1,1,147,0,0.1523658,"\int x^3 \text{csch}^{-1}(a+b x) \, dx","Int[x^3*ArcCsch[a + b*x],x]","-\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^4 \text{csch}^{-1}(a+b x)}{4 b^4}+\frac{x^2 (a+b x) \sqrt{\frac{1}{(a+b x)^2}+1}}{12 b^2}-\frac{a (a+b x)^2 \sqrt{\frac{1}{(a+b x)^2}+1}}{3 b^4}+\frac{1}{4} x^4 \text{csch}^{-1}(a+b x)","-\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^4 \text{csch}^{-1}(a+b x)}{4 b^4}+\frac{x^2 (a+b x) \sqrt{\frac{1}{(a+b x)^2}+1}}{12 b^2}-\frac{a (a+b x)^2 \sqrt{\frac{1}{(a+b x)^2}+1}}{3 b^4}+\frac{1}{4} x^4 \text{csch}^{-1}(a+b x)",1,"-((2 - 17*a^2)*(a + b*x)*Sqrt[1 + (a + b*x)^(-2)])/(12*b^4) + (x^2*(a + b*x)*Sqrt[1 + (a + b*x)^(-2)])/(12*b^2) - (a*(a + b*x)^2*Sqrt[1 + (a + b*x)^(-2)])/(3*b^4) - (a^4*ArcCsch[a + b*x])/(4*b^4) + (x^4*ArcCsch[a + b*x])/4 + (a*(1 - 2*a^2)*ArcTanh[Sqrt[1 + (a + b*x)^(-2)]])/(2*b^4)","A",8,7,10,0.7000,1,"{6322, 5469, 3782, 4048, 3770, 3767, 8}"
2,1,110,0,0.0952465,"\int x^2 \text{csch}^{-1}(a+b x) \, dx","Int[x^2*ArcCsch[a + b*x],x]","-\frac{\left(1-6 a^2\right) \tanh ^{-1}\left(\sqrt{\frac{1}{(a+b x)^2}+1}\right)}{6 b^3}+\frac{a^3 \text{csch}^{-1}(a+b x)}{3 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)","-\frac{\left(1-6 a^2\right) \tanh ^{-1}\left(\sqrt{\frac{1}{(a+b x)^2}+1}\right)}{6 b^3}+\frac{a^3 \text{csch}^{-1}(a+b x)}{3 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*(a + b*x)*Sqrt[1 + (a + b*x)^(-2)])/(6*b^3) + (x*(a + b*x)*Sqrt[1 + (a + b*x)^(-2)])/(6*b^2) + (a^3*ArcCsch[a + b*x])/(3*b^3) + (x^3*ArcCsch[a + b*x])/3 - ((1 - 6*a^2)*ArcTanh[Sqrt[1 + (a + b*x)^(-2)]])/(6*b^3)","A",7,6,10,0.6000,1,"{6322, 5469, 3782, 3770, 3767, 8}"
3,1,75,0,0.0605459,"\int x \text{csch}^{-1}(a+b x) \, dx","Int[x*ArcCsch[a + b*x],x]","-\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)","-\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 + b*x)^(-2)])/(2*b^2) - (a^2*ArcCsch[a + b*x])/(2*b^2) + (x^2*ArcCsch[a + b*x])/2 - (a*ArcTanh[Sqrt[1 + (a + b*x)^(-2)]])/b^2","A",6,6,8,0.7500,1,"{6322, 5469, 3773, 3770, 3767, 8}"
4,1,162,0,0.2866673,"\int \frac{\text{csch}^{-1}(a+b x)}{x} \, dx","Int[ArcCsch[a + b*x]/x,x]","\text{PolyLog}\left(2,\frac{a e^{\text{csch}^{-1}(a+b x)}}{1-\sqrt{a^2+1}}\right)+\text{PolyLog}\left(2,\frac{a e^{\text{csch}^{-1}(a+b x)}}{\sqrt{a^2+1}+1}\right)-\frac{1}{2} \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(a+b x)}\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)-\text{csch}^{-1}(a+b x) \log \left(1-e^{2 \text{csch}^{-1}(a+b x)}\right)","\text{PolyLog}\left(2,\frac{a e^{\text{csch}^{-1}(a+b x)}}{1-\sqrt{a^2+1}}\right)+\text{PolyLog}\left(2,\frac{a e^{\text{csch}^{-1}(a+b x)}}{\sqrt{a^2+1}+1}\right)-\frac{1}{2} \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(a+b x)}\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)-\text{csch}^{-1}(a+b x) \log \left(1-e^{2 \text{csch}^{-1}(a+b x)}\right)",1,"ArcCsch[a + b*x]*Log[1 - (a*E^ArcCsch[a + b*x])/(1 - Sqrt[1 + a^2])] + ArcCsch[a + b*x]*Log[1 - (a*E^ArcCsch[a + b*x])/(1 + Sqrt[1 + a^2])] - ArcCsch[a + b*x]*Log[1 - E^(2*ArcCsch[a + b*x])] + PolyLog[2, (a*E^ArcCsch[a + b*x])/(1 - Sqrt[1 + a^2])] + PolyLog[2, (a*E^ArcCsch[a + b*x])/(1 + Sqrt[1 + a^2])] - PolyLog[2, E^(2*ArcCsch[a + b*x])]/2","A",14,8,10,0.8000,1,"{6322, 5596, 5569, 3716, 2190, 2279, 2391, 5561}"
5,1,63,0,0.1018013,"\int \frac{\text{csch}^{-1}(a+b x)}{x^2} \, dx","Int[ArcCsch[a + b*x]/x^2,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}","\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,"-((b*ArcCsch[a + b*x])/a) - ArcCsch[a + b*x]/x + (2*b*ArcTanh[(a + Tanh[ArcCsch[a + b*x]/2])/Sqrt[1 + a^2]])/(a*Sqrt[1 + a^2])","A",6,6,10,0.6000,1,"{6322, 5469, 3783, 2660, 618, 206}"
6,1,114,0,0.2099616,"\int \frac{\text{csch}^{-1}(a+b x)}{x^3} \, dx","Int[ArcCsch[a + b*x]/x^3,x]","\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}","\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 + b*x)^(-2)])/(2*a*(1 + a^2)*x) + (b^2*ArcCsch[a + b*x])/(2*a^2) - ArcCsch[a + b*x]/(2*x^2) - ((1 + 2*a^2)*b^2*ArcTanh[(a + Tanh[ArcCsch[a + b*x]/2])/Sqrt[1 + a^2]])/(a^2*(1 + a^2)^(3/2))","A",8,8,10,0.8000,1,"{6322, 5469, 3785, 3919, 3831, 2660, 618, 206}"
7,1,501,0,0.8867688,"\int (e+f x)^3 \left(a+b \text{csch}^{-1}(c+d x)\right)^2 \, dx","Int[(e + f*x)^3*(a + b*ArcCsch[c + d*x])^2,x]","-\frac{b^2 f^2 (d e-c f) \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c+d x)}\right)}{d^4}+\frac{b^2 f^2 (d e-c f) \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c+d x)}\right)}{d^4}+\frac{2 b^2 (d e-c f)^3 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c+d x)}\right)}{d^4}-\frac{2 b^2 (d e-c f)^3 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c+d x)}\right)}{d^4}+\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 x (d e-c f)}{d^3}+\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 (d e-c f) \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c+d x)}\right)}{d^4}+\frac{b^2 f^2 (d e-c f) \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c+d x)}\right)}{d^4}+\frac{2 b^2 (d e-c f)^3 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c+d x)}\right)}{d^4}-\frac{2 b^2 (d e-c f)^3 