1,1,225,203,0.5420833,"\int x^3 \text{sech}^{-1}(a+b x) \, dx","Integrate[x^3*ArcSech[a + b*x],x]","-\frac{-3 a^4 \log (a+b x)+3 a^4 \log \left(a \sqrt{-\frac{a+b x-1}{a+b x+1}}+b x \sqrt{-\frac{a+b x-1}{a+b x+1}}+\sqrt{-\frac{a+b x-1}{a+b x+1}}+1\right)+6 i \left(2 a^2+1\right) a \log \left(2 \sqrt{-\frac{a+b x-1}{a+b x+1}} (a+b x+1)-2 i (a+b x)\right)+\sqrt{-\frac{a+b x-1}{a+b x+1}} \left(13 a^3+\left(9 a^2-4 a+2\right) b x+13 a^2+(1-3 a) b^2 x^2+2 a+b^3 x^3+2\right)-3 b^4 x^4 \text{sech}^{-1}(a+b x)}{12 b^4}","-\frac{a^4 \text{sech}^{-1}(a+b x)}{4 b^4}-\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 (a+b x) \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{3 b^4}-\frac{x^2 \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{12 b^2}+\frac{1}{4} x^4 \text{sech}^{-1}(a+b x)",1,"-1/12*(Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(2 + 2*a + 13*a^2 + 13*a^3 + (2 - 4*a + 9*a^2)*b*x + (1 - 3*a)*b^2*x^2 + b^3*x^3) - 3*b^4*x^4*ArcSech[a + b*x] - 3*a^4*Log[a + b*x] + 3*a^4*Log[1 + Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + a*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + b*x*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]] + (6*I)*a*(1 + 2*a^2)*Log[(-2*I)*(a + b*x) + 2*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(1 + a + b*x)])/b^4","C",1
2,1,200,153,0.2844221,"\int x^2 \text{sech}^{-1}(a+b x) \, dx","Integrate[x^2*ArcSech[a + b*x],x]","\frac{-2 a^3 \log (a+b x)+2 a^3 \log \left(a \sqrt{-\frac{a+b x-1}{a+b x+1}}+b x \sqrt{-\frac{a+b x-1}{a+b x+1}}+\sqrt{-\frac{a+b x-1}{a+b x+1}}+1\right)+\sqrt{-\frac{a+b x-1}{a+b x+1}} \left(5 a^2+a (4 b x+5)-b x (b x+1)\right)+i \left(6 a^2+1\right) \log \left(2 \sqrt{-\frac{a+b x-1}{a+b x+1}} (a+b x+1)-2 i (a+b x)\right)+2 b^3 x^3 \text{sech}^{-1}(a+b x)}{6 b^3}","\frac{a^3 \text{sech}^{-1}(a+b x)}{3 b^3}-\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{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,"(Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(5*a^2 - b*x*(1 + b*x) + a*(5 + 4*b*x)) + 2*b^3*x^3*ArcSech[a + b*x] - 2*a^3*Log[a + b*x] + 2*a^3*Log[1 + Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + a*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + b*x*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]] + I*(1 + 6*a^2)*Log[(-2*I)*(a + b*x) + 2*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(1 + a + b*x)])/(6*b^3)","C",1
3,1,176,107,0.1676376,"\int x \text{sech}^{-1}(a+b x) \, dx","Integrate[x*ArcSech[a + b*x],x]","\frac{a^2 \log (a+b x)-a^2 \log \left(a \sqrt{-\frac{a+b x-1}{a+b x+1}}+b x \sqrt{-\frac{a+b x-1}{a+b x+1}}+\sqrt{-\frac{a+b x-1}{a+b x+1}}+1\right)+b^2 x^2 \text{sech}^{-1}(a+b x)-\sqrt{-\frac{a+b x-1}{a+b x+1}} (a+b x+1)-2 i a \log \left(2 \sqrt{-\frac{a+b x-1}{a+b x+1}} (a+b x+1)-2 i (a+b x)\right)}{2 b^2}","-\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)) + b^2*x^2*ArcSech[a + b*x] + a^2*Log[a + b*x] - a^2*Log[1 + Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + a*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + b*x*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]] - (2*I)*a*Log[(-2*I)*(a + b*x) + 2*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(1 + a + b*x)])/(2*b^2)","C",1
4,1,125,44,0.3139857,"\int \text{sech}^{-1}(a+b x) \, dx","Integrate[ArcSech[a + b*x],x]","x \text{sech}^{-1}(a+b x)-\frac{2 b \sqrt{-\frac{a+b x-1}{a+b x+1}} \left(\sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{a+b x-1}}{\sqrt{2}}\right)-a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{-b} \sqrt{\frac{a+b x-1}{a+b x+1}}}{\sqrt{b}}\right)\right)}{(-b)^{5/2} \sqrt{\frac{a+b x-1}{a+b x+1}}}","\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,"x*ArcSech[a + b*x] - (2*b*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(Sqrt[-b]*ArcSinh[Sqrt[-1 + a + b*x]/Sqrt[2]] - a*Sqrt[b]*ArcTanh[(Sqrt[-b]*Sqrt[(-1 + a + b*x)/(1 + a + b*x)])/Sqrt[b]]))/((-b)^(5/2)*Sqrt[(-1 + a + b*x)/(1 + a + b*x)])","B",0
5,1,332,170,0.2040225,"\int \frac{\text{sech}^{-1}(a+b x)}{x} \, dx","Integrate[ArcSech[a + b*x]/x,x]","-\text{Li}_2\left(-\frac{\left(\sqrt{1-a^2}-1\right) e^{-\text{sech}^{-1}(a+b x)}}{a}\right)-\text{Li}_2\left(\frac{\left(\sqrt{1-a^2}+1\right) e^{-\text{sech}^{-1}(a+b x)}}{a}\right)+\text{sech}^{-1}(a+b x) \log \left(\frac{\left(\sqrt{1-a^2}-1\right) e^{-\text{sech}^{-1}(a+b x)}}{a}+1\right)+\text{sech}^{-1}(a+b x) \log \left(1-\frac{\left(\sqrt{1-a^2}+1\right) e^{-\text{sech}^{-1}(a+b x)}}{a}\right)+2 i \sin ^{-1}\left(\frac{\sqrt{\frac{a-1}{a}}}{\sqrt{2}}\right) \log \left(\frac{\left(\sqrt{1-a^2}-1\right) e^{-\text{sech}^{-1}(a+b x)}}{a}+1\right)-2 i \sin ^{-1}\left(\frac{\sqrt{\frac{a-1}{a}}}{\sqrt{2}}\right) \log \left(1-\frac{\left(\sqrt{1-a^2}+1\right) e^{-\text{sech}^{-1}(a+b x)}}{a}\right)-4 i \sin ^{-1}\left(\frac{\sqrt{\frac{a-1}{a}}}{\sqrt{2}}\right) \tanh ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{1-a^2}}\right)+\frac{1}{2} \text{Li}_2\left(-e^{-2 \text{sech}^{-1}(a+b x)}\right)-\text{sech}^{-1}(a+b x) \log \left(e^{-2 \text{sech}^{-1}(a+b x)}+1\right)","\text{Li}_2\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\text{Li}_2\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\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)-\frac{1}{2} \text{Li}_2\left(-e^{2 \text{sech}^{-1}(a+b x)}\right)-\text{sech}^{-1}(a+b x) \log \left(e^{2 \text{sech}^{-1}(a+b x)}+1\right)",1,"(-4*I)*ArcSin[Sqrt[(-1 + a)/a]/Sqrt[2]]*ArcTanh[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[1 - a^2]] - ArcSech[a + b*x]*Log[1 + E^(-2*ArcSech[a + b*x])] + ArcSech[a + b*x]*Log[1 + (-1 + Sqrt[1 - a^2])/(a*E^ArcSech[a + b*x])] + (2*I)*ArcSin[Sqrt[(-1 + a)/a]/Sqrt[2]]*Log[1 + (-1 + Sqrt[1 - a^2])/(a*E^ArcSech[a + b*x])] + ArcSech[a + b*x]*Log[1 - (1 + Sqrt[1 - a^2])/(a*E^ArcSech[a + b*x])] - (2*I)*ArcSin[Sqrt[(-1 + a)/a]/Sqrt[2]]*Log[1 - (1 + Sqrt[1 - a^2])/(a*E^ArcSech[a + b*x])] + PolyLog[2, -E^(-2*ArcSech[a + b*x])]/2 - PolyLog[2, -((-1 + Sqrt[1 - a^2])/(a*E^ArcSech[a + b*x]))] - PolyLog[2, (1 + Sqrt[1 - a^2])/(a*E^ArcSech[a + b*x])]","C",0
