1,1,203,0,0.1553226,"\int x^3 \text{sech}^{-1}(a+b x) \, dx","Int[x^3*ArcSech[a + b*x],x]","-\frac{\left(17 a^2+2\right) \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{12 b^4}+\frac{\left(2 a^2+1\right) a \tan ^{-1}\left(\frac{\sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{a+b x}\right)}{2 b^4}-\frac{a^4 \text{sech}^{-1}(a+b x)}{4 b^4}-\frac{x^2 \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{12 b^2}+\frac{a (a+b x) \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{3 b^4}+\frac{1}{4} x^4 \text{sech}^{-1}(a+b x)","-\frac{\left(17 a^2+2\right) \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{12 b^4}+\frac{\left(2 a^2+1\right) a \tan ^{-1}\left(\frac{\sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{a+b x}\right)}{2 b^4}-\frac{a^4 \text{sech}^{-1}(a+b x)}{4 b^4}-\frac{x^2 \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{12 b^2}+\frac{a (a+b x) \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{3 b^4}+\frac{1}{4} x^4 \text{sech}^{-1}(a+b x)",1,"-((2 + 17*a^2)*Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x))/(12*b^4) - (x^2*Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x))/(12*b^2) + (a*(a + b*x)*Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x))/(3*b^4) - (a^4*ArcSech[a + b*x])/(4*b^4) + (x^4*ArcSech[a + b*x])/4 + (a*(1 + 2*a^2)*ArcTan[(Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x))/(a + b*x)])/(2*b^4)","A",8,7,10,0.7000,1,"{6321, 5468, 3782, 4048, 3770, 3767, 8}"
2,1,153,0,0.0985505,"\int x^2 \text{sech}^{-1}(a+b x) \, dx","Int[x^2*ArcSech[a + b*x],x]","-\frac{\left(6 a^2+1\right) \tan ^{-1}\left(\frac{\sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{a+b x}\right)}{6 b^3}+\frac{a^3 \text{sech}^{-1}(a+b x)}{3 b^3}+\frac{5 a \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{6 b^3}-\frac{x \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{6 b^2}+\frac{1}{3} x^3 \text{sech}^{-1}(a+b x)","-\frac{\left(6 a^2+1\right) \tan ^{-1}\left(\frac{\sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{a+b x}\right)}{6 b^3}+\frac{a^3 \text{sech}^{-1}(a+b x)}{3 b^3}+\frac{5 a \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{6 b^3}-\frac{x \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{6 b^2}+\frac{1}{3} x^3 \text{sech}^{-1}(a+b x)",1,"(5*a*Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x))/(6*b^3) - (x*Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x))/(6*b^2) + (a^3*ArcSech[a + b*x])/(3*b^3) + (x^3*ArcSech[a + b*x])/3 - ((1 + 6*a^2)*ArcTan[(Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x))/(a + b*x)])/(6*b^3)","A",7,6,10,0.6000,1,"{6321, 5468, 3782, 3770, 3767, 8}"
3,1,107,0,0.0617878,"\int x \text{sech}^{-1}(a+b x) \, dx","Int[x*ArcSech[a + b*x],x]","-\frac{a^2 \text{sech}^{-1}(a+b x)}{2 b^2}-\frac{\sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{2 b^2}+\frac{a \tan ^{-1}\left(\frac{\sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{a+b x}\right)}{b^2}+\frac{1}{2} x^2 \text{sech}^{-1}(a+b x)","-\frac{a^2 \text{sech}^{-1}(a+b x)}{2 b^2}-\frac{\sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{2 b^2}+\frac{a \tan ^{-1}\left(\frac{\sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{a+b x}\right)}{b^2}+\frac{1}{2} x^2 \text{sech}^{-1}(a+b x)",1,"-(Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x))/(2*b^2) - (a^2*ArcSech[a + b*x])/(2*b^2) + (x^2*ArcSech[a + b*x])/2 + (a*ArcTan[(Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x))/(a + b*x)])/b^2","A",6,6,8,0.7500,1,"{6321, 5468, 3773, 3770, 3767, 8}"
4,1,44,0,0.0556131,"\int \text{sech}^{-1}(a+b x) \, dx","Int[ArcSech[a + b*x],x]","\frac{(a+b x) \text{sech}^{-1}(a+b x)}{b}-\frac{2 \tan ^{-1}\left(\sqrt{\frac{-a-b x+1}{a+b x+1}}\right)}{b}","\frac{(a+b x) \text{sech}^{-1}(a+b x)}{b}-\frac{2 \tan ^{-1}\left(\sqrt{\frac{-a-b x+1}{a+b x+1}}\right)}{b}",1,"((a + b*x)*ArcSech[a + b*x])/b - (2*ArcTan[Sqrt[(1 - a - b*x)/(1 + a + b*x)]])/b","A",4,4,6,0.6667,1,"{6313, 1961, 12, 203}"
5,1,170,0,0.2897609,"\int \frac{\text{sech}^{-1}(a+b x)}{x} \, dx","Int[ArcSech[a + b*x]/x,x]","\text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\frac{1}{2} \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a+b x)}\right)+\text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\text{sech}^{-1}(a+b x) \log \left(e^{2 \text{sech}^{-1}(a+b x)}+1\right)","\text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\frac{1}{2} \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a+b x)}\right)+\text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\text{sech}^{-1}(a+b x) \log \left(e^{2 \text{sech}^{-1}(a+b x)}+1\right)",1,"ArcSech[a + b*x]*Log[1 - (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])] + ArcSech[a + b*x]*Log[1 - (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])] - ArcSech[a + b*x]*Log[1 + E^(2*ArcSech[a + b*x])] + PolyLog[2, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])] + PolyLog[2, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])] - PolyLog[2, -E^(2*ArcSech[a + b*x])]/2","A",14,8,10,0.8000,1,"{6321, 5595, 5570, 3718, 2190, 2279, 2391, 5562}"
6,1,70,0,0.105885,"\int \frac{\text{sech}^{-1}(a+b x)}{x^2} \, dx","Int[ArcSech[a + b*x]/x^2,x]","\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{a+1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{1-a}}\right)}{a \sqrt{1-a^2}}-\frac{b \text{sech}^{-1}(a+b x)}{a}-\frac{\text{sech}^{-1}(a+b x)}{x}","\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{a+1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{1-a}}\right)}{a \sqrt{1-a^2}}-\frac{b \text{sech}^{-1}(a+b x)}{a}-\frac{\text{sech}^{-1}(a+b x)}{x}",1,"-((b*ArcSech[a + b*x])/a) - ArcSech[a + b*x]/x + (2*b*ArcTanh[(Sqrt[1 + a]*Tanh[ArcSech[a + b*x]/2])/Sqrt[1 - a]])/(a*Sqrt[1 - a^2])","A",5,5,10,0.5000,1,"{6321, 5468, 3783, 2659, 208}"
7,1,133,0,0.2037805,"\int \frac{\text{sech}^{-1}(a+b x)}{x^3} \, dx","Int[ArcSech[a + b*x]/x^3,x]","\frac{b^2 \text{sech}^{-1}(a+b x)}{2 a^2}-\frac{\left(1-2 a^2\right) b^2 \tanh ^{-1}\left(\frac{\sqrt{a+1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{1-a}}\right)}{a^2 \left(1-a^2\right)^{3/2}}+\frac{b \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{2 a \left(1-a^2\right) x}-\frac{\text{sech}^{-1}(a+b x)}{2 x^2}","\frac{b^2 \text{sech}^{-1}(a+b x)}{2 a^2}-\frac{\left(1-2 a^2\right) b^2 \tanh ^{-1}\left(\frac{\sqrt{a+1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{1-a}}\right)}{a^2 \left(1-a^2\right)^{3/2}}+\frac{b \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{2 a \left(1-a^2\right) x}-\frac{\text{sech}^{-1}(a+b x)}{2 x^2}",1,"(b*Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x))/(2*a*(1 - a^2)*x) + (b^2*ArcSech[a + b*x])/(2*a^2) - ArcSech[a + b*x]/(2*x^2) - ((1 - 2*a^2)*b^2*ArcTanh[(Sqrt[1 + a]*Tanh[ArcSech[a + b*x]/2])/Sqrt[1 - a]])/(a^2*(1 - a^2)^(3/2))","A",7,7,10,0.7000,1,"{6321, 5468, 3785, 3919, 3831, 2659, 208}"
8,1,197,0,0.3159074,"\int \frac{\text{sech}^{-1}(a+b x)}{x^4} \, dx","Int[ArcSech[a + b*x]/x^4,x]","-\frac{\left(2-5 a^2\right) b^2 \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{6 a^2 \left(1-a^2\right)^2 x}-\frac{b^3 \text{sech}^{-1}(a+b x)}{3 a^3}+\frac{\left(6 a^4-5 a^2+2\right) b^3 \tanh ^{-1}\left(\frac{\sqrt{a+1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{1-a}}\right)}{3 a^3 \left(1-a^2\right)^{5/2}}+\frac{b \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{6 a \left(1-a^2\right) x^2}-\frac{\text{sech}^{-1}(a+b x)}{3 x^3}","-\frac{\left(2-5 a^2\right) b^2 \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{6 a^2 \left(1-a^2\right)^2 x}-\frac{b^3 \text{sech}^{-1}(a+b x)}{3 a^3}+\frac{\left(6 a^4-5 a^2+2\right) b^3 \tanh ^{-1}\left(\frac{\sqrt{a+1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{1-a}}\right)}{3 a^3 \left(1-a^2\right)^{5/2}}+\frac{b \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{6 a \left(1-a^2\right) x^2}-\frac{\text{sech}^{-1}(a+b x)}{3 x^3}",1,"(b*Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x))/(6*a*(1 - a^2)*x^2) - ((2 - 5*a^2)*b^2*Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x))/(6*a^2*(1 - a^2)^2*x) - (b^3*ArcSech[a + b*x])/(3*a^3) - ArcSech[a + b*x]/(3*x^3) + ((2 - 5*a^2 + 6*a^4)*b^3*ArcTanh[(Sqrt[1 + a]*Tanh[ArcSech[a + b*x]/2])/Sqrt[1 - a]])/(3*a^3*(1 - a^2)^(5/2))","A",8,8,10,0.8000,1,"{6321, 5468, 3785, 4060, 3919, 3831, 2659, 208}"
9,1,279,0,0.2416251,"\int x^2 \text{sech}^{-1}(a+b x)^2 \, dx","Int[x^2*ArcSech[a + b*x]^2,x]","\frac{2 i a^2 \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a+b x)}\right)}{b^3}-\frac{2 i a^2 \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a+b x)}\right)}{b^3}+\frac{i \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a+b x)}\right)}{3 b^3}-\frac{i \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a+b x)}\right)}{3 b^3}+\frac{a^3 \text{sech}^{-1}(a+b x)^2}{3 b^3}-\frac{4 a^2 \text{sech}^{-1}(a+b x) \tan ^{-1}\left(e^{\text{sech}^{-1}(a+b x)}\right)}{b^3}+\frac{2 a \log (a+b x)}{b^3}+\frac{2 a \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)}{b^3}-\frac{(a+b x) \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)}{3 b^3}-\frac{2 \text{sech}^{-1}(a+b x) \tan ^{-1}\left(e^{\text{sech}^{-1}(a+b x)}\right)}{3 b^3}+\frac{1}{3} x^3 \text{sech}^{-1}(a+b x)^2-\frac{x}{3 b^2}","\frac{2 i a^2 \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a+b x)}\right)}{b^3}-\frac{2 i a^2 \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a+b x)}\right)}{b^3}+\frac{i \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a+b x)}\right)}{3 b^3}-\frac{i \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a+b x)}\right)}{3 b^3}+\frac{a^3 \text{sech}^{-1}(a+b x)^2}{3 b^3}-\frac{4 a^2 \text{sech}^{-1}(a+b x) \tan ^{-1}\left(e^{\text{sech}^{-1}(a+b x)}\right)}{b^3}+\frac{2 a \log (a+b x)}{b^3}+\frac{2 a \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)}{b^3}-\frac{(a+b x) \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)}{3 b^3}-\frac{2 \text{sech}^{-1}(a+b x) \tan ^{-1}\left(e^{\text{sech}^{-1}(a+b x)}\right)}{3 b^3}+\frac{1}{3} x^3 \text{sech}^{-1}(a+b x)^2-\frac{x}{3 b^2}",1,"-x/(3*b^2) + (2*a*Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x)*ArcSech[a + b*x])/b^3 - ((a + b*x)*Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x)*ArcSech[a + b*x])/(3*b^3) + (a^3*ArcSech[a + b*x]^2)/(3*b^3) + (x^3*ArcSech[a + b*x]^2)/3 - (2*ArcSech[a + b*x]*ArcTan[E^ArcSech[a + b*x]])/(3*b^3) - (4*a^2*ArcSech[a + b*x]*ArcTan[E^ArcSech[a + b*x]])/b^3 + (2*a*Log[a + b*x])/b^3 + ((I/3)*PolyLog[2, (-I)*E^ArcSech[a + b*x]])/b^3 + ((2*I)*a^2*PolyLog[2, (-I)*E^ArcSech[a + b*x]])/b^3 - ((I/3)*PolyLog[2, I*E^ArcSech[a + b*x]])/b^3 - ((2*I)*a^2*PolyLog[2, I*E^ArcSech[a + b*x]])/b^3","A",17,9,12,0.7500,1,"{6321, 5468, 4190, 4180, 2279, 2391, 4184, 3475, 4185}"
10,1,149,0,0.1383422,"\int x \text{sech}^{-1}(a+b x)^2 \, dx","Int[x*ArcSech[a + b*x]^2,x]","-\frac{2 i a \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}+\frac{2 i a \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}-\frac{a^2 \text{sech}^{-1}(a+b x)^2}{2 b^2}-\frac{\log (a+b x)}{b^2}-\frac{\sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)}{b^2}+\frac{4 a \text{sech}^{-1}(a+b x) \tan ^{-1}\left(e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}+\frac{1}{2} x^2 \text{sech}^{-1}(a+b x)^2","-\frac{2 i a \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}+\frac{2 i a \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}-\frac{a^2 \text{sech}^{-1}(a+b x)^2}{2 b^2}-\frac{\log (a+b x)}{b^2}-\frac{\sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)}{b^2}+\frac{4 a \text{sech}^{-1}(a+b x) \tan ^{-1}\left(e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}+\frac{1}{2} x^2 \text{sech}^{-1}(a+b x)^2",1,"-((Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x)*ArcSech[a + b*x])/b^2) - (a^2*ArcSech[a + b*x]^2)/(2*b^2) + (x^2*ArcSech[a + b*x]^2)/2 + (4*a*ArcSech[a + b*x]*ArcTan[E^ArcSech[a + b*x]])/b^2 - Log[a + b*x]/b^2 - ((2*I)*a*PolyLog[2, (-I)*E^ArcSech[a + b*x]])/b^2 + ((2*I)*a*PolyLog[2, I*E^ArcSech[a + b*x]])/b^2","A",11,8,10,0.8000,1,"{6321, 5468, 4190, 4180, 2279, 2391, 4184, 3475}"
11,1,80,0,0.067922,"\int \text{sech}^{-1}(a+b x)^2 \, dx","Int[ArcSech[a + b*x]^2,x]","\frac{2 i \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a+b x)}\right)}{b}-\frac{2 i \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \text{sech}^{-1}(a+b x)^2}{b}-\frac{4 \text{sech}^{-1}(a+b x) \tan ^{-1}\left(e^{\text{sech}^{-1}(a+b x)}\right)}{b}","\frac{2 i \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a+b x)}\right)}{b}-\frac{2 i \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \text{sech}^{-1}(a+b x)^2}{b}-\frac{4 \text{sech}^{-1}(a+b x) \tan ^{-1}\left(e^{\text{sech}^{-1}(a+b x)}\right)}{b}",1,"((a + b*x)*ArcSech[a + b*x]^2)/b - (4*ArcSech[a + b*x]*ArcTan[E^ArcSech[a + b*x]])/b + ((2*I)*PolyLog[2, (-I)*E^ArcSech[a + b*x]])/b - ((2*I)*PolyLog[2, I*E^ArcSech[a + b*x]])/b","A",8,6,8,0.7500,1,"{6315, 6279, 5418, 4180, 2279, 2391}"