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c+d x)}\right)}{d^4}+\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 x (d e-c f)}{d^3}+\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}",1,"(b^2*f^2*(d*e - c*f)*x)/d^3 + (b^2*f^3*(c + d*x)^2)/(12*d^4) - (b*f^3*(c + d*x)*Sqrt[1 + (c + d*x)^(-2)]*(a + b*ArcCsch[c + d*x]))/(3*d^4) + (3*b*f*(d*e - c*f)^2*(c + d*x)*Sqrt[1 + (c + d*x)^(-2)]*(a + b*ArcCsch[c + d*x]))/d^4 + (b*f^2*(d*e - c*f)*(c + d*x)^2*Sqrt[1 + (c + d*x)^(-2)]*(a + b*ArcCsch[c + d*x]))/d^4 + (b*f^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^(-2)]*(a + b*ArcCsch[c + d*x]))/(6*d^4) - ((d*e - c*f)^4*(a + b*ArcCsch[c + d*x])^2)/(4*d^4*f) + ((e + f*x)^4*(a + b*ArcCsch[c + d*x])^2)/(4*f) - (2*b*f^2*(d*e - c*f)*(a + b*ArcCsch[c + d*x])*ArcTanh[E^ArcCsch[c + d*x]])/d^4 + (4*b*(d*e - c*f)^3*(a + b*ArcCsch[c + d*x])*ArcTanh[E^ArcCsch[c + d*x]])/d^4 - (b^2*f^3*Log[c + d*x])/(3*d^4) + (3*b^2*f*(d*e - c*f)^2*Log[c + d*x])/d^4 - (b^2*f^2*(d*e - c*f)*PolyLog[2, -E^ArcCsch[c + d*x]])/d^4 + (2*b^2*(d*e - c*f)^3*PolyLog[2, -E^ArcCsch[c + d*x]])/d^4 + (b^2*f^2*(d*e - c*f)*PolyLog[2, E^ArcCsch[c + d*x]])/d^4 - (2*b^2*(d*e - c*f)^3*PolyLog[2, E^ArcCsch[c + d*x]])/d^4","A",20,9,20,0.4500,1,"{6322, 5469, 4190, 4182, 2279, 2391, 4184, 3475, 4185}"
8,1,351,0,0.5062503,"\int (e+f x)^2 \left(a+b \text{csch}^{-1}(c+d x)\right)^2 \, dx","Int[(e + f*x)^2*(a + b*ArcCsch[c + d*x])^2,x]","\frac{2 b^2 (d e-c f)^2 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c+d x)}\right)}{d^3}-\frac{2 b^2 (d e-c f)^2 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c+d x)}\right)}{d^3}-\frac{b^2 f^2 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c+d x)}\right)}{3 d^3}+\frac{b^2 f^2 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c+d x)}\right)}{3 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 f (d e-c f) \log (c+d x)}{d^3}+\frac{b^2 f^2 x}{3 d^2}","\frac{2 b^2 (d e-c f)^2 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c+d x)}\right)}{d^3}-\frac{2 b^2 (d e-c f)^2 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c+d x)}\right)}{d^3}-\frac{b^2 f^2 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c+d x)}\right)}{3 d^3}+\frac{b^2 f^2 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c+d x)}\right)}{3 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 f (d e-c f) \log (c+d x)}{d^3}+\frac{b^2 f^2 x}{3 d^2}",1,"(b^2*f^2*x)/(3*d^2) + (2*b*f*(d*e - c*f)*(c + d*x)*Sqrt[1 + (c + d*x)^(-2)]*(a + b*ArcCsch[c + d*x]))/d^3 + (b*f^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^(-2)]*(a + b*ArcCsch[c + d*x]))/(3*d^3) - ((d*e - c*f)^3*(a + b*ArcCsch[c + d*x])^2)/(3*d^3*f) + ((e + f*x)^3*(a + b*ArcCsch[c + d*x])^2)/(3*f) - (2*b*f^2*(a + b*ArcCsch[c + d*x])*ArcTanh[E^ArcCsch[c + d*x]])/(3*d^3) + (4*b*(d*e - c*f)^2*(a + b*ArcCsch[c + d*x])*ArcTanh[E^ArcCsch[c + d*x]])/d^3 + (2*b^2*f*(d*e - c*f)*Log[c + d*x])/d^3 - (b^2*f^2*PolyLog[2, -E^ArcCsch[c + d*x]])/(3*d^3) + (2*b^2*(d*e - c*f)^2*PolyLog[2, -E^ArcCsch[c + d*x]])/d^3 + (b^2*f^2*PolyLog[2, E^ArcCsch[c + d*x]])/(3*d^3) - (2*b^2*(d*e - c*f)^2*PolyLog[2, E^ArcCsch[c + d*x]])/d^3","A",17,9,20,0.4500,1,"{6322, 5469, 4190, 4182, 2279, 2391, 4184, 3475, 4185}"
9,1,194,0,0.2733357,"\int (e+f x) \left(a+b \text{csch}^{-1}(c+d x)\right)^2 \, dx","Int[(e + f*x)*(a + b*ArcCsch[c + d*x])^2,x]","\frac{2 b^2 (d e-c f) \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c+d x)}\right)}{d^2}-\frac{2 b^2 (d e-c f) \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c+d x)}\right)}{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{b^2 f \log (c+d x)}{d^2}","\frac{2 b^2 (d e-c f) \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c+d x)}\right)}{d^2}-\frac{2 b^2 (d e-c f) \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c+d x)}\right)}{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{b^2 f \log (c+d x)}{d^2}",1,"(b*f*(c + d*x)*Sqrt[1 + (c + d*x)^(-2)]*(a + b*ArcCsch[c + d*x]))/d^2 - ((d*e - c*f)^2*(a + b*ArcCsch[c + d*x])^2)/(2*d^2*f) + ((e + f*x)^2*(a + b*ArcCsch[c + d*x])^2)/(2*f) + (4*b*(d*e - c*f)*(a + b*ArcCsch[c + d*x])*ArcTanh[E^ArcCsch[c + d*x]])/d^2 + (b^2*f*Log[c + d*x])/d^2 + (2*b^2*(d*e - c*f)*PolyLog[2, -E^ArcCsch[c + d*x]])/d^2 - (2*b^2*(d*e - c*f)*PolyLog[2, E^ArcCsch[c + d*x]])/d^2","A",11,8,18,0.4444,1,"{6322, 5469, 4190, 4182, 2279, 2391, 4184, 3475}"
10,1,85,0,0.0831275,"\int \left(a+b \text{csch}^{-1}(c+d x)\right)^2 \, dx","Int[(a + b*ArcCsch[c + d*x])^2,x]","\frac{2 b^2 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c+d x)}\right)}{d}-\frac{2 b^2 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c+d x)}\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{PolyLog}\left(2,-e^{\text{csch}^{-1}(c+d x)}\right)}{d}-\frac{2 b^2 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c+d x)}\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}",1,"((c + d*x)*(a + b*ArcCsch[c + d*x])^2)/d + (4*b*(a + b*ArcCsch[c + d*x])*ArcTanh[E^ArcCsch[c + d*x]])/d + (2*b^2*PolyLog[2, -E^ArcCsch[c + d*x]])/d - (2*b^2*PolyLog[2, E^ArcCsch[c + d*x]])/d","A",8,6,12,0.5000,1,"{6316, 6280, 5452, 4182, 2279, 2391}"