6,1,244,70,0.2568854,"\int \frac{\text{sech}^{-1}(a+b x)}{x^2} \, dx","Integrate[ArcSech[a + b*x]/x^2,x]","\frac{b \left(\sqrt{1-a^2} \log (a+b x)-\sqrt{1-a^2} \log \left(a \sqrt{-\frac{a+b x-1}{a+b x+1}}+b x \sqrt{-\frac{a+b x-1}{a+b x+1}}+\sqrt{-\frac{a+b x-1}{a+b x+1}}+1\right)+\log \left(\sqrt{1-a^2} a \sqrt{-\frac{a+b x-1}{a+b x+1}}+\sqrt{1-a^2} b x \sqrt{-\frac{a+b x-1}{a+b x+1}}+\sqrt{1-a^2} \sqrt{-\frac{a+b x-1}{a+b x+1}}-a^2-a b x+1\right)-\log (x)\right)}{a \sqrt{1-a^2}}-\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,"-(ArcSech[a + b*x]/x) + (b*(-Log[x] + Sqrt[1 - a^2]*Log[a + b*x] - Sqrt[1 - a^2]*Log[1 + Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + a*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + b*x*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]] + Log[1 - a^2 - a*b*x + Sqrt[1 - a^2]*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + a*Sqrt[1 - a^2]*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + Sqrt[1 - a^2]*b*x*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]]))/(a*Sqrt[1 - a^2])","B",1
7,1,315,133,0.9743884,"\int \frac{\text{sech}^{-1}(a+b x)}{x^3} \, dx","Integrate[ArcSech[a + b*x]/x^3,x]","\frac{1}{2} \left(-\frac{\left(2 a^2-1\right) b^2 \log (x)}{a^2 \left(1-a^2\right)^{3/2}}-\frac{b^2 \log (a+b x)}{a^2}+\frac{b^2 \log \left(a \sqrt{-\frac{a+b x-1}{a+b x+1}}+b x \sqrt{-\frac{a+b x-1}{a+b x+1}}+\sqrt{-\frac{a+b x-1}{a+b x+1}}+1\right)}{a^2}+\frac{\left(2 a^2-1\right) b^2 \log \left(\sqrt{1-a^2} a \sqrt{-\frac{a+b x-1}{a+b x+1}}+\sqrt{1-a^2} b x \sqrt{-\frac{a+b x-1}{a+b x+1}}+\sqrt{1-a^2} \sqrt{-\frac{a+b x-1}{a+b x+1}}-a^2-a b x+1\right)}{a^2 \left(1-a^2\right)^{3/2}}-\frac{\text{sech}^{-1}(a+b x)}{x^2}-\frac{b \sqrt{-\frac{a+b x-1}{a+b x+1}} (a+b x+1)}{(a-1) a (a+1) x}\right)","\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))/((-1 + a)*a*(1 + a)*x)) - ArcSech[a + b*x]/x^2 - ((-1 + 2*a^2)*b^2*Log[x])/(a^2*(1 - a^2)^(3/2)) - (b^2*Log[a + b*x])/a^2 + (b^2*Log[1 + Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + a*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + b*x*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]])/a^2 + ((-1 + 2*a^2)*b^2*Log[1 - a^2 - a*b*x + Sqrt[1 - a^2]*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + a*Sqrt[1 - a^2]*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + Sqrt[1 - a^2]*b*x*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]])/(a^2*(1 - a^2)^(3/2)))/2","B",1
8,1,368,197,0.3885529,"\int \frac{\text{sech}^{-1}(a+b x)}{x^4} \, dx","Integrate[ArcSech[a + b*x]/x^4,x]","\frac{1}{6} \left(\frac{2 b^3 \log (a+b x)}{a^3}-\frac{2 b^3 \log \left(a \sqrt{-\frac{a+b x-1}{a+b x+1}}+b x \sqrt{-\frac{a+b x-1}{a+b x+1}}+\sqrt{-\frac{a+b x-1}{a+b x+1}}+1\right)}{a^3}-\frac{\left(6 a^4-5 a^2+2\right) b^3 \log (x)}{a^3 \left(1-a^2\right)^{5/2}}+\frac{\left(6 a^4-5 a^2+2\right) b^3 \log \left(\sqrt{1-a^2} a \sqrt{-\frac{a+b x-1}{a+b x+1}}+\sqrt{1-a^2} b x \sqrt{-\frac{a+b x-1}{a+b x+1}}+\sqrt{1-a^2} \sqrt{-\frac{a+b x-1}{a+b x+1}}-a^2-a b x+1\right)}{a^3 \left(1-a^2\right)^{5/2}}+\frac{b \sqrt{-\frac{a+b x-1}{a+b x+1}} \left(-a^4+a^3 (4 b x-1)+a^2 \left(5 b^2 x^2+5 b x+1\right)-a b x+a-2 b x (b x+1)\right)}{(a-1)^2 a^2 (a+1)^2 x^2}-\frac{2 \text{sech}^{-1}(a+b x)}{x^3}\right)","-\frac{b^3 \text{sech}^{-1}(a+b x)}{3 a^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 \sqrt{\frac{-a-b x+1}{a+b x+1}} (a+b x+1)}{6 a \left(1-a^2\right) x^2}+\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{\text{sech}^{-1}(a+b x)}{3 x^3}",1,"((b*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(a - a^4 - a*b*x - 2*b*x*(1 + b*x) + a^3*(-1 + 4*b*x) + a^2*(1 + 5*b*x + 5*b^2*x^2)))/((-1 + a)^2*a^2*(1 + a)^2*x^2) - (2*ArcSech[a + b*x])/x^3 - ((2 - 5*a^2 + 6*a^4)*b^3*Log[x])/(a^3*(1 - a^2)^(5/2)) + (2*b^3*Log[a + b*x])/a^3 - (2*b^3*Log[1 + Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + a*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + b*x*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]])/a^3 + ((2 - 5*a^2 + 6*a^4)*b^3*Log[1 - a^2 - a*b*x + Sqrt[1 - a^2]*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + a*Sqrt[1 - a^2]*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))] + Sqrt[1 - a^2]*b*x*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]])/(a^3*(1 - a^2)^(5/2)))/6","A",1
9,1,305,279,1.9954945,"\int x^2 \text{sech}^{-1}(a+b x)^2 \, dx","Integrate[x^2*ArcSech[a + b*x]^2,x]","-\frac{-\left(6 a^2+1\right) \left(2 i \text{Li}_2\left(-i e^{\text{sech}^{-1}(a+b x)}\right)-2 i \text{Li}_2\left(i e^{\text{sech}^{-1}(a+b x)}\right)-2 i \text{sech}^{-1}(a+b x) \log \left(1-i e^{\text{sech}^{-1}(a+b x)}\right)+\pi  \log \left(1-i e^{\text{sech}^{-1}(a+b x)}\right)+2 i \text{sech}^{-1}(a+b x) \log \left(1+i e^{\text{sech}^{-1}(a+b x)}\right)-\pi  \log \left(1+i e^{\text{sech}^{-1}(a+b x)}\right)-\pi  \log \left(\cot \left(\frac{1}{4} \left(\pi +2 i \text{sech}^{-1}(a+b x)\right)\right)\right)\right)+2 \left(-3 a^2 (a+b x) \text{sech}^{-1}(a+b x)^2-6 a \sqrt{-\frac{a+b x-1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)+a+b x\right)+12 a \log \left(\frac{1}{a+b x}\right)-2 (a+b x)^3 \text{sech}^{-1}(a+b x)^2+6 a (a+b x)^2 \text{sech}^{-1}(a+b x)^2+2 \sqrt{-\frac{a+b x-1}{a+b x+1}} (a+b x+1) (a+b x) \text{sech}^{-1}(a+b x)}{6 b^3}","\frac{a^3 \text{sech}^{-1}(a+b x)^2}{3 b^3}+\frac{2 i a^2 \text{Li}_2\left(-i e^{\text{sech}^{-1}(a+b x)}\right)}{b^3}-\frac{2 i a^2 \text{Li}_2\left(i e^{\text{sech}^{-1}(a+b