12,1,274,0,0.4634817,"\int \frac{\text{sech}^{-1}(a+b x)^2}{x} \, dx","Int[ArcSech[a + b*x]^2/x,x]","2 \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+2 \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-2 \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-2 \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a+b x)}\right)+\frac{1}{2} \text{PolyLog}\left(3,-e^{2 \text{sech}^{-1}(a+b x)}\right)+\text{sech}^{-1}(a+b x)^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\text{sech}^{-1}(a+b x)^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\text{sech}^{-1}(a+b x)^2 \log \left(e^{2 \text{sech}^{-1}(a+b x)}+1\right)","2 \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+2 \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-2 \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-2 \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a+b x)}\right)+\frac{1}{2} \text{PolyLog}\left(3,-e^{2 \text{sech}^{-1}(a+b x)}\right)+\text{sech}^{-1}(a+b x)^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\text{sech}^{-1}(a+b x)^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\text{sech}^{-1}(a+b x)^2 \log \left(e^{2 \text{sech}^{-1}(a+b x)}+1\right)",1,"ArcSech[a + b*x]^2*Log[1 - (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])] + ArcSech[a + b*x]^2*Log[1 - (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])] - ArcSech[a + b*x]^2*Log[1 + E^(2*ArcSech[a + b*x])] + 2*ArcSech[a + b*x]*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])] + 2*ArcSech[a + b*x]*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])] - ArcSech[a + b*x]*PolyLog[2, -E^(2*ArcSech[a + b*x])] - 2*PolyLog[3, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])] - 2*PolyLog[3, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])] + PolyLog[3, -E^(2*ArcSech[a + b*x])]/2","A",17,9,12,0.7500,1,"{6321, 5595, 5570, 3718, 2190, 2531, 2282, 6589, 5562}"
13,1,224,0,0.3889057,"\int \frac{\text{sech}^{-1}(a+b x)^2}{x^2} \, dx","Int[ArcSech[a + b*x]^2/x^2,x]","\frac{2 b \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}-\frac{2 b \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}+\frac{2 b \text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}-\frac{2 b \text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{b \text{sech}^{-1}(a+b x)^2}{a}-\frac{\text{sech}^{-1}(a+b x)^2}{x}","\frac{2 b \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}-\frac{2 b \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}+\frac{2 b \text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}-\frac{2 b \text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{b \text{sech}^{-1}(a+b x)^2}{a}-\frac{\text{sech}^{-1}(a+b x)^2}{x}",1,"-((b*ArcSech[a + b*x]^2)/a) - ArcSech[a + b*x]^2/x + (2*b*ArcSech[a + b*x]*Log[1 - (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) - (2*b*ArcSech[a + b*x]*Log[1 - (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) + (2*b*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) - (2*b*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2])","A",12,8,12,0.6667,1,"{6321, 5468, 4191, 3320, 2264, 2190, 2279, 2391}"
14,1,537,0,0.7498425,"\int \frac{\text{sech}^{-1}(a+b x)^2}{x^3} \, dx","Int[ArcSech[a + b*x]^2/x^3,x]","-\frac{2 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a^2 \sqrt{1-a^2}}+\frac{b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a^2 \left(1-a^2\right)^{3/2}}+\frac{2 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a^2 \sqrt{1-a^2}}-\frac{b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a^2 \left(1-a^2\right)^{3/2}}+\frac{b^2 \log \left(\frac{x}{a+b x}\right)}{a^2 \left(1-a^2\right)}+\frac{b^2 \text{sech}^{-1}(a+b x)^2}{2 a^2}+\frac{b^2 \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)}{a \left(1-a^2\right) (a+b x) \left(1-\frac{a}{a+b x}\right)}-\frac{2 b^2 \text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a^2 \sqrt{1-a^2}}+\frac{b^2 \text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a^2 \left(1-a^2\right)^{3/2}}+\frac{2 b^2 \text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a^2 \sqrt{1-a^2}}-\frac{b^2 \text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a^2 \left(1-a^2\right)^{3/2}}-\frac{\text{sech}^{-1}(a+b x)^2}{2 x^2}","-\frac{2 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a^2 \sqrt{1-a^2}}+\frac{b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a^2 \left(1-a^2\right)^{3/2}}+\frac{2 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a^2 \sqrt{1-a^2}}-\frac{b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a^2 \left(1-a^2\right)^{3/2}}+\frac{b^2 \log \left(\frac{x}{a+b x}\right)}{a^2 \left(1-a^2\right)}+\frac{b^2 \text{sech}^{-1}(a+b x)^2}{2 a^2}+\frac{b^2 \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)}{a \left(1-a^2\right) (a+b x) \left(1-\frac{a}{a+b x}\right)}-\frac{2 b^2 \text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a^2 \sqrt{1-a^2}}+\frac{b^2 \text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a^2 \left(1-a^2\right)^{3/2}}+\frac{2 b^2 \text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a^2 \sqrt{1-a^2}}-\frac{b^2 \text{sech}^{-1}(a+b x) \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a^2 \left(1-a^2\right)^{3/2}}-\frac{\text{sech}^{-1}(a+b x)^2}{2 x^2}",1,"(b^2*Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x)*ArcSech[a + b*x])/(a*(1 - a^2)*(a + b*x)*(1 - a/(a + b*x))) + (b^2*ArcSech[a + b*x]^2)/(2*a^2) - ArcSech[a + b*x]^2/(2*x^2) + (b^2*ArcSech[a + b*x]*Log[1 - (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a^2*(1 - a^2)^(3/2)) - (2*b^2*ArcSech[a + b*x]*Log[1 - (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a^2*Sqrt[1 - a^2]) - (b^2*ArcSech[a + b*x]*Log[1 - (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a^2*(1 - a^2)^(3/2)) + (2*b^2*ArcSech[a + b*x]*Log[1 - (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a^2*Sqrt[1 - a^2]) + (b^2*Log[x/(a + b*x)])/(a^2*(1 - a^2)) + (b^2*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a^2*(1 - a^2)^(3/2)) - (2*b^2*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a^2*Sqrt[1 - a^2]) - (b^2*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a^2*(1 - a^2)^(3/2)) + (2*b^2*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a^2*Sqrt[1 - a^2])","A",23,11,12,0.9167,1,"{6321, 5468, 4191, 3324, 3320, 2264, 2190, 2279, 2391, 2668, 31}"
15,1,260,0,0.2572065,"\int x \text{sech}^{-1}(a+b x)^3 \, dx","Int[x*ArcSech[a + b*x]^3,x]","-\frac{6 i a \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}+\frac{6 i a \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}+\frac{3 \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a+b x)}\right)}{2 b^2}+\frac{6 i a \text{PolyLog}\left(3,-i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}-\frac{6 i a \text{PolyLog}\left(3,i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}-\frac{a^2 \text{sech}^{-1}(a+b x)^3}{2 b^2}-\frac{3 \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)^2}{2 b^2}-\frac{3 \text{sech}^{-1}(a+b x)^2}{2 b^2}+\frac{3 \text{sech}^{-1}(a+b x) \log \left(e^{2 \text{sech}^{-1}(a+b x)}+1\right)}{b^2}+\frac{6 a \text{sech}^{-1}(a+b x)^2 \tan ^{-1}\left(e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}+\frac{1}{2} x^2 \text{sech}^{-1}(a+b x)^3","-\frac{6 i a \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}+\frac{6 i a \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}+\frac{3 \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a+b x)}\right)}{2 b^2}+\frac{6 i a \text{PolyLog}\left(3,-i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}-\frac{6 i a \text{PolyLog}\left(3,i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}-\frac{a^2 \text{sech}^{-1}(a+b x)^3}{2 b^2}-\frac{3 \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)^2}{2 b^2}-\frac{3 \text{sech}^{-1}(a+b x)^2}{2 b^2}+\frac{3 \text{sech}^{-1}(a+b x) \log \left(e^{2 \text{sech}^{-1}(a+b x)}+1\right)}{b^2}+\frac{6 a \text{sech}^{-1}(a+b x)^2 \tan ^{-1}\left(e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}+\frac{1}{2} x^2 \text{sech}^{-1}(a+b x)^3",1,"(-3*ArcSech[a + b*x]^2)/(2*b^2) - (3*Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x)*ArcSech[a + b*x]^2)/(2*b^2) - (a^2*ArcSech[a + b*x]^3)/(2*b^2) + (x^2*ArcSech[a + b*x]^3)/2 + (6*a*ArcSech[a + b*x]^2*ArcTan[E^ArcSech[a + b*x]])/b^2 + (3*ArcSech[a + b*x]*Log[1 + E^(2*ArcSech[a + b*x])])/b^2 - ((6*I)*a*ArcSech[a + b*x]*PolyLog[2, (-I)*E^ArcSech[a + b*x]])/b^2 + ((6*I)*a*ArcSech[a + b*x]*PolyLog[2, I*E^ArcSech[a + b*x]])/b^2 + (3*PolyLog[2, -E^(2*ArcSech[a + b*x])])/(2*b^2) + ((6*I)*a*PolyLog[3, (-I)*E^ArcSech[a + b*x]])/b^2 - ((6*I)*a*PolyLog[3, I*E^ArcSech[a + b*x]])/b^2","A",16,12,10,1.200,1,"{6321, 5468, 4190, 4180, 2531, 2282, 6589, 4184, 3718, 2190, 2279, 2391}"
16,1,136,0,0.1047826,"\int \text{sech}^{-1}(a+b x)^3 \, dx","Int[ArcSech[a + b*x]^3,x]","\frac{6 i \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a+b x)}\right)}{b}-\frac{6 i \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a+b x)}\right)}{b}-\frac{6 i \text{PolyLog}\left(3,-i e^{\text{sech}^{-1}(a+b x)}\right)}{b}+\frac{6 i \text{PolyLog}\left(3,i e^{\text{sech}^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \text{sech}^{-1}(a+b x)^3}{b}-\frac{6 \text{sech}^{-1}(a+b x)^2 \tan ^{-1}\left(e^{\text{sech}^{-1}(a+b x)}\right)}{b}","\frac{6 i \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a+b x)}\right)}{b}-\frac{6 i \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a+b x)}\right)}{b}-\frac{6 i \text{PolyLog}\left(3,-i e^{\text{sech}^{-1}(a+b x)}\right)}{b}+\frac{6 i \text{PolyLog}\left(3,i e^{\text{sech}^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \text{sech}^{-1}(a+b x)^3}{b}-\frac{6 \text{sech}^{-1}(a+b x)^2 \tan ^{-1}\left(e^{\text{sech}^{-1}(a+b x)}\right)}{b}",1,"((a + b*x)*ArcSech[a + b*x]^3)/b - (6*ArcSech[a + b*x]^2*ArcTan[E^ArcSech[a + b*x]])/b + ((6*I)*ArcSech[a + b*x]*PolyLog[2, (-I)*E^ArcSech[a + b*x]])/b - ((6*I)*ArcSech[a + b*x]*PolyLog[2, I*E^ArcSech[a + b*x]])/b - ((6*I)*PolyLog[3, (-I)*E^ArcSech[a + b*x]])/b + ((6*I)*PolyLog[3, I*E^ArcSech[a + b*x]])/b","A",10,7,8,0.8750,1,"{6315, 6279, 5418, 4180, 2531, 2282, 6589}"
17,1,378,0,0.5107701,"\int \frac{\text{sech}^{-1}(a+b x)^3}{x} \, dx","Int[ArcSech[a + b*x]^3/x,x]","3 \text{sech}^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+3 \text{sech}^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-6 \text{sech}^{-1}(a+b x) \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-6 \text{sech}^{-1}(a+b x) \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+6 \text{PolyLog}\left(4,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+6 \text{PolyLog}\left(4,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\frac{3}{2} \text{sech}^{-1}(a+b x)^2 \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a+b x)}\right)+\frac{3}{2} \text{sech}^{-1}(a+b x) \text{PolyLog}\left(3,-e^{2 \text{sech}^{-1}(a+b x)}\right)-\frac{3}{4} \text{PolyLog}\left(4,-e^{2 \text{sech}^{-1}(a+b x)}\right)+\text{sech}^{-1}(a+b x)^3 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\text{sech}^{-1}(a+b x)^3 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\text{sech}^{-1}(a+b x)^3 \log \left(e^{2 \text{sech}^{-1}(a+b x)}+1\right)","3 \text{sech}^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+3 \text{sech}^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-6 \text{sech}^{-1}(a+b x) \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-6 \text{sech}^{-1}(a+b x) \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+6 \text{PolyLog}\left(4,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+6 \text{PolyLog}\left(4,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\frac{3}{2} \text{sech}^{-1}(a+b x)^2 \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a+b x)}\right)+\frac{3}{2} \text{sech}^{-1}(a+b x) \text{PolyLog}\left(3,-e^{2 \text{sech}^{-1}(a+b x)}\right)-\frac{3}{4} \text{PolyLog}\left(4,-e^{2 \text{sech}^{-1}(a+b x)}\right)+\text{sech}^{-1}(a+b x)^3 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\text{sech}^{-1}(a+b x)^3 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\text{sech}^{-1}(a+b x)^3 \log \left(e^{2 \text{sech}^{-1}(a+b x)}+1\right)",1,"ArcSech[a + b*x]^3*Log[1 - (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])] + ArcSech[a + b*x]^3*Log[1 - (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])] - ArcSech[a + b*x]^3*Log[1 + E^(2*ArcSech[a + b*x])] + 3*ArcSech[a + b*x]^2*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])] + 3*ArcSech[a + b*x]^2*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])] - (3*ArcSech[a + b*x]^2*PolyLog[2, -E^(2*ArcSech[a + b*x])])/2 - 6*ArcSech[a + b*x]*PolyLog[3, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])] - 6*ArcSech[a + b*x]*PolyLog[3, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])] + (3*ArcSech[a + b*x]*PolyLog[3, -E^(2*ArcSech[a + b*x])])/2 + 6*PolyLog[4, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])] + 6*PolyLog[4, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])] - (3*PolyLog[4, -E^(2*ArcSech[a + b*x])])/4","A",20,10,12,0.8333,1,"{6321, 5595, 5570, 3718, 2190, 2531, 6609, 2282, 6589, 5562}"