11,1,475,0,1.0728227,"\int \frac{\left(a+b \text{csch}^{-1}(c+d x)\right)^2}{e+f x} \, dx","Int[(a + b*ArcCsch[c + d*x])^2/(e + f*x),x]","\frac{2 b \left(a+b \text{csch}^{-1}(c+d x)\right) \text{PolyLog}\left(2,-\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}}\right)}{f}+\frac{2 b \left(a+b \text{csch}^{-1}(c+d x)\right) \text{PolyLog}\left(2,-\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}\right)}{f}-\frac{b \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c+d x)}\right) \left(a+b \text{csch}^{-1}(c+d x)\right)}{f}-\frac{2 b^2 \text{PolyLog}\left(3,-\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}}\right)}{f}-\frac{2 b^2 \text{PolyLog}\left(3,-\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}\right)}{f}+\frac{b^2 \text{PolyLog}\left(3,e^{2 \text{csch}^{-1}(c+d x)}\right)}{2 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{\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 \left(a+b \text{csch}^{-1}(c+d x)\right) \text{PolyLog}\left(2,-\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}}\right)}{f}+\frac{2 b \left(a+b \text{csch}^{-1}(c+d x)\right) \text{PolyLog}\left(2,-\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}\right)}{f}-\frac{b \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c+d x)}\right) \left(a+b \text{csch}^{-1}(c+d x)\right)}{f}-\frac{2 b^2 \text{PolyLog}\left(3,-\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}}\right)}{f}-\frac{2 b^2 \text{PolyLog}\left(3,-\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}\right)}{f}+\frac{b^2 \text{PolyLog}\left(3,e^{2 \text{csch}^{-1}(c+d x)}\right)}{2 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{\log \left(1-e^{2 \text{csch}^{-1}(c+d x)}\right) \left(a+b \text{csch}^{-1}(c+d x)\right)^2}{f}",1,"-(((a + b*ArcCsch[c + d*x])^2*Log[1 - E^(2*ArcCsch[c + d*x])])/f) + ((a + b*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])])/f + ((a + b*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])])/f - (b*(a + b*ArcCsch[c + d*x])*PolyLog[2, E^(2*ArcCsch[c + d*x])])/f + (2*b*(a + b*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]))])/f + (2*b*(a + b*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]))])/f + (b^2*PolyLog[3, E^(2*ArcCsch[c + d*x])])/(2*f) - (2*b^2*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]))])/f - (2*b^2*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]))])/f","A",17,9,20,0.4500,1,"{6322, 5596, 5569, 3716, 2190, 2531, 2282, 6589, 5561}"
12,1,448,0,1.1100484,"\int \frac{\left(a+b \text{csch}^{-1}(c+d x)\right)^2}{(e+f x)^2} \, dx","Int[(a + b*ArcCsch[c + d*x])^2/(e + f*x)^2,x]","-\frac{2 b^2 d \text{PolyLog}\left(2,-\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}}\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{PolyLog}\left(2,-\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}\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)}}{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{PolyLog}\left(2,-\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}}\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{PolyLog}\left(2,-\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}\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)}}{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)}",1,"(d*(a + b*ArcCsch[c + d*x])^2)/(f*(d*e - c*f)) - (a + b*ArcCsch[c + d*x])^2/(f*(e + f*x)) - (2*b*d*(a + b*ArcCsch[c + d*x])*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])])/((d*e - c*f)*Sqrt[d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2]) + (2*b*d*(a + b*ArcCsch[c + d*x])*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])])/((d*e - c*f)*Sqrt[d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2]) - (2*b^2*d*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]))])/((d*e - c*f)*Sqrt[d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2]) + (2*b^2*d*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]))])/((d*e - c*f)*Sqrt[d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2])","A",12,8,20,0.4000,1,"{6322, 5469, 4191, 3322, 2264, 2190, 2279, 2391}"
13,1,1024,0,2.2960207,"\int \frac{\left(a+b \text{csch}^{-1}(c+d x)\right)^2}{(e+f x)^3} \, dx","Int[(a + b*ArcCsch[c + d*x])^2/(e + f*x)^3,x]","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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}","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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,"-((b*d^2*f*Sqrt[1 + (c + d*x)^(-2)]*(a + b*ArcCsch[c + d*x]))/((d*e - c*f)*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)*(f + (d*e - c*f)/(c + d*x)))) + (d^2*(a + b*ArcCsch[c + d*x])^2)/(2*f*(d*e - c*f)^2) - (a + b*ArcCsch[c + d*x])^2/(2*f*(e + f*x)^2) + (b*d^2*f^2*(a + b*ArcCsch[c + d*x])*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])])/((d*e - c*f)^2*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)^(3/2)) - (2*b*d^2*(a + b*ArcCsch[c + d*x])*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])])/((d*e - c*f)^2*Sqrt[d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2]) - (b*d^2*f^2*(a + b*ArcCsch[c + d*x])*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])])/((d*e - c*f)^2*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)^(3/2)) + (2*b*d^2*(a + b*ArcCsch[c + d*x])*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])])/((d*e - c*f)^2*Sqrt[d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2]) + (b^2*d^2*f*Log[f + (d*e - c*f)/(c + d*x)])/((d*e - c*f)^2*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)) + (b^2*d^2*f^2*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]))])/((d*e - c*f)^2*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)^(3/2)) - (2*b^2*d^2*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]))])/((d*e - c*f)^2*Sqrt[d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2]) - (b^2*d^2*f^2*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]))])/((d*e - c*f)^2*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)^(3/2)) + (2*b^2*d^2*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]))])/((d*e - c*f)^2*Sqrt[d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2])","A",23,11,20,0.5500,1,"{6322, 5469, 4191, 3322, 2264, 2190, 2279, 2391, 3324, 2668, 31}"
14,1,114,0,0.0323269,"\int x^3 \text{csch}^{-1}\left(\sqrt{x}\right) \, dx","Int[x^3*ArcCsch[Sqrt[x]],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}}","\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]*Sqrt[x])/(4*Sqrt[-x]) - ((-1 - x)^(3/2)*Sqrt[x])/(4*Sqrt[-x]) - (3*(-1 - x)^(5/2)*Sqrt[x])/(20*Sqrt[-x]) - ((-1 - x)^(7/2)*Sqrt[x])/(28*Sqrt[-x]) + (x^4*ArcCsch[Sqrt[x]])/4","A",4,3,10,0.3000,1,"{6346, 12, 43}"
15,1,89,0,0.0253573,"\int x^2 \text{csch}^{-1}\left(\sqrt{x}\right) \, dx","Int[x^2*ArcCsch[Sqrt[x]],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}}","\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]*Sqrt[x])/(3*Sqrt[-x]) + (2*(-1 - x)^(3/2)*Sqrt[x])/(9*Sqrt[-x]) + ((-1 - x)^(5/2)*Sqrt[x])/(15*Sqrt[-x]) + (x^3*ArcCsch[Sqrt[x]])/3","A",4,3,10,0.3000,1,"{6346, 12, 43}"
16,1,64,0,0.017491,"\int x \text{csch}^{-1}\left(\sqrt{x}\right) \, dx","Int[x*ArcCsch[Sqrt[x]],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}}","\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]*Sqrt[x])/(2*Sqrt[-x]) - ((-1 - x)^(3/2)*Sqrt[x])/(6*Sqrt[-x]) + (x^2*ArcCsch[Sqrt[x]])/2","A",4,3,8,0.3750,1,"{6346, 12, 43}"
17,1,31,0,0.0076117,"\int \text{csch}^{-1}\left(\sqrt{x}\right) \, dx","Int[ArcCsch[Sqrt[x]],x]","\frac{\sqrt{-x-1} \sqrt{x}}{\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]*Sqrt[x])/Sqrt[-x] + x*ArcCsch[Sqrt[x]]","A",3,3,6,0.5000,1,"{6344, 12, 32}"
18,1,46,0,0.0965395,"\int \frac{\text{csch}^{-1}\left(\sqrt{x}\right)}{x} \, dx","Int[ArcCsch[Sqrt[x]]/x,x]","-\text{PolyLog}\left(2,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)","-\text{PolyLog}\left(2,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]]^2 - 2*ArcCsch[Sqrt[x]]*Log[1 - E^(2*ArcCsch[Sqrt[x]])] - PolyLog[2, E^(2*ArcCsch[Sqrt[x]])]","A",7,6,10,0.6000,1,"{6282, 5659, 3716, 2190, 2279, 2391}"
19,1,63,0,0.0238083,"\int \frac{\text{csch}^{-1}\left(\sqrt{x}\right)}{x^2} \, dx","Int[ArcCsch[Sqrt[x]]/x^2,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}","\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]/(2*Sqrt[-x]*Sqrt[x]) - ArcCsch[Sqrt[x]]/x - (Sqrt[x]*ArcTan[Sqrt[-1 - x]])/(2*Sqrt[-x])","A",5,5,10,0.5000,1,"{6346, 12, 51, 63, 204}"
20,1,90,0,0.0281949,"\int \frac{\text{csch}^{-1}\left(\sqrt{x}\right)}{x^3} \, dx","Int[ArcCsch[Sqrt[x]]/x^3,x]","\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}}","\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]/(8*Sqrt[-x]*x^(3/2)) - (3*Sqrt[-1 - x])/(16*Sqrt[-x]*Sqrt[x]) - ArcCsch[Sqrt[x]]/(2*x^2) + (3*Sqrt[x]*ArcTan[Sqrt[-1 - x]])/(16*Sqrt[-x])","A",6,5,10,0.5000,1,"{6346, 12, 51, 63, 204}"
21,1,115,0,0.0343055,"\int \frac{\text{csch}^{-1}\left(\sqrt{x}\right)}{x^4} \, dx","Int[ArcCsch[Sqrt[x]]/x^4,x]","-\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}}","-\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]/(18*Sqrt[-x]*x^(5/2)) - (5*Sqrt[-1 - x])/(72*Sqrt[-x]*x^(3/2)) + (5*Sqrt[-1 - x])/(48*Sqrt[-x]*Sqrt[x]) - ArcCsch[Sqrt[x]]/(3*x^3) - (5*Sqrt[x]*ArcTan[Sqrt[-1 - x]])/(48*Sqrt[-x])","A",7,5,10,0.5000,1,"{6346, 12, 51, 63, 204}"
22,1,16,0,0.0060857,"\int \text{csch}^{-1}\left(\frac{1}{x}\right) \, dx","Int[ArcCsch[x^(-1)],x]","x \sinh ^{-1}(x)-\sqrt{x^2+1}","x \sinh ^{-1}(x)-\sqrt{x^2+1}",1,"-Sqrt[1 + x^2] + x*ArcSinh[x]","A",3,3,4,0.7500,1,"{6328, 5653, 261}"
23,1,61,0,0.1079177,"\int \frac{\text{csch}^{-1}\left(a x^n\right)}{x} \, dx","Int[ArcCsch[a*x^n]/x,x]","-\frac{\text{PolyLog}\left(2,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}","-\frac{\text{PolyLog}\left(2,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,"ArcCsch[a*x^n]^2/(2*n) - (ArcCsch[a*x^n]*Log[1 - E^(2*ArcCsch[a*x^n])])/n - PolyLog[2, E^(2*ArcCsch[a*x^n])]/(2*n)","A",7,6,10,0.6000,1,"{6282, 5659, 3716, 2190, 2279, 2391}"
24,1,54,0,0.1006771,"\int \frac{\text{csch}^{-1}\left(a x^5\right)}{x} \, dx","Int[ArcCsch[a*x^5]/x,x]","-\frac{1}{10} \text{PolyLog}\left(2,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)","-\frac{1}{10} \text{PolyLog}\left(2,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]^2/10 - (ArcCsch[a*x^5]*Log[1 - E^(2*ArcCsch[a*x^5])])/5 - PolyLog[2, E^(2*ArcCsch[a*x^5])]/10","A",7,6,10,0.6000,1,"{6282, 5659, 3716, 2190, 2279, 2391}"
