (a+b)^2 (1-\csc (x))}+\frac{5 a-7 b}{16 (a-b)^2 (\csc (x)+1)}+\frac{1}{16 (a+b) (1-\csc (x))^2}+\frac{1}{16 (a-b) (\csc (x)+1)^2}-\frac{\log (\sin (x))}{a}","\frac{b^6 \log (a+b \csc (x))}{a \left(a^2-b^2\right)^3}-\frac{\left(8 a^2+21 a b+15 b^2\right) \log (1-\csc (x))}{16 (a+b)^3}-\frac{\left(8 a^2-21 a b+15 b^2\right) \log (\csc (x)+1)}{16 (a-b)^3}+\frac{5 a+7 b}{16 (a+b)^2 (1-\csc (x))}+\frac{5 a-7 b}{16 (a-b)^2 (\csc (x)+1)}+\frac{1}{16 (a+b) (1-\csc (x))^2}+\frac{1}{16 (a-b) (\csc (x)+1)^2}-\frac{\log (\sin (x))}{a}",1,"1/(16*(a + b)*(1 - Csc[x])^2) + (5*a + 7*b)/(16*(a + b)^2*(1 - Csc[x])) + 1/(16*(a - b)*(1 + Csc[x])^2) + (5*a - 7*b)/(16*(a - b)^2*(1 + Csc[x])) - ((8*a^2 + 21*a*b + 15*b^2)*Log[1 - Csc[x]])/(16*(a + b)^3) - ((8*a^2 - 21*a*b + 15*b^2)*Log[1 + Csc[x]])/(16*(a - b)^3) + (b^6*Log[a + b*Csc[x]])/(a*(a^2 - b^2)^3) - Log[Sin[x]]/a","A",3,2,13,0.1538,1,"{3885, 894}"
13,1,113,0,0.1668372,"\int \frac{\tan ^3(x)}{a+b \csc (x)} \, dx","Int[Tan[x]^3/(a + b*Csc[x]),x]","\frac{b^4 \log (a+b \csc (x))}{a \left(a^2-b^2\right)^2}-\frac{1}{4 (a+b) (1-\csc (x))}-\frac{1}{4 (a-b) (\csc (x)+1)}+\frac{(2 a+3 b) \log (1-\csc (x))}{4 (a+b)^2}+\frac{(2 a-3 b) \log (\csc (x)+1)}{4 (a-b)^2}+\frac{\log (\sin (x))}{a}","\frac{b^4 \log (a+b \csc (x))}{a \left(a^2-b^2\right)^2}-\frac{1}{4 (a+b) (1-\csc (x))}-\frac{1}{4 (a-b) (\csc (x)+1)}+\frac{(2 a+3 b) \log (1-\csc (x))}{4 (a+b)^2}+\frac{(2 a-3 b) \log (\csc (x)+1)}{4 (a-b)^2}+\frac{\log (\sin (x))}{a}",1,"-1/(4*(a + b)*(1 - Csc[x])) - 1/(4*(a - b)*(1 + Csc[x])) + ((2*a + 3*b)*Log[1 - Csc[x]])/(4*(a + b)^2) + ((2*a - 3*b)*Log[1 + Csc[x]])/(4*(a - b)^2) + (b^4*Log[a + b*Csc[x]])/(a*(a^2 - b^2)^2) + Log[Sin[x]]/a","A",3,2,13,0.1538,1,"{3885, 894}"
14,1,66,0,0.0906753,"\int \frac{\tan (x)}{a+b \csc (x)} \, dx","Int[Tan[x]/(a + b*Csc[x]),x]","\frac{b^2 \log (a+b \csc (x))}{a \left(a^2-b^2\right)}-\frac{\log (1-\csc (x))}{2 (a+b)}-\frac{\log (\csc (x)+1)}{2 (a-b)}-\frac{\log (\sin (x))}{a}","\frac{b^2 \log (a+b \csc (x))}{a \left(a^2-b^2\right)}-\frac{\log (1-\csc (x))}{2 (a+b)}-\frac{\log (\csc (x)+1)}{2 (a-b)}-\frac{\log (\sin (x))}{a}",1,"-Log[1 - Csc[x]]/(2*(a + b)) - Log[1 + Csc[x]]/(2*(a - b)) + (b^2*Log[a + b*Csc[x]])/(a*(a^2 - b^2)) - Log[Sin[x]]/a","A",3,2,11,0.1818,1,"{3885, 894}"
15,1,19,0,0.024461,"\int \frac{\cot (x)}{a+b \csc (x)} \, dx","Int[Cot[x]/(a + b*Csc[x]),x]","\frac{\log (a+b \csc (x))}{a}+\frac{\log (\sin (x))}{a}","\frac{\log (a+b \csc (x))}{a}+\frac{\log (\sin (x))}{a}",1,"Log[a + b*Csc[x]]/a + Log[Sin[x]]/a","A",4,4,11,0.3636,1,"{3885, 36, 29, 31}"