18,1,330,0,0.5752158,"\int \frac{\text{sech}^{-1}(a+b x)^3}{x^2} \, dx","Int[ArcSech[a + b*x]^3/x^2,x]","\frac{6 b \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}-\frac{6 b \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{6 b \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{6 b \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}+\frac{3 b \text{sech}^{-1}(a+b x)^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}-\frac{3 b \text{sech}^{-1}(a+b x)^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{b \text{sech}^{-1}(a+b x)^3}{a}-\frac{\text{sech}^{-1}(a+b x)^3}{x}","\frac{6 b \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}-\frac{6 b \text{sech}^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{6 b \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{6 b \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}+\frac{3 b \text{sech}^{-1}(a+b x)^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}-\frac{3 b \text{sech}^{-1}(a+b x)^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{b \text{sech}^{-1}(a+b x)^3}{a}-\frac{\text{sech}^{-1}(a+b x)^3}{x}",1,"-((b*ArcSech[a + b*x]^3)/a) - ArcSech[a + b*x]^3/x + (3*b*ArcSech[a + b*x]^2*Log[1 - (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) - (3*b*ArcSech[a + b*x]^2*Log[1 - (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) + (6*b*ArcSech[a + b*x]*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) - (6*b*ArcSech[a + b*x]*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) - (6*b*PolyLog[3, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) + (6*b*PolyLog[3, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2])","A",14,9,12,0.7500,1,"{6321, 5468, 4191, 3320, 2264, 2190, 2531, 2282, 6589}"
19,1,965,0,1.3379302,"\int \frac{\text{sech}^{-1}(a+b x)^3}{x^3} \, dx","Int[ArcSech[a + b*x]^3/x^3,x]","\frac{b^2 \text{sech}^{-1}(a+b x)^3}{2 a^2}-\frac{\text{sech}^{-1}(a+b x)^3}{2 x^2}-\frac{3 b^2 \text{sech}^{-1}(a+b x)^2}{2 a^2 \left(1-a^2\right)}-\frac{3 b^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right) \text{sech}^{-1}(a+b x)^2}{a^2 \sqrt{1-a^2}}+\frac{3 b^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right) \text{sech}^{-1}(a+b x)^2}{2 a^2 \left(1-a^2\right)^{3/2}}+\frac{3 b^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right) \text{sech}^{-1}(a+b x)^2}{a^2 \sqrt{1-a^2}}-\frac{3 b^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right) \text{sech}^{-1}(a+b x)^2}{2 a^2 \left(1-a^2\right)^{3/2}}+\frac{3 b^2 \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)^2}{2 a \left(1-a^2\right) (a+b x) \left(1-\frac{a}{a+b x}\right)}+\frac{3 b^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right) \text{sech}^{-1}(a+b x)}{a^2 \left(1-a^2\right)}+\frac{3 b^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right) \text{sech}^{-1}(a+b x)}{a^2 \left(1-a^2\right)}-\frac{6 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right) \text{sech}^{-1}(a+b x)}{a^2 \sqrt{1-a^2}}+\frac{3 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right) \text{sech}^{-1}(a+b x)}{a^2 \left(1-a^2\right)^{3/2}}+\frac{6 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right) \text{sech}^{-1}(a+b x)}{a^2 \sqrt{1-a^2}}-\frac{3 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right) \text{sech}^{-1}(a+b x)}{a^2 \left(1-a^2\right)^{3/2}}+\frac{3 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a^2 \left(1-a^2\right)}+\frac{3 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a^2 \left(1-a^2\right)}+\frac{6 b^2 \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a^2 \sqrt{1-a^2}}-\frac{3 b^2 \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a^2 \left(1-a^2\right)^{3/2}}-\frac{6 b^2 \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a^2 \sqrt{1-a^2}}+\frac{3 b^2 \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a^2 \left(1-a^2\right)^{3/2}}","\frac{b^2 \text{sech}^{-1}(a+b x)^3}{2 a^2}-\frac{\text{sech}^{-1}(a+b x)^3}{2 x^2}-\frac{3 b^2 \text{sech}^{-1}(a+b x)^2}{2 a^2 \left(1-a^2\right)}-\frac{3 b^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right) \text{sech}^{-1}(a+b x)^2}{a^2 \sqrt{1-a^2}}+\frac{3 b^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right) \text{sech}^{-1}(a+b x)^2}{2 a^2 \left(1-a^2\right)^{3/2}}+\frac{3 b^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right) \text{sech}^{-1}(a+b x)^2}{a^2 \sqrt{1-a^2}}-\frac{3 b^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right) \text{sech}^{-1}(a+b x)^2}{2 a^2 \left(1-a^2\right)^{3/2}}+\frac{3 b^2 \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)^2}{2 a \left(1-a^2\right) (a+b x) \left(1-\frac{a}{a+b x}\right)}+\frac{3 b^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right) \text{sech}^{-1}(a+b x)}{a^2 \left(1-a^2\right)}+\frac{3 b^2 \log \left(1-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right) \text{sech}^{-1}(a+b x)}{a^2 \left(1-a^2\right)}-\frac{6 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right) \text{sech}^{-1}(a+b x)}{a^2 \sqrt{1-a^2}}+\frac{3 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right) \text{sech}^{-1}(a+b x)}{a^2 \left(1-a^2\right)^{3/2}}+\frac{6 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right) \text{sech}^{-1}(a+b x)}{a^2 \sqrt{1-a^2}}-\frac{3 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right) \text{sech}^{-1}(a+b x)}{a^2 \left(1-a^2\right)^{3/2}}+\frac{3 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a^2 \left(1-a^2\right)}+\frac{3 b^2 \text{PolyLog}\left(2,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a^2 \left(1-a^2\right)}+\frac{6 b^2 \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a^2 \sqrt{1-a^2}}-\frac{3 b^2 \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a^2 \left(1-a^2\right)^{3/2}}-\frac{6 b^2 \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a^2 \sqrt{1-a^2}}+\frac{3 b^2 \text{PolyLog}\left(3,\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a^2 \left(1-a^2\right)^{3/2}}",1,"(-3*b^2*ArcSech[a + b*x]^2)/(2*a^2*(1 - a^2)) + (3*b^2*Sqrt[(1 - a - b*x)/(1 + a + b*x)]*(1 + a + b*x)*ArcSech[a + b*x]^2)/(2*a*(1 - a^2)*(a + b*x)*(1 - a/(a + b*x))) + (b^2*ArcSech[a + b*x]^3)/(2*a^2) - ArcSech[a + b*x]^3/(2*x^2) + (3*b^2*ArcSech[a + b*x]*Log[1 - (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a^2*(1 - a^2)) + (3*b^2*ArcSech[a + b*x]^2*Log[1 - (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(2*a^2*(1 - a^2)^(3/2)) - (3*b^2*ArcSech[a + b*x]^2*Log[1 - (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a^2*Sqrt[1 - a^2]) + (3*b^2*ArcSech[a + b*x]*Log[1 - (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a^2*(1 - a^2)) - (3*b^2*ArcSech[a + b*x]^2*Log[1 - (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(2*a^2*(1 - a^2)^(3/2)) + (3*b^2*ArcSech[a + b*x]^2*Log[1 - (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a^2*Sqrt[1 - a^2]) + (3*b^2*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a^2*(1 - a^2)) + (3*b^2*ArcSech[a + b*x]*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a^2*(1 - a^2)^(3/2)) - (6*b^2*ArcSech[a + b*x]*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a^2*Sqrt[1 - a^2]) + (3*b^2*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a^2*(1 - a^2)) - (3*b^2*ArcSech[a + b*x]*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a^2*(1 - a^2)^(3/2)) + (6*b^2*ArcSech[a + b*x]*PolyLog[2, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a^2*Sqrt[1 - a^2]) - (3*b^2*PolyLog[3, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a^2*(1 - a^2)^(3/2)) + (6*b^2*PolyLog[3, (a*E^ArcSech[a + b*x])/(1 - Sqrt[1 - a^2])])/(a^2*Sqrt[1 - a^2]) + (3*b^2*PolyLog[3, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a^2*(1 - a^2)^(3/2)) - (6*b^2*PolyLog[3, (a*E^ArcSech[a + b*x])/(1 + Sqrt[1 - a^2])])/(a^2*Sqrt[1 - a^2])","A",32,13,12,1.083,1,"{6321, 5468, 4191, 3324, 3320, 2264, 2190, 2531, 2282, 6589, 5562, 2279, 2391}"
20,1,164,0,0.0304525,"\int x^3 \text{sech}^{-1}\left(\sqrt{x}\right) \, dx","Int[x^3*ArcSech[Sqrt[x]],x]","\frac{1}{4} x^4 \text{sech}^{-1}\left(\sqrt{x}\right)+\frac{(1-x)^4}{28 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}-\frac{3 (1-x)^3}{20 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}+\frac{(1-x)^2}{4 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}-\frac{1-x}{4 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}","\frac{1}{4} x^4 \text{sech}^{-1}\left(\sqrt{x}\right)+\frac{(1-x)^4}{28 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}-\frac{3 (1-x)^3}{20 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}+\frac{(1-x)^2}{4 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}-\frac{1-x}{4 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}",1,"-(1 - x)/(4*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*Sqrt[x]) + (1 - x)^2/(4*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*Sqrt[x]) - (3*(1 - x)^3)/(20*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*Sqrt[x]) + (1 - x)^4/(28*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*Sqrt[x]) + (x^4*ArcSech[Sqrt[x]])/4","A",4,3,10,0.3000,1,"{6345, 12, 43}"
21,1,126,0,0.0270286,"\int x^2 \text{sech}^{-1}\left(\sqrt{x}\right) \, dx","Int[x^2*ArcSech[Sqrt[x]],x]","\frac{1}{3} x^3 \text{sech}^{-1}\left(\sqrt{x}\right)-\frac{(1-x)^3}{15 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}+\frac{2 (1-x)^2}{9 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}-\frac{1-x}{3 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}","\frac{1}{3} x^3 \text{sech}^{-1}\left(\sqrt{x}\right)-\frac{(1-x)^3}{15 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}+\frac{2 (1-x)^2}{9 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}-\frac{1-x}{3 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}",1,"-(1 - x)/(3*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*Sqrt[x]) + (2*(1 - x)^2)/(9*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*Sqrt[x]) - (1 - x)^3/(15*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*Sqrt[x]) + (x^3*ArcSech[Sqrt[x]])/3","A",4,3,10,0.3000,1,"{6345, 12, 43}"
22,1,88,0,0.0183515,"\int x \text{sech}^{-1}\left(\sqrt{x}\right) \, dx","Int[x*ArcSech[Sqrt[x]],x]","\frac{1}{2} x^2 \text{sech}^{-1}\left(\sqrt{x}\right)+\frac{(1-x)^2}{6 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}-\frac{1-x}{2 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}","\frac{1}{2} x^2 \text{sech}^{-1}\left(\sqrt{x}\right)+\frac{(1-x)^2}{6 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}-\frac{1-x}{2 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}",1,"-(1 - x)/(2*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*Sqrt[x]) + (1 - x)^2/(6*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*Sqrt[x]) + (x^2*ArcSech[Sqrt[x]])/2","A",4,3,8,0.3750,1,"{6345, 12, 43}"
23,1,43,0,0.0072149,"\int \text{sech}^{-1}\left(\sqrt{x}\right) \, dx","Int[ArcSech[Sqrt[x]],x]","x \text{sech}^{-1}\left(\sqrt{x}\right)-\frac{1-x}{\sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}","x \text{sech}^{-1}\left(\sqrt{x}\right)-\frac{1-x}{\sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}",1,"-((1 - x)/(Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*Sqrt[x])) + x*ArcSech[Sqrt[x]]","A",3,3,6,0.5000,1,"{6343, 12, 32}"
24,1,46,0,0.0952382,"\int \frac{\text{sech}^{-1}\left(\sqrt{x}\right)}{x} \, dx","Int[ArcSech[Sqrt[x]]/x,x]","-\text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}\left(\sqrt{x}\right)}\right)+\text{sech}^{-1}\left(\sqrt{x}\right)^2-2 \text{sech}^{-1}\left(\sqrt{x}\right) \log \left(e^{2 \text{sech}^{-1}\left(\sqrt{x}\right)}+1\right)","-\text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}\left(\sqrt{x}\right)}\right)+\text{sech}^{-1}\left(\sqrt{x}\right)^2-2 \text{sech}^{-1}\left(\sqrt{x}\right) \log \left(e^{2 \text{sech}^{-1}\left(\sqrt{x}\right)}+1\right)",1,"ArcSech[Sqrt[x]]^2 - 2*ArcSech[Sqrt[x]]*Log[1 + E^(2*ArcSech[Sqrt[x]])] - PolyLog[2, -E^(2*ArcSech[Sqrt[x]])]","A",7,6,10,0.6000,1,"{6281, 5660, 3718, 2190, 2279, 2391}"
25,1,98,0,0.0233795,"\int \frac{\text{sech}^{-1}\left(\sqrt{x}\right)}{x^2} \, dx","Int[ArcSech[Sqrt[x]]/x^2,x]","\frac{1-x}{2 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} x^{3/2}}+\frac{\sqrt{1-x} \tanh ^{-1}\left(\sqrt{1-x}\right)}{2 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}-\frac{\text{sech}^{-1}\left(\sqrt{x}\right)}{x}","\frac{1-x}{2 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} x^{3/2}}+\frac{\sqrt{1-x} \tanh ^{-1}\left(\sqrt{1-x}\right)}{2 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}-\frac{\text{sech}^{-1}\left(\sqrt{x}\right)}{x}",1,"(1 - x)/(2*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*x^(3/2)) - ArcSech[Sqrt[x]]/x + (Sqrt[1 - x]*ArcTanh[Sqrt[1 - x]])/(2*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*Sqrt[x])","A",5,5,10,0.5000,1,"{6345, 12, 51, 63, 206}"