25,1,77,0,0.0879159,"\int \text{csch}^{-1}\left(c e^{a+b x}\right) \, dx","Int[ArcCsch[c*E^(a + b*x)],x]","-\frac{\text{PolyLog}\left(2,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}","-\frac{\text{PolyLog}\left(2,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,"ArcCsch[c*E^(a + b*x)]^2/(2*b) - (ArcCsch[c*E^(a + b*x)]*Log[1 - E^(2*ArcCsch[c*E^(a + b*x)])])/b - PolyLog[2, E^(2*ArcCsch[c*E^(a + b*x)])]/(2*b)","A",7,7,10,0.7000,1,"{2282, 6282, 5659, 3716, 2190, 2279, 2391}"
26,1,52,0,0.0398986,"\int e^{\text{csch}^{-1}(a x)} x^m \, dx","Int[E^ArcCsch[a*x]*x^m,x]","\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}","\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 - m)/2, -(1/(a^2*x^2))])/(1 + m)","A",4,4,10,0.4000,1,"{6336, 30, 339, 364}"
27,1,54,0,0.0294947,"\int e^{\text{csch}^{-1}(a x)} x^4 \, dx","Int[E^ArcCsch[a*x]*x^4,x]","\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}","\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,"(-2*(1 + 1/(a^2*x^2))^(3/2)*x^3)/(15*a^2) + x^4/(4*a) + ((1 + 1/(a^2*x^2))^(3/2)*x^5)/5","A",4,4,10,0.4000,1,"{6336, 30, 271, 264}"
28,1,75,0,0.0440765,"\int e^{\text{csch}^{-1}(a x)} x^3 \, dx","Int[E^ArcCsch[a*x]*x^3,x]","\frac{1}{4} x^4 \sqrt{\frac{1}{a^2 x^2}+1}+\frac{x^2 \sqrt{\frac{1}{a^2 x^2}+1}}{8 a^2}-\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{a^2 x^2}+1}\right)}{8 a^4}+\frac{x^3}{3 a}","\frac{1}{4} x^4 \sqrt{\frac{1}{a^2 x^2}+1}+\frac{x^2 \sqrt{\frac{1}{a^2 x^2}+1}}{8 a^2}-\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{a^2 x^2}+1}\right)}{8 a^4}+\frac{x^3}{3 a}",1,"(Sqrt[1 + 1/(a^2*x^2)]*x^2)/(8*a^2) + x^3/(3*a) + (Sqrt[1 + 1/(a^2*x^2)]*x^4)/4 - ArcTanh[Sqrt[1 + 1/(a^2*x^2)]]/(8*a^4)","A",7,7,10,0.7000,1,"{6336, 30, 266, 47, 51, 63, 208}"
29,1,31,0,0.0219103,"\int e^{\text{csch}^{-1}(a x)} x^2 \, dx","Int[E^ArcCsch[a*x]*x^2,x]","\frac{1}{3} x^3 \left(\frac{1}{a^2 x^2}+1\right)^{3/2}+\frac{x^2}{2 a}","\frac{1}{3} x^3 \left(\frac{1}{a^2 x^2}+1\right)^{3/2}+\frac{x^2}{2 a}",1,"x^2/(2*a) + ((1 + 1/(a^2*x^2))^(3/2)*x^3)/3","A",3,3,10,0.3000,1,"{6336, 30, 264}"
30,1,47,0,0.0264616,"\int e^{\text{csch}^{-1}(a x)} x \, dx","Int[E^ArcCsch[a*x]*x,x]","\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}","\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,"x/a + (Sqrt[1 + 1/(a^2*x^2)]*x^2)/2 + ArcTanh[Sqrt[1 + 1/(a^2*x^2)]]/(2*a^2)","A",6,6,8,0.7500,1,"{6336, 8, 266, 47, 63, 208}"
31,1,31,0,0.015288,"\int e^{\text{csch}^{-1}(a x)} \, dx","Int[E^ArcCsch[a*x],x]","x \sqrt{\frac{1}{a^2 x^2}+1}+\frac{\log (x)}{a}-\frac{\text{csch}^{-1}(a x)}{a}","\frac{\log (x)}{a}+x e^{\text{csch}^{-1}(a x)}-\frac{\text{csch}^{-1}(a x)}{a}",1,"Sqrt[1 + 1/(a^2*x^2)]*x - ArcCsch[a*x]/a + Log[x]/a","A",5,5,6,0.8333,0,"{6331, 29, 242, 277, 215}"
32,1,38,0,0.034632,"\int \frac{e^{\text{csch}^{-1}(a x)}}{x} \, dx","Int[E^ArcCsch[a*x]/x,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}","-\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) + ArcTanh[Sqrt[1 + 1/(a^2*x^2)]]","A",6,6,10,0.6000,1,"{6336, 30, 266, 50, 63, 208}"
33,1,40,0,0.028842,"\int \frac{e^{\text{csch}^{-1}(a x)}}{x^2} \, dx","Int[E^ArcCsch[a*x]/x^2,x]","-\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)","-\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*a*x^2) - Sqrt[1 + 1/(a^2*x^2)]/(2*x) - (a*ArcCsch[a*x])/2","A",5,5,10,0.5000,1,"{6336, 30, 335, 195, 215}"
34,1,31,0,0.0219248,"\int \frac{e^{\text{csch}^{-1}(a x)}}{x^3} \, dx","Int[E^ArcCsch[a*x]/x^3,x]","-\frac{1}{3} a^2 \left(\frac{1}{a^2 x^2}+1\right)^{3/2}-\frac{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,"-(a^2*(1 + 1/(a^2*x^2))^(3/2))/3 - 1/(3*a*x^3)","A",3,3,10,0.3000,1,"{6336, 30, 261}"
35,1,65,0,0.0434752,"\int \frac{e^{\text{csch}^{-1}(a x)}}{x^4} \, dx","Int[E^ArcCsch[a*x]/x^4,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}{8} a^3 \text{csch}^{-1}(a x)-\frac{1}{4 a x^4}","-\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}{8} a^3 \text{csch}^{-1}(a x)-\frac{1}{4 a x^4}",1,"-1/(4*a*x^4) - Sqrt[1 + 1/(a^2*x^2)]/(4*x^3) - (a^2*Sqrt[1 + 1/(a^2*x^2)])/(8*x) + (a^3*ArcCsch[a*x])/8","A",6,6,10,0.6000,1,"{6336, 30, 335, 279, 321, 215}"
36,1,51,0,0.0384009,"\int \frac{e^{\text{csch}^{-1}(a x)}}{x^5} \, dx","Int[E^ArcCsch[a*x]/x^5,x]","-\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}","-\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,"(a^4*(1 + 1/(a^2*x^2))^(3/2))/3 - (a^4*(1 + 1/(a^2*x^2))^(5/2))/5 - 1/(5*a*x^5)","A",5,4,10,0.4000,1,"{6336, 30, 266, 43}"
37,1,59,0,0.0415475,"\int e^{\text{csch}^{-1}\left(a x^2\right)} x^m \, dx","Int[E^ArcCsch[a*x^2]*x^m,x]","\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)}","\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)/(a*(1 - m))) + (x^(1 + m)*Hypergeometric2F1[-1/2, (-1 - m)/4, (3 - m)/4, -(1/(a^2*x^4))])/(1 + m)","A",4,4,12,0.3333,1,"{6336, 30, 339, 364}"
