1,1,149,147,0.2997469,"\int x^3 \text{csch}^{-1}(a+b x) \, dx","Integrate[x^3*ArcCsch[a + b*x],x]","\frac{-3 a^4 \sinh ^{-1}\left(\frac{1}{a+b x}\right)+6 \left(1-2 a^2\right) a \log \left((a+b x) \left(\sqrt{\frac{a^2+2 a b x+b^2 x^2+1}{(a+b x)^2}}+1\right)\right)+\sqrt{\frac{a^2+2 a b x+b^2 x^2+1}{(a+b x)^2}} \left(13 a^3+9 a^2 b x-3 a b^2 x^2-2 a+b^3 x^3-2 b x\right)+3 b^4 x^4 \text{csch}^{-1}(a+b x)}{12 b^4}","-\frac{a^4 \text{csch}^{-1}(a+b x)}{4 b^4}-\frac{\left(2-17 a^2\right) (a+b x) \sqrt{\frac{1}{(a+b x)^2}+1}}{12 b^4}+\frac{\left(1-2 a^2\right) a \tanh ^{-1}\left(\sqrt{\frac{1}{(a+b x)^2}+1}\right)}{2 b^4}-\frac{a (a+b x)^2 \sqrt{\frac{1}{(a+b x)^2}+1}}{3 b^4}+\frac{x^2 (a+b x) \sqrt{\frac{1}{(a+b x)^2}+1}}{12 b^2}+\frac{1}{4} x^4 \text{csch}^{-1}(a+b x)",1,"(Sqrt[(1 + a^2 + 2*a*b*x + b^2*x^2)/(a + b*x)^2]*(-2*a + 13*a^3 - 2*b*x + 9*a^2*b*x - 3*a*b^2*x^2 + b^3*x^3) + 3*b^4*x^4*ArcCsch[a + b*x] - 3*a^4*ArcSinh[(a + b*x)^(-1)] + 6*a*(1 - 2*a^2)*Log[(a + b*x)*(1 + Sqrt[(1 + a^2 + 2*a*b*x + b^2*x^2)/(a + b*x)^2])])/(12*b^4)","A",1
2,1,129,110,0.1765466,"\int x^2 \text{csch}^{-1}(a+b x) \, dx","Integrate[x^2*ArcCsch[a + b*x],x]","\frac{2 a^3 \sinh ^{-1}\left(\frac{1}{a+b x}\right)+\left(-5 a^2-4 a b x+b^2 x^2\right) \sqrt{\frac{a^2+2 a b x+b^2 x^2+1}{(a+b x)^2}}+\left(6 a^2-1\right) \log \left((a+b x) \left(\sqrt{\frac{a^2+2 a b x+b^2 x^2+1}{(a+b x)^2}}+1\right)\right)+2 b^3 x^3 \text{csch}^{-1}(a+b x)}{6 b^3}","\frac{a^3 \text{csch}^{-1}(a+b x)}{3 b^3}-\frac{\left(1-6 a^2\right) \tanh ^{-1}\left(\sqrt{\frac{1}{(a+b x)^2}+1}\right)}{6 b^3}-\frac{5 a (a+b x) \sqrt{\frac{1}{(a+b x)^2}+1}}{6 b^3}+\frac{x (a+b x) \sqrt{\frac{1}{(a+b x)^2}+1}}{6 b^2}+\frac{1}{3} x^3 \text{csch}^{-1}(a+b x)",1,"((-5*a^2 - 4*a*b*x + b^2*x^2)*Sqrt[(1 + a^2 + 2*a*b*x + b^2*x^2)/(a + b*x)^2] + 2*b^3*x^3*ArcCsch[a + b*x] + 2*a^3*ArcSinh[(a + b*x)^(-1)] + (-1 + 6*a^2)*Log[(a + b*x)*(1 + Sqrt[(1 + a^2 + 2*a*b*x + b^2*x^2)/(a + b*x)^2])])/(6*b^3)","A",1
3,1,110,75,0.1050314,"\int x \text{csch}^{-1}(a+b x) \, dx","Integrate[x*ArcCsch[a + b*x],x]","\frac{(a+b x) \sqrt{\frac{a^2+2 a b x+b^2 x^2+1}{(a+b x)^2}}-2 a \log \left((a+b x) \left(\sqrt{\frac{a^2+2 a b x+b^2 x^2+1}{(a+b x)^2}}+1\right)\right)+a^2 \left(-\sinh ^{-1}\left(\frac{1}{a+b x}\right)\right)+b^2 x^2 \text{csch}^{-1}(a+b x)}{2 b^2}","-\frac{a^2 \text{csch}^{-1}(a+b x)}{2 b^2}+\frac{(a+b x) \sqrt{\frac{1}{(a+b x)^2}+1}}{2 b^2}-\frac{a \tanh ^{-1}\left(\sqrt{\frac{1}{(a+b x)^2}+1}\right)}{b^2}+\frac{1}{2} x^2 \text{csch}^{-1}(a+b x)",1,"((a + b*x)*Sqrt[(1 + a^2 + 2*a*b*x + b^2*x^2)/(a + b*x)^2] + b^2*x^2*ArcCsch[a + b*x] - a^2*ArcSinh[(a + b*x)^(-1)] - 2*a*Log[(a + b*x)*(1 + Sqrt[(1 + a^2 + 2*a*b*x + b^2*x^2)/(a + b*x)^2])])/(2*b^2)","A",1
4,1,427,162,0.403272,"\int \frac{\text{csch}^{-1}(a+b x)}{x} \, dx","Integrate[ArcCsch[a + b*x]/x,x]","\frac{1}{8} \left(8 \text{Li}_2\left(\frac{\left(\sqrt{a^2+1}-1\right) e^{\text{csch}^{-1}(a+b x)}}{a}\right)+8 \text{Li}_2\left(-\frac{\left(\sqrt{a^2+1}+1\right) e^{\text{csch}^{-1}(a+b x)}}{a}\right)+8 \text{csch}^{-1}(a+b x) \log \left(1-\frac{\left(\sqrt{a^2+1}-1\right) e^{\text{csch}^{-1}(a+b x)}}{a}\right)+8 \text{csch}^{-1}(a+b x) \log \left(\frac{\left(\sqrt{a^2+1}+1\right) e^{\text{csch}^{-1}(a+b x)}}{a}+1\right)+4 i \pi  \log \left(1-\frac{\left(\sqrt{a^2+1}-1\right) e^{\text{csch}^{-1}(a+b x)}}{a}\right)+4 i \pi  \log \left(\frac{\left(\sqrt{a^2+1}+1\right) e^{\text{csch}^{-1}(a+b x)}}{a}+1\right)+16 i \sin ^{-1}\left(\frac{\sqrt{\frac{a-i}{a}}}{\sqrt{2}}\right) \log \left(1-\frac{\left(\sqrt{a^2+1}-1\right) e^{\text{csch}^{-1}(a+b x)}}{a}\right)-16 i \sin ^{-1}\left(\frac{\sqrt{\frac{a-i}{a}}}{\sqrt{2}}\right) \log \left(\frac{\left(\sqrt{a^2+1}+1\right) e^{\text{csch}^{-1}(a+b x)}}{a}+1\right)-32 \sin ^{-1}\left(\frac{\sqrt{\frac{a-i}{a}}}{\sqrt{2}}\right) \tan ^{-1}\left(\frac{(1-i a) \cot \left(\frac{1}{4} \left(\pi +2 i \text{csch}^{-1}(a+b x)\right)\right)}{\sqrt{a^2+1}}\right)+4 \text{Li}_2\left(e^{-2 \text{csch}^{-1}(a+b x)}\right)-4 i \pi  \log \left(\frac{b x}{a+b x}\right)-8 \text{csch}^{-1}(a+b x)^2-4 i \pi  \text{csch}^{-1}(a+b x)-8 \text{csch}^{-1}(a+b x) \log \left(1-e^{-2 \text{csch}^{-1}(a+b x)}\right)+\pi ^2\right)","\text{Li}_2\left(\frac{a e^{\text{csch}^{-1}(a+b x)}}{1-\sqrt{a^2+1}}\right)+\text{Li}_2\left(\frac{a e^{\text{csch}^{-1}(a+b x)}}{\sqrt{a^2+1}+1}\right)+\text{csch}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{csch}^{-1}(a+b x)}}{1-\sqrt{a^2+1}}\right)+\text{csch}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{csch}^{-1}(a+b x)}}{\sqrt{a^2+1}+1}\right)-\frac{1}{2} \text{Li}_2\left(e^{2 \text{csch}^{-1}(a+b x)}\right)-\text{csch}^{-1}(a+b x) \log \left(1-e^{2 \text{csch}^{-1}(a+b x)}\right)",1,"(Pi^2 - (4*I)*Pi*ArcCsch[a + b*x] - 8*ArcCsch[a + b*x]^2 - 32*ArcSin[Sqrt[(-I + a)/a]/Sqrt[2]]*ArcTan[((1 - I*a)*Cot[(Pi + (2*I)*ArcCsch[a + b*x])/4])/Sqrt[1 + a^2]] - 8*ArcCsch[a + b*x]*Log[1 - E^(-2*ArcCsch[a + b*x])] + (4*I)*Pi*Log[1 - ((-1 + Sqrt[1 + a^2])*E^ArcCsch[a + b*x])/a] + 8*ArcCsch[a + b*x]*Log[1 - ((-1 + Sqrt[1 + a^2])*E^ArcCsch[a + b*x])/a] + (16*I)*ArcSin[Sqrt[(-I + a)/a]/Sqrt[2]]*Log[1 - ((-1 + Sqrt[1 + a^2])*E^ArcCsch[a + b*x])/a] + (4*I)*Pi*Log[1 + ((1 + Sqrt[1 + a^2])*E^ArcCsch[a + b*x])/a] + 8*ArcCsch[a + b*x]*Log[1 + ((1 + Sqrt[1 + a^2])*E^ArcCsch[a + b*x])/a] - (16*I)*ArcSin[Sqrt[(-I + a)/a]/Sqrt[2]]*Log[1 + ((1 + Sqrt[1 + a^2])*E^ArcCsch[a + b*x])/a] - (4*I)*Pi*Log[(b*x)/(a + b*x)] + 4*PolyLog[2, E^(-2*ArcCsch[a + b*x])] + 8*PolyLog[2, ((-1 + Sqrt[1 + a^2])*E^ArcCsch[a + b*x])/a] + 8*PolyLog[2, -(((1 + Sqrt[1 + a^2])*E^ArcCsch[a + b*x])/a)])/8","C",0
5,1,141,63,0.1645279,"\int \frac{\text{csch}^{-1}(a+b x)}{x^2} \, dx","Integrate[ArcCsch[a + b*x]/x^2,x]","-\frac{b \left(-\log \left(\sqrt{a^2+1} a \sqrt{\frac{a^2+2 a b x+b^2 x^2+1}{(a+b x)^2}}+\sqrt{a^2+1} b x \sqrt{\frac{a^2+2 a b x+b^2 x^2+1}{(a+b x)^2}}+a^2+a b x+1\right)+\sqrt{a^2+1} \sinh ^{-1}\left(\frac{1}{a+b x}\right)+\log (x)\right)}{a \sqrt{a^2+1}}-\frac{\text{csch}^{-1}(a+b x)}{x}","\frac{2 b \tanh ^{-1}\left(\frac{\tanh \left(\frac{1}{2} \text{csch}^{-1}(a+b x)\right)+a}{\sqrt{a^2+1}}\right)}{a \sqrt{a^2+1}}-\frac{b \text{csch}^{-1}(a+b x)}{a}-\frac{\text{csch}^{-1}(a+b x)}{x}",1,"-(ArcCsch[a + b*x]/x) - (b*(Sqrt[1 + a^2]*ArcSinh[(a + b*x)^(-1)] + Log[x] - Log[1 + a^2 + a*b*x + a*Sqrt[1 + a^2]*Sqrt[(1 + a^2 + 2*a*b*x + b^2*x^2)/(a + b*x)^2] + Sqrt[1 + a^2]*b*x*Sqrt[(1 + a^2 + 2*a*b*x + b^2*x^2)/(a + b*x)^2]]))/(a*Sqrt[1 + a^2])","B",1
6,1,220,114,0.4767635,"\int \frac{\text{csch}^{-1}(a+b x)}{x^3} \, dx","Integrate[ArcCsch[a + b*x]/x^3,x]","\frac{1}{2} \left(\frac{b (a+b x) \sqrt{\frac{a^2+2 a b x+b^2 x^2+1}{(a+b x)^2}}}{a \left(a^2+1\right) x}-\frac{\left(2 a^2+1\right) b^2 \log \left(\sqrt{a^2+1} a \sqrt{\frac{a^2+2 a b x+b^2 x^2+1}{(a+b x)^2}}+\sqrt{a^2+1} b x \sqrt{\frac{a^2+2 a b x+b^2 x^2+1}{(a+b x)^2}}+a^2+a b x+1\right)}{a^2 \left(a^2+1\right)^{3/2}}+\frac{\left(2 a^2+1\right) b^2 \log (x)}{a^2 \left(a^2+1\right)^{3/2}}+\frac{b^2 \sinh ^{-1}\left(\frac{1}{a+b x}\right)}{a^2}-\frac{\text{csch}^{-1}(a+b x)}{x^2}\right)","\frac{b^2 \text{csch}^{-1}(a+b x)}{2 a^2}-\frac{\left(2 a^2+1\right) b^2 \tanh ^{-1}\left(\frac{\tanh \left(\frac{1}{2} \text{csch}^{-1}(a+b x)\right)+a}{\sqrt{a^2+1}}\right)}{a^2 \left(a^2+1\right)^{3/2}}+\frac{b (a+b x) \sqrt{\frac{1}{(a+b x)^2}+1}}{2 a \left(a^2+1\right) x}-\frac{\text{csch}^{-1}(a+b x)}{2 x^2}",1,"((b*(a + b*x)*Sqrt[(1 + a^2 + 2*a*b*x + b^2*x^2)/(a + b*x)^2])/(a*(1 + a^2)*x) - ArcCsch[a + b*x]/x^2 + (b^2*ArcSinh[(a + b*x)^(-1)])/a^2 + ((1 + 2*a^2)*b^2*Log[x])/(a^2*(1 + a^2)^(3/2)) - ((1 + 2*a^2)*b^2*Log[1 + a^2 + a*b*x + a*Sqrt[1 + a^2]*Sqrt[(1 + a^2 + 2*a*b*x + b^2*x^2)/(a + b*x)^2] + Sqrt[1 + a^2]*b*x*Sqrt[(1 + a^2 + 2*a*b*x + b^2*x^2)/(a + b*x)^2]])/(a^2*(1 + a^2)^(3/2)))/2","A",1