26,1,136,0,0.0332407,"\int \frac{\text{sech}^{-1}\left(\sqrt{x}\right)}{x^3} \, dx","Int[ArcSech[Sqrt[x]]/x^3,x]","\frac{3 (1-x)}{16 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} x^{3/2}}+\frac{1-x}{8 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} x^{5/2}}-\frac{\text{sech}^{-1}\left(\sqrt{x}\right)}{2 x^2}+\frac{3 \sqrt{1-x} \tanh ^{-1}\left(\sqrt{1-x}\right)}{16 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}","\frac{3 (1-x)}{16 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} x^{3/2}}+\frac{1-x}{8 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} x^{5/2}}-\frac{\text{sech}^{-1}\left(\sqrt{x}\right)}{2 x^2}+\frac{3 \sqrt{1-x} \tanh ^{-1}\left(\sqrt{1-x}\right)}{16 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}",1,"(1 - x)/(8*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*x^(5/2)) + (3*(1 - x))/(16*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*x^(3/2)) - ArcSech[Sqrt[x]]/(2*x^2) + (3*Sqrt[1 - x]*ArcTanh[Sqrt[1 - x]])/(16*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*Sqrt[x])","A",6,5,10,0.5000,1,"{6345, 12, 51, 63, 206}"
27,1,172,0,0.039765,"\int \frac{\text{sech}^{-1}\left(\sqrt{x}\right)}{x^4} \, dx","Int[ArcSech[Sqrt[x]]/x^4,x]","\frac{5 (1-x)}{48 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} x^{3/2}}+\frac{5 (1-x)}{72 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} x^{5/2}}+\frac{1-x}{18 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} x^{7/2}}-\frac{\text{sech}^{-1}\left(\sqrt{x}\right)}{3 x^3}+\frac{5 \sqrt{1-x} \tanh ^{-1}\left(\sqrt{1-x}\right)}{48 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}","\frac{5 (1-x)}{48 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} x^{3/2}}+\frac{5 (1-x)}{72 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} x^{5/2}}+\frac{1-x}{18 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} x^{7/2}}-\frac{\text{sech}^{-1}\left(\sqrt{x}\right)}{3 x^3}+\frac{5 \sqrt{1-x} \tanh ^{-1}\left(\sqrt{1-x}\right)}{48 \sqrt{\frac{1}{\sqrt{x}}-1} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}}",1,"(1 - x)/(18*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*x^(7/2)) + (5*(1 - x))/(72*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*x^(5/2)) + (5*(1 - x))/(48*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*x^(3/2)) - ArcSech[Sqrt[x]]/(3*x^3) + (5*Sqrt[1 - x]*ArcTanh[Sqrt[1 - x]])/(48*Sqrt[-1 + 1/Sqrt[x]]*Sqrt[1 + 1/Sqrt[x]]*Sqrt[x])","A",7,5,10,0.5000,1,"{6345, 12, 51, 63, 206}"
28,1,21,0,0.0069606,"\int \text{sech}^{-1}\left(\frac{1}{x}\right) \, dx","Int[ArcSech[x^(-1)],x]","x \cosh ^{-1}(x)-\sqrt{x-1} \sqrt{x+1}","x \cosh ^{-1}(x)-\sqrt{x-1} \sqrt{x+1}",1,"-(Sqrt[-1 + x]*Sqrt[1 + x]) + x*ArcCosh[x]","A",3,3,4,0.7500,1,"{6327, 5654, 74}"
29,1,61,0,0.1053666,"\int \frac{\text{sech}^{-1}\left(a x^n\right)}{x} \, dx","Int[ArcSech[a*x^n]/x,x]","-\frac{\text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}\left(a x^n\right)}\right)}{2 n}+\frac{\text{sech}^{-1}\left(a x^n\right)^2}{2 n}-\frac{\text{sech}^{-1}\left(a x^n\right) \log \left(e^{2 \text{sech}^{-1}\left(a x^n\right)}+1\right)}{n}","-\frac{\text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}\left(a x^n\right)}\right)}{2 n}+\frac{\text{sech}^{-1}\left(a x^n\right)^2}{2 n}-\frac{\text{sech}^{-1}\left(a x^n\right) \log \left(e^{2 \text{sech}^{-1}\left(a x^n\right)}+1\right)}{n}",1,"ArcSech[a*x^n]^2/(2*n) - (ArcSech[a*x^n]*Log[1 + E^(2*ArcSech[a*x^n])])/n - PolyLog[2, -E^(2*ArcSech[a*x^n])]/(2*n)","A",7,6,10,0.6000,1,"{6281, 5660, 3718, 2190, 2279, 2391}"
30,1,54,0,0.1072383,"\int \frac{\text{sech}^{-1}\left(a x^5\right)}{x} \, dx","Int[ArcSech[a*x^5]/x,x]","-\frac{1}{10} \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}\left(a x^5\right)}\right)+\frac{1}{10} \text{sech}^{-1}\left(a x^5\right)^2-\frac{1}{5} \text{sech}^{-1}\left(a x^5\right) \log \left(e^{2 \text{sech}^{-1}\left(a x^5\right)}+1\right)","-\frac{1}{10} \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}\left(a x^5\right)}\right)+\frac{1}{10} \text{sech}^{-1}\left(a x^5\right)^2-\frac{1}{5} \text{sech}^{-1}\left(a x^5\right) \log \left(e^{2 \text{sech}^{-1}\left(a x^5\right)}+1\right)",1,"ArcSech[a*x^5]^2/10 - (ArcSech[a*x^5]*Log[1 + E^(2*ArcSech[a*x^5])])/5 - PolyLog[2, -E^(2*ArcSech[a*x^5])]/10","A",7,6,10,0.6000,1,"{6281, 5660, 3718, 2190, 2279, 2391}"
31,1,77,0,0.1011717,"\int \text{sech}^{-1}\left(c e^{a+b x}\right) \, dx","Int[ArcSech[c*E^(a + b*x)],x]","-\frac{\text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}+\frac{\text{sech}^{-1}\left(c e^{a+b x}\right)^2}{2 b}-\frac{\text{sech}^{-1}\left(c e^{a+b x}\right) \log \left(e^{2 \text{sech}^{-1}\left(c e^{a+b x}\right)}+1\right)}{b}","-\frac{\text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}+\frac{\text{sech}^{-1}\left(c e^{a+b x}\right)^2}{2 b}-\frac{\text{sech}^{-1}\left(c e^{a+b x}\right) \log \left(e^{2 \text{sech}^{-1}\left(c e^{a+b x}\right)}+1\right)}{b}",1,"ArcSech[c*E^(a + b*x)]^2/(2*b) - (ArcSech[c*E^(a + b*x)]*Log[1 + E^(2*ArcSech[c*E^(a + b*x)])])/b - PolyLog[2, -E^(2*ArcSech[c*E^(a + b*x)])]/(2*b)","A",7,7,10,0.7000,1,"{2282, 6281, 5660, 3718, 2190, 2279, 2391}"
32,1,83,0,0.0384958,"\int e^{\text{sech}^{-1}(a x)} x^4 \, dx","Int[E^ArcSech[a*x]*x^4,x]","-\frac{x^2 \sqrt{1-a x}}{15 a^3 \sqrt{\frac{1}{a x+1}}}-\frac{2 \sqrt{1-a x}}{15 a^5 \sqrt{\frac{1}{a x+1}}}+\frac{x^4}{20 a}+\frac{1}{5} x^5 e^{\text{sech}^{-1}(a x)}","\frac{x^2}{15 a^3}-\frac{x^3 e^{\text{sech}^{-1}(a x)}}{15 a^2}-\frac{2 x e^{\text{sech}^{-1}(a x)}}{15 a^4}+\frac{x^4}{20 a}+\frac{1}{5} x^5 e^{\text{sech}^{-1}(a x)}",1,"x^4/(20*a) + (E^ArcSech[a*x]*x^5)/5 - (2*Sqrt[1 - a*x])/(15*a^5*Sqrt[(1 + a*x)^(-1)]) - (x^2*Sqrt[1 - a*x])/(15*a^3*Sqrt[(1 + a*x)^(-1)])","A",5,5,10,0.5000,0,"{6335, 30, 100, 12, 74}"
33,1,84,0,0.0319382,"\int e^{\text{sech}^{-1}(a x)} x^3 \, dx","Int[E^ArcSech[a*x]*x^3,x]","-\frac{x \sqrt{1-a x}}{8 a^3 \sqrt{\frac{1}{a x+1}}}+\frac{\sqrt{\frac{1}{a x+1}} \sqrt{a x+1} \sin ^{-1}(a x)}{8 a^4}+\frac{x^3}{12 a}+\frac{1}{4} x^4 e^{\text{sech}^{-1}(a x)}","-\frac{x \sqrt{1-a x}}{8 a^3 \sqrt{\frac{1}{a x+1}}}+\frac{\sqrt{\frac{1}{a x+1}} \sqrt{a x+1} \sin ^{-1}(a x)}{8 a^4}+\frac{x^3}{12 a}+\frac{1}{4} x^4 e^{\text{sech}^{-1}(a x)}",1,"x^3/(12*a) + (E^ArcSech[a*x]*x^4)/4 - (x*Sqrt[1 - a*x])/(8*a^3*Sqrt[(1 + a*x)^(-1)]) + (Sqrt[(1 + a*x)^(-1)]*Sqrt[1 + a*x]*ArcSin[a*x])/(8*a^4)","A",5,5,10,0.5000,1,"{6335, 30, 90, 41, 216}"
34,1,52,0,0.024187,"\int e^{\text{sech}^{-1}(a x)} x^2 \, dx","Int[E^ArcSech[a*x]*x^2,x]","-\frac{\sqrt{1-a x}}{3 a^3 \sqrt{\frac{1}{a x+1}}}+\frac{x^2}{6 a}+\frac{1}{3} x^3 e^{\text{sech}^{-1}(a x)}","-\frac{x e^{\text{sech}^{-1}(a x)}}{3 a^2}+\frac{x^2}{6 a}+\frac{1}{3} x^3 e^{\text{sech}^{-1}(a x)}",1,"x^2/(6*a) + (E^ArcSech[a*x]*x^3)/3 - Sqrt[1 - a*x]/(3*a^3*Sqrt[(1 + a*x)^(-1)])","A",3,3,10,0.3000,0,"{6335, 30, 74}"
35,1,53,0,0.0181567,"\int e^{\text{sech}^{-1}(a x)} x \, dx","Int[E^ArcSech[a*x]*x,x]","\frac{\sqrt{\frac{1}{a x+1}} \sqrt{a x+1} \sin ^{-1}(a x)}{2 a^2}+\frac{1}{2} x^2 e^{\text{sech}^{-1}(a x)}+\frac{x}{2 a}","\frac{\sqrt{\frac{1}{a x+1}} \sqrt{a x+1} \sin ^{-1}(a x)}{2 a^2}+\frac{1}{2} x^2 e^{\text{sech}^{-1}(a x)}+\frac{x}{2 a}",1,"x/(2*a) + (E^ArcSech[a*x]*x^2)/2 + (Sqrt[(1 + a*x)^(-1)]*Sqrt[1 + a*x]*ArcSin[a*x])/(2*a^2)","A",4,4,8,0.5000,1,"{6335, 8, 41, 216}"
36,1,39,0,0.1369781,"\int e^{\text{sech}^{-1}(a x)} \, dx","Int[E^ArcSech[a*x],x]","\frac{\log (x)}{a}-\frac{2 \tanh ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)}{a}+x e^{\text{sech}^{-1}(a x)}","\frac{\log (x)}{a}+x e^{\text{sech}^{-1}(a x)}-\frac{\text{sech}^{-1}(a x)}{a}",1,"E^ArcSech[a*x]*x - (2*ArcTanh[Sqrt[(1 - a*x)/(1 + a*x)]])/a + Log[x]/a","A",3,3,6,0.5000,0,"{6329, 1962, 208}"
37,1,64,0,0.0308311,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x} \, dx","Int[E^ArcSech[a*x]/x,x]","-\frac{\sqrt{1-a x}}{a x \sqrt{\frac{1}{a x+1}}}-\frac{1}{a x}-\sqrt{\frac{1}{a x+1}} \sqrt{a x+1} \sin ^{-1}(a x)","2 \tan ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)-\frac{2}{1-\sqrt{\frac{1-a x}{a x+1}}}",1,"-(1/(a*x)) - Sqrt[1 - a*x]/(a*x*Sqrt[(1 + a*x)^(-1)]) - Sqrt[(1 + a*x)^(-1)]*Sqrt[1 + a*x]*ArcSin[a*x]","A",5,5,10,0.5000,0,"{6334, 97, 12, 41, 216}"
38,1,99,0,0.0412326,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x^2} \, dx","Int[E^ArcSech[a*x]/x^2,x]","\frac{\sqrt{1-a x}}{2 a x^2 \sqrt{\frac{1}{a x+1}}}+\frac{1}{2 a x^2}+\frac{1}{2} a \sqrt{\frac{1}{a x+1}} \sqrt{a x+1} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)-\frac{e^{\text{sech}^{-1}(a x)}}{x}","a \tanh ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)-\frac{e^{\text{sech}^{-1}(a x)}}{2 x}",1,"1/(2*a*x^2) - E^ArcSech[a*x]/x + Sqrt[1 - a*x]/(2*a*x^2*Sqrt[(1 + a*x)^(-1)]) + (a*Sqrt[(1 + a*x)^(-1)]*Sqrt[1 + a*x]*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/2","B",6,6,10,0.6000,0,"{6335, 30, 103, 12, 92, 208}"
39,1,84,0,0.0366551,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x^3} \, dx","Int[E^ArcSech[a*x]/x^3,x]","\frac{\sqrt{1-a x}}{6 a x^3 \sqrt{\frac{1}{a x+1}}}+\frac{1}{6 a x^3}-\frac{e^{\text{sech}^{-1}(a x)}}{2 x^2}+\frac{a \sqrt{1-a x}}{3 x \sqrt{\frac{1}{a x+1}}}","-\frac{8 a^2 \left(\frac{1-a x}{a x+1}\right)^{3/2}}{3 \left(1-\frac{1-a x}{a x+1}\right)^3}-\frac{1}{3 a x^3}",1,"1/(6*a*x^3) - E^ArcSech[a*x]/(2*x^2) + Sqrt[1 - a*x]/(6*a*x^3*Sqrt[(1 + a*x)^(-1)]) + (a*Sqrt[1 - a*x])/(3*x*Sqrt[(1 + a*x)^(-1)])","C",5,5,10,0.5000,0,"{6335, 30, 103, 12, 95}"
40,1,132,0,0.058869,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x^4} \, dx","Int[E^ArcSech[a*x]/x^4,x]","\frac{1}{8} a^3 \sqrt{\frac{1}{a x+1}} \sqrt{a x+1} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)+\frac{a \sqrt{1-a x}}{8 x^2 \sqrt{\frac{1}{a x+1}}}+\frac{\sqrt{1-a x}}{12 a x^4 \sqrt{\frac{1}{a x+1}}}+\frac{1}{12 a x^4}-\frac{e^{\text{sech}^{-1}(a x)}}{3 x^3}","\frac{1}{8} a^3 \sqrt{\frac{1}{a x+1}} \sqrt{a x+1} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)+\frac{a \sqrt{1-a x}}{8 x^2 \sqrt{\frac{1}{a x+1}}}+\frac{\sqrt{1-a x}}{12 a x^4 \sqrt{\frac{1}{a x+1}}}+\frac{1}{12 a x^4}-\frac{e^{\text{sech}^{-1}(a x)}}{3 x^3}",1,"1/(12*a*x^4) - E^ArcSech[a*x]/(3*x^3) + Sqrt[1 - a*x]/(12*a*x^4*Sqrt[(1 + a*x)^(-1)]) + (a*Sqrt[1 - a*x])/(8*x^2*Sqrt[(1 + a*x)^(-1)]) + (a^3*Sqrt[(1 + a*x)^(-1)]*Sqrt[1 + a*x]*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/8","A",8,6,10,0.6000,1,"{6335, 30, 103, 12, 92, 208}"
41,1,115,0,0.051863,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x^5} \, dx","Int[E^ArcSech[a*x]/x^5,x]","\frac{2 a^3 \sqrt{1-a x}}{15 x \sqrt{\frac{1}{a x+1}}}+\frac{a \sqrt{1-a x}}{15 x^3 \sqrt{\frac{1}{a x+1}}}+\frac{\sqrt{1-a x}}{20 a x^5 \sqrt{\frac{1}{a x+1}}}+\frac{1}{20 a x^5}-\frac{e^{\text{sech}^{-1}(a x)}}{4 x^4}","\frac{2 a^3 \sqrt{1-a x}}{15 x \sqrt{\frac{1}{a x+1}}}+\frac{a \sqrt{1-a x}}{15 x^3 \sqrt{\frac{1}{a x+1}}}+\frac{\sqrt{1-a x}}{20 a x^5 \sqrt{\frac{1}{a x+1}}}+\frac{1}{20 a x^5}-\frac{e^{\text{sech}^{-1}(a x)}}{4 x^4}",1,"1/(20*a*x^5) - E^ArcSech[a*x]/(4*x^4) + Sqrt[1 - a*x]/(20*a*x^5*Sqrt[(1 + a*x)^(-1)]) + (a*Sqrt[1 - a*x])/(15*x^3*Sqrt[(1 + a*x)^(-1)]) + (2*a^3*Sqrt[1 - a*x])/(15*x*Sqrt[(1 + a*x)^(-1)])","A",7,5,10,0.5000,1,"{6335, 30, 103, 12, 95}"
42,1,163,0,0.0769087,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x^6} \, dx","Int[E^ArcSech[a*x]/x^6,x]","\frac{a^3 \sqrt{1-a x}}{16 x^2 \sqrt{\frac{1}{a x+1}}}+\frac{1}{16} a^5 \sqrt{\frac{1}{a x+1}} \sqrt{a x+1} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)+\frac{a \sqrt{1-a x}}{24 x^4 \sqrt{\frac{1}{a x+1}}}+\frac{\sqrt{1-a x}}{30 a x^6 \sqrt{\frac{1}{a x+1}}}+\frac{1}{30 a x^6}-\frac{e^{\text{sech}^{-1}(a x)}}{5 x^5}","\frac{a^3 \sqrt{1-a x}}{16 x^2 \sqrt{\frac{1}{a x+1}}}+\frac{1}{16} a^5 \sqrt{\frac{1}{a x+1}} \sqrt{a x+1} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)+\frac{a \sqrt{1-a x}}{24 x^4 \sqrt{\frac{1}{a x+1}}}+\frac{\sqrt{1-a x}}{30 a x^6 \sqrt{\frac{1}{a x+1}}}+\frac{1}{30 a x^6}-\frac{e^{\text{sech}^{-1}(a x)}}{5 x^5}",1,"1/(30*a*x^6) - E^ArcSech[a*x]/(5*x^5) + Sqrt[1 - a*x]/(30*a*x^6*Sqrt[(1 + a*x)^(-1)]) + (a*Sqrt[1 - a*x])/(24*x^4*Sqrt[(1 + a*x)^(-1)]) + (a^3*Sqrt[1 - a*x])/(16*x^2*Sqrt[(1 + a*x)^(-1)]) + (a^5*Sqrt[(1 + a*x)^(-1)]*Sqrt[1 + a*x]*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/16","A",10,6,10,0.6000,1,"{6335, 30, 103, 12, 92, 208}"
43,1,146,0,0.0711514,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x^7} \, dx","Int[E^ArcSech[a*x]/x^7,x]","\frac{4 a^3 \sqrt{1-a x}}{105 x^3 \sqrt{\frac{1}{a x+1}}}+\frac{8 a^5 \sqrt{1-a x}}{105 x \sqrt{\frac{1}{a x+1}}}+\frac{a \sqrt{1-a x}}{35 x^5 \sqrt{\frac{1}{a x+1}}}+\frac{\sqrt{1-a x}}{42 a x^7 \sqrt{\frac{1}{a x+1}}}+\frac{1}{42 a x^7}-\frac{e^{\text{sech}^{-1}(a x)}}{6 x^6}","\frac{4 a^3 \sqrt{1-a x}}{105 x^3 \sqrt{\frac{1}{a x+1}}}+\frac{8 a^5 \sqrt{1-a x}}{105 x \sqrt{\frac{1}{a x+1}}}+\frac{a \sqrt{1-a x}}{35 x^5 \sqrt{\frac{1}{a x+1}}}+\frac{\sqrt{1-a x}}{42 a x^7 \sqrt{\frac{1}{a x+1}}}+\frac{1}{42 a x^7}-\frac{e^{\text{sech}^{-1}(a x)}}{6 x^6}",1,"1/(42*a*x^7) - E^ArcSech[a*x]/(6*x^6) + Sqrt[1 - a*x]/(42*a*x^7*Sqrt[(1 + a*x)^(-1)]) + (a*Sqrt[1 - a*x])/(35*x^5*Sqrt[(1 + a*x)^(-1)]) + (4*a^3*Sqrt[1 - a*x])/(105*x^3*Sqrt[(1 + a*x)^(-1)]) + (8*a^5*Sqrt[1 - a*x])/(105*x*Sqrt[(1 + a*x)^(-1)])","A",9,5,10,0.5000,1,"{6335, 30, 103, 12, 95}"