38,1,202,0,0.1247436,"\int e^{\text{csch}^{-1}\left(a x^2\right)} x^4 \, dx","Int[E^ArcCsch[a*x^2]*x^4,x]","\frac{1}{5} x^5 \sqrt{\frac{1}{a^2 x^4}+1}+\frac{2 x \sqrt{\frac{1}{a^2 x^4}+1}}{5 a^2}-\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}","\frac{1}{5} x^5 \sqrt{\frac{1}{a^2 x^4}+1}+\frac{2 x \sqrt{\frac{1}{a^2 x^4}+1}}{5 a^2}-\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,"(-2*Sqrt[1 + 1/(a^2*x^4)])/(5*a^2*(a + x^(-2))*x) + (2*Sqrt[1 + 1/(a^2*x^4)]*x)/(5*a^2) + x^3/(3*a) + (Sqrt[1 + 1/(a^2*x^4)]*x^5)/5 + (2*Sqrt[(a^2 + x^(-4))/(a + x^(-2))^2]*(a + x^(-2))*EllipticE[2*ArcCot[Sqrt[a]*x], 1/2])/(5*a^(7/2)*Sqrt[1 + 1/(a^2*x^4)]) - (Sqrt[(a^2 + x^(-4))/(a + x^(-2))^2]*(a + x^(-2))*EllipticF[2*ArcCot[Sqrt[a]*x], 1/2])/(5*a^(7/2)*Sqrt[1 + 1/(a^2*x^4)])","A",8,8,12,0.6667,1,"{6336, 30, 335, 277, 325, 305, 220, 1196}"
39,1,52,0,0.0383185,"\int e^{\text{csch}^{-1}\left(a x^2\right)} x^3 \, dx","Int[E^ArcCsch[a*x^2]*x^3,x]","\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}","\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,"x^2/(2*a) + (Sqrt[1 + 1/(a^2*x^4)]*x^4)/4 + ArcTanh[Sqrt[1 + 1/(a^2*x^4)]]/(4*a^2)","A",6,6,12,0.5000,1,"{6336, 30, 266, 47, 63, 208}"
40,1,86,0,0.0532904,"\int e^{\text{csch}^{-1}\left(a x^2\right)} x^2 \, dx","Int[E^ArcCsch[a*x^2]*x^2,x]","\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}","\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,"x/a + (Sqrt[1 + 1/(a^2*x^4)]*x^3)/3 - (Sqrt[(a^2 + x^(-4))/(a + x^(-2))^2]*(a + x^(-2))*EllipticF[2*ArcCot[Sqrt[a]*x], 1/2])/(3*a^(5/2)*Sqrt[1 + 1/(a^2*x^4)])","A",5,5,12,0.4167,1,"{6336, 8, 335, 277, 220}"
41,1,40,0,0.0362239,"\int e^{\text{csch}^{-1}\left(a x^2\right)} x \, dx","Int[E^ArcCsch[a*x^2]*x,x]","\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}","\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,"(Sqrt[1 + 1/(a^2*x^4)]*x^2)/2 - ArcCsch[a*x^2]/(2*a) + Log[x]/a","A",6,6,10,0.6000,1,"{6336, 29, 335, 275, 277, 215}"
42,1,165,0,0.0803542,"\int e^{\text{csch}^{-1}\left(a x^2\right)} \, dx","Int[E^ArcCsch[a*x^2],x]","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}","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,"-(1/(a*x)) - (2*Sqrt[1 + 1/(a^2*x^4)])/((a + x^(-2))*x) + Sqrt[1 + 1/(a^2*x^4)]*x + (2*Sqrt[(a^2 + x^(-4))/(a + x^(-2))^2]*(a + x^(-2))*EllipticE[2*ArcCot[Sqrt[a]*x], 1/2])/(a^(3/2)*Sqrt[1 + 1/(a^2*x^4)]) - (Sqrt[(a^2 + x^(-4))/(a + x^(-2))^2]*(a + x^(-2))*EllipticF[2*ArcCot[Sqrt[a]*x], 1/2])/(a^(3/2)*Sqrt[1 + 1/(a^2*x^4)])","A",7,7,8,0.8750,1,"{6331, 30, 242, 277, 305, 220, 1196}"
43,1,46,0,0.0327176,"\int \frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{x} \, dx","Int[E^ArcCsch[a*x^2]/x,x]","-\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}","-\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,"-Sqrt[1 + 1/(a^2*x^4)]/2 - 1/(2*a*x^2) + ArcTanh[Sqrt[1 + 1/(a^2*x^4)]]/2","A",6,6,12,0.5000,1,"{6336, 30, 266, 50, 63, 208}"
44,1,91,0,0.0472524,"\int \frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{x^2} \, dx","Int[E^ArcCsch[a*x^2]/x^2,x]","-\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}","-\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*x^3) - Sqrt[1 + 1/(a^2*x^4)]/(3*x) - (Sqrt[(a^2 + x^(-4))/(a + x^(-2))^2]*(a + x^(-2))*EllipticF[2*ArcCot[Sqrt[a]*x], 1/2])/(3*Sqrt[a]*Sqrt[1 + 1/(a^2*x^4)])","A",5,5,12,0.4167,1,"{6336, 30, 335, 195, 220}"
45,1,42,0,0.039321,"\int \frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{x^3} \, dx","Int[E^ArcCsch[a*x^2]/x^3,x]","-\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)","-\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/(4*a*x^4) - Sqrt[1 + 1/(a^2*x^4)]/(4*x^2) - (a*ArcCsch[a*x^2])/4","A",6,6,12,0.5000,1,"{6336, 30, 335, 275, 195, 215}"
46,1,181,0,0.0954163,"\int \frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{x^4} \, dx","Int[E^ArcCsch[a*x^2]/x^4,x]","-\frac{2 a^2 \sqrt{\frac{1}{a^2 x^4}+1}}{5 x \left(a+\frac{1}{x^2}\right)}-\frac{\sqrt{\frac{1}{a^2 x^4}+1}}{5 x^3}-\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}","-\frac{2 a^2 \sqrt{\frac{1}{a^2 x^4}+1}}{5 x \left(a+\frac{1}{x^2}\right)}-\frac{\sqrt{\frac{1}{a^2 x^4}+1}}{5 x^3}-\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,"-1/(5*a*x^5) - Sqrt[1 + 1/(a^2*x^4)]/(5*x^3) - (2*a^2*Sqrt[1 + 1/(a^2*x^4)])/(5*(a + x^(-2))*x) + (2*Sqrt[a]*Sqrt[(a^2 + x^(-4))/(a + x^(-2))^2]*(a + x^(-2))*EllipticE[2*ArcCot[Sqrt[a]*x], 1/2])/(5*Sqrt[1 + 1/(a^2*x^4)]) - (Sqrt[a]*Sqrt[(a^2 + x^(-4))/(a + x^(-2))^2]*(a + x^(-2))*EllipticF[2*ArcCot[Sqrt[a]*x], 1/2])/(5*Sqrt[1 + 1/(a^2*x^4)])","A",7,7,12,0.5833,1,"{6336, 30, 335, 279, 305, 220, 1196}"
47,1,31,0,0.0216713,"\int \frac{e^{\text{csch}^{-1}\left(a x^2\right)}}{x^5} \, dx","Int[E^ArcCsch[a*x^2]/x^5,x]","-\frac{1}{6} a^2 \left(\frac{1}{a^2 x^4}+1\right)^{3/2}-\frac{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,"-(a^2*(1 + 1/(a^2*x^4))^(3/2))/6 - 1/(6*a*x^6)","A",3,3,12,0.2500,1,"{6336, 30, 261}"
48,1,64,0,0.3218775,"\int e^{2 \text{csch}^{-1}(a x)} x^m \, dx","Int[E^(2*ArcCsch[a*x])*x^m,x]","\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}","\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,"(-2*x^(-1 + m))/(a^2*(1 - m)) + x^(1 + m)/(1 + m) + (2*x^m*Hypergeometric2F1[-1/2, -m/2, 1 - m/2, -(1/(a^2*x^2))])/(a*m)","A",5,4,12,0.3333,1,"{6338, 6742, 339, 364}"