7,1,1429,501,12.8023446,"\int (e+f x)^3 \left(a+b \text{csch}^{-1}(c+d x)\right)^2 \, dx","Integrate[(e + f*x)^3*(a + b*ArcCsch[c + d*x])^2,x]","\frac{1}{4} a^2 f^3 x^4+a^2 e f^2 x^3-\frac{b^2 f^3 \left(3 \text{csch}^{-1}(c+d x)^2 \text{csch}^4\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)-\frac{2 \text{csch}^{-1}(c+d x) \left(6 c \text{csch}^{-1}(c+d x)-1\right) \text{csch}^4\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)}{c+d x}+2 \left(36 c^2 \text{csch}^{-1}(c+d x)^2-3 \text{csch}^{-1}(c+d x)^2-24 c \text{csch}^{-1}(c+d x)+2\right) \text{csch}^2\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)+3 \text{csch}^{-1}(c+d x)^2 \text{sech}^4\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)-32 (c+d x)^3 \text{csch}^{-1}(c+d x) \left(6 c \text{csch}^{-1}(c+d x)+1\right) \sinh ^4\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)-2 \left(36 c^2 \text{csch}^{-1}(c+d x)^2-3 \text{csch}^{-1}(c+d x)^2+24 c \text{csch}^{-1}(c+d x)+2\right) \text{sech}^2\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)-16 \left(6 \text{csch}^{-1}(c+d x)^2 c^3-18 \text{csch}^{-1}(c+d x) c^2-3 \left(\text{csch}^{-1}(c+d x)^2-2\right) c+2 \text{csch}^{-1}(c+d x)\right) \coth \left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)-64 \left(9 c^2-1\right) \log \left(\frac{1}{c+d x}\right)+192 c \left(2 c^2-1\right) \left(\text{csch}^{-1}(c+d x) \left(\log \left(1-e^{-\text{csch}^{-1}(c+d x)}\right)-\log \left(1+e^{-\text{csch}^{-1}(c+d x)}\right)\right)+\text{Li}_2\left(-e^{-\text{csch}^{-1}(c+d x)}\right)-\text{Li}_2\left(e^{-\text{csch}^{-1}(c+d x)}\right)\right)+16 \left(6 \text{csch}^{-1}(c+d x)^2 c^3+18 \text{csch}^{-1}(c+d x) c^2-3 \left(\text{csch}^{-1}(c+d x)^2-2\right) c-2 \text{csch}^{-1}(c+d x)\right) \tanh \left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)\right) x^3}{192 d (c+d x)^3 \left(\frac{c}{c+d x}-1\right)^3}+\frac{3}{2} a^2 e^2 f x^2+a^2 e^3 x-\frac{3 b^2 d e^2 f \left(\frac{(c+d x)^2 \text{csch}^{-1}(c+d x)^2}{2 d^2}-\frac{c \coth \left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right) \text{csch}^{-1}(c+d x)^2}{2 d^2}+\frac{c \tanh \left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right) \text{csch}^{-1}(c+d x)^2}{2 d^2}+\frac{(c+d x) \sqrt{1+\frac{1}{(c+d x)^2}} \text{csch}^{-1}(c+d x)}{d^2}-\frac{\log \left(\frac{1}{c+d x}\right)}{d^2}-\frac{2 i c \left(i \text{csch}^{-1}(c+d x) \left(\log \left(1-e^{-\text{csch}^{-1}(c+d x)}\right)-\log \left(1+e^{-\text{csch}^{-1}(c+d x)}\right)\right)+i \left(\text{Li}_2\left(-e^{-\text{csch}^{-1}(c+d x)}\right)-\text{Li}_2\left(e^{-\text{csch}^{-1}(c+d x)}\right)\right)\right)}{d^2}\right) x}{(c+d x) \left(\frac{c}{c+d x}-1\right)}+\frac{1}{6} a b \left(3 x \left(4 e^3+6 f x e^2+4 f^2 x^2 e+f^3 x^3\right) \text{csch}^{-1}(c+d x)+\frac{f (c+d x) \sqrt{\frac{c^2+2 d x c+d^2 x^2+1}{(c+d x)^2}} \left(\left(18 e^2+6 f x e+f^2 x^2\right) d^2-2 c f (15 e+2 f x) d+\left(13 c^2-2\right) f^2\right)-3 c \left(-4 d^3 e^3+6 c d^2 f e^2-4 c^2 d f^2 e+c^3 f^3\right) \sinh ^{-1}\left(\frac{1}{c+d x}\right)+6 \left(2 d^3 e^3-6 c d^2 f e^2+\left(6 c^2-1\right) d f^2 e+c \left(1-2 c^2\right) f^3\right) \log \left((c+d x) \left(\sqrt{\frac{c^2+2 d x c+d^2 x^2+1}{(c+d x)^2}}+1\right)\right)}{d^4}\right)-\frac{b^2 e^3 \left(-\text{csch}^{-1}(c+d x) \left((c+d x) \text{csch}^{-1}(c+d x)-2 \log \left(1-e^{-\text{csch}^{-1}(c+d x)}\right)+2 \log \left(1+e^{-\text{csch}^{-1}(c+d x)}\right)\right)+2 \text{Li}_2\left(-e^{-\text{csch}^{-1}(c+d x)}\right)-2 \text{Li}_2\left(e^{-\text{csch}^{-1}(c+d x)}\right)\right)}{d}-\frac{b^2 e f^2 \left(-\frac{\text{csch}^{-1}(c+d x)^2 \text{csch}^4\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)}{2 (c+d x)}+2 \text{csch}^{-1}(c+d x) \left(3 c \text{csch}^{-1}(c+d x)-1\right) \text{csch}^2\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)-8 (c+d x)^3 \text{csch}^{-1}(c+d x)^2 \sinh ^4\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)-2 \text{csch}^{-1}(c+d x) \left(3 c \text{csch}^{-1}(c+d x)+1\right) \text{sech}^2\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)+2 \left(-6 c^2 \text{csch}^{-1}(c+d x)^2+\text{csch}^{-1}(c+d x)^2+12 c \text{csch}^{-1}(c+d x)-2\right) \coth \left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)-48 c \log \left(\frac{1}{c+d x}\right)+8 \left(6 c^2-1\right) \left(\text{csch}^{-1}(c+d x) \left(\log \left(1-e^{-\text{csch}^{-1}(c+d x)}\right)-\log \left(1+e^{-\text{csch}^{-1}(c+d x)}\right)\right)+\text{Li}_2\left(-e^{-\text{csch}^{-1}(c+d x)}\right)-\text{Li}_2\left(e^{-\text{csch}^{-1}(c+d x)}\right)\right)+2 \left(6 c^2 \text{csch}^{-1}(c+d x)^2-\text{csch}^{-1}(c+d x)^2+12 c \text{csch}^{-1}(c+d x)+2\right) \tanh \left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)\right)}{8 d^3}","\frac{b f^2 (c+d x)^2 \sqrt{\frac{1}{(c+d x)^2}+1} (d e-c f) \left(a+b \text{csch}^{-1}(c+d x)\right)}{d^4}-\frac{2 b f^2 (d e-c f) \tanh ^{-1}\left(e^{\text{csch}^{-1}(c+d x)}\right) \left(a+b \text{csch}^{-1}(c+d x)\right)}{d^4}-\frac{(d e-c f)^4 \left(a+b \text{csch}^{-1}(c+d x)\right)^2}{4 d^4 f}+\frac{3 b f (c+d x) \sqrt{\frac{1}{(c+d x)^2}+1} (d e-c f)^2 \left(a+b \text{csch}^{-1}(c+d x)\right)}{d^4}+\frac{4 b (d e-c f)^3 \tanh ^{-1}\left(e^{\text{csch}^{-1}(c+d x)}\right) \left(a+b \text{csch}^{-1}(c+d x)\right)}{d^4}+\frac{b f^3 (c+d x)^3 \sqrt{\frac{1}{(c+d x)^2}+1} \left(a+b \text{csch}^{-1}(c+d x)\right)}{6 d^4}-\frac{b f^3 (c+d x) \sqrt{\frac{1}{(c+d x)^2}+1} \left(a+b \text{csch}^{-1}(c+d x)\right)}{3 d^4}+\frac{(e+f x)^4 \left(a+b \text{csch}^{-1}(c+d x)\right)^2}{4 f}-\frac{b^2 f^2 (d e-c f) \text{Li}_2\left(-e^{\text{csch}^{-1}(c+d x)}\right)}{d^4}+\frac{b^2 f^2 (d e-c f) \text{Li}_2\left(e^{\text{csch}^{-1}(c+d x)}\right)}{d^4}+\frac{2 b^2 (d e-c f)^3 \text{Li}_2\left(-e^{\text{csch}^{-1}(c+d x)}\right)}{d^4}-\frac{2 b^2 (d e-c f)^3 \text{Li}_2\left(e^{\text{csch}^{-1}(c+d x)}\right)}{d^4}+\frac{3 b^2 f (d e-c f)^2 \log (c+d x)}{d^4}+\frac{b^2 f^3 (c+d x)^2}{12 d^4}-\frac{b^2 f^3 \log (c+d x)}{3 d^4}+\frac{b^2 f^2 x (d e-c f)}{d^3}",1,"a^2*e^3*x + (3*a^2*e^2*f*x^2)/2 + a^2*e*f^2*x^3 + (a^2*f^3*x^4)/4 + (a*b*(3*x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3)*ArcCsch[c + d*x] + (f*(c + d*x)*Sqrt[(1 + c^2 + 2*c*d*x + d^2*x^2)/(c + d*x)^2]*((-2 + 13*c^2)*f^2 - 2*c*d*f*(15*e + 2*f*x) + d^2*(18*e^2 + 6*e*f*x + f^2*x^2)) - 3*c*(-4*d^3*e^3 + 6*c*d^2*e^2*f - 4*c^2*d*e*f^2 + c^3*f^3)*ArcSinh[(c + d*x)^(-1)] + 6*(2*d^3*e^3 - 6*c*d^2*e^2*f + (-1 + 6*c^2)*d*e*f^2 + c*(1 - 2*c^2)*f^3)*Log[(c + d*x)*(1 + Sqrt[(1 + c^2 + 2*c*d*x + d^2*x^2)/(c + d*x)^2])])/d^4))/6 - (b^2*e^3*(-(ArcCsch[c + d*x]*((c + d*x)*ArcCsch[c + d*x] - 2*Log[1 - E^(-ArcCsch[c + d*x])] + 2*Log[1 + E^(-ArcCsch[c + d*x])])) + 2*PolyLog[2, -E^(-ArcCsch[c + d*x])] - 2*PolyLog[2, E^(-ArcCsch[c + d*x])]))/d - (3*b^2*d*e^2*f*x*(((c + d*x)*Sqrt[1 + (c + d*x)^(-2)]*ArcCsch[c + d*x])/d^2 + ((c + d*x)^2*ArcCsch[c + d*x]^2)/(2*d^2) - (c*ArcCsch[c + d*x]^2*Coth[ArcCsch[c + d*x]/2])/(2*d^2) - Log[(c + d*x)^(-1)]/d^2 - ((2*I)*c*(I*ArcCsch[c + d*x]*(Log[1 - E^(-ArcCsch[c + d*x])] - Log[1 + E^(-ArcCsch[c + d*x])]) + I*(PolyLog[2, -E^(-ArcCsch[c + d*x])] - PolyLog[2, E^(-ArcCsch[c + d*x])])))/d^2 + (c*ArcCsch[c + d*x]^2*Tanh[ArcCsch[c + d*x]/2])/(2*d^2)))/((c + d*x)*(-1 + c/(c + d*x))) - (b^2*e*f^2*(2*(-2 + 12*c*ArcCsch[c + d*x] + ArcCsch[c + d*x]^2 - 6*c^2*ArcCsch[c + d*x]^2)*Coth[ArcCsch[c + d*x]/2] + 2*ArcCsch[c + d*x]*(-1 + 3*c*ArcCsch[c + d*x])*Csch[ArcCsch[c + d*x]/2]^2 - (ArcCsch[c + d*x]^2*Csch[ArcCsch[c + d*x]/2]^4)/(2*(c + d*x)) - 48*c*Log[(c + d*x)^(-1)] + 8*(-1 + 6*c^2)*(ArcCsch[c + d*x]*(Log[1 - E^(-ArcCsch[c + d*x])] - Log[1 + E^(-ArcCsch[c + d*x])]) + PolyLog[2, -E^(-ArcCsch[c + d*x])] - PolyLog[2, E^(-ArcCsch[c + d*x])]) - 2*ArcCsch[c + d*x]*(1 + 3*c*ArcCsch[c + d*x])*Sech[ArcCsch[c + d*x]/2]^2 - 8*(c + d*x)^3*ArcCsch[c + d*x]^2*Sinh[ArcCsch[c + d*x]/2]^4 + 2*(2 + 12*c*ArcCsch[c + d*x] - ArcCsch[c + d*x]^2 + 6*c^2*ArcCsch[c + d*x]^2)*Tanh[ArcCsch[c + d*x]/2]))/(8*d^3) - (b^2*f^3*x^3*(-16*(2*ArcCsch[c + d*x] - 18*c^2*ArcCsch[c + d*x] + 6*c^3*ArcCsch[c + d*x]^2 - 3*c*(-2 + ArcCsch[c + d*x]^2))*Coth[ArcCsch[c + d*x]/2] + 2*(2 - 24*c*ArcCsch[c + d*x] - 3*ArcCsch[c + d*x]^2 + 36*c^2*ArcCsch[c + d*x]^2)*Csch[ArcCsch[c + d*x]/2]^2 + 3*ArcCsch[c + d*x]^2*Csch[ArcCsch[c + d*x]/2]^4 - (2*ArcCsch[c + d*x]*(-1 + 6*c*ArcCsch[c + d*x])*Csch[ArcCsch[c + d*x]/2]^4)/(c + d*x) - 64*(-1 + 9*c^2)*Log[(c + d*x)^(-1)] + 192*c*(-1 + 2*c^2)*(ArcCsch[c + d*x]*(Log[1 - E^(-ArcCsch[c + d*x])] - Log[1 + E^(-ArcCsch[c + d*x])]) + PolyLog[2, -E^(-ArcCsch[c + d*x])] - PolyLog[2, E^(-ArcCsch[c + d*x])]) - 2*(2 + 24*c*ArcCsch[c + d*x] - 3*ArcCsch[c + d*x]^2 + 36*c^2*ArcCsch[c + d*x]^2)*Sech[ArcCsch[c + d*x]/2]^2 + 3*ArcCsch[c + d*x]^2*Sech[ArcCsch[c + d*x]/2]^4 - 32*(c + d*x)^3*ArcCsch[c + d*x]*(1 + 6*c*ArcCsch[c + d*x])*Sinh[ArcCsch[c + d*x]/2]^4 + 16*(-2*ArcCsch[c + d*x] + 18*c^2*ArcCsch[c + d*x] + 6*c^3*ArcCsch[c + d*x]^2 - 3*c*(-2 + ArcCsch[c + d*x]^2))*Tanh[ArcCsch[c + d*x]/2]))/(192*d*(c + d*x)^3*(-1 + c/(c + d*x))^3)","C",0
8,1,864,351,9.2443236,"\int (e+f x)^2 \left(a+b \text{csch}^{-1}(c+d x)\right)^2 \, dx","Integrate[(e + f*x)^2*(a + b*ArcCsch[c + d*x])^2,x]","\frac{1}{3} a^2 f^2 x^3+a^2 e f x^2+a^2 e^2 x-\frac{2 b^2 d e f \left(\frac{(c+d x)^2 \text{csch}^{-1}(c+d x)^2}{2 d^2}-\frac{c \coth \left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right) \text{csch}^{-1}(c+d x)^2}{2 d^2}+\frac{c \tanh \left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right) \text{csch}^{-1}(c+d x)^2}{2 d^2}+\frac{(c+d x) \sqrt{1+\frac{1}{(c+d x)^2}} \text{csch}^{-1}(c+d x)}{d^2}-\frac{\log \left(\frac{1}{c+d x}\right)}{d^2}-\frac{2 i c \left(i \text{csch}^{-1}(c+d x) \left(\log \left(1-e^{-\text{csch}^{-1}(c+d x)}\right)-\log \left(1+e^{-\text{csch}^{-1}(c+d x)}\right)\right)+i \left(\text{Li}_2\left(-e^{-\text{csch}^{-1}(c+d x)}\right)-\text{Li}_2\left(e^{-\text{csch}^{-1}(c+d x)}\right)\right)\right)}{d^2}\right) x}{(c+d x) \left(\frac{c}{c+d x}-1\right)}+\frac{1}{3} a b \left(2 x \left(3 e^2+3 f x e+f^2 x^2\right) \text{csch}^{-1}(c+d x)+\frac{-f (c+d x) \sqrt{\frac{c^2+2 d x c+d^2 x^2+1}{(c+d x)^2}} (5 c f-d (6 e+f x))+2 c \left(3 d^2 e^2-3 c d f e+c^2 f^2\right) \sinh ^{-1}\left(\frac{1}{c+d x}\right)+\left(6 d^2 e^2-12 c d f e+\left(6 c^2-1\right) f^2\right) \log \left((c+d x) \left(\sqrt{\frac{c^2+2 d x c+d^2 x^2+1}{(c+d x)^2}}+1\right)\right)}{d^3}\right)-\frac{b^2 