44,1,194,0,0.0984763,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x^8} \, dx","Int[E^ArcSech[a*x]/x^8,x]","\frac{5 a^5 \sqrt{1-a x}}{128 x^2 \sqrt{\frac{1}{a x+1}}}+\frac{5 a^3 \sqrt{1-a x}}{192 x^4 \sqrt{\frac{1}{a x+1}}}+\frac{5}{128} a^7 \sqrt{\frac{1}{a x+1}} \sqrt{a x+1} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)+\frac{a \sqrt{1-a x}}{48 x^6 \sqrt{\frac{1}{a x+1}}}+\frac{\sqrt{1-a x}}{56 a x^8 \sqrt{\frac{1}{a x+1}}}+\frac{1}{56 a x^8}-\frac{e^{\text{sech}^{-1}(a x)}}{7 x^7}","\frac{5 a^5 \sqrt{1-a x}}{128 x^2 \sqrt{\frac{1}{a x+1}}}+\frac{5 a^3 \sqrt{1-a x}}{192 x^4 \sqrt{\frac{1}{a x+1}}}+\frac{5}{128} a^7 \sqrt{\frac{1}{a x+1}} \sqrt{a x+1} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)+\frac{a \sqrt{1-a x}}{48 x^6 \sqrt{\frac{1}{a x+1}}}+\frac{\sqrt{1-a x}}{56 a x^8 \sqrt{\frac{1}{a x+1}}}+\frac{1}{56 a x^8}-\frac{e^{\text{sech}^{-1}(a x)}}{7 x^7}",1,"1/(56*a*x^8) - E^ArcSech[a*x]/(7*x^7) + Sqrt[1 - a*x]/(56*a*x^8*Sqrt[(1 + a*x)^(-1)]) + (a*Sqrt[1 - a*x])/(48*x^6*Sqrt[(1 + a*x)^(-1)]) + (5*a^3*Sqrt[1 - a*x])/(192*x^4*Sqrt[(1 + a*x)^(-1)]) + (5*a^5*Sqrt[1 - a*x])/(128*x^2*Sqrt[(1 + a*x)^(-1)]) + (5*a^7*Sqrt[(1 + a*x)^(-1)]*Sqrt[1 + a*x]*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/128","A",12,6,10,0.6000,1,"{6335, 30, 103, 12, 92, 208}"
45,1,111,0,0.0616554,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x^7 \, dx","Int[E^ArcSech[a*x^2]*x^7,x]","-\frac{x^2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sqrt{1-a^2 x^4}}{16 a^3}+\frac{\sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sin ^{-1}\left(a x^2\right)}{16 a^4}+\frac{x^6}{24 a}+\frac{1}{8} x^8 e^{\text{sech}^{-1}\left(a x^2\right)}","-\frac{x^2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sqrt{1-a^2 x^4}}{16 a^3}+\frac{\sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sin ^{-1}\left(a x^2\right)}{16 a^4}+\frac{x^6}{24 a}+\frac{1}{8} x^8 e^{\text{sech}^{-1}\left(a x^2\right)}",1,"x^6/(24*a) + (E^ArcSech[a*x^2]*x^8)/8 - (x^2*Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*Sqrt[1 - a^2*x^4])/(16*a^3) + (Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*ArcSin[a*x^2])/(16*a^4)","A",6,6,12,0.5000,1,"{6335, 30, 259, 275, 321, 216}"
46,1,115,0,0.051338,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x^6 \, dx","Int[E^ArcSech[a*x^2]*x^6,x]","-\frac{2 x \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sqrt{1-a^2 x^4}}{21 a^3}+\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{21 a^{7/2}}+\frac{2 x^5}{35 a}+\frac{1}{7} x^7 e^{\text{sech}^{-1}\left(a x^2\right)}","-\frac{2 x \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sqrt{1-a^2 x^4}}{21 a^3}+\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{21 a^{7/2}}+\frac{2 x^5}{35 a}+\frac{1}{7} x^7 e^{\text{sech}^{-1}\left(a x^2\right)}",1,"(2*x^5)/(35*a) + (E^ArcSech[a*x^2]*x^7)/7 - (2*x*Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*Sqrt[1 - a^2*x^4])/(21*a^3) + (2*Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*EllipticF[ArcSin[Sqrt[a]*x], -1])/(21*a^(7/2))","A",5,5,12,0.4167,1,"{6335, 30, 259, 321, 221}"
47,1,71,0,0.0412168,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x^5 \, dx","Int[E^ArcSech[a*x^2]*x^5,x]","-\frac{\sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sqrt{1-a^2 x^4}}{6 a^3}+\frac{x^4}{12 a}+\frac{1}{6} x^6 e^{\text{sech}^{-1}\left(a x^2\right)}","-\frac{\sqrt{1-a x^2}}{6 a^3 \sqrt{\frac{1}{a x^2+1}}}+\frac{x^4}{12 a}+\frac{1}{6} x^6 e^{\text{sech}^{-1}\left(a x^2\right)}",1,"x^4/(12*a) + (E^ArcSech[a*x^2]*x^6)/6 - (Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*Sqrt[1 - a^2*x^4])/(6*a^3)","A",4,4,12,0.3333,0,"{6335, 30, 259, 261}"
48,1,112,0,0.0665785,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x^4 \, dx","Int[E^ArcSech[a*x^2]*x^4,x]","-\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{5 a^{5/2}}+\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} E\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{5 a^{5/2}}+\frac{2 x^3}{15 a}+\frac{1}{5} x^5 e^{\text{sech}^{-1}\left(a x^2\right)}","-\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{5 a^{5/2}}+\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} E\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{5 a^{5/2}}+\frac{2 x^3}{15 a}+\frac{1}{5} x^5 e^{\text{sech}^{-1}\left(a x^2\right)}",1,"(2*x^3)/(15*a) + (E^ArcSech[a*x^2]*x^5)/5 + (2*Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*EllipticE[ArcSin[Sqrt[a]*x], -1])/(5*a^(5/2)) - (2*Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*EllipticF[ArcSin[Sqrt[a]*x], -1])/(5*a^(5/2))","A",7,7,12,0.5833,1,"{6335, 30, 259, 307, 221, 1199, 424}"
49,1,63,0,0.0368681,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x^3 \, dx","Int[E^ArcSech[a*x^2]*x^3,x]","\frac{\sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sin ^{-1}\left(a x^2\right)}{4 a^2}+\frac{x^2}{4 a}+\frac{1}{4} x^4 e^{\text{sech}^{-1}\left(a x^2\right)}","\frac{\sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sin ^{-1}\left(a x^2\right)}{4 a^2}+\frac{x^2}{4 a}+\frac{1}{4} x^4 e^{\text{sech}^{-1}\left(a x^2\right)}",1,"x^2/(4*a) + (E^ArcSech[a*x^2]*x^4)/4 + (Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*ArcSin[a*x^2])/(4*a^2)","A",5,5,12,0.4167,1,"{6335, 30, 259, 275, 216}"
50,1,67,0,0.0279784,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x^2 \, dx","Int[E^ArcSech[a*x^2]*x^2,x]","\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{3 a^{3/2}}+\frac{1}{3} x^3 e^{\text{sech}^{-1}\left(a x^2\right)}+\frac{2 x}{3 a}","\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{3 a^{3/2}}+\frac{1}{3} x^3 e^{\text{sech}^{-1}\left(a x^2\right)}+\frac{2 x}{3 a}",1,"(2*x)/(3*a) + (E^ArcSech[a*x^2]*x^3)/3 + (2*Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*EllipticF[ArcSin[Sqrt[a]*x], -1])/(3*a^(3/2))","A",4,4,12,0.3333,1,"{6335, 8, 248, 221}"
51,1,68,0,0.0425703,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x \, dx","Int[E^ArcSech[a*x^2]*x,x]","-\frac{\sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \tanh ^{-1}\left(\sqrt{1-a^2 x^4}\right)}{2 a}+\frac{1}{2} x^2 e^{\text{sech}^{-1}\left(a x^2\right)}+\frac{\log (x)}{a}","-\frac{\sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \tanh ^{-1}\left(\sqrt{1-a^2 x^4}\right)}{2 a}+\frac{1}{2} x^2 e^{\text{sech}^{-1}\left(a x^2\right)}+\frac{\log (x)}{a}",1,"(E^ArcSech[a*x^2]*x^2)/2 - (Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*ArcTanh[Sqrt[1 - a^2*x^4]])/(2*a) + Log[x]/a","A",6,6,10,0.6000,1,"{6335, 29, 259, 266, 63, 208}"
52,1,147,0,0.0680163,"\int e^{\text{sech}^{-1}\left(a x^2\right)} \, dx","Int[E^ArcSech[a*x^2],x]","-\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sqrt{1-a^2 x^4}}{a x}+x e^{\text{sech}^{-1}\left(a x^2\right)}+\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{\sqrt{a}}-\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} E\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{\sqrt{a}}-\frac{2}{a x}","-\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sqrt{1-a^2 x^4}}{a x}+x e^{\text{sech}^{-1}\left(a x^2\right)}+\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{\sqrt{a}}-\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} E\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{\sqrt{a}}-\frac{2}{a x}",1,"-2/(a*x) + E^ArcSech[a*x^2]*x - (2*Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*Sqrt[1 - a^2*x^4])/(a*x) - (2*Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*EllipticE[ArcSin[Sqrt[a]*x], -1])/Sqrt[a] + (2*Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*EllipticF[ArcSin[Sqrt[a]*x], -1])/Sqrt[a]","A",8,8,8,1.000,1,"{6330, 30, 259, 325, 307, 221, 1199, 424}"
53,1,93,0,0.0530153,"\int \frac{e^{\text{sech}^{-1}\left(a x^2\right)}}{x} \, dx","Int[E^ArcSech[a*x^2]/x,x]","-\frac{\sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sqrt{1-a^2 x^4}}{2 a x^2}-\frac{1}{2 a x^2}-\frac{1}{2} \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sin ^{-1}\left(a x^2\right)","-\frac{\sqrt{1-a x^2}}{2 a x^2 \sqrt{\frac{1}{a x^2+1}}}-\frac{1}{2 a x^2}-\frac{1}{2} \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sin ^{-1}\left(a x^2\right)",1,"-1/(2*a*x^2) - (Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*Sqrt[1 - a^2*x^4])/(2*a*x^2) - (Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*ArcSin[a*x^2])/2","A",5,5,12,0.4167,0,"{6334, 259, 275, 277, 216}"
54,1,115,0,0.0510283,"\int \frac{e^{\text{sech}^{-1}\left(a x^2\right)}}{x^2} \, dx","Int[E^ArcSech[a*x^2]/x^2,x]","\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sqrt{1-a^2 x^4}}{3 a x^3}+\frac{2}{3 a x^3}-\frac{e^{\text{sech}^{-1}\left(a x^2\right)}}{x}-\frac{2}{3} \sqrt{a} \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)","\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sqrt{1-a^2 x^4}}{3 a x^3}+\frac{2}{3 a x^3}-\frac{e^{\text{sech}^{-1}\left(a x^2\right)}}{x}-\frac{2}{3} \sqrt{a} \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)",1,"2/(3*a*x^3) - E^ArcSech[a*x^2]/x + (2*Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*Sqrt[1 - a^2*x^4])/(3*a*x^3) - (2*Sqrt[a]*Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*EllipticF[ArcSin[Sqrt[a]*x], -1])/3","A",5,5,12,0.4167,1,"{6335, 30, 259, 325, 221}"
55,1,118,0,0.0611727,"\int \frac{e^{\text{sech}^{-1}\left(a x^2\right)}}{x^3} \, dx","Int[E^ArcSech[a*x^2]/x^3,x]","\frac{\sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sqrt{1-a^2 x^4}}{4 a x^4}+\frac{1}{4} a \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \tanh ^{-1}\left(\sqrt{1-a^2 x^4}\right)+\frac{1}{4 a x^4}-\frac{e^{\text{sech}^{-1}\left(a x^2\right)}}{2 x^2}","\frac{\sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sqrt{1-a^2 x^4}}{4 a x^4}+\frac{1}{4} a \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \tanh ^{-1}\left(\sqrt{1-a^2 x^4}\right)+\frac{1}{4 a x^4}-\frac{e^{\text{sech}^{-1}\left(a x^2\right)}}{2 x^2}",1,"1/(4*a*x^4) - E^ArcSech[a*x^2]/(2*x^2) + (Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*Sqrt[1 - a^2*x^4])/(4*a*x^4) + (a*Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*ArcTanh[Sqrt[1 - a^2*x^4]])/4","A",7,7,12,0.5833,1,"{6335, 30, 259, 266, 51, 63, 208}"
56,1,109,0,0.0677183,"\int e^{\text{sech}^{-1}\left(a x^3\right)} x^m \, dx","Int[E^ArcSech[a*x^3]*x^m,x]","-\frac{3 \sqrt{\frac{1}{a x^3+1}} \sqrt{a x^3+1} x^{m-2} \, _2F_1\left(\frac{1}{2},\frac{m-2}{6};\frac{m+4}{6};a^2 x^6\right)}{a \left(-m^2+m+2\right)}-\frac{3 x^{m-2}}{a \left(-m^2+m+2\right)}+\frac{x^{m+1} e^{\text{sech}^{-1}\left(a x^3\right)}}{m+1}","-\frac{3 \sqrt{\frac{1}{a x^3+1}} \sqrt{a x^3+1} x^{m-2} \, _2F_1\left(\frac{1}{2},\frac{m-2}{6};\frac{m+4}{6};a^2 x^6\right)}{a \left(-m^2+m+2\right)}-\frac{3 x^{m-2}}{a \left(-m^2+m+2\right)}+\frac{x^{m+1} e^{\text{sech}^{-1}\left(a x^3\right)}}{m+1}",1,"(-3*x^(-2 + m))/(a*(2 + m - m^2)) + (E^ArcSech[a*x^3]*x^(1 + m))/(1 + m) - (3*x^(-2 + m)*Sqrt[(1 + a*x^3)^(-1)]*Sqrt[1 + a*x^3]*Hypergeometric2F1[1/2, (-2 + m)/6, (4 + m)/6, a^2*x^6])/(a*(2 + m - m^2))","A",4,4,12,0.3333,1,"{6335, 30, 259, 364}"
57,1,107,0,0.0557968,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x^m \, dx","Int[E^ArcSech[a*x^2]*x^m,x]","-\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} x^{m-1} \, _2F_1\left(\frac{1}{2},\frac{m-1}{4};\frac{m+3}{4};a^2 x^4\right)}{a \left(1-m^2\right)}-\frac{2 x^{m-1}}{a \left(1-m^2\right)}+\frac{x^{m+1} e^{\text{sech}^{-1}\left(a x^2\right)}}{m+1}","-\frac{2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} x^{m-1} \, _2F_1\left(\frac{1}{2},\frac{m-1}{4};\frac{m+3}{4};a^2 x^4\right)}{a \left(1-m^2\right)}-\frac{2 x^{m-1}}{a \left(1-m^2\right)}+\frac{x^{m+1} e^{\text{sech}^{-1}\left(a x^2\right)}}{m+1}",1,"(-2*x^(-1 + m))/(a*(1 - m^2)) + (E^ArcSech[a*x^2]*x^(1 + m))/(1 + m) - (2*x^(-1 + m)*Sqrt[(1 + a*x^2)^(-1)]*Sqrt[1 + a*x^2]*Hypergeometric2F1[1/2, (-1 + m)/4, (3 + m)/4, a^2*x^4])/(a*(1 - m^2))","A",4,4,12,0.3333,1,"{6335, 30, 259, 364}"
58,1,91,0,0.0395333,"\int e^{\text{sech}^{-1}(a x)} x^m \, dx","Int[E^ArcSech[a*x]*x^m,x]","\frac{\sqrt{\frac{1}{a x+1}} \sqrt{a x+1} x^m \, _2F_1\left(\frac{1}{2},\frac{m}{2};\frac{m+2}{2};a^2 x^2\right)}{a m (m+1)}+\frac{x^m}{a m (m+1)}+\frac{x^{m+1} e^{\text{sech}^{-1}(a x)}}{m+1}","\frac{\sqrt{\frac{1}{a x+1}} \sqrt{a x+1} x^m \, _2F_1\left(\frac{1}{2},\frac{m}{2};\frac{m+2}{2};a^2 x^2\right)}{a m (m+1)}+\frac{x^m}{a m (m+1)}+\frac{x^{m+1} e^{\text{sech}^{-1}(a x)}}{m+1}",1,"x^m/(a*m*(1 + m)) + (E^ArcSech[a*x]*x^(1 + m))/(1 + m) + (x^m*Sqrt[(1 + a*x)^(-1)]*Sqrt[1 + a*x]*Hypergeometric2F1[1/2, m/2, (2 + m)/2, a^2*x^2])/(a*m*(1 + m))","A",4,4,10,0.4000,1,"{6335, 30, 125, 364}"