49,1,85,0,0.2541382,"\int e^{2 \text{csch}^{-1}(a x)} x^4 \, dx","Int[E^(2*ArcCsch[a*x])*x^4,x]","\frac{x^4 \sqrt{\frac{1}{a^2 x^2}+1}}{2 a}+\frac{2 x^3}{3 a^2}+\frac{x^2 \sqrt{\frac{1}{a^2 x^2}+1}}{4 a^3}-\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{a^2 x^2}+1}\right)}{4 a^5}+\frac{x^5}{5}","\frac{x^4 \sqrt{\frac{1}{a^2 x^2}+1}}{2 a}+\frac{2 x^3}{3 a^2}+\frac{x^2 \sqrt{\frac{1}{a^2 x^2}+1}}{4 a^3}-\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{a^2 x^2}+1}\right)}{4 a^5}+\frac{x^5}{5}",1,"(Sqrt[1 + 1/(a^2*x^2)]*x^2)/(4*a^3) + (2*x^3)/(3*a^2) + (Sqrt[1 + 1/(a^2*x^2)]*x^4)/(2*a) + x^5/5 - ArcTanh[Sqrt[1 + 1/(a^2*x^2)]]/(4*a^5)","A",8,7,12,0.5833,1,"{6338, 6742, 266, 47, 51, 63, 208}"
50,1,38,0,0.2247857,"\int e^{2 \text{csch}^{-1}(a x)} x^3 \, dx","Int[E^(2*ArcCsch[a*x])*x^3,x]","\frac{2 x^3 \left(\frac{1}{a^2 x^2}+1\right)^{3/2}}{3 a}+\frac{x^2}{a^2}+\frac{x^4}{4}","\frac{2 x^3 \left(\frac{1}{a^2 x^2}+1\right)^{3/2}}{3 a}+\frac{x^2}{a^2}+\frac{x^4}{4}",1,"x^2/a^2 + (2*(1 + 1/(a^2*x^2))^(3/2)*x^3)/(3*a) + x^4/4","A",4,3,12,0.2500,1,"{6338, 6742, 264}"
51,1,52,0,0.2397378,"\int e^{2 \text{csch}^{-1}(a x)} x^2 \, dx","Int[E^(2*ArcCsch[a*x])*x^2,x]","\frac{x^2 \sqrt{\frac{1}{a^2 x^2}+1}}{a}+\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{a^2 x^2}+1}\right)}{a^3}+\frac{2 x}{a^2}+\frac{x^3}{3}","\frac{x^2 \sqrt{\frac{1}{a^2 x^2}+1}}{a}+\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{a^2 x^2}+1}\right)}{a^3}+\frac{2 x}{a^2}+\frac{x^3}{3}",1,"(2*x)/a^2 + (Sqrt[1 + 1/(a^2*x^2)]*x^2)/a + x^3/3 + ArcTanh[Sqrt[1 + 1/(a^2*x^2)]]/a^3","A",7,6,12,0.5000,1,"{6338, 6742, 266, 47, 63, 208}"
52,1,43,0,0.1579097,"\int e^{2 \text{csch}^{-1}(a x)} x \, dx","Int[E^(2*ArcCsch[a*x])*x,x]","\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}","\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,"(2*Sqrt[1 + 1/(a^2*x^2)]*x)/a + x^2/2 - (2*ArcCsch[a*x])/a^2 + (2*Log[x])/a^2","A",6,5,10,0.5000,1,"{6338, 6742, 242, 277, 215}"
53,1,47,0,0.0718435,"\int e^{2 \text{csch}^{-1}(a x)} \, dx","Int[E^(2*ArcCsch[a*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","-\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*ArcTanh[Sqrt[1 + 1/(a^2*x^2)]])/a","A",7,6,8,0.7500,1,"{6333, 6742, 266, 50, 63, 208}"
54,1,38,0,0.2143969,"\int \frac{e^{2 \text{csch}^{-1}(a x)}}{x} \, dx","Int[E^(2*ArcCsch[a*x])/x,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)","-\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^2*x^2)) - Sqrt[1 + 1/(a^2*x^2)]/(a*x) - ArcCsch[a*x] + Log[x]","A",6,5,12,0.4167,1,"{6338, 6742, 335, 195, 215}"
55,1,54,0,0.2035544,"\int \frac{e^{2 \text{csch}^{-1}(a x)}}{x^2} \, dx","Int[E^(2*ArcCsch[a*x])/x^2,x]","-\frac{1}{6} a \left(\sqrt{\frac{1}{a^2 x^2}+1}+\frac{1}{a x}\right)^3-\frac{1}{2} a \sqrt{\frac{1}{a^2 x^2}+1}-\frac{1}{2 x}","-\frac{2}{3} a \left(\frac{1}{a^2 x^2}+1\right)^{3/2}-\frac{2}{3 a^2 x^3}-\frac{1}{x}",1,"-(a*Sqrt[1 + 1/(a^2*x^2)])/2 - (a*(Sqrt[1 + 1/(a^2*x^2)] + 1/(a*x))^3)/6 - 1/(2*x)","A",4,3,12,0.2500,1,"{6338, 6715, 2117}"
56,1,73,0,0.2338418,"\int \frac{e^{2 \text{csch}^{-1}(a x)}}{x^3} \, dx","Int[E^(2*ArcCsch[a*x])/x^3,x]","-\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}{2 a^2 x^4}+\frac{1}{4} a^2 \text{csch}^{-1}(a x)-\frac{1}{2 x^2}","-\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}{2 a^2 x^4}+\frac{1}{4} a^2 \text{csch}^{-1}(a x)-\frac{1}{2 x^2}",1,"-1/(2*a^2*x^4) - Sqrt[1 + 1/(a^2*x^2)]/(2*a*x^3) - 1/(2*x^2) - (a*Sqrt[1 + 1/(a^2*x^2)])/(4*x) + (a^2*ArcCsch[a*x])/4","A",7,6,12,0.5000,1,"{6338, 6742, 335, 279, 321, 215}"
57,1,58,0,0.2330015,"\int \frac{e^{2 \text{csch}^{-1}(a x)}}{x^4} \, dx","Int[E^(2*ArcCsch[a*x])/x^4,x]","-\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{2}{5 a^2 x^5}-\frac{1}{3 x^3}","-\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{2}{5 a^2 x^5}-\frac{1}{3 x^3}",1,"(2*a^3*(1 + 1/(a^2*x^2))^(3/2))/3 - (2*a^3*(1 + 1/(a^2*x^2))^(5/2))/5 - 2/(5*a^2*x^5) - 1/(3*x^3)","A",6,4,12,0.3333,1,"{6338, 6742, 266, 43}"
58,1,96,0,0.2525606,"\int \frac{e^{2 \text{csch}^{-1}(a x)}}{x^5} \, dx","Int[E^(2*ArcCsch[a*x])/x^5,x]","\frac{a^3 \sqrt{\frac{1}{a^2 x^2}+1}}{8 x}-\frac{a \sqrt{\frac{1}{a^2 x^2}+1}}{12 x^3}-\frac{\sqrt{\frac{1}{a^2 x^2}+1}}{3 a x^5}-\frac{1}{3 a^2 x^6}-\frac{1}{8} a^4 \text{csch}^{-1}(a x)-\frac{1}{4 x^4}","\frac{a^3 \sqrt{\frac{1}{a^2 x^2}+1}}{8 x}-\frac{a \sqrt{\frac{1}{a^2 x^2}+1}}{12 x^3}-\frac{\sqrt{\frac{1}{a^2 x^2}+1}}{3 a x^5}-\frac{1}{3 a^2 x^6}-\frac{1}{8} a^4 \text{csch}^{-1}(a x)-\frac{1}{4 x^4}",1,"-1/(3*a^2*x^6) - Sqrt[1 + 1/(a^2*x^2)]/(3*a*x^5) - 1/(4*x^4) - (a*Sqrt[1 + 1/(a^2*x^2)])/(12*x^3) + (a^3*Sqrt[1 + 1/(a^2*x^2)])/(8*x) - (a^4*ArcCsch[a*x])/8","A",8,6,12,0.5000,1,"{6338, 6742, 335, 279, 321, 215}"
59,1,85,0,0.1037344,"\int \frac{e^{\text{csch}^{-1}(c x)} (d x)^m}{1+c^2 x^2} \, dx","Int[(E^ArcCsch[c*x]*(d*x)^m)/(1 + c^2*x^2),x]","\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)}","\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*(d*x)^(-1 + m)*Hypergeometric2F1[1/2, (1 - m)/2, (3 - m)/2, -(1/(c^2*x^2))])/(c^2*(1 - m))) + ((d*x)^m*Hypergeometric2F1[1, m/2, (2 + m)/2, -(c^2*x^2)])/(c*m)","A",4,3,23,0.1304,1,"{6342, 339, 364}"