e^2 \left(-\text{csch}^{-1}(c+d x) \left((c+d x) \text{csch}^{-1}(c+d x)-2 \log \left(1-e^{-\text{csch}^{-1}(c+d x)}\right)+2 \log \left(1+e^{-\text{csch}^{-1}(c+d x)}\right)\right)+2 \text{Li}_2\left(-e^{-\text{csch}^{-1}(c+d x)}\right)-2 \text{Li}_2\left(e^{-\text{csch}^{-1}(c+d x)}\right)\right)}{d}-\frac{b^2 f^2 \left(-\frac{\text{csch}^{-1}(c+d x)^2 \text{csch}^4\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)}{2 (c+d x)}+2 \text{csch}^{-1}(c+d x) \left(3 c \text{csch}^{-1}(c+d x)-1\right) \text{csch}^2\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)-8 (c+d x)^3 \text{csch}^{-1}(c+d x)^2 \sinh ^4\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)-2 \text{csch}^{-1}(c+d x) \left(3 c \text{csch}^{-1}(c+d x)+1\right) \text{sech}^2\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)+2 \left(-6 c^2 \text{csch}^{-1}(c+d x)^2+\text{csch}^{-1}(c+d x)^2+12 c \text{csch}^{-1}(c+d x)-2\right) \coth \left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)-48 c \log \left(\frac{1}{c+d x}\right)+8 \left(6 c^2-1\right) \left(\text{csch}^{-1}(c+d x) \left(\log \left(1-e^{-\text{csch}^{-1}(c+d x)}\right)-\log \left(1+e^{-\text{csch}^{-1}(c+d x)}\right)\right)+\text{Li}_2\left(-e^{-\text{csch}^{-1}(c+d x)}\right)-\text{Li}_2\left(e^{-\text{csch}^{-1}(c+d x)}\right)\right)+2 \left(6 c^2 \text{csch}^{-1}(c+d x)^2-\text{csch}^{-1}(c+d x)^2+12 c \text{csch}^{-1}(c+d x)+2\right) \tanh \left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)\right)}{24 d^3}","-\frac{(d e-c f)^3 \left(a+b \text{csch}^{-1}(c+d x)\right)^2}{3 d^3 f}+\frac{2 b f (c+d x) \sqrt{\frac{1}{(c+d x)^2}+1} (d e-c f) \left(a+b \text{csch}^{-1}(c+d x)\right)}{d^3}+\frac{4 b (d e-c f)^2 \tanh ^{-1}\left(e^{\text{csch}^{-1}(c+d x)}\right) \left(a+b \text{csch}^{-1}(c+d x)\right)}{d^3}+\frac{b f^2 (c+d x)^2 \sqrt{\frac{1}{(c+d x)^2}+1} \left(a+b \text{csch}^{-1}(c+d x)\right)}{3 d^3}-\frac{2 b f^2 \tanh ^{-1}\left(e^{\text{csch}^{-1}(c+d x)}\right) \left(a+b \text{csch}^{-1}(c+d x)\right)}{3 d^3}+\frac{(e+f x)^3 \left(a+b \text{csch}^{-1}(c+d x)\right)^2}{3 f}+\frac{2 b^2 (d e-c f)^2 \text{Li}_2\left(-e^{\text{csch}^{-1}(c+d x)}\right)}{d^3}-\frac{2 b^2 (d e-c f)^2 \text{Li}_2\left(e^{\text{csch}^{-1}(c+d x)}\right)}{d^3}+\frac{2 b^2 f (d e-c f) \log (c+d x)}{d^3}-\frac{b^2 f^2 \text{Li}_2\left(-e^{\text{csch}^{-1}(c+d x)}\right)}{3 d^3}+\frac{b^2 f^2 \text{Li}_2\left(e^{\text{csch}^{-1}(c+d x)}\right)}{3 d^3}+\frac{b^2 f^2 x}{3 d^2}",1,"a^2*e^2*x + a^2*e*f*x^2 + (a^2*f^2*x^3)/3 + (a*b*(2*x*(3*e^2 + 3*e*f*x + f^2*x^2)*ArcCsch[c + d*x] + (-(f*(c + d*x)*Sqrt[(1 + c^2 + 2*c*d*x + d^2*x^2)/(c + d*x)^2]*(5*c*f - d*(6*e + f*x))) + 2*c*(3*d^2*e^2 - 3*c*d*e*f + c^2*f^2)*ArcSinh[(c + d*x)^(-1)] + (6*d^2*e^2 - 12*c*d*e*f + (-1 + 6*c^2)*f^2)*Log[(c + d*x)*(1 + Sqrt[(1 + c^2 + 2*c*d*x + d^2*x^2)/(c + d*x)^2])])/d^3))/3 - (b^2*e^2*(-(ArcCsch[c + d*x]*((c + d*x)*ArcCsch[c + d*x] - 2*Log[1 - E^(-ArcCsch[c + d*x])] + 2*Log[1 + E^(-ArcCsch[c + d*x])])) + 2*PolyLog[2, -E^(-ArcCsch[c + d*x])] - 2*PolyLog[2, E^(-ArcCsch[c + d*x])]))/d - (2*b^2*d*e*f*x*(((c + d*x)*Sqrt[1 + (c + d*x)^(-2)]*ArcCsch[c + d*x])/d^2 + ((c + d*x)^2*ArcCsch[c + d*x]^2)/(2*d^2) - (c*ArcCsch[c + d*x]^2*Coth[ArcCsch[c + d*x]/2])/(2*d^2) - Log[(c + d*x)^(-1)]/d^2 - ((2*I)*c*(I*ArcCsch[c + d*x]*(Log[1 - E^(-ArcCsch[c + d*x])] - Log[1 + E^(-ArcCsch[c + d*x])]) + I*(PolyLog[2, -E^(-ArcCsch[c + d*x])] - PolyLog[2, E^(-ArcCsch[c + d*x])])))/d^2 + (c*ArcCsch[c + d*x]^2*Tanh[ArcCsch[c + d*x]/2])/(2*d^2)))/((c + d*x)*(-1 + c/(c + d*x))) - (b^2*f^2*(2*(-2 + 12*c*ArcCsch[c + d*x] + ArcCsch[c + d*x]^2 - 6*c^2*ArcCsch[c + d*x]^2)*Coth[ArcCsch[c + d*x]/2] + 2*ArcCsch[c + d*x]*(-1 + 3*c*ArcCsch[c + d*x])*Csch[ArcCsch[c + d*x]/2]^2 - (ArcCsch[c + d*x]^2*Csch[ArcCsch[c + d*x]/2]^4)/(2*(c + d*x)) - 48*c*Log[(c + d*x)^(-1)] + 8*(-1 + 6*c^2)*(ArcCsch[c + d*x]*(Log[1 - E^(-ArcCsch[c + d*x])] - Log[1 + E^(-ArcCsch[c + d*x])]) + PolyLog[2, -E^(-ArcCsch[c + d*x])] - PolyLog[2, E^(-ArcCsch[c + d*x])]) - 2*ArcCsch[c + d*x]*(1 + 3*c*ArcCsch[c + d*x])*Sech[ArcCsch[c + d*x]/2]^2 - 8*(c + d*x)^3*ArcCsch[c + d*x]^2*Sinh[ArcCsch[c + d*x]/2]^4 + 2*(2 + 12*c*ArcCsch[c + d*x] - ArcCsch[c + d*x]^2 + 6*c^2*ArcCsch[c + d*x]^2)*Tanh[ArcCsch[c + d*x]/2]))/(24*d^3)","C",0
9,1,401,194,1.4612458,"\int (e+f x) \left(a+b \text{csch}^{-1}(c+d x)\right)^2 \, dx","Integrate[(e + f*x)*(a + b*ArcCsch[c + d*x])^2,x]","\frac{2 a^2 (c+d x) (d e-c f)+a^2 f (c+d x)^2+2 a b d e \left(2 (c+d x) \text{csch}^{-1}(c+d x)-2 \log \left(2 (c+d x) \sinh ^2\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)\right)\right)+2 a b f (c+d x) \left(\sqrt{\frac{1}{(c+d x)^2}+1}+(c+d x) \text{csch}^{-1}(c+d x)\right)+2 a b c f \left(2 \log \left(2 (c+d x) \sinh ^2\left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)\right)-2 (c+d x) \text{csch}^{-1}(c+d x)\right)+2 b^2 d e \left(-2 \text{Li}_2\left(-e^{-\text{csch}^{-1}(c+d x)}\right)+2 \text{Li}_2\left(e^{-\text{csch}^{-1}(c+d x)}\right)+\text{csch}^{-1}(c+d x) \left((c+d x) \text{csch}^{-1}(c+d x)-2 \log \left(1-e^{-\text{csch}^{-1}(c+d x)}\right)+2 \log \left(e^{-\text{csch}^{-1}(c+d x)}+1\right)\right)\right)-2 b^2 c f \left(-2 \text{Li}_2\left(-e^{-\text{csch}^{-1}(c+d x)}\right)+2 \text{Li}_2\left(e^{-\text{csch}^{-1}(c+d x)}\right)+\text{csch}^{-1}(c+d x) \left((c+d x) \text{csch}^{-1}(c+d x)-2 \log \left(1-e^{-\text{csch}^{-1}(c+d x)}\right)+2 \log \left(e^{-\text{csch}^{-1}(c+d x)}+1\right)\right)\right)+2 b^2 f \left(-\log \left(\frac{1}{c+d x}\right)+\frac{1}{2} (c+d x)^2 \text{csch}^{-1}(c+d x)^2+(c+d x) \sqrt{\frac{1}{(c+d x)^2}+1} \text{csch}^{-1}(c+d x)\right)}{2 d^2}","-\frac{(d e-c f)^2 \left(a+b \text{csch}^{-1}(c+d x)\right)^2}{2 d^2 f}+\frac{4 b (d e-c f) \tanh ^{-1}\left(e^{\text{csch}^{-1}(c+d x)}\right) \left(a+b \text{csch}^{-1}(c+d x)\right)}{d^2}+\frac{b f (c+d x) \sqrt{\frac{1}{(c+d x)^2}+1} \left(a+b \text{csch}^{-1}(c+d x)\right)}{d^2}+\frac{(e+f x)^2 \left(a+b \text{csch}^{-1}(c+d x)\right)^2}{2 f}+\frac{2 b^2 (d e-c f) \text{Li}_2\left(-e^{\text{csch}^{-1}(c+d x)}\right)}{d^2}-\frac{2 b^2 (d e-c f) \text{Li}_2\left(e^{\text{csch}^{-1}(c+d x)}\right)}{d^2}+\frac{b^2 f \log (c+d x)}{d^2}",1,"(2*a^2*(d*e - c*f)*(c + d*x) + a^2*f*(c + d*x)^2 + 2*a*b*f*(c + d*x)*(Sqrt[1 + (c + d*x)^(-2)] + (c + d*x)*ArcCsch[c + d*x]) + 2*b^2*f*((c + d*x)*Sqrt[1 + (c + d*x)^(-2)]*ArcCsch[c + d*x] + ((c + d*x)^2*ArcCsch[c + d*x]^2)/2 - Log[(c + d*x)^(-1)]) + 2*a*b*d*e*(2*(c + d*x)*ArcCsch[c + d*x] - 2*Log[2*(c + d*x)*Sinh[ArcCsch[c + d*x]/2]^2]) + 2*a*b*c*f*(-2*(c + d*x)*ArcCsch[c + d*x] + 2*Log[2*(c + d*x)*Sinh[ArcCsch[c + d*x]/2]^2]) + 2*b^2*d*e*(ArcCsch[c + d*x]*((c + d*x)*ArcCsch[c + d*x] - 2*Log[1 - E^(-ArcCsch[c + d*x])] + 2*Log[1 + E^(-ArcCsch[c + d*x])]) - 2*PolyLog[2, -E^(-ArcCsch[c + d*x])] + 2*PolyLog[2, E^(-ArcCsch[c + d*x])]) - 2*b^2*c*f*(ArcCsch[c + d*x]*((c + d*x)*ArcCsch[c + d*x] - 2*Log[1 - E^(-ArcCsch[c + d*x])] + 2*Log[1 + E^(-ArcCsch[c + d*x])]) - 2*PolyLog[2, -E^(-ArcCsch[c + d*x])] + 2*PolyLog[2, E^(-ArcCsch[c + d*x])]))/(2*d^2)","B",0
10,1,160,85,0.263094,"\int \left(a+b \text{csch}^{-1}(c+d x)\right)^2 \, dx","Integrate[(a + b*ArcCsch[c + d*x])^2,x]","\frac{a^2 c+a^2 d x+2 a b (c+d x) \text{csch}^{-1}(c+d x)-2 a b \log \left(\tanh \left(\frac{1}{2} \text{csch}^{-1}(c+d x)\right)\right)-2 b^2 \text{Li}_2\left(-e^{-\text{csch}^{-1}(c+d x)}\right)+2 b^2 \text{Li}_2\left(e^{-\text{csch}^{-1}(c+d x)}\right)+b^2 c \text{csch}^{-1}(c+d x)^2+b^2 d x \text{csch}^{-1}(c+d x)^2-2 b^2 \text{csch}^{-1}(c+d x) \log \left(1-e^{-\text{csch}^{-1}(c+d x)}\right)+2 b^2 \text{csch}^{-1}(c+d x) \log \left(e^{-\text{csch}^{-1}(c+d x)}+1\right)}{d}","\frac{(c+d x) \left(a+b \text{csch}^{-1}(c+d x)\right)^2}{d}+\frac{4 b \tanh ^{-1}\left(e^{\text{csch}^{-1}(c+d x)}\right) \left(a+b \text{csch}^{-1}(c+d x)\right)}{d}+\frac{2 b^2 \text{Li}_2\left(-e^{\text{csch}^{-1}(c+d x)}\right)}{d}-\frac{2 b^2 \text{Li}_2\left(e^{\text{csch}^{-1}(c+d x)}\right)}{d}",1,"(a^2*c + a^2*d*x + 2*a*b*(c + d*x)*ArcCsch[c + d*x] + b^2*c*ArcCsch[c + d*x]^2 + b^2*d*x*ArcCsch[c + d*x]^2 - 2*b^2*ArcCsch[c + d*x]*Log[1 - E^(-ArcCsch[c + d*x])] + 2*b^2*ArcCsch[c + d*x]*Log[1 + E^(-ArcCsch[c + d*x])] - 2*a*b*Log[Tanh[ArcCsch[c + d*x]/2]] - 2*b^2*PolyLog[2, -E^(-ArcCsch[c + d*x])] + 2*b^2*PolyLog[2, E^(-ArcCsch[c + d*x])])/d","A",0