16,1,38,0,0.0629755,"\int \frac{\cot ^3(x)}{a+b \csc (x)} \, dx","Int[Cot[x]^3/(a + b*Csc[x]),x]","-\frac{\left(1-\frac{a^2}{b^2}\right) \log (a+b \csc (x))}{a}-\frac{\log (\sin (x))}{a}-\frac{\csc (x)}{b}","-\frac{\left(1-\frac{a^2}{b^2}\right) \log (a+b \csc (x))}{a}-\frac{\log (\sin (x))}{a}-\frac{\csc (x)}{b}",1,"-(Csc[x]/b) - ((1 - a^2/b^2)*Log[a + b*Csc[x]])/a - Log[Sin[x]]/a","A",3,2,13,0.1538,1,"{3885, 894}"
17,1,72,0,0.0834981,"\int \frac{\cot ^5(x)}{a+b \csc (x)} \, dx","Int[Cot[x]^5/(a + b*Csc[x]),x]","-\frac{\left(a^2-2 b^2\right) \csc (x)}{b^3}+\frac{\left(a^2-b^2\right)^2 \log (a+b \csc (x))}{a b^4}+\frac{a \csc ^2(x)}{2 b^2}+\frac{\log (\sin (x))}{a}-\frac{\csc ^3(x)}{3 b}","-\frac{\left(a^2-2 b^2\right) \csc (x)}{b^3}+\frac{\left(a^2-b^2\right)^2 \log (a+b \csc (x))}{a b^4}+\frac{a \csc ^2(x)}{2 b^2}+\frac{\log (\sin (x))}{a}-\frac{\csc ^3(x)}{3 b}",1,"-(((a^2 - 2*b^2)*Csc[x])/b^3) + (a*Csc[x]^2)/(2*b^2) - Csc[x]^3/(3*b) + ((a^2 - b^2)^2*Log[a + b*Csc[x]])/(a*b^4) + Log[Sin[x]]/a","A",3,2,13,0.1538,1,"{3885, 894}"
18,1,122,0,0.1231513,"\int \frac{\cot ^7(x)}{a+b \csc (x)} \, dx","Int[Cot[x]^7/(a + b*Csc[x]),x]","-\frac{\left(a^2-3 b^2\right) \csc ^3(x)}{3 b^3}+\frac{a \left(a^2-3 b^2\right) \csc ^2(x)}{2 b^4}-\frac{\left(-3 a^2 b^2+a^4+3 b^4\right) \csc (x)}{b^5}+\frac{\left(a^2-b^2\right)^3 \log (a+b \csc (x))}{a b^6}+\frac{a \csc ^4(x)}{4 b^2}-\frac{\log (\sin (x))}{a}-\frac{\csc ^5(x)}{5 b}","-\frac{\left(a^2-3 b^2\right) \csc ^3(x)}{3 b^3}+\frac{a \left(a^2-3 b^2\right) \csc ^2(x)}{2 b^4}-\frac{\left(-3 a^2 b^2+a^4+3 b^4\right) \csc (x)}{b^5}+\frac{\left(a^2-b^2\right)^3 \log (a+b \csc (x))}{a b^6}+\frac{a \csc ^4(x)}{4 b^2}-\frac{\log (\sin (x))}{a}-\frac{\csc ^5(x)}{5 b}",1,"-(((a^4 - 3*a^2*b^2 + 3*b^4)*Csc[x])/b^5) + (a*(a^2 - 3*b^2)*Csc[x]^2)/(2*b^4) - ((a^2 - 3*b^2)*Csc[x]^3)/(3*b^3) + (a*Csc[x]^4)/(4*b^2) - Csc[x]^5/(5*b) + ((a^2 - b^2)^3*Log[a + b*Csc[x]])/(a*b^6) - Log[Sin[x]]/a","A",3,2,13,0.1538,1,"{3885, 894}"