59,1,109,0,0.0751257,"\int e^{\text{sech}^{-1}\left(\frac{a}{x}\right)} x^m \, dx","Int[E^ArcSech[a/x]*x^m,x]","-\frac{\sqrt{\frac{1}{\frac{a}{x}+1}} \sqrt{\frac{a}{x}+1} x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-m-2);-\frac{m}{2};\frac{a^2}{x^2}\right)}{a \left(m^2+3 m+2\right)}-\frac{x^{m+2}}{a \left(m^2+3 m+2\right)}+\frac{x^{m+1} e^{\text{sech}^{-1}\left(\frac{a}{x}\right)}}{m+1}","-\frac{\sqrt{\frac{1}{\frac{a}{x}+1}} \sqrt{\frac{a}{x}+1} x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-m-2);-\frac{m}{2};\frac{a^2}{x^2}\right)}{a \left(m^2+3 m+2\right)}-\frac{x^{m+2}}{a \left(m^2+3 m+2\right)}+\frac{x^{m+1} e^{\text{sech}^{-1}\left(\frac{a}{x}\right)}}{m+1}",1,"(E^ArcSech[a/x]*x^(1 + m))/(1 + m) - x^(2 + m)/(a*(2 + 3*m + m^2)) - (Sqrt[(1 + a/x)^(-1)]*Sqrt[1 + a/x]*x^(2 + m)*Hypergeometric2F1[1/2, (-2 - m)/2, -m/2, a^2/x^2])/(a*(2 + 3*m + m^2))","A",5,5,12,0.4167,1,"{6335, 30, 259, 339, 364}"
60,1,133,0,0.0834416,"\int e^{\text{sech}^{-1}\left(a x^p\right)} x^m \, dx","Int[E^ArcSech[a*x^p]*x^m,x]","\frac{p \sqrt{\frac{1}{a x^p+1}} \sqrt{a x^p+1} x^{m-p+1} \, _2F_1\left(\frac{1}{2},\frac{m-p+1}{2 p};\frac{m+p+1}{2 p};a^2 x^{2 p}\right)}{a (m+1) (m-p+1)}+\frac{p x^{m-p+1}}{a (m+1) (m-p+1)}+\frac{x^{m+1} e^{\text{sech}^{-1}\left(a x^p\right)}}{m+1}","\frac{p \sqrt{\frac{1}{a x^p+1}} \sqrt{a x^p+1} x^{m-p+1} \, _2F_1\left(\frac{1}{2},\frac{m-p+1}{2 p};\frac{m+p+1}{2 p};a^2 x^{2 p}\right)}{a (m+1) (m-p+1)}+\frac{p x^{m-p+1}}{a (m+1) (m-p+1)}+\frac{x^{m+1} e^{\text{sech}^{-1}\left(a x^p\right)}}{m+1}",1,"(E^ArcSech[a*x^p]*x^(1 + m))/(1 + m) + (p*x^(1 + m - p))/(a*(1 + m)*(1 + m - p)) + (p*x^(1 + m - p)*Sqrt[(1 + a*x^p)^(-1)]*Sqrt[1 + a*x^p]*Hypergeometric2F1[1/2, (1 + m - p)/(2*p), (1 + m + p)/(2*p), a^2*x^(2*p)])/(a*(1 + m)*(1 + m - p))","A",4,4,12,0.3333,1,"{6335, 30, 259, 364}"
61,1,119,0,0.0528343,"\int e^{\text{sech}^{-1}\left(a x^p\right)} x \, dx","Int[E^ArcSech[a*x^p]*x,x]","\frac{p x^{2-p} \sqrt{\frac{1}{a x^p+1}} \sqrt{a x^p+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(\frac{2}{p}-1\right);\frac{1}{2} \left(1+\frac{2}{p}\right);a^2 x^{2 p}\right)}{2 a (2-p)}+\frac{p x^{2-p}}{2 a (2-p)}+\frac{1}{2} x^2 e^{\text{sech}^{-1}\left(a x^p\right)}","\frac{p x^{2-p} \sqrt{\frac{1}{a x^p+1}} \sqrt{a x^p+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(\frac{2}{p}-1\right);\frac{1}{2} \left(1+\frac{2}{p}\right);a^2 x^{2 p}\right)}{2 a (2-p)}+\frac{p x^{2-p}}{2 a (2-p)}+\frac{1}{2} x^2 e^{\text{sech}^{-1}\left(a x^p\right)}",1,"(E^ArcSech[a*x^p]*x^2)/2 + (p*x^(2 - p))/(2*a*(2 - p)) + (p*x^(2 - p)*Sqrt[(1 + a*x^p)^(-1)]*Sqrt[1 + a*x^p]*Hypergeometric2F1[1/2, (-1 + 2/p)/2, (1 + 2/p)/2, a^2*x^(2*p)])/(2*a*(2 - p))","A",4,4,10,0.4000,1,"{6335, 30, 259, 364}"
62,1,105,0,0.0468155,"\int e^{\text{sech}^{-1}\left(a x^p\right)} \, dx","Int[E^ArcSech[a*x^p],x]","\frac{p x^{1-p} \sqrt{\frac{1}{a x^p+1}} \sqrt{a x^p+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(\frac{1}{p}-1\right);\frac{p+1}{2 p};a^2 x^{2 p}\right)}{a (1-p)}+\frac{p x^{1-p}}{a (1-p)}+x e^{\text{sech}^{-1}\left(a x^p\right)}","\frac{p x^{1-p} \sqrt{\frac{1}{a x^p+1}} \sqrt{a x^p+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(\frac{1}{p}-1\right);\frac{p+1}{2 p};a^2 x^{2 p}\right)}{a (1-p)}+\frac{p x^{1-p}}{a (1-p)}+x e^{\text{sech}^{-1}\left(a x^p\right)}",1,"E^ArcSech[a*x^p]*x + (p*x^(1 - p))/(a*(1 - p)) + (p*x^(1 - p)*Sqrt[(1 + a*x^p)^(-1)]*Sqrt[1 + a*x^p]*Hypergeometric2F1[1/2, (-1 + p^(-1))/2, (1 + p)/(2*p), a^2*x^(2*p)])/(a*(1 - p))","A",4,4,8,0.5000,1,"{6330, 30, 259, 364}"
63,1,106,0,0.0689316,"\int \frac{e^{\text{sech}^{-1}\left(a x^p\right)}}{x} \, dx","Int[E^ArcSech[a*x^p]/x,x]","-\frac{x^{-p} \sqrt{\frac{1}{a x^p+1}} \sqrt{a x^p+1} \sqrt{1-a^2 x^{2 p}}}{a p}-\frac{x^{-p}}{a p}-\frac{\sqrt{\frac{1}{a x^p+1}} \sqrt{a x^p+1} \csc ^{-1}\left(\frac{x^{-p}}{a}\right)}{p}","-\frac{x^{-p} \sqrt{1-a x^p}}{a p \sqrt{\frac{1}{a x^p+1}}}-\frac{x^{-p}}{a p}-\frac{\sqrt{\frac{1}{a x^p+1}} \sqrt{a x^p+1} \sin ^{-1}\left(a x^p\right)}{p}",1,"-(1/(a*p*x^p)) - (Sqrt[(1 + a*x^p)^(-1)]*Sqrt[1 + a*x^p]*Sqrt[1 - a^2*x^(2*p)])/(a*p*x^p) - (Sqrt[(1 + a*x^p)^(-1)]*Sqrt[1 + a*x^p]*ArcCsc[1/(a*x^p)])/p","A",6,6,12,0.5000,0,"{6334, 259, 345, 242, 277, 216}"
64,1,107,0,0.0604132,"\int \frac{e^{\text{sech}^{-1}\left(a x^p\right)}}{x^2} \, dx","Int[E^ArcSech[a*x^p]/x^2,x]","\frac{p x^{-p-1} \sqrt{\frac{1}{a x^p+1}} \sqrt{a x^p+1} \, _2F_1\left(\frac{1}{2},-\frac{p+1}{2 p};-\frac{1-p}{2 p};a^2 x^{2 p}\right)}{a (p+1)}+\frac{p x^{-p-1}}{a (p+1)}-\frac{e^{\text{sech}^{-1}\left(a x^p\right)}}{x}","\frac{p x^{-p-1} \sqrt{\frac{1}{a x^p+1}} \sqrt{a x^p+1} \, _2F_1\left(\frac{1}{2},-\frac{p+1}{2 p};-\frac{1-p}{2 p};a^2 x^{2 p}\right)}{a (p+1)}+\frac{p x^{-p-1}}{a (p+1)}-\frac{e^{\text{sech}^{-1}\left(a x^p\right)}}{x}",1,"-(E^ArcSech[a*x^p]/x) + (p*x^(-1 - p))/(a*(1 + p)) + (p*x^(-1 - p)*Sqrt[(1 + a*x^p)^(-1)]*Sqrt[1 + a*x^p]*Hypergeometric2F1[1/2, -(1 + p)/(2*p), -(1 - p)/(2*p), a^2*x^(2*p)])/(a*(1 + p))","A",4,4,12,0.3333,1,"{6335, 30, 259, 364}"
65,1,203,0,0.699971,"\int e^{2 \text{sech}^{-1}(a x)} x^4 \, dx","Int[E^(2*ArcSech[a*x])*x^4,x]","\frac{(1-a x) (a x+1)^4}{5 a^5}+\frac{\sqrt{\frac{1-a x}{a x+1}} \left(5-6 \sqrt{\frac{1-a x}{a x+1}}\right) (a x+1)^4}{10 a^5}-\frac{\left(45 \sqrt{\frac{1-a x}{a x+1}}+4\right) (a x+1)^3}{30 a^5}+\frac{5 \sqrt{\frac{1-a x}{a x+1}} (a x+1)^2}{4 a^5}+\frac{\left(4-\sqrt{\frac{1-a x}{a x+1}}\right) (a x+1)}{4 a^5}-\frac{\tan ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)}{2 a^5}","\frac{(1-a x) (a x+1)^4}{5 a^5}+\frac{\sqrt{\frac{1-a x}{a x+1}} \left(5-6 \sqrt{\frac{1-a x}{a x+1}}\right) (a x+1)^4}{10 a^5}-\frac{\left(45 \sqrt{\frac{1-a x}{a x+1}}+4\right) (a x+1)^3}{30 a^5}+\frac{5 \sqrt{\frac{1-a x}{a x+1}} (a x+1)^2}{4 a^5}+\frac{\left(4-\sqrt{\frac{1-a x}{a x+1}}\right) (a x+1)}{4 a^5}-\frac{\tan ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)}{2 a^5}",1,"(5*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2)/(4*a^5) + ((1 - a*x)*(1 + a*x)^4)/(5*a^5) + (Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^4*(5 - 6*Sqrt[(1 - a*x)/(1 + a*x)]))/(10*a^5) + ((1 + a*x)*(4 - Sqrt[(1 - a*x)/(1 + a*x)]))/(4*a^5) - ((1 + a*x)^3*(4 + 45*Sqrt[(1 - a*x)/(1 + a*x)]))/(30*a^5) - ArcTan[Sqrt[(1 - a*x)/(1 + a*x)]]/(2*a^5)","A",9,6,12,0.5000,1,"{6337, 1804, 1811, 1814, 639, 203}"
66,1,117,0,0.5464329,"\int e^{2 \text{sech}^{-1}(a x)} x^3 \, dx","Int[E^(2*ArcSech[a*x])*x^3,x]","\frac{(1-a x) (a x+1)^3}{4 a^4}+\frac{\sqrt{\frac{1-a x}{a x+1}} \left(4-3 \sqrt{\frac{1-a x}{a x+1}}\right) (a x+1)^3}{6 a^4}+\frac{\left(3-8 \sqrt{\frac{1-a x}{a x+1}}\right) (a x+1)^2}{6 a^4}-\frac{x}{a^3}","\frac{(1-a x) (a x+1)^3}{4 a^4}+\frac{\sqrt{\frac{1-a x}{a x+1}} \left(4-3 \sqrt{\frac{1-a x}{a x+1}}\right) (a x+1)^3}{6 a^4}+\frac{\left(3-8 \sqrt{\frac{1-a x}{a x+1}}\right) (a x+1)^2}{6 a^4}-\frac{x}{a^3}",1,"-(x/a^3) + ((1 - a*x)*(1 + a*x)^3)/(4*a^4) + ((1 + a*x)^2*(3 - 8*Sqrt[(1 - a*x)/(1 + a*x)]))/(6*a^4) + (Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^3*(4 - 3*Sqrt[(1 - a*x)/(1 + a*x)]))/(6*a^4)","A",8,6,12,0.5000,1,"{6337, 1804, 1811, 1814, 12, 261}"
67,1,169,0,0.4650503,"\int e^{2 \text{sech}^{-1}(a x)} x^2 \, dx","Int[E^(2*ArcSech[a*x])*x^2,x]","\frac{(a x+1)^3 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^4}{12 a^3}-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)^2 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^3}{6 a^3}+\frac{(a x+1) \left(1-\sqrt{\frac{1-a x}{a x+1}}\right) \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}{2 a^3}-\frac{2 \tan ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)}{a^3}","\frac{(a x+1)^3 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^4}{12 a^3}-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)^2 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^3}{6 a^3}+\frac{(a x+1) \left(1-\sqrt{\frac{1-a x}{a x+1}}\right) \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}{2 a^3}-\frac{2 \tan ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)}{a^3}",1,"((1 + a*x)*(1 - Sqrt[(1 - a*x)/(1 + a*x)])*(1 + Sqrt[(1 - a*x)/(1 + a*x)]))/(2*a^3) - (Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^3)/(6*a^3) + ((1 + a*x)^3*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^4)/(12*a^3) - (2*ArcTan[Sqrt[(1 - a*x)/(1 + a*x)]])/a^3","A",7,6,12,0.5000,1,"{6337, 821, 12, 729, 723, 203}"
68,1,85,0,0.4342263,"\int e^{2 \text{sech}^{-1}(a x)} x \, dx","Int[E^(2*ArcSech[a*x])*x,x]","-\frac{(a x+1)^2}{2 a^2}+\frac{\left(2 \sqrt{\frac{1-a x}{a x+1}}+1\right) (a x+1)}{a^2}+\frac{2 \log (a x+1)}{a^2}+\frac{4 \log \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}{a^2}","-\frac{(a x+1)^2}{2 a^2}+\frac{\left(2 \sqrt{\frac{1-a x}{a x+1}}+1\right) (a x+1)}{a^2}+\frac{2 \log (a x+1)}{a^2}+\frac{4 \log \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}{a^2}",1,"-(1 + a*x)^2/(2*a^2) + ((1 + a*x)*(1 + 2*Sqrt[(1 - a*x)/(1 + a*x)]))/a^2 + (2*Log[1 + a*x])/a^2 + (4*Log[1 - Sqrt[(1 - a*x)/(1 + a*x)]])/a^2","A",8,5,10,0.5000,1,"{6337, 1647, 1593, 801, 260}"
69,1,57,0,0.1735856,"\int e^{2 \text{sech}^{-1}(a x)} \, dx","Int[E^(2*ArcSech[a*x]),x]","-\frac{4}{a \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}+\frac{4 \tan ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)}{a}-x","-\frac{4}{a \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}+\frac{4 \tan ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)}{a}-x",1,"-x - 4/(a*(1 - Sqrt[(1 - a*x)/(1 + a*x)])) + (4*ArcTan[Sqrt[(1 - a*x)/(1 + a*x)]])/a","A",7,5,8,0.6250,1,"{6332, 1647, 12, 801, 203}"
70,1,86,0,0.4455473,"\int \frac{e^{2 \text{sech}^{-1}(a x)}}{x} \, dx","Int[E^(2*ArcSech[a*x])/x,x]","\frac{2}{1-\sqrt{\frac{1-a x}{a x+1}}}-\frac{2}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}-\log (a x+1)-2 \log \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)","\frac{2}{1-\sqrt{\frac{1-a x}{a x+1}}}-\frac{2}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}-\log (a x+1)-2 \log \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)",1,"-2/(1 - Sqrt[(1 - a*x)/(1 + a*x)])^2 + 2/(1 - Sqrt[(1 - a*x)/(1 + a*x)]) - Log[1 + a*x] - 2*Log[1 - Sqrt[(1 - a*x)/(1 + a*x)]]","A",5,3,12,0.2500,1,"{6337, 1629, 260}"
71,1,57,0,0.390062,"\int \frac{e^{2 \text{sech}^{-1}(a x)}}{x^2} \, dx","Int[E^(2*ArcSech[a*x])/x^2,x]","\frac{2 a}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}-\frac{4 a}{3 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}","\frac{2 a}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}-\frac{4 a}{3 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}",1,"(-4*a)/(3*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^3) + (2*a)/(1 - Sqrt[(1 - a*x)/(1 + a*x)])^2","A",4,2,12,0.1667,1,"{6337, 43}"
72,1,147,0,0.45291,"\int \frac{e^{2 \text{sech}^{-1}(a x)}}{x^3} \, dx","Int[E^(2*ArcSech[a*x])/x^3,x]","\frac{a^2}{2 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}-\frac{3 a^2}{2 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}+\frac{2 a^2}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}-\frac{a^2}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^4}+\frac{1}{2} a^2 \tanh ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)","\frac{a^2}{2 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}-\frac{3 a^2}{2 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}+\frac{2 a^2}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}-\frac{a^2}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^4}+\frac{1}{2} a^2 \tanh ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)",1,"-(a^2/(1 - Sqrt[(1 - a*x)/(1 + a*x)])^4) + (2*a^2)/(1 - Sqrt[(1 - a*x)/(1 + a*x)])^3 - (3*a^2)/(2*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^2) + a^2/(2*(1 - Sqrt[(1 - a*x)/(1 + a*x)])) + (a^2*ArcTanh[Sqrt[(1 - a*x)/(1 + a*x)]])/2","A",5,3,12,0.2500,1,"{6337, 1612, 207}"
73,1,183,0,0.5049215,"\int \frac{e^{2 \text{sech}^{-1}(a x)}}{x^4} \, dx","Int[E^(2*ArcSech[a*x])/x^4,x]","-\frac{a^3}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}-\frac{a^3}{4 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}+\frac{3 a^3}{2 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}-\frac{7 a^3}{3 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}+\frac{2 a^3}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^4}-\frac{4 a^3}{5 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^5}","-\frac{a^3}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}-\frac{a^3}{4 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}+\frac{3 a^3}{2 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}-\frac{7 a^3}{3 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}+\frac{2 a^3}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^4}-\frac{4 a^3}{5 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^5}",1,"(-4*a^3)/(5*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^5) + (2*a^3)/(1 - Sqrt[(1 - a*x)/(1 + a*x)])^4 - (7*a^3)/(3*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^3) + (3*a^3)/(2*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^2) - a^3/(4*(1 - Sqrt[(1 - a*x)/(1 + a*x)])) - a^3/(4*(1 + Sqrt[(1 - a*x)/(1 + a*x)]))","A",4,2,12,0.1667,1,"{6337, 1612}"