11,1,1008,475,2.9799377,"\int \frac{\left(a+b \text{csch}^{-1}(c+d x)\right)^2}{e+f x} \, dx","Integrate[(a + b*ArcCsch[c + d*x])^2/(e + f*x),x]","\frac{6 \log (e+f x) a^2+6 b \left(\frac{1}{4} \left(\pi -2 i \text{csch}^{-1}(c+d x)\right)^2-\text{csch}^{-1}(c+d x)^2-8 \sin ^{-1}\left(\sqrt{\frac{d e-c f+i f}{2 d e-2 c f}}\right) \tan ^{-1}\left(\frac{(i d e-i c f+f) \cot \left(\frac{1}{4} \left(2 i \text{csch}^{-1}(c+d x)+\pi \right)\right)}{\sqrt{f^2+(d e-c f)^2}}\right)-2 \text{csch}^{-1}(c+d x) \log \left(1-e^{-2 \text{csch}^{-1}(c+d x)}\right)+\left(2 \text{csch}^{-1}(c+d x)+i \left(4 \sin ^{-1}\left(\sqrt{\frac{d e-c f+i f}{2 d e-2 c f}}\right)+\pi \right)\right) \log \left(\frac{d e-e^{\text{csch}^{-1}(c+d x)} f-c f+e^{\text{csch}^{-1}(c+d x)} \sqrt{f^2+(d e-c f)^2}}{d e-c f}\right)+\left(2 \text{csch}^{-1}(c+d x)+i \left(\pi -4 \sin ^{-1}\left(\sqrt{\frac{d e-c f+i f}{2 d e-2 c f}}\right)\right)\right) \log \left(-\frac{-d e+e^{\text{csch}^{-1}(c+d x)} f+c f+e^{\text{csch}^{-1}(c+d x)} \sqrt{f^2+(d e-c f)^2}}{d e-c f}\right)+2 \text{csch}^{-1}(c+d x) \log \left(\frac{d (e+f x)}{c+d x}\right)-\left(2 \text{csch}^{-1}(c+d x)+i \pi \right) \log \left(\frac{d (e+f x)}{c+d x}\right)+\text{Li}_2\left(e^{-2 \text{csch}^{-1}(c+d x)}\right)+2 \text{Li}_2\left(\frac{e^{\text{csch}^{-1}(c+d x)} \left(f-\sqrt{f^2+(d e-c f)^2}\right)}{d e-c f}\right)+2 \text{Li}_2\left(\frac{e^{\text{csch}^{-1}(c+d x)} \left(f+\sqrt{f^2+(d e-c f)^2}\right)}{d e-c f}\right)\right) a+b^2 \left(-2 \text{csch}^{-1}(c+d x)^3-6 \log \left(1+e^{-\text{csch}^{-1}(c+d x)}\right) \text{csch}^{-1}(c+d x)^2-6 \log \left(1-e^{\text{csch}^{-1}(c+d x)}\right) \text{csch}^{-1}(c+d x)^2+6 \log \left(\frac{e^{\text{csch}^{-1}(c+d x)} (c f-d e)}{\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}-f}+1\right) \text{csch}^{-1}(c+d x)^2+6 \log \left(\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f+\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}+1\right) \text{csch}^{-1}(c+d x)^2+12 \text{Li}_2\left(-e^{-\text{csch}^{-1}(c+d x)}\right) \text{csch}^{-1}(c+d x)-12 \text{Li}_2\left(e^{\text{csch}^{-1}(c+d x)}\right) \text{csch}^{-1}(c+d x)+12 \text{Li}_2\left(\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}-f}\right) \text{csch}^{-1}(c+d x)+12 \text{Li}_2\left(\frac{e^{\text{csch}^{-1}(c+d x)} (c f-d e)}{f+\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}\right) \text{csch}^{-1}(c+d x)+12 \text{Li}_3\left(-e^{-\text{csch}^{-1}(c+d x)}\right)+12 \text{Li}_3\left(e^{\text{csch}^{-1}(c+d x)}\right)-12 \text{Li}_3\left(\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}-f}\right)-12 \text{Li}_3\left(\frac{e^{\text{csch}^{-1}(c+d x)} (c f-d e)}{f+\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}\right)-i \pi ^3\right)}{6 f}","\frac{2 b \left(a+b \text{csch}^{-1}(c+d x)\right) \text{Li}_2\left(-\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f-\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}\right)}{f}+\frac{2 b \left(a+b \text{csch}^{-1}(c+d x)\right) \text{Li}_2\left(-\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f+\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}\right)}{f}+\frac{\left(a+b \text{csch}^{-1}(c+d x)\right)^2 \log \left(\frac{(d e-c f) e^{\text{csch}^{-1}(c+d x)}}{f-\sqrt{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}}+1\right)}{f}+\frac{\left(a+b \text{csch}^{-1}(c+d x)\right)^2 \log \left(\frac{(d e-c f) e^{\text{csch}^{-1}(c+d x)}}{\sqrt{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}+f}+1\right)}{f}-\frac{b \text{Li}_2\left(e^{2 \text{csch}^{-1}(c+d x)}\right) \left(a+b \text{csch}^{-1}(c+d x)\right)}{f}-\frac{\log \left(1-e^{2 \text{csch}^{-1}(c+d x)}\right) \left(a+b \text{csch}^{-1}(c+d x)\right)^2}{f}-\frac{2 b^2 \text{Li}_3\left(-\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f-\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}\right)}{f}-\frac{2 b^2 \text{Li}_3\left(-\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f+\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}\right)}{f}+\frac{b^2 \text{Li}_3\left(e^{2 \text{csch}^{-1}(c+d x)}\right)}{2 f}",1,"(6*a^2*Log[e + f*x] + 6*a*b*((Pi - (2*I)*ArcCsch[c + d*x])^2/4 - ArcCsch[c + d*x]^2 - 8*ArcSin[Sqrt[(d*e + I*f - c*f)/(2*d*e - 2*c*f)]]*ArcTan[((I*d*e + f - I*c*f)*Cot[(Pi + (2*I)*ArcCsch[c + d*x])/4])/Sqrt[f^2 + (d*e - c*f)^2]] - 2*ArcCsch[c + d*x]*Log[1 - E^(-2*ArcCsch[c + d*x])] + (2*ArcCsch[c + d*x] + I*(Pi + 4*ArcSin[Sqrt[(d*e + I*f - c*f)/(2*d*e - 2*c*f)]]))*Log[(d*e - c*f - E^ArcCsch[c + d*x]*f + E^ArcCsch[c + d*x]*Sqrt[f^2 + (d*e - c*f)^2])/(d*e - c*f)] + (2*ArcCsch[c + d*x] + I*(Pi - 4*ArcSin[Sqrt[(d*e + I*f - c*f)/(2*d*e - 2*c*f)]]))*Log[-((-(d*e) + c*f + E^ArcCsch[c + d*x]*f + E^ArcCsch[c + d*x]*Sqrt[f^2 + (d*e - c*f)^2])/(d*e - c*f))] + 2*ArcCsch[c + d*x]*Log[(d*(e + f*x))/(c + d*x)] - (I*Pi + 2*ArcCsch[c + d*x])*Log[(d*(e + f*x))/(c + d*x)] + PolyLog[2, E^(-2*ArcCsch[c + d*x])] + 2*PolyLog[2, (E^ArcCsch[c + d*x]*(f - Sqrt[f^2 + (d*e - c*f)^2]))/(d*e - c*f)] + 2*PolyLog[2, (E^ArcCsch[c + d*x]*(f + Sqrt[f^2 + (d*e - c*f)^2]))/(d*e - c*f)]) + b^2*((-I)*Pi^3 - 2*ArcCsch[c + d*x]^3 - 6*ArcCsch[c + d*x]^2*Log[1 + E^(-ArcCsch[c + d*x])] - 6*ArcCsch[c + d*x]^2*Log[1 - E^ArcCsch[c + d*x]] + 6*ArcCsch[c + d*x]^2*Log[1 + (E^ArcCsch[c + d*x]*(-(d*e) + c*f))/(-f + Sqrt[d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2])] + 6*ArcCsch[c + d*x]^2*Log[1 + (E^ArcCsch[c + d*x]*(d*e - c*f))/(f + Sqrt[d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2])] + 12*ArcCsch[c + d*x]*PolyLog[2, -E^(-ArcCsch[c + d*x])] - 12*ArcCsch[c + d*x]*PolyLog[2, E^ArcCsch[c + d*x]] + 12*ArcCsch[c + d*x]*PolyLog[2, (E^ArcCsch[c + d*x]*(d*e - c*f))/(-f + Sqrt[d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2])] + 12*ArcCsch[c + d*x]*PolyLog[2, (E^ArcCsch[c + d*x]*(-(d*e) + c*f))/(f + Sqrt[d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2])] + 12*PolyLog[3, -E^(-ArcCsch[c + d*x])] + 12*PolyLog[3, E^ArcCsch[c + d*x]] - 12*PolyLog[3, (E^ArcCsch[c + d*x]*(d*e - c*f))/(-f + Sqrt[d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2])] - 12*PolyLog[3, (E^ArcCsch[c + d*x]*(-(d*e) + c*f))/(f + Sqrt[d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2])]))/(6*f)","C",0
12,1,2061,448,12.8836051,"\int \frac{\left(a+b \text{csch}^{-1}(c+d x)\right)^2}{(e+f x)^2} \, dx","Integrate[(a + b*ArcCsch[c + d*x])^2/(e + f*x)^2,x]","\text{Result too large to show}","-\frac{2 b d \left(a+b \text{csch}^{-1}(c+d x)\right) \log \left(\frac{(d e-c f) e^{\text{csch}^{-1}(c+d x)}}{f-\sqrt{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}}+1\right)}{(d e-c f) \sqrt{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}}+\frac{2 b d \left(a+b \text{csch}^{-1}(c+d x)\right) \log \left(\frac{(d e-c f) e^{\text{csch}^{-1}(c+d x)}}{\sqrt{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}+f}+1\right)}{(d e-c f) \sqrt{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}}+\frac{d \left(a+b \text{csch}^{-1}(c+d x)\right)^2}{f (d e-c f)}-\frac{\left(a+b \text{csch}^{-1}(c+d x)\right)^2}{f (e+f x)}-\frac{2 b^2 d \text{Li}_2\left(-\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f-\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}\right)}{(d e-c f) \sqrt{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}}+\frac{2 b^2 d \text{Li}_2\left(-\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f+\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}\right)}{(d e-c f) \sqrt{\left(c^2+1\right) f^2-2 c d e f+d^2 e^2}}",1,"-(a^2/(f*(e + f*x))) - (2*a*b*(c + d*x)^2*(f + (d*e - c*f)/(c + d*x))^2*(ArcCsch[c + d*x]/(f + (d*e)/(c + d*x) - (c*f)/(c + d*x)) - (2*ArcTan[(d*e - c*f - f*Tanh[ArcCsch[c + d*x]/2])/Sqrt[-(d^2*e^2) + 2*c*d*e*f - (1 + c^2)*f^2]])/Sqrt[-(d^2*e^2) + 2*c*d*e*f - (1 + c^2)*f^2]))/(d*(-(d*e) + c*f)*(e + f*x)^2) - (b^2*(c + d*x)^2*(f + (d*e - c*f)/(c + d*x))^2*(ArcCsch[c + d*x]^2/((-(d*e) + c*f)*(f + (d*e)/(c + d*x) - (c*f)/(c + d*x))) + (2*(((-I)*Pi*ArcTanh[(-(d*e) + c*f + f*Tanh[ArcCsch[c + d*x]/2])/Sqrt[f^2 + (d*e - c*f)^2]])/Sqrt[f^2 + (d*e - c*f)^2] - (2*(Pi/2 - I*ArcCsch[c + d*x])*ArcTanh[((f - I*(d*e - c*f))*Cot[(Pi/2 - I*ArcCsch[c + d*x])/2])/Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]] - 2*ArcCos[((-I)*f)/(d*e - c*f)]*ArcTanh[((-f - I*(d*e - c*f))*Tan[(Pi/2 - I*ArcCsch[c + d*x])/2])/Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]] + (ArcCos[((-I)*f)/(d*e - c*f)] - (2*I)*(ArcTanh[((f - I*(d*e - c*f))*Cot[(Pi/2 - I*ArcCsch[c + d*x])/2])/Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]] - ArcTanh[((-f - I*(d*e - c*f))*Tan[(Pi/2 - I*ArcCsch[c + d*x])/2])/Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]]))*Log[Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]/(Sqrt[2]*E^((I/2)*(Pi/2 - I*ArcCsch[c + d*x]))*Sqrt[(-I)*(d*e - c*f)]*Sqrt[f + (d*e - c*f)/(c + d*x)])] + (ArcCos[((-I)*f)/(d*e - c*f)] + (2*I)*(ArcTanh[((f - I*(d*e - c*f))*Cot[(Pi/2 - I*ArcCsch[c + d*x])/2])/Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]] - ArcTanh[((-f - I*(d*e - c*f))*Tan[(Pi/2 - I*ArcCsch[c + d*x])/2])/Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]]))*Log[(E^((I/2)*(Pi/2 - I*ArcCsch[c + d*x]))*Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2])/(Sqrt[2]*Sqrt[(-I)*(d*e - c*f)]*Sqrt[f + (d*e - c*f)/(c + d*x)])] - (ArcCos[((-I)*f)/(d*e - c*f)] + (2*I)*ArcTanh[((-f - I*(d*e - c*f))*Tan[(Pi/2 - I*ArcCsch[c + d*x])/2])/Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]])*Log[1 - (I*(f - I*Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2])*(f - I*(d*e - c*f) - Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]*Tan[(Pi/2 - I*ArcCsch[c + d*x])/2]))/((d*e - c*f)*(f - I*(d*e - c*f) + Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]*Tan[(Pi/2 - I*ArcCsch[c + d*x])/2]))] + (-ArcCos[((-I)*f)/(d*e - c*f)] + (2*I)*ArcTanh[((-f - I*(d*e - c*f))*Tan[(Pi/2 - I*ArcCsch[c + d*x])/2])/Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]])*Log[1 - (I*(f + I*Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2])*(f - I*(d*e - c*f) - Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]*Tan[(Pi/2 - I*ArcCsch[c + d*x])/2]))/((d*e - c*f)*(f - I*(d*e - c*f) + Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]*Tan[(Pi/2 - I*ArcCsch[c + d*x])/2]))] + I*(PolyLog[2, (I*(f - I*Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2])*(f - I*(d*e - c*f) - Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]*Tan[(Pi/2 - I*ArcCsch[c + d*x])/2]))/((d*e - c*f)*(f - I*(d*e - c*f) + Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]*Tan[(Pi/2 - I*ArcCsch[c + d*x])/2]))] - PolyLog[2, (I*(f + I*Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2])*(f - I*(d*e - c*f) - Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]*Tan[(Pi/2 - I*ArcCsch[c + d*x])/2]))/((d*e - c*f)*(f - I*(d*e - c*f) + Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]*Tan[(Pi/2 - I*ArcCsch[c + d*x])/2]))]))/Sqrt[-(d^2*e^2) + 2*c*d*e*f - f^2 - c^2*f^2]))/(d*e - c*f)))/(d*(e + f*x)^2)","C",0