60,1,92,0,0.1080445,"\int \frac{e^{\text{csch}^{-1}(c x)} x^5}{1+c^2 x^2} \, dx","Int[(E^ArcCsch[c*x]*x^5)/(1 + c^2*x^2),x]","\frac{x^4 \sqrt{\frac{1}{c^2 x^2}+1}}{4 c^2}+\frac{x^3}{3 c^3}-\frac{3 x^2 \sqrt{\frac{1}{c^2 x^2}+1}}{8 c^4}+\frac{3 \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{8 c^6}-\frac{x}{c^5}+\frac{\tan ^{-1}(c x)}{c^6}","\frac{x^4 \sqrt{\frac{1}{c^2 x^2}+1}}{4 c^2}+\frac{x^3}{3 c^3}-\frac{3 x^2 \sqrt{\frac{1}{c^2 x^2}+1}}{8 c^4}+\frac{3 \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{8 c^6}-\frac{x}{c^5}+\frac{\tan ^{-1}(c x)}{c^6}",1,"-(x/c^5) - (3*Sqrt[1 + 1/(c^2*x^2)]*x^2)/(8*c^4) + x^3/(3*c^3) + (Sqrt[1 + 1/(c^2*x^2)]*x^4)/(4*c^2) + ArcTan[c*x]/c^6 + (3*ArcTanh[Sqrt[1 + 1/(c^2*x^2)]])/(8*c^6)","A",9,7,21,0.3333,1,"{6342, 266, 51, 63, 208, 302, 203}"
61,1,72,0,0.0975695,"\int \frac{e^{\text{csch}^{-1}(c x)} x^4}{1+c^2 x^2} \, dx","Int[(E^ArcCsch[c*x]*x^4)/(1 + c^2*x^2),x]","\frac{x^3 \sqrt{\frac{1}{c^2 x^2}+1}}{3 c^2}+\frac{x^2}{2 c^3}-\frac{2 x \sqrt{\frac{1}{c^2 x^2}+1}}{3 c^4}-\frac{\log \left(c^2 x^2+1\right)}{2 c^5}","\frac{x^3 \sqrt{\frac{1}{c^2 x^2}+1}}{3 c^2}+\frac{x^2}{2 c^3}-\frac{2 x \sqrt{\frac{1}{c^2 x^2}+1}}{3 c^4}-\frac{\log \left(c^2 x^2+1\right)}{2 c^5}",1,"(-2*Sqrt[1 + 1/(c^2*x^2)]*x)/(3*c^4) + x^2/(2*c^3) + (Sqrt[1 + 1/(c^2*x^2)]*x^3)/(3*c^2) - Log[1 + c^2*x^2]/(2*c^5)","A",6,5,21,0.2381,1,"{6342, 271, 191, 266, 43}"
62,1,59,0,0.0897483,"\int \frac{e^{\text{csch}^{-1}(c x)} x^3}{1+c^2 x^2} \, dx","Int[(E^ArcCsch[c*x]*x^3)/(1 + c^2*x^2),x]","\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}+\frac{x}{c^3}-\frac{\tan ^{-1}(c x)}{c^4}","\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}+\frac{x}{c^3}-\frac{\tan ^{-1}(c x)}{c^4}",1,"x/c^3 + (Sqrt[1 + 1/(c^2*x^2)]*x^2)/(2*c^2) - ArcTan[c*x]/c^4 - ArcTanh[Sqrt[1 + 1/(c^2*x^2)]]/(2*c^4)","A",7,7,21,0.3333,1,"{6342, 266, 51, 63, 208, 321, 203}"
63,1,36,0,0.0698466,"\int \frac{e^{\text{csch}^{-1}(c x)} x^2}{1+c^2 x^2} \, dx","Int[(E^ArcCsch[c*x]*x^2)/(1 + c^2*x^2),x]","\frac{x \sqrt{\frac{1}{c^2 x^2}+1}}{c^2}+\frac{\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,"(Sqrt[1 + 1/(c^2*x^2)]*x)/c^2 + Log[1 + c^2*x^2]/(2*c^3)","A",3,3,21,0.1429,1,"{6342, 191, 260}"
64,1,27,0,0.0592035,"\int \frac{e^{\text{csch}^{-1}(c x)} x}{1+c^2 x^2} \, dx","Int[(E^ArcCsch[c*x]*x)/(1 + c^2*x^2),x]","\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\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 + ArcTanh[Sqrt[1 + 1/(c^2*x^2)]]/c^2","A",5,5,19,0.2632,1,"{6342, 266, 63, 208, 203}"
65,1,33,0,0.0428856,"\int \frac{e^{\text{csch}^{-1}(c x)}}{1+c^2 x^2} \, dx","Int[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{\text{csch}^{-1}(c x)}{c}","-\frac{\log \left(c^2 x^2+1\right)}{2 c}+\frac{\log (x)}{c}-\frac{\text{csch}^{-1}(c x)}{c}",1,"-(ArcCsch[c*x]/c) + Log[x]/c - Log[1 + c^2*x^2]/(2*c)","A",7,7,18,0.3889,1,"{6340, 335, 215, 266, 36, 29, 31}"
66,1,30,0,0.071148,"\int \frac{e^{\text{csch}^{-1}(c x)}}{x \left(1+c^2 x^2\right)} \, dx","Int[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",4,4,21,0.1905,1,"{6342, 261, 325, 203}"
67,1,60,0,0.0970317,"\int \frac{e^{\text{csch}^{-1}(c x)}}{x^2 \left(1+c^2 x^2\right)} \, dx","Int[E^ArcCsch[c*x]/(x^2*(1 + c^2*x^2)),x]","-\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)","-\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/(2*c*x^2) - Sqrt[1 + 1/(c^2*x^2)]/(2*x) + (c*ArcCsch[c*x])/2 - c*Log[x] + (c*Log[1 + c^2*x^2])/2","A",7,6,21,0.2857,1,"{6342, 335, 321, 215, 266, 44}"
68,1,61,0,0.0945817,"\int \frac{e^{\text{csch}^{-1}(c x)}}{x^3 \left(1+c^2 x^2\right)} \, dx","Int[E^ArcCsch[c*x]/(x^3*(1 + c^2*x^2)),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}","-\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,"c^2*Sqrt[1 + 1/(c^2*x^2)] - (c^2*(1 + 1/(c^2*x^2))^(3/2))/3 - 1/(3*c*x^3) + c/x + c^2*ArcTan[c*x]","A",7,5,21,0.2381,1,"{6342, 266, 43, 325, 203}"
69,1,61,0,0.0977974,"\int \frac{\text{csch}^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx","Int[ArcCsch[a + b*x]/((a*d)/b + d*x),x]","-\frac{\text{PolyLog}\left(2,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}","-\frac{\text{PolyLog}\left(2,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]^2/(2*d) - (ArcCsch[a + b*x]*Log[1 - E^(2*ArcCsch[a + b*x])])/d - PolyLog[2, E^(2*ArcCsch[a + b*x])]/(2*d)","A",8,8,19,0.4211,1,"{6320, 12, 6282, 5659, 3716, 2190, 2279, 2391}"
70,1,46,0,0.0582378,"\int x^3 \text{csch}^{-1}\left(a+b x^4\right) \, dx","Int[x^3*ArcCsch[a + b*x^4],x]","\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}","\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)*ArcCsch[a + b*x^4])/(4*b) + ArcTanh[Sqrt[1 + (a + b*x^4)^(-2)]]/(4*b)","A",6,6,12,0.5000,1,"{6715, 6314, 372, 266, 63, 207}"
71,1,46,0,0.0702649,"\int x^{-1+n} \text{csch}^{-1}\left(a+b x^n\right) \, dx","Int[x^(-1 + n)*ArcCsch[a + b*x^n],x]","\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}","\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)*ArcCsch[a + b*x^n])/(b*n) + ArcTanh[Sqrt[1 + (a + b*x^n)^(-2)]]/(b*n)","A",6,6,14,0.4286,1,"{6715, 6314, 372, 266, 63, 207}"