19,1,205,0,0.323515,"\int \frac{\tan ^4(x)}{a+b \csc (x)} \, dx","Int[Tan[x]^4/(a + b*Csc[x]),x]","\frac{b^4 x}{a \left(a^2-b^2\right)^2}-\frac{a b^2 x}{\left(a^2-b^2\right)^2}+\frac{a x}{a^2-b^2}+\frac{a \tan ^3(x)}{3 \left(a^2-b^2\right)}+\frac{a b^2 \tan (x)}{\left(a^2-b^2\right)^2}-\frac{a \tan (x)}{a^2-b^2}-\frac{b \sec ^3(x)}{3 \left(a^2-b^2\right)}-\frac{b^3 \sec (x)}{\left(a^2-b^2\right)^2}+\frac{b \sec (x)}{a^2-b^2}+\frac{2 b^5 \tanh ^{-1}\left(\frac{a+b \tan \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{a \left(a^2-b^2\right)^{5/2}}","\frac{a \tan ^3(x)}{3 \left(a^2-b^2\right)}+\frac{a b^2 \tan (x)}{\left(a^2-b^2\right)^2}-\frac{a \tan (x)}{a^2-b^2}-\frac{b \sec ^3(x)}{3 \left(a^2-b^2\right)}-\frac{b^3 \sec (x)}{\left(a^2-b^2\right)^2}+\frac{b \sec (x)}{a^2-b^2}+\frac{2 b^5 \tanh ^{-1}\left(\frac{a+b \tan \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{a \left(a^2-b^2\right)^{5/2}}+\frac{x}{a}",1,"-((a*b^2*x)/(a^2 - b^2)^2) + (b^4*x)/(a*(a^2 - b^2)^2) + (a*x)/(a^2 - b^2) + (2*b^5*ArcTanh[(a + b*Tan[x/2])/Sqrt[a^2 - b^2]])/(a*(a^2 - b^2)^(5/2)) - (b^3*Sec[x])/(a^2 - b^2)^2 + (b*Sec[x])/(a^2 - b^2) - (b*Sec[x]^3)/(3*(a^2 - b^2)) + (a*b^2*Tan[x])/(a^2 - b^2)^2 - (a*Tan[x])/(a^2 - b^2) + (a*Tan[x]^3)/(3*(a^2 - b^2))","A",16,9,13,0.6923,1,"{3898, 2902, 2606, 3473, 8, 2735, 2660, 618, 206}"
20,1,112,0,0.1874512,"\int \frac{\tan ^2(x)}{a+b \csc (x)} \, dx","Int[Tan[x]^2/(a + b*Csc[x]),x]","\frac{b^2 x}{a \left(a^2-b^2\right)}-\frac{a x}{a^2-b^2}+\frac{a \tan (x)}{a^2-b^2}-\frac{b \sec (x)}{a^2-b^2}+\frac{2 b^3 \tanh ^{-1}\left(\frac{a+b \tan \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{a \left(a^2-b^2\right)^{3/2}}","\frac{a \tan (x)}{a^2-b^2}-\frac{b \sec (x)}{a^2-b^2}+\frac{2 b^3 \tanh ^{-1}\left(\frac{a+b \tan \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{a \left(a^2-b^2\right)^{3/2}}-\frac{x}{a}",1,"-((a*x)/(a^2 - b^2)) + (b^2*x)/(a*(a^2 - b^2)) + (2*b^3*ArcTanh[(a + b*Tan[x/2])/Sqrt[a^2 - b^2]])/(a*(a^2 - b^2)^(3/2)) - (b*Sec[x])/(a^2 - b^2) + (a*Tan[x])/(a^2 - b^2)","A",10,9,13,0.6923,1,"{3898, 2902, 2606, 8, 3473, 2735, 2660, 618, 206}"
21,1,61,0,0.1760358,"\int \frac{\cot ^2(x)}{a+b \csc (x)} \, dx","Int[Cot[x]^2/(a + b*Csc[x]),x]","\frac{2 \sqrt{a^2-b^2} \tanh ^{-1}\left(\frac{a+b \tan \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{a b}-\frac{x}{a}-\frac{\tanh ^{-1}(\cos (x))}{b}","\frac{2 \sqrt{a^2-b^2} \tanh ^{-1}\left(\frac{a+b \tan \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{a b}-\frac{x}{a}-\frac{\tanh ^{-1}(\cos (x))}{b}",1,"-(x/a) - ArcTanh[Cos[x]]/b + (2*Sqrt[a^2 - b^2]*ArcTanh[(a + b*Tan[x/2])/Sqrt[a^2 - b^2]])/(a*b)","A",8,8,13,0.6154,1,"{3894, 4051, 3770, 3919, 3831, 2660, 618, 206}"