13,1,8350,1024,14.291738,"\int \frac{\left(a+b \text{csch}^{-1}(c+d x)\right)^2}{(e+f x)^3} \, dx","Integrate[(a + b*ArcCsch[c + d*x])^2/(e + f*x)^3,x]","\text{Result too large to show}","\frac{\left(a+b \text{csch}^{-1}(c+d x)\right)^2 d^2}{2 f (d e-c f)^2}-\frac{b f \sqrt{1+\frac{1}{(c+d x)^2}} \left(a+b \text{csch}^{-1}(c+d x)\right) d^2}{(d e-c f) \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right) \left(f+\frac{d e-c f}{c+d x}\right)}-\frac{2 b \left(a+b \text{csch}^{-1}(c+d x)\right) \log \left(\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f-\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}+1\right) d^2}{(d e-c f)^2 \sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}+\frac{b f^2 \left(a+b \text{csch}^{-1}(c+d x)\right) \log \left(\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f-\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}+1\right) d^2}{(d e-c f)^2 \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)^{3/2}}+\frac{2 b \left(a+b \text{csch}^{-1}(c+d x)\right) \log \left(\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f+\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}+1\right) d^2}{(d e-c f)^2 \sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}-\frac{b f^2 \left(a+b \text{csch}^{-1}(c+d x)\right) \log \left(\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f+\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}+1\right) d^2}{(d e-c f)^2 \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)^{3/2}}+\frac{b^2 f \log \left(f+\frac{d e-c f}{c+d x}\right) d^2}{(d e-c f)^2 \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)}-\frac{2 b^2 \text{Li}_2\left(-\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f-\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}\right) d^2}{(d e-c f)^2 \sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}+\frac{b^2 f^2 \text{Li}_2\left(-\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f-\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}\right) d^2}{(d e-c f)^2 \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)^{3/2}}+\frac{2 b^2 \text{Li}_2\left(-\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f+\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}\right) d^2}{(d e-c f)^2 \sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}-\frac{b^2 f^2 \text{Li}_2\left(-\frac{e^{\text{csch}^{-1}(c+d x)} (d e-c f)}{f+\sqrt{d^2 e^2-2 c d f e+\left(c^2+1\right) f^2}}\right) d^2}{(d e-c f)^2 \left(d^2 e^2-2 c d f e+\left(c^2+1\right) f^2\right)^{3/2}}-\frac{\left(a+b \text{csch}^{-1}(c+d x)\right)^2}{2 f (e+f x)^2}",1,"Result too large to show","C",0
14,1,47,114,0.0359319,"\int x^3 \text{csch}^{-1}\left(\sqrt{x}\right) \, dx","Integrate[x^3*ArcCsch[Sqrt[x]],x]","\frac{1}{4} x^4 \text{csch}^{-1}\left(\sqrt{x}\right)+\frac{1}{140} \sqrt{\frac{1}{x}+1} \left(5 x^3-6 x^2+8 x-16\right) \sqrt{x}","\frac{1}{4} x^4 \text{csch}^{-1}\left(\sqrt{x}\right)-\frac{(-x-1)^{7/2} \sqrt{x}}{28 \sqrt{-x}}-\frac{3 (-x-1)^{5/2} \sqrt{x}}{20 \sqrt{-x}}-\frac{(-x-1)^{3/2} \sqrt{x}}{4 \sqrt{-x}}-\frac{\sqrt{-x-1} \sqrt{x}}{4 \sqrt{-x}}",1,"(Sqrt[1 + x^(-1)]*Sqrt[x]*(-16 + 8*x - 6*x^2 + 5*x^3))/140 + (x^4*ArcCsch[Sqrt[x]])/4","A",1
15,1,42,89,0.0287911,"\int x^2 \text{csch}^{-1}\left(\sqrt{x}\right) \, dx","Integrate[x^2*ArcCsch[Sqrt[x]],x]","\frac{1}{3} x^3 \text{csch}^{-1}\left(\sqrt{x}\right)+\frac{1}{45} \sqrt{\frac{1}{x}+1} \left(3 x^2-4 x+8\right) \sqrt{x}","\frac{1}{3} x^3 \text{csch}^{-1}\left(\sqrt{x}\right)+\frac{(-x-1)^{5/2} \sqrt{x}}{15 \sqrt{-x}}+\frac{2 (-x-1)^{3/2} \sqrt{x}}{9 \sqrt{-x}}+\frac{\sqrt{-x-1} \sqrt{x}}{3 \sqrt{-x}}",1,"(Sqrt[1 + x^(-1)]*Sqrt[x]*(8 - 4*x + 3*x^2))/45 + (x^3*ArcCsch[Sqrt[x]])/3","A",1
16,1,35,64,0.0265182,"\int x \text{csch}^{-1}\left(\sqrt{x}\right) \, dx","Integrate[x*ArcCsch[Sqrt[x]],x]","\frac{1}{2} x^2 \text{csch}^{-1}\left(\sqrt{x}\right)+\frac{1}{6} \sqrt{\frac{1}{x}+1} (x-2) \sqrt{x}","\frac{1}{2} x^2 \text{csch}^{-1}\left(\sqrt{x}\right)-\frac{(-x-1)^{3/2} \sqrt{x}}{6 \sqrt{-x}}-\frac{\sqrt{-x-1} \sqrt{x}}{2 \sqrt{-x}}",1,"(Sqrt[1 + x^(-1)]*(-2 + x)*Sqrt[x])/6 + (x^2*ArcCsch[Sqrt[x]])/2","A",1
17,1,24,31,0.0107391,"\int \text{csch}^{-1}\left(\sqrt{x}\right) \, dx","Integrate[ArcCsch[Sqrt[x]],x]","\sqrt{\frac{1}{x}+1} \sqrt{x}+x \text{csch}^{-1}\left(\sqrt{x}\right)","\frac{\sqrt{-x-1} \sqrt{x}}{\sqrt{-x}}+x \text{csch}^{-1}\left(\sqrt{x}\right)",1,"Sqrt[1 + x^(-1)]*Sqrt[x] + x*ArcCsch[Sqrt[x]]","A",1
18,1,45,46,0.0367348,"\int \frac{\text{csch}^{-1}\left(\sqrt{x}\right)}{x} \, dx","Integrate[ArcCsch[Sqrt[x]]/x,x]","\text{Li}_2\left(e^{-2 \text{csch}^{-1}\left(\sqrt{x}\right)}\right)-\text{csch}^{-1}\left(\sqrt{x}\right) \left(\text{csch}^{-1}\left(\sqrt{x}\right)+2 \log \left(1-e^{-2 \text{csch}^{-1}\left(\sqrt{x}\right)}\right)\right)","-\text{Li}_2\left(e^{2 \text{csch}^{-1}\left(\sqrt{x}\right)}\right)+\text{csch}^{-1}\left(\sqrt{x}\right)^2-2 \text{csch}^{-1}\left(\sqrt{x}\right) \log \left(1-e^{2 \text{csch}^{-1}\left(\sqrt{x}\right)}\right)",1,"-(ArcCsch[Sqrt[x]]*(ArcCsch[Sqrt[x]] + 2*Log[1 - E^(-2*ArcCsch[Sqrt[x]])])) + PolyLog[2, E^(-2*ArcCsch[Sqrt[x]])]","A",0
19,1,42,63,0.0246922,"\int \frac{\text{csch}^{-1}\left(\sqrt{x}\right)}{x^2} \, dx","Integrate[ArcCsch[Sqrt[x]]/x^2,x]","\frac{\sqrt{\frac{x+1}{x}}}{2 \sqrt{x}}-\frac{1}{2} \sinh ^{-1}\left(\frac{1}{\sqrt{x}}\right)-\frac{\text{csch}^{-1}\left(\sqrt{x}\right)}{x}","\frac{\sqrt{-x-1}}{2 \sqrt{-x} \sqrt{x}}-\frac{\sqrt{x} \tan ^{-1}\left(\sqrt{-x-1}\right)}{2 \sqrt{-x}}-\frac{\text{csch}^{-1}\left(\sqrt{x}\right)}{x}",1,"Sqrt[(1 + x)/x]/(2*Sqrt[x]) - ArcCsch[Sqrt[x]]/x - ArcSinh[1/Sqrt[x]]/2","A",1
20,1,47,90,0.0368565,"\int \frac{\text{csch}^{-1}\left(\sqrt{x}\right)}{x^3} \, dx","Integrate[ArcCsch[Sqrt[x]]/x^3,x]","\frac{3 x^2 \sinh ^{-1}\left(\frac{1}{\sqrt{x}}\right)+\sqrt{\frac{1}{x}+1} (2-3 x) \sqrt{x}-8 \text{csch}^{-1}\left(\sqrt{x}\right)}{16 x^2}","\frac{\sqrt{-x-1}}{8 \sqrt{-x} x^{3/2}}-\frac{\text{csch}^{-1}\left(\sqrt{x}\right)}{2 x^2}-\frac{3 \sqrt{-x-1}}{16 \sqrt{-x} \sqrt{x}}+\frac{3 \sqrt{x} \tan ^{-1}\left(\sqrt{-x-1}\right)}{16 \sqrt{-x}}",1,"(Sqrt[1 + x^(-1)]*(2 - 3*x)*Sqrt[x] - 8*ArcCsch[Sqrt[x]] + 3*x^2*ArcSinh[1/Sqrt[x]])/(16*x^2)","A",1
21,1,52,115,0.0435022,"\int \frac{\text{csch}^{-1}\left(\sqrt{x}\right)}{x^4} \, dx","Integrate[ArcCsch[Sqrt[x]]/x^4,x]","\frac{-15 x^3 \sinh ^{-1}\left(\frac{1}{\sqrt{x}}\right)+\sqrt{\frac{1}{x}+1} \left(15 x^2-10 x+8\right) \sqrt{x}-48 \text{csch}^{-1}\left(\sqrt{x}\right)}{144 x^3}","-\frac{5 \sqrt{-x-1}}{72 \sqrt{-x} x^{3/2}}+\frac{\sqrt{-x-1}}{18 \sqrt{-x} x^{5/2}}-\frac{\text{csch}^{-1}\left(\sqrt{x}\right)}{3 x^3}+\frac{5 \sqrt{-x-1}}{48 \sqrt{-x} \sqrt{x}}-\frac{5 \sqrt{x} \tan ^{-1}\left(\sqrt{-x-1}\right)}{48 \sqrt{-x}}",1,"(Sqrt[1 + x^(-1)]*Sqrt[x]*(8 - 10*x + 15*x^2) - 48*ArcCsch[Sqrt[x]] - 15*x^3*ArcSinh[1/Sqrt[x]])/(144*x^3)","A",1
22,1,18,16,0.0030849,"\int \text{csch}^{-1}\left(\frac{1}{x}\right) \, dx","Integrate[ArcCsch[x^(-1)],x]","x \text{csch}^{-1}\left(\frac{1}{x}\right)-\sqrt{x^2+1}","x \sinh ^{-1}(x)-\sqrt{x^2+1}",1,"-Sqrt[1 + x^2] + x*ArcCsch[x^(-1)]","A",1
23,1,64,61,0.1042851,"\int \frac{\text{csch}^{-1}\left(a x^n\right)}{x} \, dx","Integrate[ArcCsch[a*x^n]/x,x]","\log (x) \left(\text{csch}^{-1}\left(a x^n\right)-\sinh ^{-1}\left(\frac{x^{-n}}{a}\right)\right)-\frac{x^{-n} \, _3F_2\left(\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-\frac{x^{-2 n}}{a^2}\right)}{a n}","-\frac{\text{Li}_2\left(e^{2 \text{csch}^{-1}\left(a x^n\right)}\right)}{2 n}+\frac{\text{csch}^{-1}\left(a x^n\right)^2}{2 n}-\frac{\text{csch}^{-1}\left(a x^n\right) \log \left(1-e^{2 \text{csch}^{-1}\left(a x^n\right)}\right)}{n}",1,"-(HypergeometricPFQ[{1/2, 1/2, 1/2}, {3/2, 3/2}, -(1/(a^2*x^(2*n)))]/(a*n*x^n)) + (ArcCsch[a*x^n] - ArcSinh[1/(a*x^n)])*Log[x]","C",1