74,1,267,0,0.5425055,"\int \frac{e^{2 \text{sech}^{-1}(a x)}}{x^5} \, dx","Int[E^(2*ArcSech[a*x])/x^5,x]","\frac{3 a^4}{8 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}+\frac{a^4}{8 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}-\frac{11 a^4}{8 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}-\frac{a^4}{8 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}+\frac{8 a^4}{3 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}-\frac{3 a^4}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^4}+\frac{2 a^4}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^5}-\frac{2 a^4}{3 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^6}+\frac{1}{4} a^4 \tanh ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)","\frac{3 a^4}{8 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}+\frac{a^4}{8 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}-\frac{11 a^4}{8 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}-\frac{a^4}{8 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}+\frac{8 a^4}{3 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}-\frac{3 a^4}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^4}+\frac{2 a^4}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^5}-\frac{2 a^4}{3 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^6}+\frac{1}{4} a^4 \tanh ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)",1,"(-2*a^4)/(3*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^6) + (2*a^4)/(1 - Sqrt[(1 - a*x)/(1 + a*x)])^5 - (3*a^4)/(1 - Sqrt[(1 - a*x)/(1 + a*x)])^4 + (8*a^4)/(3*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^3) - (11*a^4)/(8*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^2) + (3*a^4)/(8*(1 - Sqrt[(1 - a*x)/(1 + a*x)])) - a^4/(8*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^2) + a^4/(8*(1 + Sqrt[(1 - a*x)/(1 + a*x)])) + (a^4*ArcTanh[Sqrt[(1 - a*x)/(1 + a*x)]])/4","A",5,3,12,0.2500,1,"{6337, 1612, 207}"
75,1,301,0,0.5758366,"\int \frac{e^{2 \text{sech}^{-1}(a x)}}{x^6} \, dx","Int[E^(2*ArcSech[a*x])/x^6,x]","-\frac{a^5}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}-\frac{a^5}{4 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}+\frac{11 a^5}{8 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}+\frac{a^5}{8 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}-\frac{35 a^5}{12 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}-\frac{a^5}{12 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^3}+\frac{4 a^5}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^4}-\frac{18 a^5}{5 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^5}+\frac{2 a^5}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^6}-\frac{4 a^5}{7 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^7}","-\frac{a^5}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}-\frac{a^5}{4 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}+\frac{11 a^5}{8 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}+\frac{a^5}{8 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}-\frac{35 a^5}{12 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}-\frac{a^5}{12 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^3}+\frac{4 a^5}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^4}-\frac{18 a^5}{5 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^5}+\frac{2 a^5}{\left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^6}-\frac{4 a^5}{7 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^7}",1,"(-4*a^5)/(7*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^7) + (2*a^5)/(1 - Sqrt[(1 - a*x)/(1 + a*x)])^6 - (18*a^5)/(5*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^5) + (4*a^5)/(1 - Sqrt[(1 - a*x)/(1 + a*x)])^4 - (35*a^5)/(12*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^3) + (11*a^5)/(8*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^2) - a^5/(4*(1 - Sqrt[(1 - a*x)/(1 + a*x)])) - a^5/(12*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^3) + a^5/(8*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^2) - a^5/(4*(1 + Sqrt[(1 - a*x)/(1 + a*x)]))","A",4,2,12,0.1667,1,"{6337, 1612}"
76,1,147,0,0.6192084,"\int e^{-\text{sech}^{-1}(a x)} x^4 \, dx","Int[x^4/E^ArcSech[a*x],x]","-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)^5}{5 a^5}+\frac{\left(16 \sqrt{\frac{1-a x}{a x+1}}+5\right) (a x+1)^4}{20 a^5}-\frac{\left(17 \sqrt{\frac{1-a x}{a x+1}}+15\right) (a x+1)^3}{15 a^5}+\frac{\left(4 \sqrt{\frac{1-a x}{a x+1}}+9\right) (a x+1)^2}{6 a^5}-\frac{x}{a^4}","-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)^5}{5 a^5}+\frac{\left(16 \sqrt{\frac{1-a x}{a x+1}}+5\right) (a x+1)^4}{20 a^5}-\frac{\left(17 \sqrt{\frac{1-a x}{a x+1}}+15\right) (a x+1)^3}{15 a^5}+\frac{\left(4 \sqrt{\frac{1-a x}{a x+1}}+9\right) (a x+1)^2}{6 a^5}-\frac{x}{a^4}",1,"-(x/a^4) - (Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^5)/(5*a^5) + ((1 + a*x)^2*(9 + 4*Sqrt[(1 - a*x)/(1 + a*x)]))/(6*a^5) + ((1 + a*x)^4*(5 + 16*Sqrt[(1 - a*x)/(1 + a*x)]))/(20*a^5) - ((1 + a*x)^3*(15 + 17*Sqrt[(1 - a*x)/(1 + a*x)]))/(15*a^5)","A",8,5,12,0.4167,1,"{6337, 1804, 1814, 12, 261}"
77,1,163,0,0.5694601,"\int e^{-\text{sech}^{-1}(a x)} x^3 \, dx","Int[x^3/E^ArcSech[a*x],x]","-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)^4}{4 a^4}+\frac{\left(9 \sqrt{\frac{1-a x}{a x+1}}+4\right) (a x+1)^3}{12 a^4}-\frac{\left(5 \sqrt{\frac{1-a x}{a x+1}}+8\right) (a x+1)^2}{8 a^4}+\frac{\left(\sqrt{\frac{1-a x}{a x+1}}+8\right) (a x+1)}{8 a^4}+\frac{\tan ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)}{4 a^4}","-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)^4}{4 a^4}+\frac{\left(9 \sqrt{\frac{1-a x}{a x+1}}+4\right) (a x+1)^3}{12 a^4}-\frac{\left(5 \sqrt{\frac{1-a x}{a x+1}}+8\right) (a x+1)^2}{8 a^4}+\frac{\left(\sqrt{\frac{1-a x}{a x+1}}+8\right) (a x+1)}{8 a^4}+\frac{\tan ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)}{4 a^4}",1,"-(Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^4)/(4*a^4) + ((1 + a*x)*(8 + Sqrt[(1 - a*x)/(1 + a*x)]))/(8*a^4) - ((1 + a*x)^2*(8 + 5*Sqrt[(1 - a*x)/(1 + a*x)]))/(8*a^4) + ((1 + a*x)^3*(4 + 9*Sqrt[(1 - a*x)/(1 + a*x)]))/(12*a^4) + ArcTan[Sqrt[(1 - a*x)/(1 + a*x)]]/(4*a^4)","A",7,5,12,0.4167,1,"{6337, 1804, 1814, 639, 203}"
78,1,75,0,0.5132538,"\int e^{-\text{sech}^{-1}(a x)} x^2 \, dx","Int[x^2/E^ArcSech[a*x],x]","-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)^3}{3 a^3}+\frac{\left(4 \sqrt{\frac{1-a x}{a x+1}}+3\right) (a x+1)^2}{6 a^3}-\frac{x}{a^2}","-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)^3}{3 a^3}+\frac{\left(4 \sqrt{\frac{1-a x}{a x+1}}+3\right) (a x+1)^2}{6 a^3}-\frac{x}{a^2}",1,"-(x/a^2) - (Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^3)/(3*a^3) + ((1 + a*x)^2*(3 + 4*Sqrt[(1 - a*x)/(1 + a*x)]))/(6*a^3)","A",6,5,12,0.4167,1,"{6337, 1804, 1814, 12, 261}"
79,1,94,0,0.3087492,"\int e^{-\text{sech}^{-1}(a x)} x \, dx","Int[x/E^ArcSech[a*x],x]","\frac{(a x+1)^2 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}{4 a^2}+\frac{(a x+1) \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}{2 a^2}+\frac{\tan ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)}{a^2}","\frac{(a x+1)^2 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}{4 a^2}+\frac{(a x+1) \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}{2 a^2}+\frac{\tan ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)}{a^2}",1,"((1 + a*x)^2*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^2)/(4*a^2) + ((1 + a*x)*(1 + Sqrt[(1 - a*x)/(1 + a*x)]))/(2*a^2) + ArcTan[Sqrt[(1 - a*x)/(1 + a*x)]]/a^2","A",5,4,10,0.4000,1,"{6337, 819, 639, 203}"
80,1,65,0,0.1656415,"\int e^{-\text{sech}^{-1}(a x)} \, dx","Int[E^(-ArcSech[a*x]),x]","-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)}{a}+\frac{\log (a x+1)}{a}+\frac{2 \log \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}{a}","-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)}{a}+\frac{\log (a x+1)}{a}+\frac{2 \log \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}{a}",1,"-((Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x))/a) + Log[1 + a*x]/a + (2*Log[1 + Sqrt[(1 - a*x)/(1 + a*x)]])/a","A",6,4,8,0.5000,1,"{6332, 1647, 801, 260}"
81,1,46,0,0.4012553,"\int \frac{e^{-\text{sech}^{-1}(a x)}}{x} \, dx","Int[1/(E^ArcSech[a*x]*x),x]","-\frac{2}{\sqrt{\frac{1-a x}{a x+1}}+1}-2 \tan ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)","-\frac{2}{\sqrt{\frac{1-a x}{a x+1}}+1}-2 \tan ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)",1,"-2/(1 + Sqrt[(1 - a*x)/(1 + a*x)]) - 2*ArcTan[Sqrt[(1 - a*x)/(1 + a*x)]]","A",5,3,12,0.2500,1,"{6337, 801, 203}"
82,1,72,0,0.3827688,"\int \frac{e^{-\text{sech}^{-1}(a x)}}{x^2} \, dx","Int[1/(E^ArcSech[a*x]*x^2),x]","\frac{a}{\sqrt{\frac{1-a x}{a x+1}}+1}-\frac{a}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}+a \left(-\tanh ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)\right)","\frac{a}{\sqrt{\frac{1-a x}{a x+1}}+1}-\frac{a}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}+a \left(-\tanh ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)\right)",1,"-(a/(1 + Sqrt[(1 - a*x)/(1 + a*x)])^2) + a/(1 + Sqrt[(1 - a*x)/(1 + a*x)]) - a*ArcTanh[Sqrt[(1 - a*x)/(1 + a*x)]]","A",5,3,12,0.2500,1,"{6337, 77, 207}"
83,1,116,0,0.4238089,"\int \frac{e^{-\text{sech}^{-1}(a x)}}{x^3} \, dx","Int[1/(E^ArcSech[a*x]*x^3),x]","-\frac{a^2}{2 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}-\frac{a^2}{2 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}+\frac{a^2}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}-\frac{2 a^2}{3 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^3}","-\frac{a^2}{2 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}-\frac{a^2}{2 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}+\frac{a^2}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}-\frac{2 a^2}{3 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^3}",1,"-a^2/(2*(1 - Sqrt[(1 - a*x)/(1 + a*x)])) - (2*a^2)/(3*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^3) + a^2/(1 + Sqrt[(1 - a*x)/(1 + a*x)])^2 - a^2/(2*(1 + Sqrt[(1 - a*x)/(1 + a*x)]))","A",4,2,12,0.1667,1,"{6337, 1612}"
84,1,200,0,0.5004691,"\int \frac{e^{-\text{sech}^{-1}(a x)}}{x^4} \, dx","Int[1/(E^ArcSech[a*x]*x^4),x]","\frac{a^3}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}+\frac{a^3}{2 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}-\frac{a^3}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}-\frac{a^3}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}+\frac{a^3}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^3}-\frac{a^3}{2 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^4}-\frac{1}{4} a^3 \tanh ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)","\frac{a^3}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}+\frac{a^3}{2 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}-\frac{a^3}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}-\frac{a^3}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}+\frac{a^3}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^3}-\frac{a^3}{2 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^4}-\frac{1}{4} a^3 \tanh ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)",1,"-a^3/(4*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^2) + a^3/(4*(1 - Sqrt[(1 - a*x)/(1 + a*x)])) - a^3/(2*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^4) + a^3/(1 + Sqrt[(1 - a*x)/(1 + a*x)])^3 - a^3/(1 + Sqrt[(1 - a*x)/(1 + a*x)])^2 + a^3/(2*(1 + Sqrt[(1 - a*x)/(1 + a*x)])) - (a^3*ArcTanh[Sqrt[(1 - a*x)/(1 + a*x)]])/4","A",5,3,12,0.2500,1,"{6337, 1612, 207}"
85,1,233,0,0.4998711,"\int \frac{e^{-\text{sech}^{-1}(a x)}}{x^5} \, dx","Int[1/(E^ArcSech[a*x]*x^5),x]","-\frac{3 a^4}{8 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}-\frac{3 a^4}{8 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}+\frac{a^4}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}+\frac{a^4}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}-\frac{a^4}{6 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}-\frac{4 a^4}{3 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^3}+\frac{a^4}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^4}-\frac{2 a^4}{5 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^5}","-\frac{3 a^4}{8 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}-\frac{3 a^4}{8 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}+\frac{a^4}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}+\frac{a^4}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}-\frac{a^4}{6 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}-\frac{4 a^4}{3 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^3}+\frac{a^4}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^4}-\frac{2 a^4}{5 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^5}",1,"-a^4/(6*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^3) + a^4/(4*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^2) - (3*a^4)/(8*(1 - Sqrt[(1 - a*x)/(1 + a*x)])) - (2*a^4)/(5*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^5) + a^4/(1 + Sqrt[(1 - a*x)/(1 + a*x)])^4 - (4*a^4)/(3*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^3) + a^4/(1 + Sqrt[(1 - a*x)/(1 + a*x)])^2 - (3*a^4)/(8*(1 + Sqrt[(1 - a*x)/(1 + a*x)]))","A",4,2,12,0.1667,1,"{6337, 1612}"