x)}\right)}{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{i \text{Li}_2\left(-i e^{\text{sech}^{-1}(a+b x)}\right)}{3 b^3}-\frac{i \text{Li}_2\left(i e^{\text{sech}^{-1}(a+b x)}\right)}{3 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,"-1/6*(2*(a + b*x)*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(1 + a + b*x)*ArcSech[a + b*x] + 6*a*(a + b*x)^2*ArcSech[a + b*x]^2 - 2*(a + b*x)^3*ArcSech[a + b*x]^2 + 2*(a + b*x - 6*a*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(1 + a + b*x)*ArcSech[a + b*x] - 3*a^2*(a + b*x)*ArcSech[a + b*x]^2) + 12*a*Log[(a + b*x)^(-1)] - (1 + 6*a^2)*(Pi*Log[1 - I*E^ArcSech[a + b*x]] - (2*I)*ArcSech[a + b*x]*Log[1 - I*E^ArcSech[a + b*x]] - Pi*Log[1 + I*E^ArcSech[a + b*x]] + (2*I)*ArcSech[a + b*x]*Log[1 + I*E^ArcSech[a + b*x]] - Pi*Log[Cot[(Pi + (2*I)*ArcSech[a + b*x])/4]] + (2*I)*PolyLog[2, (-I)*E^ArcSech[a + b*x]] - (2*I)*PolyLog[2, I*E^ArcSech[a + b*x]]))/b^3","A",0
10,1,172,149,0.4296658,"\int x \text{sech}^{-1}(a+b x)^2 \, dx","Integrate[x*ArcSech[a + b*x]^2,x]","\frac{-4 i a \left(\text{Li}_2\left(-i e^{-\text{sech}^{-1}(a+b x)}\right)-\text{Li}_2\left(i e^{-\text{sech}^{-1}(a+b x)}\right)\right)+2 \log \left(\frac{1}{a+b x}\right)+(a+b x)^2 \text{sech}^{-1}(a+b x)^2-2 a (a+b x) \text{sech}^{-1}(a+b x)^2-2 \sqrt{-\frac{a+b x-1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)-4 i a \text{sech}^{-1}(a+b x) \left(\log \left(1-i e^{-\text{sech}^{-1}(a+b x)}\right)-\log \left(1+i e^{-\text{sech}^{-1}(a+b x)}\right)\right)}{2 b^2}","-\frac{a^2 \text{sech}^{-1}(a+b x)^2}{2 b^2}-\frac{2 i a \text{Li}_2\left(-i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}+\frac{2 i a \text{Li}_2\left(i e^{\text{sech}^{-1}(a+b x)}\right)}{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,"(-2*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(1 + a + b*x)*ArcSech[a + b*x] - 2*a*(a + b*x)*ArcSech[a + b*x]^2 + (a + b*x)^2*ArcSech[a + b*x]^2 - (4*I)*a*ArcSech[a + b*x]*(Log[1 - I/E^ArcSech[a + b*x]] - Log[1 + I/E^ArcSech[a + b*x]]) + 2*Log[(a + b*x)^(-1)] - (4*I)*a*(PolyLog[2, (-I)/E^ArcSech[a + b*x]] - PolyLog[2, I/E^ArcSech[a + b*x]]))/(2*b^2)","A",0
11,1,105,80,0.2274255,"\int \text{sech}^{-1}(a+b x)^2 \, dx","Integrate[ArcSech[a + b*x]^2,x]","\frac{i \left(2 \text{Li}_2\left(-i e^{-\text{sech}^{-1}(a+b x)}\right)-2 \text{Li}_2\left(i e^{-\text{sech}^{-1}(a+b x)}\right)+\text{sech}^{-1}(a+b x) \left(-i (a+b x) \text{sech}^{-1}(a+b x)+2 \log \left(1-i e^{-\text{sech}^{-1}(a+b x)}\right)-2 \log \left(1+i e^{-\text{sech}^{-1}(a+b x)}\right)\right)\right)}{b}","\frac{2 i \text{Li}_2\left(-i e^{\text{sech}^{-1}(a+b x)}\right)}{b}-\frac{2 i \text{Li}_2\left(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,"(I*(ArcSech[a + b*x]*((-I)*(a + b*x)*ArcSech[a + b*x] + 2*Log[1 - I/E^ArcSech[a + b*x]] - 2*Log[1 + I/E^ArcSech[a + b*x]]) + 2*PolyLog[2, (-I)/E^ArcSech[a + b*x]] - 2*PolyLog[2, I/E^ArcSech[a + b*x]]))/b","A",0
12,1,280,274,0.3045881,"\int \frac{\text{sech}^{-1}(a+b x)^2}{x} \, dx","Integrate[ArcSech[a + b*x]^2/x,x]","2 \text{sech}^{-1}(a+b x) \text{Li}_2\left(-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}-1}\right)+2 \text{sech}^{-1}(a+b x) \text{Li}_2\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-2 \text{Li}_3\left(-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}-1}\right)-2 \text{Li}_3\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+\text{sech}^{-1}(a+b x)^2 \log \left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}-1}+1\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) \text{Li}_2\left(-e^{-2 \text{sech}^{-1}(a+b x)}\right)+\frac{1}{2} \text{Li}_3\left(-e^{-2 \text{sech}^{-1}(a+b x)}\right)-\frac{2}{3} \text{sech}^{-1}(a+b x)^3-\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{Li}_2\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+2 \text{sech}^{-1}(a+b x) \text{Li}_2\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-2 \text{Li}_3\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-2 \text{Li}_3\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\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) \text{Li}_2\left(-e^{2 \text{sech}^{-1}(a+b x)}\right)+\frac{1}{2} \text{Li}_3\left(-e^{2 \text{sech}^{-1}(a+b x)}\right)-\text{sech}^{-1}(a+b x)^2 \log \left(e^{2 \text{sech}^{-1}(a+b x)}+1\right)",1,"(-2*ArcSech[a + b*x]^3)/3 - ArcSech[a + b*x]^2*Log[1 + E^(-2*ArcSech[a + b*x])] + 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]*PolyLog[2, -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])] + PolyLog[3, -E^(-2*ArcSech[a + b*x])]/2 - 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])]","A",0
13,1,678,224,2.6900873,"\int \frac{\text{sech}^{-1}(a+b x)^2}{x^2} \, dx","Integrate[ArcSech[a + b*x]^2/x^2,x]","\frac{-\frac{(a+b x) \text{sech}^{-1}(a+b x)^2}{x}+\frac{2 b \left(i \left(\text{Li}_2\left(\frac{\left(-i \sqrt{a^2-1}-1\right) \left(a-i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}{a \left(a+i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}\right)-\text{Li}_2\left(\frac{\left(\sqrt{a^2-1}+i\right) \left(a-i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}{a \left(\sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-i (a-1)\right)}\right)\right)+2 \text{sech}^{-1}(a+b x) \tan ^{-1}\left(\frac{(a-1) \coth \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)-2 i \cos ^{-1}\left(\frac{1}{a}\right) \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)-\log \left(-\frac{(a-1) \left(-i \sqrt{a^2-1}+a+1\right) \left(\tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}{a \left(i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)+a-1\right)}\right) \left(2 \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)+\cos ^{-1}\left(\frac{1}{a}\right)\right)-\log \left(\frac{(a-1) \left(i \sqrt{a^2-1}+a+1\right) \left(\tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)+1\right)}{a \left(i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)+a-1\right)}\right) \left(\cos ^{-1}\left(\frac{1}{a}\right)-2 \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right)+\log \left(\frac{\sqrt{a^2-1} e^{-\frac{1}{2} \text{sech}^{-1}(a+b x)}}{\sqrt{2} \sqrt{a} \sqrt{-\frac{b x}{a+b x}}}\right) \left(2 \left(\tan ^{-1}\left(\frac{(a-1) \coth \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)+\tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right)+\cos ^{-1}\left(\frac{1}{a}\right)\right)+\log \left(\frac{\sqrt{a^2-1} e^{\frac{1}{2} \text{sech}^{-1}(a+b x)}}{\sqrt{2} \sqrt{a} \sqrt{-\frac{b x}{a+b x}}}\right) \left(\cos ^{-1}\left(\frac{1}{a}\right)-2 \left(\tan ^{-1}\left(\frac{(a-1) \coth \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)+\tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right)\right)\right)}{\sqrt{a^2-1}}}{a}","\frac{2 b \text{Li}_2\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}-\frac{2 b \text{Li}_2\left(\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,"(-(((a + b*x)*ArcSech[a + b*x]^2)/x) + (2*b*(2*ArcSech[a + b*x]*ArcTan[((-1 + a)*Coth[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]] - (2*I)*ArcCos[a^(-1)]*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]] + (ArcCos[a^(-1)] + 2*(ArcTan[((-1 + a)*Coth[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]] + ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]))*Log[Sqrt[-1 + a^2]/(Sqrt[2]*Sqrt[a]*E^(ArcSech[a + b*x]/2)*Sqrt[-((b*x)/(a + b*x))])] + (ArcCos[a^(-1)] - 2*(ArcTan[((-1 + a)*Coth[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]] + ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]))*Log[(Sqrt[-1 + a^2]*E^(ArcSech[a + b*x]/2))/(Sqrt[2]*Sqrt[a]*Sqrt[-((b*x)/(a + b*x))])] - (ArcCos[a^(-1)] + 2*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]])*Log[-(((-1 + a)*(1 + a - I*Sqrt[-1 + a^2])*(-1 + Tanh[ArcSech[a + b*x]/2]))/(a*(-1 + a + I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2])))] - (ArcCos[a^(-1)] - 2*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]])*Log[((-1 + a)*(1 + a + I*Sqrt[-1 + a^2])*(1 + Tanh[ArcSech[a + b*x]/2]))/(a*(-1 + a + I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))] + I*(PolyLog[2, ((-1 - I*Sqrt[-1 + a^2])*(-1 + a - I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))/(a*(-1 + a + I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))] - PolyLog[2, ((I + Sqrt[-1 + a^2])*(-1 + a - I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))/(a*((-I)*(-1 + a) + Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))])))/Sqrt[-1 + a^2])/a","C",1
14,1,1439,537,7.5763255,"\int \frac{\text{sech}^{-1}(a+b x)^2}{x^3} \, dx","Integrate[ArcSech[a + b*x]^2/x^3,x]","\frac{\log \left(\frac{b x}{a+b x}\right) b^2}{a^2-a^4}+\frac{\left(2 \text{sech}^{-1}(a+b x) \tan ^{-1}\left(\frac{(a-1) \coth \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)-2 i \cos ^{-1}\left(\frac{1}{a}\right) \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)+\left(\cos ^{-1}\left(\frac{1}{a}\right)+2 \left(\tan ^{-1}\left(\frac{(a-1) \coth \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)+\tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right)\right) \log \left(\frac{\sqrt{a^2-1} e^{-\frac{1}{2} \text{sech}^{-1}(a+b x)}}{\sqrt{2} \sqrt{a} \sqrt{-\frac{b x}{a+b x}}}\right)+\left(\cos ^{-1}\left(\frac{1}{a}\right)-2 \left(\tan ^{-1}\left(\frac{(a-1) \coth \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)+\tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right)\right) \log \left(\frac{\sqrt{a^2-1} e^{\frac{1}{2} \text{sech}^{-1}(a+b x)}}{\sqrt{2} \sqrt{a} \sqrt{-\frac{b x}{a+b x}}}\right)-\left(\cos ^{-1}\left(\frac{1}{a}\right)+2 \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right) \log \left(-\frac{(a-1) \left(a-i \sqrt{a^2-1}+1\right) \left(\tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}{a \left(a+i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}\right)-\left(\cos ^{-1}\left(\frac{1}{a}\right)-2 \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right) \log \left(\frac{(a-1) \left(a+i \sqrt{a^2-1}+1\right) \left(\tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)+1\right)}{a \left(a+i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}\right)+i \left(\text{Li}_2\left(\frac{\left(-i \sqrt{a^2-1}-1\right) \left(a-i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}{a \left(a+i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}\right)-\text{Li}_2\left(\frac{\left(\sqrt{a^2-1}+i\right) \left(a-i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}{a \left(\sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-i (a-1)\right)}\right)\right)\right) b^2}{a^2 \left(a^2-1\right)^{3/2}}-\frac{2 \left(2 \text{sech}^{-1}(a+b x) \tan ^{-1}\left(\frac{(a-1) \coth \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)-2 i \cos ^{-1}\left(\frac{1}{a}\right) \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)+\left(\cos ^{-1}\left(\frac{1}{a}\right)+2 \left(\tan ^{-1}\left(\frac{(a-1) \coth \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)+\tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right)\right) \log \left(\frac{\sqrt{a^2-1} e^{-\frac{1}{2} \text{sech}^{-1}(a+b x)}}{\sqrt{2} \sqrt{a} \sqrt{-\frac{b x}{a+b x}}}\right)+\left(\cos ^{-1}\left(\frac{1}{a}\right)-2 \left(\tan ^{-1}\left(\frac{(a-1) \coth \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)+\tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right)\right) \log \left(\frac{\sqrt{a^2-1} e^{\frac{1}{2} \text{sech}^{-1}(a+b x)}}{\sqrt{2} \sqrt{a} \sqrt{-\frac{b x}{a+b x}}}\right)-\left(\cos ^{-1}\left(\frac{1}{a}\right)+2 \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right) \log \left(-\frac{(a-1) \left(a-i \sqrt{a^2-1}+1\right) \left(\tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}{a \left(a+i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}\right)-\left(\cos ^{-1}\left(\frac{1}{a}\right)-2 \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right) \log \left(\frac{(a-1) \left(a+i \sqrt{a^2-1}+1\right) \left(\tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)+1\right)}{a \left(a+i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}\right)+i \left(\text{Li}_2\left(\frac{\left(-i \sqrt{a^2-1}-1\right) \left(a-i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}{a \left(a+i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}\right)-\text{Li}_2\left(\frac{\left(\sqrt{a^2-1}+i\right) \left(a-i \sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-1\right)}{a \left(\sqrt{a^2-1} \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-i (a-1)\right)}\right)\right)\right) b^2}{\left(a^2-1\right)^{3/2}}+\frac{\text{sech}^{-1}(a+b x) \left(\left(a^2-1\right) (a+b x) \text{sech}^{-1}(a+b x)-a \sqrt{-\frac{a+b x-1}{a+b x+1}} (a+b x+1)\right) b}{(a-1) a^2 (a+1) x}-\frac{(a+b x)^2 \text{sech}^{-1}(a+b x)^2}{2 a^2 x^2}","-\frac{2 b^2 \text{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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,"-1/2*((a + b*x)^2*ArcSech[a + b*x]^2)/(a^2*x^2) + (b*ArcSech[a + b*x]*(-(a*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(1 + a + b*x)) + (-1 + a^2)*(a + b*x)*ArcSech[a + b*x]))/((-1 + a)*a^2*(1 + a)*x) + (b^2*Log[(b*x)/(a + b*x)])/(a^2 - a^4) - (2*b^2*(2*ArcSech[a + b*x]*ArcTan[((-1 + a)*Coth[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]] - (2*I)*ArcCos[a^(-1)]*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]] + (ArcCos[a^(-1)] + 2*(ArcTan[((-1 + a)*Coth[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]] + ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]))*Log[Sqrt[-1 + a^2]/(Sqrt[2]*Sqrt[a]*E^(ArcSech[a + b*x]/2)*Sqrt[-((b*x)/(a + b*x))])] + (ArcCos[a^(-1)] - 2*(ArcTan[((-1 + a)*Coth[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]] + ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]))*Log[(Sqrt[-1 + a^2]*E^(ArcSech[a + b*x]/2))/(Sqrt[2]*Sqrt[a]*Sqrt[-((b*x)/(a + b*x))])] - (ArcCos[a^(-1)] + 2*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]])*Log[-(((-1 + a)*(1 + a - I*Sqrt[-1 + a^2])*(-1 + Tanh[ArcSech[a + b*x]/2]))/(a*(-1 + a + I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2])))] - (ArcCos[a^(-1)] - 2*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]])*Log[((-1 + a)*(1 + a + I*Sqrt[-1 + a^2])*(1 + Tanh[ArcSech[a + b*x]/2]))/(a*(-1 + a + I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))] + I*(PolyLog[2, ((-1 - I*Sqrt[-1 + a^2])*(-1 + a - I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))/(a*(-1 + a + I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))] - PolyLog[2, ((I + Sqrt[-1 + a^2])*(-1 + a - I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))/(a*((-I)*(-1 + a) + Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))])))/(-1 + a^2)^(3/2) + (b^2*(2*ArcSech[a + b*x]*ArcTan[((-1 + a)*Coth[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]] - (2*I)*ArcCos[a^(-1)]*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]] + (ArcCos[a^(-1)] + 2*(ArcTan[((-1 + a)*Coth[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]] + ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]))*Log[Sqrt[-1 + a^2]/(Sqrt[2]*Sqrt[a]*E^(ArcSech[a + b*x]/2)*Sqrt[-((b*x)/(a + b*x))])] + (ArcCos[a^(-1)] - 2*(ArcTan[((-1 + a)*Coth[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]] + ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]))*Log[(Sqrt[-1 + a^2]*E^(ArcSech[a + b*x]/2))/(Sqrt[2]*Sqrt[a]*Sqrt[-((b*x)/(a + b*x))])] - (ArcCos[a^(-1)] + 2*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]])*Log[-(((-1 + a)*(1 + a - I*Sqrt[-1 + a^2])*(-1 + Tanh[ArcSech[a + b*x]/2]))/(a*(-1 + a + I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2])))] - (ArcCos[a^(-1)] - 2*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]])*Log[((-1 + a)*(1 + a + I*Sqrt[-1 + a^2])*(1 + Tanh[ArcSech[a + b*x]/2]))/(a*(-1 + a + I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))] + I*(PolyLog[2, ((-1 - I*Sqrt[-1 + a^2])*(-1 + a - I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))/(a*(-1 + a + I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))] - PolyLog[2, ((I + Sqrt[-1 + a^2])*(-1 + a - I*Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))/(a*((-I)*(-1 + a) + Sqrt[-1 + a^2]*Tanh[ArcSech[a + b*x]/2]))])))/(a^2*(-1 + a^2)^(3/2))","C",1
15,1,254,260,0.5422305,"\int x \text{sech}^{-1}(a+b x)^3 \, dx","Integrate[x*ArcSech[a + b*x]^3,x]","\frac{-3 \text{Li}_2\left(-e^{-2 \text{sech}^{-1}(a+b x)}\right)+6 i a \left(-2 \text{sech}^{-1}(a+b x) \left(\text{Li}_2\left(-i e^{-\text{sech}^{-1}(a+b x)}\right)-\text{Li}_2\left(i e^{-\text{sech}^{-1}(a+b x)}\right)\right)-2 \text{Li}_3\left(-i e^{-\text{sech}^{-1}(a+b x)}\right)+2 \text{Li}_3\left(i e^{-\text{sech}^{-1}(a+b x)}\right)-\left(\text{sech}^{-1}(a+b x)^2 \left(\log \left(1-i e^{-\text{sech}^{-1}(a+b x)}\right)-\log \left(1+i e^{-\text{sech}^{-1}(a+b x)}\right)\right)\right)\right)+(a+b x)^2 \text{sech}^{-1}(a+b x)^3-2 a (a+b x) \text{sech}^{-1}(a+b x)^3-3 \sqrt{-\frac{a+b x-1}{a+b x+1}} (a+b x+1) \text{sech}^{-1}(a+b x)^2+3 \text{sech}^{-1}(a+b x) \left(\text{sech}^{-1}(a+b x)+2 \log \left(e^{-2 \text{sech}^{-1}(a+b x)}+1\right)\right)}{2 b^2}","-\frac{a^2 \text{sech}^{-1}(a+b x)^3}{2 b^2}-\frac{6 i a \text{sech}^{-1}(a+b x) \text{Li}_2\left(-i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}+\frac{6 i a \text{sech}^{-1}(a+b x) \text{Li}_2\left(i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}+\frac{3 \text{Li}_2\left(-e^{2 \text{sech}^{-1}(a+b x)}\right)}{2 b^2}+\frac{6 i a \text{Li}_3\left(-i e^{\text{sech}^{-1}(a+b x)}\right)}{b^2}-\frac{6 i a \text{Li}_3\left(i e^{\text{sech}^{-1}(a+b x)}\right)}{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*Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(1 + a + b*x)*ArcSech[a + b*x]^2 - 2*a*(a + b*x)*ArcSech[a + b*x]^3 + (a + b*x)^2*ArcSech[a + b*x]^3 + 3*ArcSech[a + b*x]*(ArcSech[a + b*x] + 2*Log[1 + E^(-2*ArcSech[a + b*x])]) - 3*PolyLog[2, -E^(-2*ArcSech[a + b*x])] + (6*I)*a*(-(ArcSech[a + b*x]^2*(Log[1 - I/E^ArcSech[a + b*x]] - Log[1 + I/E^ArcSech[a + b*x]])) - 2*ArcSech[a + b*x]*(PolyLog[2, (-I)/E^ArcSech[a + b*x]] - PolyLog[2, I/E^ArcSech[a + b*x]]) - 2*PolyLog[3, (-I)/E^ArcSech[a + b*x]] + 2*PolyLog[3, I/E^ArcSech[a + b*x]]))/(2*b^2)","A",0