24,1,49,54,0.0454982,"\int \frac{\text{csch}^{-1}\left(a x^5\right)}{x} \, dx","Integrate[ArcCsch[a*x^5]/x,x]","\frac{1}{10} \left(\text{Li}_2\left(e^{-2 \text{csch}^{-1}\left(a x^5\right)}\right)-\text{csch}^{-1}\left(a x^5\right) \left(\text{csch}^{-1}\left(a x^5\right)+2 \log \left(1-e^{-2 \text{csch}^{-1}\left(a x^5\right)}\right)\right)\right)","-\frac{1}{10} \text{Li}_2\left(e^{2 \text{csch}^{-1}\left(a x^5\right)}\right)+\frac{1}{10} \text{csch}^{-1}\left(a x^5\right)^2-\frac{1}{5} \text{csch}^{-1}\left(a x^5\right) \log \left(1-e^{2 \text{csch}^{-1}\left(a x^5\right)}\right)",1,"(-(ArcCsch[a*x^5]*(ArcCsch[a*x^5] + 2*Log[1 - E^(-2*ArcCsch[a*x^5])])) + PolyLog[2, E^(-2*ArcCsch[a*x^5])])/10","A",0
25,1,236,77,0.6031863,"\int \text{csch}^{-1}\left(c e^{a+b x}\right) \, dx","Integrate[ArcCsch[c*E^(a + b*x)],x]","\frac{e^{-a-b x} \sqrt{c^2 e^{2 (a+b x)}+1} \left(-4 \text{Li}_2\left(\frac{1}{2} \left(1-\sqrt{e^{2 (a+b x)} c^2+1}\right)\right)+\log ^2\left(-c^2 e^{2 (a+b x)}\right)+2 \log ^2\left(\frac{1}{2} \left(\sqrt{c^2 e^{2 (a+b x)}+1}+1\right)\right)-4 \log \left(\frac{1}{2} \left(\sqrt{c^2 e^{2 (a+b x)}+1}+1\right)\right) \log \left(-c^2 e^{2 (a+b x)}\right)+\left(4 \log \left(-c^2 e^{2 (a+b x)}\right)-8 b x\right) \tanh ^{-1}\left(\sqrt{c^2 e^{2 (a+b x)}+1}\right)\right)}{8 b c \sqrt{\frac{e^{-2 (a+b x)}}{c^2}+1}}+x \text{csch}^{-1}\left(c e^{a+b x}\right)","-\frac{\text{Li}_2\left(e^{2 \text{csch}^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}+\frac{\text{csch}^{-1}\left(c e^{a+b x}\right)^2}{2 b}-\frac{\text{csch}^{-1}\left(c e^{a+b x}\right) \log \left(1-e^{2 \text{csch}^{-1}\left(c e^{a+b x}\right)}\right)}{b}",1,"x*ArcCsch[c*E^(a + b*x)] + (E^(-a - b*x)*Sqrt[1 + c^2*E^(2*(a + b*x))]*(Log[-(c^2*E^(2*(a + b*x)))]^2 + ArcTanh[Sqrt[1 + c^2*E^(2*(a + b*x))]]*(-8*b*x + 4*Log[-(c^2*E^(2*(a + b*x)))]) - 4*Log[-(c^2*E^(2*(a + b*x)))]*Log[(1 + Sqrt[1 + c^2*E^(2*(a + b*x))])/2] + 2*Log[(1 + Sqrt[1 + c^2*E^(2*(a + b*x))])/2]^2 - 4*PolyLog[2, (1 - Sqrt[1 + c^2*E^(2*(a + b*x))])/2]))/(8*b*c*Sqrt[1 + 1/(c^2*E^(2*(a + b*x)))])","B",1
26,1,54,52,0.0473198,"\int e^{\text{csch}^{-1}(a x)} x^m \, dx","Integrate[E^ArcCsch[a*x]*x^m,x]","\frac{x^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{2} (-m-1);\frac{1}{2} (-m-1)+1;-\frac{1}{a^2 x^2}\right)}{m+1}+\frac{x^m}{a m}","\frac{x^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};-\frac{1}{a^2 x^2}\right)}{m+1}+\frac{x^m}{a m}",1,"x^m/(a*m) + (x^(1 + m)*Hypergeometric2F1[-1/2, (-1 - m)/2, 1 + (-1 - m)/2, -(1/(a^2*x^2))])/(1 + m)","A",1
27,1,49,54,0.0510965,"\int e^{\text{csch}^{-1}(a x)} x^4 \, dx","Integrate[E^ArcCsch[a*x]*x^4,x]","\frac{x \sqrt{\frac{1}{a^2 x^2}+1} \left(3 a^4 x^4+a^2 x^2-2\right)}{15 a^4}+\frac{x^4}{4 a}","\frac{1}{5} x^5 \left(\frac{1}{a^2 x^2}+1\right)^{3/2}-\frac{2 x^3 \left(\frac{1}{a^2 x^2}+1\right)^{3/2}}{15 a^2}+\frac{x^4}{4 a}",1,"x^4/(4*a) + (Sqrt[1 + 1/(a^2*x^2)]*x*(-2 + a^2*x^2 + 3*a^4*x^4))/(15*a^4)","A",1
28,1,76,75,0.0591365,"\int e^{\text{csch}^{-1}(a x)} x^3 \, dx","Integrate[E^ArcCsch[a*x]*x^3,x]","\frac{a^2 x^2 \left(6 a^2 x^2 \sqrt{\frac{1}{a^2 x^2}+1}+3 \sqrt{\frac{1}{a^2 x^2}+1}+8 a x\right)-3 \log \left(x \left(\sqrt{\frac{1}{a^2 x^2}+1}+1\right)\right)}{24 a^4}","\frac{x^2 \sqrt{\frac{1}{a^2 x^2}+1}}{8 a^2}+\frac{1}{4} x^4 \sqrt{\frac{1}{a^2 x^2}+1}-\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{a^2 x^2}+1}\right)}{8 a^4}+\frac{x^3}{3 a}",1,"(a^2*x^2*(3*Sqrt[1 + 1/(a^2*x^2)] + 8*a*x + 6*a^2*Sqrt[1 + 1/(a^2*x^2)]*x^2) - 3*Log[(1 + Sqrt[1 + 1/(a^2*x^2)])*x])/(24*a^4)","A",0
29,1,38,31,0.0392912,"\int e^{\text{csch}^{-1}(a x)} x^2 \, dx","Integrate[E^ArcCsch[a*x]*x^2,x]","\frac{2 \sqrt{\frac{1}{a^2 x^2}+1} \left(a^2 x^3+x\right)+3 a x^2}{6 a^2}","\frac{1}{3} x^3 \left(\frac{1}{a^2 x^2}+1\right)^{3/2}+\frac{x^2}{2 a}",1,"(3*a*x^2 + 2*Sqrt[1 + 1/(a^2*x^2)]*(x + a^2*x^3))/(6*a^2)","A",1
30,1,47,47,0.0312921,"\int e^{\text{csch}^{-1}(a x)} x \, dx","Integrate[E^ArcCsch[a*x]*x,x]","\frac{a x \left(a x \sqrt{\frac{1}{a^2 x^2}+1}+2\right)+\log \left(x \left(\sqrt{\frac{1}{a^2 x^2}+1}+1\right)\right)}{2 a^2}","\frac{1}{2} x^2 \sqrt{\frac{1}{a^2 x^2}+1}+\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{a^2 x^2}+1}\right)}{2 a^2}+\frac{x}{a}",1,"(a*x*(2 + a*Sqrt[1 + 1/(a^2*x^2)]*x) + Log[(1 + Sqrt[1 + 1/(a^2*x^2)])*x])/(2*a^2)","A",0
31,1,35,24,0.0166657,"\int e^{\text{csch}^{-1}(a x)} \, dx","Integrate[E^ArcCsch[a*x],x]","\frac{a x \sqrt{\frac{1}{a^2 x^2}+1}+\log (a x)-\sinh ^{-1}\left(\frac{1}{a x}\right)}{a}","\frac{\log (x)}{a}+x e^{\text{csch}^{-1}(a x)}-\frac{\text{csch}^{-1}(a x)}{a}",1,"(a*Sqrt[1 + 1/(a^2*x^2)]*x - ArcSinh[1/(a*x)] + Log[a*x])/a","A",0
32,1,42,38,0.0304025,"\int \frac{e^{\text{csch}^{-1}(a x)}}{x} \, dx","Integrate[E^ArcCsch[a*x]/x,x]","-\sqrt{\frac{1}{a^2 x^2}+1}+\log \left(x \left(\sqrt{\frac{1}{a^2 x^2}+1}+1\right)\right)-\frac{1}{a x}","-\sqrt{\frac{1}{a^2 x^2}+1}+\tanh ^{-1}\left(\sqrt{\frac{1}{a^2 x^2}+1}\right)-\frac{1}{a x}",1,"-Sqrt[1 + 1/(a^2*x^2)] - 1/(a*x) + Log[(1 + Sqrt[1 + 1/(a^2*x^2)])*x]","A",0
33,1,43,40,0.0299959,"\int \frac{e^{\text{csch}^{-1}(a x)}}{x^2} \, dx","Integrate[E^ArcCsch[a*x]/x^2,x]","-\frac{a x \sqrt{\frac{1}{a^2 x^2}+1}+a^2 x^2 \sinh ^{-1}\left(\frac{1}{a x}\right)+1}{2 a x^2}","-\frac{\sqrt{\frac{1}{a^2 x^2}+1}}{2 x}-\frac{1}{2 a x^2}-\frac{1}{2} a \text{csch}^{-1}(a x)",1,"-1/2*(1 + a*Sqrt[1 + 1/(a^2*x^2)]*x + a^2*x^2*ArcSinh[1/(a*x)])/(a*x^2)","A",0
34,1,37,31,0.0372116,"\int \frac{e^{\text{csch}^{-1}(a x)}}{x^3} \, dx","Integrate[E^ArcCsch[a*x]/x^3,x]","-\frac{a x \sqrt{\frac{1}{a^2 x^2}+1} \left(a^2 x^2+1\right)+1}{3 a x^3}","-\frac{1}{3} a^2 \left(\frac{1}{a^2 x^2}+1\right)^{3/2}-\frac{1}{3 a x^3}",1,"-1/3*(1 + a*Sqrt[1 + 1/(a^2*x^2)]*x*(1 + a^2*x^2))/(a*x^3)","A",1
35,1,53,65,0.0513499,"\int \frac{e^{\text{csch}^{-1}(a x)}}{x^4} \, dx","Integrate[E^ArcCsch[a*x]/x^4,x]","\frac{a^4 x^4 \sinh ^{-1}\left(\frac{1}{a x}\right)-a x \sqrt{\frac{1}{a^2 x^2}+1} \left(a^2 x^2+2\right)-2}{8 a x^4}","\frac{1}{8} a^3 \text{csch}^{-1}(a x)-\frac{a^2 \sqrt{\frac{1}{a^2 x^2}+1}}{8 x}-\frac{\sqrt{\frac{1}{a^2 x^2}+1}}{4 x^3}-\frac{1}{4 a x^4}",1,"(-2 - a*Sqrt[1 + 1/(a^2*x^2)]*x*(2 + a^2*x^2) + a^4*x^4*ArcSinh[1/(a*x)])/(8*a*x^4)","A",0
36,1,46,51,0.0426419,"\int \frac{e^{\text{csch}^{-1}(a x)}}{x^5} \, dx","Integrate[E^ArcCsch[a*x]/x^5,x]","\frac{a x \sqrt{\frac{1}{a^2 x^2}+1} \left(2 a^4 x^4-a^2 x^2-3\right)-3}{15 a x^5}","-\frac{1}{5} a^4 \left(\frac{1}{a^2 x^2}+1\right)^{5/2}+\frac{1}{3} a^4 \left(\frac{1}{a^2 x^2}+1\right)^{3/2}-\frac{1}{5 a x^5}",1,"(-3 + a*Sqrt[1 + 1/(a^2*x^2)]*x*(-3 - a^2*x^2 + 2*a^4*x^4))/(15*a*x^5)","A",1
37,1,55,59,0.0630361,"\int e^{\text{csch}^{-1}\left(a x^2\right)} x^m \, dx","Integrate[E^ArcCsch[a*x^2]*x^m,x]","x^{m-1} \left(\frac{x^2 \, _2F_1\left(-\frac{1}{2},-\frac{m}{4}-\frac{1}{4};\frac{3}{4}-\frac{m}{4};-\frac{1}{a^2 x^4}\right)}{m+1}+\frac{1}{a (m-1)}\right)","\frac{x^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{4} (-m-1);\frac{3-m}{4};-\frac{1}{a^2 x^4}\right)}{m+1}-\frac{x^{m-1}}{a (1-m)}",1,"x^(-1 + m)*(1/(a*(-1 + m)) + (x^2*Hypergeometric2F1[-1/2, -1/4 - m/4, 3/4 - m/4, -(1/(a^2*x^4))])/(1 + m))","A",1
38,1,112,202,0.2517254,"\int e^{\text{csch}^{-1}\left(a x^2\right)} x^4 \, dx","Integrate[E^ArcCsch[a*x^2]*x^4,x]","\frac{4 \sqrt{2} x^5 e^{-\text{csch}^{-1}\left(a x^2\right)} \left(\frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{e^{2 \text{csch}^{-1}\left(a x^2\right)}-1}\right)^{5/2} \left(4 \left(1-e^{2 \text{csch}^{-1}\left(a x^2\right)}\right)^{5/2} \, _2F_1\left(\frac{3}{4},\frac{7}{2};\frac{7}{4};e^{2 \text{csch}^{-1}\left(a x^2\right)}\right)+7 e^{2 \text{csch}^{-1}\left(a x^2\right)}-4\right)}{21 \left(a x^2\right)^{5/2}}","\frac{2 x \sqrt{\frac{1}{a^2 x^4}+1}}{5 a^2}+\frac{1}{5} x^5 \sqrt{\frac{1}{a^2 x^4}+1}-\frac{2 \sqrt{\frac{1}{a^2 x^4}+1}}{5 a^2 x \left(a+\frac{1}{x^2}\right)}-\frac{\sqrt{\frac{a^2+\frac{1}{x^4}}{\left(a+\frac{1}{x^2}\right)^2}} \left(a+\frac{1}{x^2}\right) F\left(2 \cot ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{5 a^{7/2} \sqrt{\frac{1}{a^2 x^4}+1}}+\frac{2 \sqrt{\frac{a^2+\frac{1}{x^4}}{\left(a+\frac{1}{x^2}\right)^2}} \left(a+\frac{1}{x^2}\right) E\left(2 \cot ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{5 a^{7/2} \sqrt{\frac{1}{a^2 x^4}+1}}+\frac{x^3}{3 a}",1,"(4*Sqrt[2]*(E^ArcCsch[a*x^2]/(-1 + E^(2*ArcCsch[a*x^2])))^(5/2)*x^5*(-4 + 7*E^(2*ArcCsch[a*x^2]) + 4*(1 - E^(2*ArcCsch[a*x^2]))^(5/2)*Hypergeometric2F1[3/4, 7/2, 7/4, E^(2*ArcCsch[a*x^2])]))/(21*E^ArcCsch[a*x^2]*(a*x^2)^(5/2))","C",0
39,1,53,52,0.0519951,"\int e^{\text{csch}^{-1}\left(a x^2\right)} x^3 \, dx","Integrate[E^ArcCsch[a*x^2]*x^3,x]","\frac{a x^2 \left(a x^2 \sqrt{\frac{1}{a^2 x^4}+1}+2\right)+\log \left(x^2 \left(\sqrt{\frac{1}{a^2 x^4}+1}+1\right)\right)}{4 a^2}","\frac{1}{4} x^4 \sqrt{\frac{1}{a^2 x^4}+1}+\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{a^2 x^4}+1}\right)}{4 a^2}+\frac{x^2}{2 a}",1,"(a*x^2*(2 + a*Sqrt[1 + 1/(a^2*x^4)]*x^2) + Log[(1 + Sqrt[1 + 1/(a^2*x^4)])*x^2])/(4*a^2)","A",0