22,1,91,0,0.2888459,"\int \frac{\cot ^4(x)}{a+b \csc (x)} \, dx","Int[Cot[x]^4/(a + b*Csc[x]),x]","-\frac{\left(2 a^2-3 b^2\right) \tanh ^{-1}(\cos (x))}{2 b^3}+\frac{2 \left(a^2-b^2\right)^{3/2} \tanh ^{-1}\left(\frac{a+b \tan \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{a b^3}+\frac{a \cot (x)}{b^2}+\frac{x}{a}-\frac{\cot (x) \csc (x)}{2 b}","-\frac{\left(2 a^2-3 b^2\right) \tanh ^{-1}(\cos (x))}{2 b^3}+\frac{2 \left(a^2-b^2\right)^{3/2} \tanh ^{-1}\left(\frac{a+b \tan \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{a b^3}+\frac{a \cot (x)}{b^2}+\frac{x}{a}-\frac{\cot (x) \csc (x)}{2 b}",1,"x/a - ((2*a^2 - 3*b^2)*ArcTanh[Cos[x]])/(2*b^3) + (2*(a^2 - b^2)^(3/2)*ArcTanh[(a + b*Tan[x/2])/Sqrt[a^2 - b^2]])/(a*b^3) + (a*Cot[x])/b^2 - (Cot[x]*Csc[x])/(2*b)","A",7,7,13,0.5385,1,"{3898, 2893, 3057, 2660, 618, 206, 3770}"
23,1,186,0,0.2777522,"\int \frac{\cot ^6(x)}{a+b \csc (x)} \, dx","Int[Cot[x]^6/(a + b*Csc[x]),x]","\frac{a \left(a^2-3 b^2\right) \cot (x)}{b^4}-\frac{\left(a^2-3 b^2\right) \tanh ^{-1}(\cos (x))}{2 b^3}-\frac{\left(-3 a^2 b^2+a^4+3 b^4\right) \tanh ^{-1}(\cos (x))}{b^5}+\frac{2 \left(a^2-b^2\right)^{5/2} \tanh ^{-1}\left(\frac{a+b \tan \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{a b^5}-\frac{\left(a^2-3 b^2\right) \cot (x) \csc (x)}{2 b^3}+\frac{a \cot ^3(x)}{3 b^2}+\frac{a \cot (x)}{b^2}-\frac{x}{a}-\frac{3 \tanh ^{-1}(\cos (x))}{8 b}-\frac{\cot (x) \csc ^3(x)}{4 b}-\frac{3 \cot (x) \csc (x)}{8 b}","\frac{a \left(a^2-3 b^2\right) \cot (x)}{b^4}-\frac{\left(a^2-3 b^2\right) \tanh ^{-1}(\cos (x))}{2 b^3}-\frac{\left(-3 a^2 b^2+a^4+3 b^4\right) \tanh ^{-1}(\cos (x))}{b^5}+\frac{2 \left(a^2-b^2\right)^{5/2} \tanh ^{-1}\left(\frac{a+b \tan \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{a b^5}-\frac{\left(a^2-3 b^2\right) \cot (x) \csc (x)}{2 b^3}+\frac{a \cot ^3(x)}{3 b^2}+\frac{a \cot (x)}{b^2}-\frac{x}{a}-\frac{3 \tanh ^{-1}(\cos (x))}{8 b}-\frac{\cot (x) \csc ^3(x)}{4 b}-\frac{3 \cot (x) \csc (x)}{8 b}",1,"-(x/a) - (3*ArcTanh[Cos[x]])/(8*b) - ((a^2 - 3*b^2)*ArcTanh[Cos[x]])/(2*b^3) - ((a^4 - 3*a^2*b^2 + 3*b^4)*ArcTanh[Cos[x]])/b^5 + (2*(a^2 - b^2)^(5/2)*ArcTanh[(a + b*Tan[x/2])/Sqrt[a^2 - b^2]])/(a*b^5) + (a*Cot[x])/b^2 + (a*(a^2 - 3*b^2)*Cot[x])/b^4 + (a*Cot[x]^3)/(3*b^2) - (3*Cot[x]*Csc[x])/(8*b) - ((a^2 - 3*b^2)*Cot[x]*Csc[x])/(2*b^3) - (Cot[x]*Csc[x]^3)/(4*b)","A",16,9,13,0.6923,1,"{3898, 2897, 3770, 3767, 8, 3768, 2660, 618, 206}"