86,1,320,0,0.5668792,"\int \frac{e^{-\text{sech}^{-1}(a x)}}{x^6} \, dx","Int[1/(E^ArcSech[a*x]*x^6),x]","\frac{a^5}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}+\frac{3 a^5}{8 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}-\frac{3 a^5}{8 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}-\frac{a^5}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}+\frac{a^5}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}+\frac{19 a^5}{12 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^3}-\frac{a^5}{8 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^4}-\frac{13 a^5}{8 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^4}+\frac{a^5}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^5}-\frac{a^5}{3 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^6}-\frac{1}{8} a^5 \tanh ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)","\frac{a^5}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}+\frac{3 a^5}{8 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}-\frac{3 a^5}{8 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}-\frac{a^5}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}+\frac{a^5}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}+\frac{19 a^5}{12 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^3}-\frac{a^5}{8 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^4}-\frac{13 a^5}{8 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^4}+\frac{a^5}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^5}-\frac{a^5}{3 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^6}-\frac{1}{8} a^5 \tanh ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)",1,"-a^5/(8*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^4) + a^5/(4*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^3) - (3*a^5)/(8*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^2) + a^5/(4*(1 - Sqrt[(1 - a*x)/(1 + a*x)])) - a^5/(3*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^6) + a^5/(1 + Sqrt[(1 - a*x)/(1 + a*x)])^5 - (13*a^5)/(8*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^4) + (19*a^5)/(12*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^3) - a^5/(1 + Sqrt[(1 - a*x)/(1 + a*x)])^2 + (3*a^5)/(8*(1 + Sqrt[(1 - a*x)/(1 + a*x)])) - (a^5*ArcTanh[Sqrt[(1 - a*x)/(1 + a*x)]])/8","A",5,3,12,0.2500,1,"{6337, 1612, 207}"
87,1,353,0,0.6049048,"\int \frac{e^{-\text{sech}^{-1}(a x)}}{x^7} \, dx","Int[1/(E^ArcSech[a*x]*x^7),x]","-\frac{5 a^6}{16 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}-\frac{5 a^6}{16 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}+\frac{3 a^6}{8 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}+\frac{a^6}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}-\frac{5 a^6}{12 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}-\frac{11 a^6}{6 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^3}+\frac{a^6}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^4}+\frac{9 a^6}{4 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^4}-\frac{a^6}{10 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^5}-\frac{19 a^6}{10 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^5}+\frac{a^6}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^6}-\frac{2 a^6}{7 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^7}","-\frac{5 a^6}{16 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)}-\frac{5 a^6}{16 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)}+\frac{3 a^6}{8 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^2}+\frac{a^6}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^2}-\frac{5 a^6}{12 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^3}-\frac{11 a^6}{6 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^3}+\frac{a^6}{4 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^4}+\frac{9 a^6}{4 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^4}-\frac{a^6}{10 \left(1-\sqrt{\frac{1-a x}{a x+1}}\right)^5}-\frac{19 a^6}{10 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^5}+\frac{a^6}{\left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^6}-\frac{2 a^6}{7 \left(\sqrt{\frac{1-a x}{a x+1}}+1\right)^7}",1,"-a^6/(10*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^5) + a^6/(4*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^4) - (5*a^6)/(12*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^3) + (3*a^6)/(8*(1 - Sqrt[(1 - a*x)/(1 + a*x)])^2) - (5*a^6)/(16*(1 - Sqrt[(1 - a*x)/(1 + a*x)])) - (2*a^6)/(7*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^7) + a^6/(1 + Sqrt[(1 - a*x)/(1 + a*x)])^6 - (19*a^6)/(10*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^5) + (9*a^6)/(4*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^4) - (11*a^6)/(6*(1 + Sqrt[(1 - a*x)/(1 + a*x)])^3) + a^6/(1 + Sqrt[(1 - a*x)/(1 + a*x)])^2 - (5*a^6)/(16*(1 + Sqrt[(1 - a*x)/(1 + a*x)]))","A",4,2,12,0.1667,1,"{6337, 1612}"
88,1,89,0,0.2721187,"\int \frac{e^{\text{sech}^{-1}(c x)} (d x)^m}{1-c^2 x^2} \, dx","Int[(E^ArcSech[c*x]*(d*x)^m)/(1 - c^2*x^2),x]","\frac{\sqrt{\frac{1}{c x+1}} \sqrt{c x+1} (d x)^m \, _2F_1\left(\frac{1}{2},\frac{m}{2};\frac{m+2}{2};c^2 x^2\right)}{c m}+\frac{(d x)^m \, _2F_1\left(1,\frac{m}{2};\frac{m+2}{2};c^2 x^2\right)}{c m}","\frac{\sqrt{\frac{1}{c x+1}} \sqrt{c x+1} (d x)^m \, _2F_1\left(\frac{1}{2},\frac{m}{2};\frac{m+2}{2};c^2 x^2\right)}{c m}+\frac{(d x)^m \, _2F_1\left(1,\frac{m}{2};\frac{m+2}{2};c^2 x^2\right)}{c m}",1,"((d*x)^m*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Hypergeometric2F1[1/2, m/2, (2 + m)/2, c^2*x^2])/(c*m) + ((d*x)^m*Hypergeometric2F1[1, m/2, (2 + m)/2, c^2*x^2])/(c*m)","A",5,4,24,0.1667,1,"{6341, 6677, 125, 364}"
89,1,88,0,0.1808969,"\int \frac{e^{\text{sech}^{-1}(c x)} x^4}{1-c^2 x^2} \, dx","Int[(E^ArcSech[c*x]*x^4)/(1 - c^2*x^2),x]","-\frac{x^2 \sqrt{1-c x}}{3 c^3 \sqrt{\frac{1}{c x+1}}}-\frac{x^2}{2 c^3}-\frac{\log \left(1-c^2 x^2\right)}{2 c^5}-\frac{2 \sqrt{1-c x}}{3 c^5 \sqrt{\frac{1}{c x+1}}}","-\frac{x^2 \sqrt{1-c x}}{3 c^3 \sqrt{\frac{1}{c x+1}}}-\frac{x^2}{2 c^3}-\frac{\log \left(1-c^2 x^2\right)}{2 c^5}-\frac{2 \sqrt{1-c x}}{3 c^5 \sqrt{\frac{1}{c x+1}}}",1,"-x^2/(2*c^3) - (2*Sqrt[1 - c*x])/(3*c^5*Sqrt[(1 + c*x)^(-1)]) - (x^2*Sqrt[1 - c*x])/(3*c^3*Sqrt[(1 + c*x)^(-1)]) - Log[1 - c^2*x^2]/(2*c^5)","A",8,7,22,0.3182,1,"{6341, 1956, 100, 12, 74, 266, 43}"
90,1,75,0,0.1651227,"\int \frac{e^{\text{sech}^{-1}(c x)} x^3}{1-c^2 x^2} \, dx","Int[(E^ArcSech[c*x]*x^3)/(1 - c^2*x^2),x]","-\frac{x \sqrt{1-c x}}{2 c^3 \sqrt{\frac{1}{c x+1}}}-\frac{x}{c^3}+\frac{\sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{2 c^4}+\frac{\tanh ^{-1}(c x)}{c^4}","-\frac{x \sqrt{1-c x}}{2 c^3 \sqrt{\frac{1}{c x+1}}}-\frac{x}{c^3}+\frac{\sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{2 c^4}+\frac{\tanh ^{-1}(c x)}{c^4}",1,"-(x/c^3) - (x*Sqrt[1 - c*x])/(2*c^3*Sqrt[(1 + c*x)^(-1)]) + (Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/(2*c^4) + ArcTanh[c*x]/c^4","A",7,7,22,0.3182,1,"{6341, 1956, 90, 41, 216, 321, 206}"
91,1,45,0,0.1250383,"\int \frac{e^{\text{sech}^{-1}(c x)} x^2}{1-c^2 x^2} \, dx","Int[(E^ArcSech[c*x]*x^2)/(1 - c^2*x^2),x]","-\frac{\log \left(1-c^2 x^2\right)}{2 c^3}-\frac{\sqrt{1-c x}}{c^3 \sqrt{\frac{1}{c x+1}}}","-\frac{\log \left(1-c^2 x^2\right)}{2 c^3}-\frac{\sqrt{1-c x}}{c^3 \sqrt{\frac{1}{c x+1}}}",1,"-(Sqrt[1 - c*x]/(c^3*Sqrt[(1 + c*x)^(-1)])) - Log[1 - c^2*x^2]/(2*c^3)","A",4,4,22,0.1818,1,"{6341, 1956, 74, 260}"
92,1,37,0,0.113641,"\int \frac{e^{\text{sech}^{-1}(c x)} x}{1-c^2 x^2} \, dx","Int[(E^ArcSech[c*x]*x)/(1 - c^2*x^2),x]","\frac{\sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{c^2}+\frac{\tanh ^{-1}(c x)}{c^2}","\frac{\sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{c^2}+\frac{\tanh ^{-1}(c x)}{c^2}",1,"(Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/c^2 + ArcTanh[c*x]/c^2","A",5,5,20,0.2500,1,"{6341, 6677, 41, 216, 206}"
93,1,71,0,0.1194087,"\int \frac{e^{\text{sech}^{-1}(c x)}}{1-c^2 x^2} \, dx","Int[E^ArcSech[c*x]/(1 - c^2*x^2),x]","-\frac{\log \left(1-c^2 x^2\right)}{2 c}+\frac{\log (x)}{c}-\frac{\sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c x} \sqrt{c x+1}\right)}{c}","-\frac{\log \left(1-c^2 x^2\right)}{2 c}+\frac{\log (x)}{c}-\frac{\sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c x} \sqrt{c x+1}\right)}{c}",1,"-((Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[1 - c*x]*Sqrt[1 + c*x]])/c) + Log[x]/c - Log[1 - c^2*x^2]/(2*c)","A",8,8,19,0.4211,1,"{6339, 1956, 92, 208, 266, 36, 29, 31}"
94,1,42,0,0.1426128,"\int \frac{e^{\text{sech}^{-1}(c x)}}{x \left(1-c^2 x^2\right)} \, dx","Int[E^ArcSech[c*x]/(x*(1 - c^2*x^2)),x]","-\frac{\sqrt{1-c x}}{c x \sqrt{\frac{1}{c x+1}}}-\frac{1}{c x}+\tanh ^{-1}(c x)","-\frac{\sqrt{1-c x}}{c x \sqrt{\frac{1}{c x+1}}}-\frac{1}{c x}+\tanh ^{-1}(c x)",1,"-(1/(c*x)) - Sqrt[1 - c*x]/(c*x*Sqrt[(1 + c*x)^(-1)]) + ArcTanh[c*x]","A",5,5,22,0.2273,1,"{6341, 1956, 95, 325, 206}"
95,1,108,0,0.1764611,"\int \frac{e^{\text{sech}^{-1}(c x)}}{x^2 \left(1-c^2 x^2\right)} \, dx","Int[E^ArcSech[c*x]/(x^2*(1 - c^2*x^2)),x]","-\frac{1}{2} c \log \left(1-c^2 x^2\right)-\frac{\sqrt{1-c x}}{2 c x^2 \sqrt{\frac{1}{c x+1}}}-\frac{1}{2 c x^2}+c \log (x)-\frac{1}{2} c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c x} \sqrt{c x+1}\right)","-\frac{1}{2} c \log \left(1-c^2 x^2\right)-\frac{\sqrt{1-c x}}{2 c x^2 \sqrt{\frac{1}{c x+1}}}-\frac{1}{2 c x^2}+c \log (x)-\frac{1}{2} c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c x} \sqrt{c x+1}\right)",1,"-1/(2*c*x^2) - Sqrt[1 - c*x]/(2*c*x^2*Sqrt[(1 + c*x)^(-1)]) - (c*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[1 - c*x]*Sqrt[1 + c*x]])/2 + c*Log[x] - (c*Log[1 - c^2*x^2])/2","A",9,8,22,0.3636,1,"{6341, 1956, 103, 12, 92, 208, 266, 44}"
96,1,85,0,0.1653157,"\int \frac{e^{\text{sech}^{-1}(c x)}}{x^3 \left(1-c^2 x^2\right)} \, dx","Int[E^ArcSech[c*x]/(x^3*(1 - c^2*x^2)),x]","c^2 \tanh ^{-1}(c x)-\frac{\sqrt{1-c x}}{3 c x^3 \sqrt{\frac{1}{c x+1}}}-\frac{1}{3 c x^3}-\frac{2 c \sqrt{1-c x}}{3 x \sqrt{\frac{1}{c x+1}}}-\frac{c}{x}","c^2 \tanh ^{-1}(c x)-\frac{\sqrt{1-c x}}{3 c x^3 \sqrt{\frac{1}{c x+1}}}-\frac{1}{3 c x^3}-\frac{2 c \sqrt{1-c x}}{3 x \sqrt{\frac{1}{c x+1}}}-\frac{c}{x}",1,"-1/(3*c*x^3) - c/x - Sqrt[1 - c*x]/(3*c*x^3*Sqrt[(1 + c*x)^(-1)]) - (2*c*Sqrt[1 - c*x])/(3*x*Sqrt[(1 + c*x)^(-1)]) + c^2*ArcTanh[c*x]","A",8,7,22,0.3182,1,"{6341, 1956, 103, 12, 95, 325, 206}"
97,1,26,0,1.0515824,"\int \frac{x \left(-1+a e^{\text{sech}^{-1}(a x)} x\right)}{1-a^2 x^2} \, dx","Int[(x*(-1 + a*E^ArcSech[a*x]*x))/(1 - a^2*x^2),x]","-\frac{\sqrt{1-a x}}{a^2 \sqrt{\frac{1}{a x+1}}}","-\frac{x e^{\text{sech}^{-1}(a x)}}{a}",1,"-(Sqrt[1 - a*x]/(a^2*Sqrt[(1 + a*x)^(-1)]))","B",7,5,25,0.2000,0,"{6725, 260, 6341, 1956, 74}"
98,1,61,0,0.0977936,"\int \frac{\text{sech}^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx","Int[ArcSech[a + b*x]/((a*d)/b + d*x),x]","-\frac{\text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a+b x)}\right)}{2 d}+\frac{\text{sech}^{-1}(a+b x)^2}{2 d}-\frac{\text{sech}^{-1}(a+b x) \log \left(e^{2 \text{sech}^{-1}(a+b x)}+1\right)}{d}","-\frac{\text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a+b x)}\right)}{2 d}+\frac{\text{sech}^{-1}(a+b x)^2}{2 d}-\frac{\text{sech}^{-1}(a+b x) \log \left(e^{2 \text{sech}^{-1}(a+b x)}+1\right)}{d}",1,"ArcSech[a + b*x]^2/(2*d) - (ArcSech[a + b*x]*Log[1 + E^(2*ArcSech[a + b*x])])/d - PolyLog[2, -E^(2*ArcSech[a + b*x])]/(2*d)","A",8,8,19,0.4211,1,"{6319, 12, 6281, 5660, 3718, 2190, 2279, 2391}"
99,1,57,0,0.115012,"\int x^3 \text{sech}^{-1}\left(a+b x^4\right) \, dx","Int[x^3*ArcSech[a + b*x^4],x]","\frac{\left(a+b x^4\right) \text{sech}^{-1}\left(a+b x^4\right)}{4 b}-\frac{\tan ^{-1}\left(\sqrt{\frac{-a-b x^4+1}{a+b x^4+1}}\right)}{2 b}","\frac{\left(a+b x^4\right) \text{sech}^{-1}\left(a+b x^4\right)}{4 b}-\frac{\tan ^{-1}\left(\sqrt{\frac{-a-b x^4+1}{a+b x^4+1}}\right)}{2 b}",1,"((a + b*x^4)*ArcSech[a + b*x^4])/(4*b) - ArcTan[Sqrt[(1 - a - b*x^4)/(1 + a + b*x^4)]]/(2*b)","A",5,5,12,0.4167,1,"{6715, 6313, 1961, 12, 203}"
100,1,58,0,0.1130964,"\int x^{-1+n} \text{sech}^{-1}\left(a+b x^n\right) \, dx","Int[x^(-1 + n)*ArcSech[a + b*x^n],x]","\frac{\left(a+b x^n\right) \text{sech}^{-1}\left(a+b x^n\right)}{b n}-\frac{2 \tan ^{-1}\left(\sqrt{\frac{-a-b x^n+1}{a+b x^n+1}}\right)}{b n}","\frac{\left(a+b x^n\right) \text{sech}^{-1}\left(a+b x^n\right)}{b n}-\frac{2 \tan ^{-1}\left(\sqrt{\frac{-a-b x^n+1}{a+b x^n+1}}\right)}{b n}",1,"((a + b*x^n)*ArcSech[a + b*x^n])/(b*n) - (2*ArcTan[Sqrt[(1 - a - b*x^n)/(1 + a + b*x^n)]])/(b*n)","A",5,5,14,0.3571,1,"{6715, 6313, 1961, 12, 203}"