40,1,113,86,0.2324068,"\int e^{\text{csch}^{-1}\left(a x^2\right)} x^2 \, dx","Integrate[E^ArcCsch[a*x^2]*x^2,x]","-\frac{2 \sqrt{2} x e^{-\text{csch}^{-1}\left(a x^2\right)} \left(\frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{e^{2 \text{csch}^{-1}\left(a x^2\right)}-1}\right)^{3/2} \left(\left(1-e^{2 \text{csch}^{-1}\left(a x^2\right)}\right)^{3/2} \left(-\, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};e^{2 \text{csch}^{-1}\left(a x^2\right)}\right)\right)-2 e^{2 \text{csch}^{-1}\left(a x^2\right)}+1\right)}{3 a \sqrt{a x^2}}","\frac{1}{3} x^3 \sqrt{\frac{1}{a^2 x^4}+1}-\frac{\sqrt{\frac{a^2+\frac{1}{x^4}}{\left(a+\frac{1}{x^2}\right)^2}} \left(a+\frac{1}{x^2}\right) F\left(2 \cot ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{3 a^{5/2} \sqrt{\frac{1}{a^2 x^4}+1}}+\frac{x}{a}",1,"(-2*Sqrt[2]*(E^ArcCsch[a*x^2]/(-1 + E^(2*ArcCsch[a*x^2])))^(3/2)*x*(1 - 2*E^(2*ArcCsch[a*x^2]) - (1 - E^(2*ArcCsch[a*x^2]))^(3/2)*Hypergeometric2F1[1/4, 1/2, 5/4, E^(2*ArcCsch[a*x^2])]))/(3*a*E^ArcCsch[a*x^2]*Sqrt[a*x^2])","C",0
41,1,42,40,0.0307444,"\int e^{\text{csch}^{-1}\left(a x^2\right)} x \, dx","Integrate[E^ArcCsch[a*x^2]*x,x]","\frac{a x^2 \sqrt{\frac{1}{a^2 x^4}+1}+\log \left(a x^2\right)-\sinh ^{-1}\left(\frac{1}{a x^2}\right)}{2 a}","\frac{1}{2} x^2 \sqrt{\frac{1}{a^2 x^4}+1}-\frac{\text{csch}^{-1}\left(a x^2\right)}{2 a}+\frac{\log (x)}{a}",1,"(a*Sqrt[1 + 1/(a^2*x^4)]*x^2 - ArcSinh[1/(a*x^2)] + Log[a*x^2])/(2*a)","A",0
42,1,96,165,0.1485027,"\int e^{\text{csch}^{-1}\left(a x^2\right)} \, dx","Integrate[E^ArcCsch[a*x^2],x]","\frac{\sqrt{2} x e^{\text{csch}^{-1}\left(a x^2\right)} \sqrt{\frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{e^{2 \text{csch}^{-1}\left(a x^2\right)}-1}} \left(4 \sqrt{1-e^{2 \text{csch}^{-1}\left(a x^2\right)}} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};e^{2 \text{csch}^{-1}\left(a x^2\right)}\right)-3\right)}{3 \sqrt{a x^2}}","x \sqrt{\frac{1}{a^2 x^4}+1}-\frac{2 \sqrt{\frac{1}{a^2 x^4}+1}}{x \left(a+\frac{1}{x^2}\right)}-\frac{\sqrt{\frac{a^2+\frac{1}{x^4}}{\left(a+\frac{1}{x^2}\right)^2}} \left(a+\frac{1}{x^2}\right) F\left(2 \cot ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{a^{3/2} \sqrt{\frac{1}{a^2 x^4}+1}}+\frac{2 \sqrt{\frac{a^2+\frac{1}{x^4}}{\left(a+\frac{1}{x^2}\right)^2}} \left(a+\frac{1}{x^2}\right) E\left(2 \cot ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{a^{3/2} \sqrt{\frac{1}{a^2 x^4}+1}}-\frac{1}{a x}",1,"(Sqrt[2]*E^ArcCsch[a*x^2]*Sqrt[E^ArcCsch[a*x^2]/(-1 + E^(2*ArcCsch[a*x^2]))]*x*(-3 + 4*Sqrt[1 - E^(2*ArcCsch[a*x^2])]*Hypergeometric2F1[3/4, 3/2, 7/4, E^(2*ArcCsch[a*x^2])]))/(3*Sqrt[a*x^2])","C",0
43,1,22,46,0.047165,"\int \frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{x} \, dx","Integrate[E^ArcCsch[a*x^2]/x,x]","\tanh ^{-1}\left(e^{\text{csch}^{-1}\left(a x^2\right)}\right)-\frac{1}{2} e^{\text{csch}^{-1}\left(a x^2\right)}","-\frac{1}{2} \sqrt{\frac{1}{a^2 x^4}+1}+\frac{1}{2} \tanh ^{-1}\left(\sqrt{\frac{1}{a^2 x^4}+1}\right)-\frac{1}{2 a x^2}",1,"-1/2*E^ArcCsch[a*x^2] + ArcTanh[E^ArcCsch[a*x^2]]","A",0
44,1,96,91,0.1621137,"\int \frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{x^2} \, dx","Integrate[E^ArcCsch[a*x^2]/x^2,x]","-\frac{a x \sqrt{\frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{2 e^{2 \text{csch}^{-1}\left(a x^2\right)}-2}} \left(4 \sqrt{1-e^{2 \text{csch}^{-1}\left(a x^2\right)}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};e^{2 \text{csch}^{-1}\left(a x^2\right)}\right)+e^{2 \text{csch}^{-1}\left(a x^2\right)}-1\right)}{3 \sqrt{a x^2}}","-\frac{\sqrt{\frac{1}{a^2 x^4}+1}}{3 x}-\frac{\sqrt{\frac{a^2+\frac{1}{x^4}}{\left(a+\frac{1}{x^2}\right)^2}} \left(a+\frac{1}{x^2}\right) F\left(2 \cot ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{3 \sqrt{a} \sqrt{\frac{1}{a^2 x^4}+1}}-\frac{1}{3 a x^3}",1,"-1/3*(a*Sqrt[E^ArcCsch[a*x^2]/(-2 + 2*E^(2*ArcCsch[a*x^2]))]*x*(-1 + E^(2*ArcCsch[a*x^2]) + 4*Sqrt[1 - E^(2*ArcCsch[a*x^2])]*Hypergeometric2F1[1/4, 1/2, 5/4, E^(2*ArcCsch[a*x^2])]))/Sqrt[a*x^2]","C",0
45,1,24,42,0.0476675,"\int \frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{x^3} \, dx","Integrate[E^ArcCsch[a*x^2]/x^3,x]","-\frac{1}{8} a \left(2 \text{csch}^{-1}\left(a x^2\right)+e^{2 \text{csch}^{-1}\left(a x^2\right)}\right)","-\frac{\sqrt{\frac{1}{a^2 x^4}+1}}{4 x^2}-\frac{1}{4 a x^4}-\frac{1}{4} a \text{csch}^{-1}\left(a x^2\right)",1,"-1/8*(a*(E^(2*ArcCsch[a*x^2]) + 2*ArcCsch[a*x^2]))","A",0
46,1,114,181,0.2060574,"\int \frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{x^4} \, dx","Integrate[E^ArcCsch[a*x^2]/x^4,x]","\frac{\left(a x^2\right)^{3/2} \left(4 e^{2 \text{csch}^{-1}\left(a x^2\right)} \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{7}{4};e^{2 \text{csch}^{-1}\left(a x^2\right)}\right)+3 \left(1-e^{2 \text{csch}^{-1}\left(a x^2\right)}\right)^{3/2}\right)}{6 x^3 \sqrt{2-2 e^{2 \text{csch}^{-1}\left(a x^2\right)}} \sqrt{\frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{e^{2 \text{csch}^{-1}\left(a x^2\right)}-1}}}","-\frac{\sqrt{\frac{1}{a^2 x^4}+1}}{5 x^3}-\frac{2 a^2 \sqrt{\frac{1}{a^2 x^4}+1}}{5 x \left(a+\frac{1}{x^2}\right)}-\frac{\sqrt{a} \sqrt{\frac{a^2+\frac{1}{x^4}}{\left(a+\frac{1}{x^2}\right)^2}} \left(a+\frac{1}{x^2}\right) F\left(2 \cot ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{5 \sqrt{\frac{1}{a^2 x^4}+1}}+\frac{2 \sqrt{a} \sqrt{\frac{a^2+\frac{1}{x^4}}{\left(a+\frac{1}{x^2}\right)^2}} \left(a+\frac{1}{x^2}\right) E\left(2 \cot ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{5 \sqrt{\frac{1}{a^2 x^4}+1}}-\frac{1}{5 a x^5}",1,"((a*x^2)^(3/2)*(3*(1 - E^(2*ArcCsch[a*x^2]))^(3/2) + 4*E^(2*ArcCsch[a*x^2])*Hypergeometric2F1[-1/2, 3/4, 7/4, E^(2*ArcCsch[a*x^2])]))/(6*Sqrt[2 - 2*E^(2*ArcCsch[a*x^2])]*Sqrt[E^ArcCsch[a*x^2]/(-1 + E^(2*ArcCsch[a*x^2]))]*x^3)","C",0
47,1,39,31,0.0539826,"\int \frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{x^5} \, dx","Integrate[E^ArcCsch[a*x^2]/x^5,x]","-\frac{a x^2 \sqrt{\frac{1}{a^2 x^4}+1} \left(a^2 x^4+1\right)+1}{6 a x^6}","-\frac{1}{6} a^2 \left(\frac{1}{a^2 x^4}+1\right)^{3/2}-\frac{1}{6 a x^6}",1,"-1/6*(1 + a*Sqrt[1 + 1/(a^2*x^4)]*x^2*(1 + a^2*x^4))/(a*x^6)","A",1
48,1,57,64,0.0676977,"\int e^{2 \text{csch}^{-1}(a x)} x^m \, dx","Integrate[E^(2*ArcCsch[a*x])*x^m,x]","x^m \left(\frac{2 \, _2F_1\left(-\frac{1}{2},-\frac{m}{2};1-\frac{m}{2};-\frac{1}{a^2 x^2}\right)}{a m}+\frac{2}{a^2 (m-1) x}+\frac{x}{m+1}\right)","\frac{2 x^m \, _2F_1\left(-\frac{1}{2},-\frac{m}{2};1-\frac{m}{2};-\frac{1}{a^2 x^2}\right)}{a m}-\frac{2 x^{m-1}}{a^2 (1-m)}+\frac{x^{m+1}}{m+1}",1,"x^m*(2/(a^2*(-1 + m)*x) + x/(1 + m) + (2*Hypergeometric2F1[-1/2, -1/2*m, 1 - m/2, -(1/(a^2*x^2))])/(a*m))","A",1
49,1,84,85,0.0704705,"\int e^{2 \text{csch}^{-1}(a x)} x^4 \, dx","Integrate[E^(2*ArcCsch[a*x])*x^4,x]","\frac{a^2 x^2 \left(12 a^3 x^3+30 a^2 x^2 \sqrt{\frac{1}{a^2 x^2}+1}+15 \sqrt{\frac{1}{a^2 x^2}+1}+40 a x\right)-15 \log \left(x \left(\sqrt{\frac{1}{a^2 x^2}+1}+1\right)\right)}{60 a^5}","\frac{2 x^3}{3 a^2}+\frac{x^4 \sqrt{\frac{1}{a^2 x^2}+1}}{2 a}-\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{a^2 x^2}+1}\right)}{4 a^5}+\frac{x^2 \sqrt{\frac{1}{a^2 x^2}+1}}{4 a^3}+\frac{x^5}{5}",1,"(a^2*x^2*(15*Sqrt[1 + 1/(a^2*x^2)] + 40*a*x + 30*a^2*Sqrt[1 + 1/(a^2*x^2)]*x^2 + 12*a^3*x^3) - 15*Log[(1 + Sqrt[1 + 1/(a^2*x^2)])*x])/(60*a^5)","A",0
50,1,44,38,0.0507613,"\int e^{2 \text{csch}^{-1}(a x)} x^3 \, dx","Integrate[E^(2*ArcCsch[a*x])*x^3,x]","\frac{x^2}{a^2}+\frac{2 \sqrt{\frac{1}{a^2 x^2}+1} \left(a^2 x^3+x\right)}{3 a^3}+\frac{x^4}{4}","\frac{x^2}{a^2}+\frac{2 x^3 \left(\frac{1}{a^2 x^2}+1\right)^{3/2}}{3 a}+\frac{x^4}{4}",1,"x^2/a^2 + x^4/4 + (2*Sqrt[1 + 1/(a^2*x^2)]*(x + a^2*x^3))/(3*a^3)","A",1
51,1,57,52,0.0374479,"\int e^{2 \text{csch}^{-1}(a x)} x^2 \, dx","Integrate[E^(2*ArcCsch[a*x])*x^2,x]","\frac{a x \left(a^2 x^2+3 a x \sqrt{\frac{1}{a^2 x^2}+1}+6\right)+3 \log \left(x \left(\sqrt{\frac{1}{a^2 x^2}+1}+1\right)\right)}{3 a^3}","\frac{x^2 \sqrt{\frac{1}{a^2 x^2}+1}}{a}+\frac{2 x}{a^2}+\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{a^2 x^2}+1}\right)}{a^3}+\frac{x^3}{3}",1,"(a*x*(6 + 3*a*Sqrt[1 + 1/(a^2*x^2)]*x + a^2*x^2) + 3*Log[(1 + Sqrt[1 + 1/(a^2*x^2)])*x])/(3*a^3)","A",0
52,1,44,43,0.0512256,"\int e^{2 \text{csch}^{-1}(a x)} x \, dx","Integrate[E^(2*ArcCsch[a*x])*x,x]","\frac{a x \left(4 \sqrt{\frac{1}{a^2 x^2}+1}+a x\right)-4 \sinh ^{-1}\left(\frac{1}{a x}\right)+4 \log (x)}{2 a^2}","\frac{2 x \sqrt{\frac{1}{a^2 x^2}+1}}{a}+\frac{2 \log (x)}{a^2}-\frac{2 \text{csch}^{-1}(a x)}{a^2}+\frac{x^2}{2}",1,"(a*x*(4*Sqrt[1 + 1/(a^2*x^2)] + a*x) - 4*ArcSinh[1/(a*x)] + 4*Log[x])/(2*a^2)","A",0
53,1,52,47,0.0377616,"\int e^{2 \text{csch}^{-1}(a x)} \, dx","Integrate[E^(2*ArcCsch[a*x]),x]","-\frac{2 \sqrt{\frac{1}{a^2 x^2}+1}}{a}+\frac{2 \log \left(a x \left(\sqrt{\frac{1}{a^2 x^2}+1}+1\right)\right)}{a}-\frac{2}{a^2 x}+x","-\frac{2 \sqrt{\frac{1}{a^2 x^2}+1}}{a}+\frac{2 \tanh ^{-1}\left(\sqrt{\frac{1}{a^2 x^2}+1}\right)}{a}-\frac{2}{a^2 x}+x",1,"(-2*Sqrt[1 + 1/(a^2*x^2)])/a - 2/(a^2*x) + x + (2*Log[a*(1 + Sqrt[1 + 1/(a^2*x^2)])*x])/a","A",0
54,1,39,38,0.0608288,"\int \frac{e^{2 \text{csch}^{-1}(a x)}}{x} \, dx","Integrate[E^(2*ArcCsch[a*x])/x,x]","-\frac{a x \sqrt{\frac{1}{a^2 x^2}+1}+1}{a^2 x^2}-\sinh ^{-1}\left(\frac{1}{a x}\right)+\log (x)","-\frac{\sqrt{\frac{1}{a^2 x^2}+1}}{a x}-\frac{1}{a^2 x^2}-\text{csch}^{-1}(a x)+\log (x)",1,"-((1 + a*Sqrt[1 + 1/(a^2*x^2)]*x)/(a^2*x^2)) - ArcSinh[1/(a*x)] + Log[x]","A",0
55,1,46,34,0.0439221,"\int \frac{e^{2 \text{csch}^{-1}(a x)}}{x^2} \, dx","Integrate[E^(2*ArcCsch[a*x])/x^2,x]","-\frac{3 a^2 x^2+2 a x \sqrt{\frac{1}{a^2 x^2}+1} \left(a^2 x^2+1\right)+2}{3 a^2 x^3}","-\frac{2}{3 a^2 x^3}-\frac{2}{3} a \left(\frac{1}{a^2 x^2}+1\right)^{3/2}-\frac{1}{x}",1,"-1/3*(2 + 3*a^2*x^2 + 2*a*Sqrt[1 + 1/(a^2*x^2)]*x*(1 + a^2*x^2))/(a^2*x^3)","A",1
56,1,73,73,0.0520972,"\int \frac{e^{2 \text{csch}^{-1}(a x)}}{x^3} \, dx","Integrate[E^(2*ArcCsch[a*x])/x^3,x]","-\frac{1}{2 a^2 x^4}+\left(-\frac{1}{2 a x^3}-\frac{a}{4 x}\right) \sqrt{\frac{a^2 x^2+1}{a^2 x^2}}+\frac{1}{4} a^2 \sinh ^{-1}\left(\frac{1}{a x}\right)-\frac{1}{2 x^2}","-\frac{1}{2 a^2 x^4}-\frac{a \sqrt{\frac{1}{a^2 x^2}+1}}{4 x}-\frac{\sqrt{\frac{1}{a^2 x^2}+1}}{2 a x^3}+\frac{1}{4} a^2 \text{csch}^{-1}(a x)-\frac{1}{2 x^2}",1,"-1/2*1/(a^2*x^4) - 1/(2*x^2) + (-1/2*1/(a*x^3) - a/(4*x))*Sqrt[(1 + a^2*x^2)/(a^2*x^2)] + (a^2*ArcSinh[1/(a*x)])/4","A",0
57,1,54,58,0.0564404,"\int \frac{e^{2 \text{csch}^{-1}(a x)}}{x^4} \, dx","Integrate[E^(2*ArcCsch[a*x])/x^4,x]","-\frac{5 a^2 x^2+2 a x \sqrt{\frac{1}{a^2 x^2}+1} \left(-2 a^4 x^4+a^2 x^2+3\right)+6}{15 a^2 x^5}","-\frac{2}{5 a^2 x^5}-\frac{2}{5} a^3 \left(\frac{1}{a^2 x^2}+1\right)^{5/2}+\frac{2}{3} a^3 \left(\frac{1}{a^2 x^2}+1\right)^{3/2}-\frac{1}{3 x^3}",1,"-1/15*(6 + 5*a^2*x^2 + 2*a*Sqrt[1 + 1/(a^2*x^2)]*x*(3 + a^2*x^2 - 2*a^4*x^4))/(a^2*x^5)","A",1
58,1,74,96,0.076624,"\int \frac{e^{2 \text{csch}^{-1}(a x)}}{x^5} \, dx","Integrate[E^(2*ArcCsch[a*x])/x^5,x]","\frac{\frac{\left(3 a^2 x^2+4\right) \left(-2 a x \sqrt{\frac{1}{a^2 x^2}+1}+a^3 x^3 \sqrt{\frac{1}{a^2 x^2}+1}-2\right)}{x^6}-3 a^6 \sinh ^{-1}\left(\frac{1}{a x}\right)}{24 a^2}","-\frac{1}{8} a^4 \text{csch}^{-1}(a x)-\frac{1}{3 a^2 x^6}-\frac{\sqrt{\frac{1}{a^2 x^2}+1}}{3 a x^5}-\frac{a \sqrt{\frac{1}{a^2 x^2}+1}}{12 x^3}+\frac{a^3 \sqrt{\frac{1}{a^2 x^2}+1}}{8 x}-\frac{1}{4 x^4}",1,"(((4 + 3*a^2*x^2)*(-2 - 2*a*Sqrt[1 + 1/(a^2*x^2)]*x + a^3*Sqrt[1 + 1/(a^2*x^2)]*x^3))/x^6 - 3*a^6*ArcSinh[1/(a*x)])/(24*a^2)","A",0
59,1,88,85,0.2453938,"\int \frac{e^{\text{csch}^{-1}(c x)} (d x)^m}{1+c^2 x^2} \, dx","Integrate[(E^ArcCsch[c*x]*(d*x)^m)/(1 + c^2*x^2),x]","\frac{(d x)^m \left(\frac{x \sqrt{\frac{1}{c^2 x^2}+1} \, _2F_1\left(\frac{1}{2},\frac{m}{2};\frac{m}{2}+1;-c^2 x^2\right)}{\sqrt{c^2 x^2+1}}+\frac{\, _2F_1\left(1,\frac{m}{2};\frac{m}{2}+1;-c^2 x^2\right)}{c}\right)}{m}","\frac{(d x)^m \, _2F_1\left(1,\frac{m}{2};\frac{m+2}{2};-c^2 x^2\right)}{c m}-\frac{d (d x)^{m-1} \, _2F_1\left(\frac{1}{2},\frac{1-m}{2};\frac{3-m}{2};-\frac{1}{c^2 x^2}\right)}{c^2 (1-m)}",1,"((d*x)^m*((Sqrt[1 + 1/(c^2*x^2)]*x*Hypergeometric2F1[1/2, m/2, 1 + m/2, -(c^2*x^2)])/Sqrt[1 + c^2*x^2] + Hypergeometric2F1[1, m/2, 1 + m/2, -(c^2*x^2)]/c))/m","A",0
60,1,85,92,0.2009908,"\int \frac{e^{\text{csch}^{-1}(c x)} x^5}{1+c^2 x^2} \, dx","Integrate[(E^ArcCsch[c*x]*x^5)/(1 + c^2*x^2),x]","\frac{9 \log \left(x \left(\sqrt{\frac{1}{c^2 x^2}+1}+1\right)\right)+c x \left(8 c^2 x^2-9 c x \sqrt{\frac{1}{c^2 x^2}+1}+6 c^3 x^3 \sqrt{\frac{1}{c^2 x^2}+1}-24\right)+24 \tan ^{-1}(c x)}{24 c^6}","\frac{\tan ^{-1}(c x)}{c^6}-\frac{x}{c^5}+\frac{x^3}{3 c^3}+\frac{x^4 \sqrt{\frac{1}{c^2 x^2}+1}}{4 c^2}+\frac{3 \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{8 c^6}-\frac{3 x^2 \sqrt{\frac{1}{c^2 x^2}+1}}{8 c^4}",1,"(c*x*(-24 - 9*c*Sqrt[1 + 1/(c^2*x^2)]*x + 8*c^2*x^2 + 6*c^3*Sqrt[1 + 1/(c^2*x^2)]*x^3) + 24*ArcTan[c*x] + 9*Log[(1 + Sqrt[1 + 1/(c^2*x^2)])*x])/(24*c^6)","A",0
61,1,64,72,0.1286397,"\int \frac{e^{\text{csch}^{-1}(c x)} x^4}{1+c^2 x^2} \, dx","Integrate[(E^ArcCsch[c*x]*x^4)/(1 + c^2*x^2),x]","\frac{c x \left(2 c^2 x^2 \sqrt{\frac{1}{c^2 x^2}+1}-4 \sqrt{\frac{1}{c^2 x^2}+1}+3 c x\right)-3 \log \left(c^2 x^2+1\right)}{6 c^5}","\frac{x^2}{2 c^3}+\frac{x^3 \sqrt{\frac{1}{c^2 x^2}+1}}{3 c^2}-\frac{\log \left(c^2 x^2+1\right)}{2 c^5}-\frac{2 x \sqrt{\frac{1}{c^2 x^2}+1}}{3 c^4}",1,"(c*x*(-4*Sqrt[1 + 1/(c^2*x^2)] + 3*c*x + 2*c^2*Sqrt[1 + 1/(c^2*x^2)]*x^2) - 3*Log[1 + c^2*x^2])/(6*c^5)","A",1
62,1,54,59,0.1310569,"\int \frac{e^{\text{csch}^{-1}(c x)} x^3}{1+c^2 x^2} \, dx","Integrate[(E^ArcCsch[c*x]*x^3)/(1 + c^2*x^2),x]","-\frac{-c x \left(c x \sqrt{\frac{1}{c^2 x^2}+1}+2\right)+\log \left(x \left(\sqrt{\frac{1}{c^2 x^2}+1}+1\right)\right)+2 \tan ^{-1}(c x)}{2 c^4}","-\frac{\tan ^{-1}(c x)}{c^4}+\frac{x}{c^3}+\frac{x^2 \sqrt{\frac{1}{c^2 x^2}+1}}{2 c^2}-\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{2 c^4}",1,"-1/2*(-(c*x*(2 + c*Sqrt[1 + 1/(c^2*x^2)]*x)) + 2*ArcTan[c*x] + Log[(1 + Sqrt[1 + 1/(c^2*x^2)])*x])/c^4","A",0
63,1,35,36,0.0636326,"\int \frac{e^{\text{csch}^{-1}(c x)} x^2}{1+c^2 x^2} \, dx","Integrate[(E^ArcCsch[c*x]*x^2)/(1 + c^2*x^2),x]","\frac{2 c x \sqrt{\frac{1}{c^2 x^2}+1}+\log \left(c^2 x^2+1\right)}{2 c^3}","\frac{x \sqrt{\frac{1}{c^2 x^2}+1}}{c^2}+\frac{\log \left(c^2 x^2+1\right)}{2 c^3}",1,"(2*c*Sqrt[1 + 1/(c^2*x^2)]*x + Log[1 + c^2*x^2])/(2*c^3)","A",1
64,1,38,27,0.0424364,"\int \frac{e^{\text{csch}^{-1}(c x)} x}{1+c^2 x^2} \, dx","Integrate[(E^ArcCsch[c*x]*x)/(1 + c^2*x^2),x]","\frac{\log \left(x \left(\sqrt{\frac{c^2 x^2+1}{c^2 x^2}}+1\right)\right)}{c^2}+\frac{\tan ^{-1}(c x)}{c^2}","\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{c^2}+\frac{\tan ^{-1}(c x)}{c^2}",1,"ArcTan[c*x]/c^2 + Log[x*(1 + Sqrt[(1 + c^2*x^2)/(c^2*x^2)])]/c^2","A",0
65,1,37,33,0.0318279,"\int \frac{e^{\text{csch}^{-1}(c x)}}{1+c^2 x^2} \, dx","Integrate[E^ArcCsch[c*x]/(1 + c^2*x^2),x]","-\frac{\log \left(c^2 x^2+1\right)}{2 c}+\frac{\log (x)}{c}-\frac{\sinh ^{-1}\left(\frac{1}{c x}\right)}{c}","-\frac{\log \left(c^2 x^2+1\right)}{2 c}+\frac{\log (x)}{c}-\frac{\text{csch}^{-1}(c x)}{c}",1,"-(ArcSinh[1/(c*x)]/c) + Log[x]/c - Log[1 + c^2*x^2]/(2*c)","A",0
66,1,30,30,0.0954637,"\int \frac{e^{\text{csch}^{-1}(c x)}}{x \left(1+c^2 x^2\right)} \, dx","Integrate[E^ArcCsch[c*x]/(x*(1 + c^2*x^2)),x]","-\sqrt{\frac{1}{c^2 x^2}+1}-\frac{1}{c x}-\tan ^{-1}(c x)","-\sqrt{\frac{1}{c^2 x^2}+1}-\frac{1}{c x}-\tan ^{-1}(c x)",1,"-Sqrt[1 + 1/(c^2*x^2)] - 1/(c*x) - ArcTan[c*x]","A",1
67,1,58,60,0.1114153,"\int \frac{e^{\text{csch}^{-1}(c x)}}{x^2 \left(1+c^2 x^2\right)} \, dx","Integrate[E^ArcCsch[c*x]/(x^2*(1 + c^2*x^2)),x]","\frac{1}{2} \left(-\frac{\sqrt{\frac{1}{c^2 x^2}+1}}{x}+c \log \left(c^2 x^2+1\right)-\frac{1}{c x^2}-2 c \log (x)+c \sinh ^{-1}\left(\frac{1}{c x}\right)\right)","-\frac{\sqrt{\frac{1}{c^2 x^2}+1}}{2 x}+\frac{1}{2} c \log \left(c^2 x^2+1\right)-\frac{1}{2 c x^2}-c \log (x)+\frac{1}{2} c \text{csch}^{-1}(c x)",1,"(-(1/(c*x^2)) - Sqrt[1 + 1/(c^2*x^2)]/x + c*ArcSinh[1/(c*x)] - 2*c*Log[x] + c*Log[1 + c^2*x^2])/2","A",0
68,1,54,61,0.1414331,"\int \frac{e^{\text{csch}^{-1}(c x)}}{x^3 \left(1+c^2 x^2\right)} \, dx","Integrate[E^ArcCsch[c*x]/(x^3*(1 + c^2*x^2)),x]","\frac{\sqrt{\frac{1}{c^2 x^2}+1} \left(2 c^2 x^2-1\right)}{3 x^2}+c^2 \tan ^{-1}(c x)-\frac{1}{3 c x^3}+\frac{c}{x}","-\frac{1}{3} c^2 \left(\frac{1}{c^2 x^2}+1\right)^{3/2}+c^2 \sqrt{\frac{1}{c^2 x^2}+1}+c^2 \tan ^{-1}(c x)-\frac{1}{3 c x^3}+\frac{c}{x}",1,"-1/3*1/(c*x^3) + c/x + (Sqrt[1 + 1/(c^2*x^2)]*(-1 + 2*c^2*x^2))/(3*x^2) + c^2*ArcTan[c*x]","A",1
69,1,52,61,0.0603395,"\int \frac{\text{csch}^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx","Integrate[ArcCsch[a + b*x]/((a*d)/b + d*x),x]","\frac{\text{Li}_2\left(e^{-2 \text{csch}^{-1}(a+b x)}\right)-\text{csch}^{-1}(a+b x) \left(\text{csch}^{-1}(a+b x)+2 \log \left(1-e^{-2 \text{csch}^{-1}(a+b x)}\right)\right)}{2 d}","-\frac{\text{Li}_2\left(e^{2 \text{csch}^{-1}(a+b x)}\right)}{2 d}+\frac{\text{csch}^{-1}(a+b x)^2}{2 d}-\frac{\text{csch}^{-1}(a+b x) \log \left(1-e^{2 \text{csch}^{-1}(a+b x)}\right)}{d}",1,"(-(ArcCsch[a + b*x]*(ArcCsch[a + b*x] + 2*Log[1 - E^(-2*ArcCsch[a + b*x])])) + PolyLog[2, E^(-2*ArcCsch[a + b*x])])/(2*d)","A",0
70,1,74,46,0.1461699,"\int x^3 \text{csch}^{-1}\left(a+b x^4\right) \, dx","Integrate[x^3*ArcCsch[a + b*x^4],x]","\frac{\frac{\sqrt{\left(a+b x^4\right)^2+1} \sinh ^{-1}\left(a+b x^4\right)}{\sqrt{\frac{1}{\left(a+b x^4\right)^2}+1}}+\left(a+b x^4\right)^2 \text{csch}^{-1}\left(a+b x^4\right)}{4 b \left(a+b x^4\right)}","\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{\left(a+b x^4\right)^2}+1}\right)}{4 b}+\frac{\left(a+b x^4\right) \text{csch}^{-1}\left(a+b x^4\right)}{4 b}",1,"((a + b*x^4)^2*ArcCsch[a + b*x^4] + (Sqrt[1 + (a + b*x^4)^2]*ArcSinh[a + b*x^4])/Sqrt[1 + (a + b*x^4)^(-2)])/(4*b*(a + b*x^4))","A",1
71,1,74,46,0.1805608,"\int x^{-1+n} \text{csch}^{-1}\left(a+b x^n\right) \, dx","Integrate[x^(-1 + n)*ArcCsch[a + b*x^n],x]","\frac{\frac{\sqrt{\left(a+b x^n\right)^2+1} \sinh ^{-1}\left(a+b x^n\right)}{\sqrt{\frac{1}{\left(a+b x^n\right)^2}+1}}+\left(a+b x^n\right)^2 \text{csch}^{-1}\left(a+b x^n\right)}{b n \left(a+b x^n\right)}","\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{\left(a+b x^n\right)^2}+1}\right)}{b n}+\frac{\left(a+b x^n\right) \text{csch}^{-1}\left(a+b x^n\right)}{b n}",1,"((a + b*x^n)^2*ArcCsch[a + b*x^n] + (Sqrt[1 + (a + b*x^n)^2]*ArcSinh[a + b*x^n])/Sqrt[1 + (a + b*x^n)^(-2)])/(b*n*(a + b*x^n))","A",1