16,1,153,136,0.1412785,"\int \text{sech}^{-1}(a+b x)^3 \, dx","Integrate[ArcSech[a + b*x]^3,x]","-\frac{-(a+b x) \text{sech}^{-1}(a+b x)^3+3 i \left(-2 \text{sech}^{-1}(a+b x) \left(\text{Li}_2\left(-i e^{-\text{sech}^{-1}(a+b x)}\right)-\text{Li}_2\left(i e^{-\text{sech}^{-1}(a+b x)}\right)\right)-2 \left(\text{Li}_3\left(-i e^{-\text{sech}^{-1}(a+b x)}\right)-\text{Li}_3\left(i e^{-\text{sech}^{-1}(a+b x)}\right)\right)-\left(\text{sech}^{-1}(a+b x)^2 \left(\log \left(1-i e^{-\text{sech}^{-1}(a+b x)}\right)-\log \left(1+i e^{-\text{sech}^{-1}(a+b x)}\right)\right)\right)\right)}{b}","\frac{6 i \text{sech}^{-1}(a+b x) \text{Li}_2\left(-i e^{\text{sech}^{-1}(a+b x)}\right)}{b}-\frac{6 i \text{sech}^{-1}(a+b x) \text{Li}_2\left(i e^{\text{sech}^{-1}(a+b x)}\right)}{b}-\frac{6 i \text{Li}_3\left(-i e^{\text{sech}^{-1}(a+b x)}\right)}{b}+\frac{6 i \text{Li}_3\left(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) + (3*I)*(-(ArcSech[a + b*x]^2*(Log[1 - I/E^ArcSech[a + b*x]] - Log[1 + I/E^ArcSech[a + b*x]])) - 2*ArcSech[a + b*x]*(PolyLog[2, (-I)/E^ArcSech[a + b*x]] - PolyLog[2, I/E^ArcSech[a + b*x]]) - 2*(PolyLog[3, (-I)/E^ArcSech[a + b*x]] - PolyLog[3, I/E^ArcSech[a + b*x]])))/b)","A",0
17,1,384,378,0.3242039,"\int \frac{\text{sech}^{-1}(a+b x)^3}{x} \, dx","Integrate[ArcSech[a + b*x]^3/x,x]","3 \text{sech}^{-1}(a+b x)^2 \text{Li}_2\left(-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}-1}\right)+3 \text{sech}^{-1}(a+b x)^2 \text{Li}_2\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-6 \text{sech}^{-1}(a+b x) \text{Li}_3\left(-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}-1}\right)-6 \text{sech}^{-1}(a+b x) \text{Li}_3\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+6 \text{Li}_4\left(-\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}-1}\right)+6 \text{Li}_4\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+\text{sech}^{-1}(a+b x)^3 \log \left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}-1}+1\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)+\frac{3}{2} \text{sech}^{-1}(a+b x)^2 \text{Li}_2\left(-e^{-2 \text{sech}^{-1}(a+b x)}\right)+\frac{3}{2} \text{sech}^{-1}(a+b x) \text{Li}_3\left(-e^{-2 \text{sech}^{-1}(a+b x)}\right)+\frac{3}{4} \text{Li}_4\left(-e^{-2 \text{sech}^{-1}(a+b x)}\right)-\frac{1}{2} \text{sech}^{-1}(a+b x)^4-\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{Li}_2\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+3 \text{sech}^{-1}(a+b x)^2 \text{Li}_2\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-6 \text{sech}^{-1}(a+b x) \text{Li}_3\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-6 \text{sech}^{-1}(a+b x) \text{Li}_3\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+6 \text{Li}_4\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+6 \text{Li}_4\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\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)-\frac{3}{2} \text{sech}^{-1}(a+b x)^2 \text{Li}_2\left(-e^{2 \text{sech}^{-1}(a+b x)}\right)+\frac{3}{2} \text{sech}^{-1}(a+b x) \text{Li}_3\left(-e^{2 \text{sech}^{-1}(a+b x)}\right)-\frac{3}{4} \text{Li}_4\left(-e^{2 \text{sech}^{-1}(a+b x)}\right)-\text{sech}^{-1}(a+b x)^3 \log \left(e^{2 \text{sech}^{-1}(a+b x)}+1\right)",1,"-1/2*ArcSech[a + b*x]^4 - ArcSech[a + b*x]^3*Log[1 + E^(-2*ArcSech[a + b*x])] + 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])] + (3*ArcSech[a + b*x]^2*PolyLog[2, -E^(-2*ArcSech[a + b*x])])/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, (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*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*PolyLog[4, -E^(-2*ArcSech[a + b*x])])/4 + 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])]","A",0
18,1,1849,330,46.9157695,"\int \frac{\text{sech}^{-1}(a+b x)^3}{x^2} \, dx","Integrate[ArcSech[a + b*x]^3/x^2,x]","-\frac{\sqrt{a^2-1} b x \text{sech}^{-1}(a+b x)^3+a \sqrt{a^2-1} \text{sech}^{-1}(a+b x)^3-3 b x \cos ^{-1}\left(-\frac{1}{a}\right) \text{sech}^{-1}(a+b x)^2-3 i b x \log \left(\frac{\left(i a+\sqrt{a^2-1}-i\right) \left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}-i\right)}{a \left(\tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)+1\right)}\right) \text{sech}^{-1}(a+b x)^2+3 i b x \log \left(\frac{\left(-i a+\sqrt{a^2-1}+i\right) \left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}+i\right)}{a \left(\tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)+1\right)}\right) \text{sech}^{-1}(a+b x)^2+12 b x \cos ^{-1}\left(-\frac{1}{a}\right) \tanh ^{-1}\left(\tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)\right) \text{sech}^{-1}(a+b x)-6 b x \cos ^{-1}\left(-\frac{1}{a}\right) \log \left(\frac{\sqrt{a^2-1} e^{-i \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)}}{\sqrt{2} \sqrt{a} \sqrt{a \cos \left(2 \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right)+1}}\right) \text{sech}^{-1}(a+b x)+12 i b x \tanh ^{-1}\left(\coth \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)\right) \log \left(\frac{\sqrt{a^2-1} e^{-i \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)}}{\sqrt{2} \sqrt{a} \sqrt{a \cos \left(2 \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right)+1}}\right) \text{sech}^{-1}(a+b x)-12 i b x \tanh ^{-1}\left(\tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)\right) \log \left(\frac{\sqrt{a^2-1} e^{-i \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)}}{\sqrt{2} \sqrt{a} \sqrt{a \cos \left(2 \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right)+1}}\right) \text{sech}^{-1}(a+b x)-6 b x \cos ^{-1}\left(-\frac{1}{a}\right) \log \left(\frac{\sqrt{a^2-1} e^{i \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)}}{\sqrt{2} \sqrt{a} \sqrt{a \cos \left(2 \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right)+1}}\right) \text{sech}^{-1}(a+b x)-12 i b x \tanh ^{-1}\left(\coth \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)\right) \log \left(\frac{\sqrt{a^2-1} e^{i \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)}}{\sqrt{2} \sqrt{a} \sqrt{a \cos \left(2 \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right)+1}}\right) \text{sech}^{-1}(a+b x)+12 i b x \tanh ^{-1}\left(\tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)\right) \log \left(\frac{\sqrt{a^2-1} e^{i \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)}}{\sqrt{2} \sqrt{a} \sqrt{a \cos \left(2 \tan ^{-1}\left(\frac{(a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)}{\sqrt{a^2-1}}\right)\right)+1}}\right) \text{sech}^{-1}(a+b x)+6 b x \cos ^{-1}\left(-\frac{1}{a}\right) \log \left(\frac{i (a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)+\sqrt{a^2-1}}{2 \sqrt{a} \sqrt{-\frac{\left(a^2-1\right) (a+b x)}{b x}} \sqrt{-\frac{b x}{(a-1) (a+b x+1)}}}\right) \text{sech}^{-1}(a+b x)+12 i b x \tanh ^{-1}\left(\coth \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)\right) \log \left(\frac{i (a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)+\sqrt{a^2-1}}{2 \sqrt{a} \sqrt{-\frac{\left(a^2-1\right) (a+b x)}{b x}} \sqrt{-\frac{b x}{(a-1) (a+b x+1)}}}\right) \text{sech}^{-1}(a+b x)-12 i b x \tanh ^{-1}\left(\tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)\right) \log \left(\frac{i (a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)+\sqrt{a^2-1}}{2 \sqrt{a} \sqrt{-\frac{\left(a^2-1\right) (a+b x)}{b x}} \sqrt{-\frac{b x}{(a-1) (a+b x+1)}}}\right) \text{sech}^{-1}(a+b x)+6 b x \cos ^{-1}\left(-\frac{1}{a}\right) \log \left(-\frac{i \left(a^2-1\right) \sqrt{-\frac{b x}{(a-1) (a+b x+1)}}}{\sqrt{a} \sqrt{-\frac{\left(a^2-1\right) (a+b x)}{b x}} \left((a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-i \sqrt{a^2-1}\right)}\right) \text{sech}^{-1}(a+b x)-12 i b x \tanh ^{-1}\left(\coth \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)\right) \log \left(-\frac{i \left(a^2-1\right) \sqrt{-\frac{b x}{(a-1) (a+b x+1)}}}{\sqrt{a} \sqrt{-\frac{\left(a^2-1\right) (a+b x)}{b x}} \left((a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-i \sqrt{a^2-1}\right)}\right) \text{sech}^{-1}(a+b x)+12 i b x \tanh ^{-1}\left(\tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)\right) \log \left(-\frac{i \left(a^2-1\right) \sqrt{-\frac{b x}{(a-1) (a+b x+1)}}}{\sqrt{a} \sqrt{-\frac{\left(a^2-1\right) (a+b x)}{b x}} \left((a+1) \tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)-i \sqrt{a^2-1}\right)}\right) \text{sech}^{-1}(a+b x)-6 i b x \text{Li}_2\left(\frac{\left(1-i \sqrt{a^2-1}\right) \left(1-\sqrt{-\frac{a+b x-1}{a+b x+1}} (a+b x+1)\right)}{a (a+b x)}\right) \text{sech}^{-1}(a+b x)+6 i b x \text{Li}_2\left(\frac{\left(i \sqrt{a^2-1}+1\right) \left(1-\sqrt{-\frac{a+b x-1}{a+b x+1}} (a+b x+1)\right)}{a (a+b x)}\right) \text{sech}^{-1}(a+b x)-12 b x \cos ^{-1}\left(-\frac{1}{a}\right) \tanh ^{-1}\left(\tanh \left(\frac{1}{2} \text{sech}^{-1}(a+b x)\right)\right)^2-6 i b x \text{Li}_3\left(\frac{\left(1-i \sqrt{a^2-1}\right) \left(1-\sqrt{-\frac{a+b x-1}{a+b x+1}} (a+b x+1)\right)}{a (a+b x)}\right)+6 i b x \text{Li}_3\left(\frac{\left(i \sqrt{a^2-1}+1\right) \left(1-\sqrt{-\frac{a+b x-1}{a+b x+1}} (a+b x+1)\right)}{a (a+b x)}\right)}{a \sqrt{a^2-1} x}","\frac{6 b \text{sech}^{-1}(a+b x) \text{Li}_2\left(\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{Li}_2\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{6 b \text{Li}_3\left(\frac{a e^{\text{sech}^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{6 b \text{Li}_3\left(\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,"-((-3*b*x*ArcCos[-a^(-1)]*ArcSech[a + b*x]^2 + a*Sqrt[-1 + a^2]*ArcSech[a + b*x]^3 + Sqrt[-1 + a^2]*b*x*ArcSech[a + b*x]^3 + 12*b*x*ArcCos[-a^(-1)]*ArcSech[a + b*x]*ArcTanh[Tanh[ArcSech[a + b*x]/2]] - 12*b*x*ArcCos[-a^(-1)]*ArcTanh[Tanh[ArcSech[a + b*x]/2]]^2 - 6*b*x*ArcCos[-a^(-1)]*ArcSech[a + b*x]*Log[Sqrt[-1 + a^2]/(Sqrt[2]*Sqrt[a]*E^(I*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]])*Sqrt[1 + a*Cos[2*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]]])] + (12*I)*b*x*ArcSech[a + b*x]*ArcTanh[Coth[ArcSech[a + b*x]/2]]*Log[Sqrt[-1 + a^2]/(Sqrt[2]*Sqrt[a]*E^(I*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]])*Sqrt[1 + a*Cos[2*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]]])] - (12*I)*b*x*ArcSech[a + b*x]*ArcTanh[Tanh[ArcSech[a + b*x]/2]]*Log[Sqrt[-1 + a^2]/(Sqrt[2]*Sqrt[a]*E^(I*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]])*Sqrt[1 + a*Cos[2*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]]])] - 6*b*x*ArcCos[-a^(-1)]*ArcSech[a + b*x]*Log[(Sqrt[-1 + a^2]*E^(I*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]))/(Sqrt[2]*Sqrt[a]*Sqrt[1 + a*Cos[2*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]]])] - (12*I)*b*x*ArcSech[a + b*x]*ArcTanh[Coth[ArcSech[a + b*x]/2]]*Log[(Sqrt[-1 + a^2]*E^(I*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]))/(Sqrt[2]*Sqrt[a]*Sqrt[1 + a*Cos[2*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]]])] + (12*I)*b*x*ArcSech[a + b*x]*ArcTanh[Tanh[ArcSech[a + b*x]/2]]*Log[(Sqrt[-1 + a^2]*E^(I*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]))/(Sqrt[2]*Sqrt[a]*Sqrt[1 + a*Cos[2*ArcTan[((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]]]])] + 6*b*x*ArcCos[-a^(-1)]*ArcSech[a + b*x]*Log[(Sqrt[-1 + a^2] + I*(1 + a)*Tanh[ArcSech[a + b*x]/2])/(2*Sqrt[a]*Sqrt[-(((-1 + a^2)*(a + b*x))/(b*x))]*Sqrt[-((b*x)/((-1 + a)*(1 + a + b*x)))])] + (12*I)*b*x*ArcSech[a + b*x]*ArcTanh[Coth[ArcSech[a + b*x]/2]]*Log[(Sqrt[-1 + a^2] + I*(1 + a)*Tanh[ArcSech[a + b*x]/2])/(2*Sqrt[a]*Sqrt[-(((-1 + a^2)*(a + b*x))/(b*x))]*Sqrt[-((b*x)/((-1 + a)*(1 + a + b*x)))])] - (12*I)*b*x*ArcSech[a + b*x]*ArcTanh[Tanh[ArcSech[a + b*x]/2]]*Log[(Sqrt[-1 + a^2] + I*(1 + a)*Tanh[ArcSech[a + b*x]/2])/(2*Sqrt[a]*Sqrt[-(((-1 + a^2)*(a + b*x))/(b*x))]*Sqrt[-((b*x)/((-1 + a)*(1 + a + b*x)))])] + 6*b*x*ArcCos[-a^(-1)]*ArcSech[a + b*x]*Log[((-I)*(-1 + a^2)*Sqrt[-((b*x)/((-1 + a)*(1 + a + b*x)))])/(Sqrt[a]*Sqrt[-(((-1 + a^2)*(a + b*x))/(b*x))]*((-I)*Sqrt[-1 + a^2] + (1 + a)*Tanh[ArcSech[a + b*x]/2]))] - (12*I)*b*x*ArcSech[a + b*x]*ArcTanh[Coth[ArcSech[a + b*x]/2]]*Log[((-I)*(-1 + a^2)*Sqrt[-((b*x)/((-1 + a)*(1 + a + b*x)))])/(Sqrt[a]*Sqrt[-(((-1 + a^2)*(a + b*x))/(b*x))]*((-I)*Sqrt[-1 + a^2] + (1 + a)*Tanh[ArcSech[a + b*x]/2]))] + (12*I)*b*x*ArcSech[a + b*x]*ArcTanh[Tanh[ArcSech[a + b*x]/2]]*Log[((-I)*(-1 + a^2)*Sqrt[-((b*x)/((-1 + a)*(1 + a + b*x)))])/(Sqrt[a]*Sqrt[-(((-1 + a^2)*(a + b*x))/(b*x))]*((-I)*Sqrt[-1 + a^2] + (1 + a)*Tanh[ArcSech[a + b*x]/2]))] - (3*I)*b*x*ArcSech[a + b*x]^2*Log[((-I + I*a + Sqrt[-1 + a^2])*(-I + ((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]))/(a*(1 + Tanh[ArcSech[a + b*x]/2]))] + (3*I)*b*x*ArcSech[a + b*x]^2*Log[((I - I*a + Sqrt[-1 + a^2])*(I + ((1 + a)*Tanh[ArcSech[a + b*x]/2])/Sqrt[-1 + a^2]))/(a*(1 + Tanh[ArcSech[a + b*x]/2]))] - (6*I)*b*x*ArcSech[a + b*x]*PolyLog[2, ((1 - I*Sqrt[-1 + a^2])*(1 - Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(1 + a + b*x)))/(a*(a + b*x))] + (6*I)*b*x*ArcSech[a + b*x]*PolyLog[2, ((1 + I*Sqrt[-1 + a^2])*(1 - Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(1 + a + b*x)))/(a*(a + b*x))] - (6*I)*b*x*PolyLog[3, ((1 - I*Sqrt[-1 + a^2])*(1 - Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(1 + a + b*x)))/(a*(a + b*x))] + (6*I)*b*x*PolyLog[3, ((1 + I*Sqrt[-1 + a^2])*(1 - Sqrt[-((-1 + a + b*x)/(1 + a + b*x))]*(1 + a + b*x)))/(a*(a + b*x))])/(a*Sqrt[-1 + a^2]*x))","C",0
19,0,0,965,9.9541495,"\int \frac{\text{sech}^{-1}(a+b x)^3}{x^3} \, dx","Integrate[ArcSech[a + b*x]^3/x^3,x]","\int \frac{\text{sech}^{-1}(a+b x)^3}{x^3} \, dx","\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_2\left(\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{Li}_3\left(\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{Li}_3\left(\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{Li}_3\left(\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{Li}_3\left(\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,"Integrate[ArcSech[a + b*x]^3/x^3, x]","F",-1
20,1,84,164,0.0435449,"\int x^3 \text{sech}^{-1}\left(\sqrt{x}\right) \, dx","Integrate[x^3*ArcSech[Sqrt[x]],x]","\frac{1}{4} x^4 \text{sech}^{-1}\left(\sqrt{x}\right)-\frac{1}{140} \sqrt{\frac{1-\sqrt{x}}{\sqrt{x}+1}} \left(5 x^{7/2}+6 x^{5/2}+8 x^{3/2}+5 x^3+6 x^2+8 x+16 \sqrt{x}+16\right)","\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,"-1/140*(Sqrt[(1 - Sqrt[x])/(1 + Sqrt[x])]*(16 + 16*Sqrt[x] + 8*x + 8*x^(3/2) + 6*x^2 + 6*x^(5/2) + 5*x^3 + 5*x^(7/2))) + (x^4*ArcSech[Sqrt[x]])/4","A",1
21,1,72,126,0.0306019,"\int x^2 \text{sech}^{-1}\left(\sqrt{x}\right) \, dx","Integrate[x^2*ArcSech[Sqrt[x]],x]","\frac{1}{3} x^3 \text{sech}^{-1}\left(\sqrt{x}\right)-\frac{1}{45} \sqrt{\frac{1-\sqrt{x}}{\sqrt{x}+1}} \left(3 x^{5/2}+4 x^{3/2}+3 x^2+4 x+8 \sqrt{x}+8\right)","\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,"-1/45*(Sqrt[(1 - Sqrt[x])/(1 + Sqrt[x])]*(8 + 8*Sqrt[x] + 4*x + 4*x^(3/2) + 3*x^2 + 3*x^(5/2))) + (x^3*ArcSech[Sqrt[x]])/3","A",1
22,1,56,88,0.026395,"\int x \text{sech}^{-1}\left(\sqrt{x}\right) \, dx","Integrate[x*ArcSech[Sqrt[x]],x]","\frac{1}{2} x^2 \text{sech}^{-1}\left(\sqrt{x}\right)-\frac{1}{6} \sqrt{\frac{1-\sqrt{x}}{\sqrt{x}+1}} \left(x^{3/2}+x+2 \sqrt{x}+2\right)","\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,"-1/6*(Sqrt[(1 - Sqrt[x])/(1 + Sqrt[x])]*(2 + 2*Sqrt[x] + x + x^(3/2))) + (x^2*ArcSech[Sqrt[x]])/2","A",1
23,1,67,43,0.0964322,"\int \text{sech}^{-1}\left(\sqrt{x}\right) \, dx","Integrate[ArcSech[Sqrt[x]],x]","x \text{sech}^{-1}\left(\sqrt{x}\right)-\frac{\sqrt{\frac{1-\sqrt{x}}{\sqrt{x}+1}} \sqrt{\sqrt{x}+1} \sqrt{1-x}}{\sqrt{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,"-((Sqrt[(1 - Sqrt[x])/(1 + Sqrt[x])]*Sqrt[1 + Sqrt[x]]*Sqrt[1 - x])/Sqrt[1 - Sqrt[x]]) + x*ArcSech[Sqrt[x]]","A",1
24,1,45,46,0.039436,"\int \frac{\text{sech}^{-1}\left(\sqrt{x}\right)}{x} \, dx","Integrate[ArcSech[Sqrt[x]]/x,x]","\text{Li}_2\left(-e^{-2 \text{sech}^{-1}\left(\sqrt{x}\right)}\right)-\text{sech}^{-1}\left(\sqrt{x}\right) \left(\text{sech}^{-1}\left(\sqrt{x}\right)+2 \log \left(e^{-2 \text{sech}^{-1}\left(\sqrt{x}\right)}+1\right)\right)","-\text{Li}_2\left(-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]]*(ArcSech[Sqrt[x]] + 2*Log[1 + E^(-2*ArcSech[Sqrt[x]])])) + PolyLog[2, -E^(-2*ArcSech[Sqrt[x]])]","A",0
25,1,111,98,0.0768651,"\int \frac{\text{sech}^{-1}\left(\sqrt{x}\right)}{x^2} \, dx","Integrate[ArcSech[Sqrt[x]]/x^2,x]","\frac{\sqrt{\frac{1-\sqrt{x}}{\sqrt{x}+1}} \left(\sqrt{x}+1\right)+x \log \left(\sqrt{x} \sqrt{\frac{1-\sqrt{x}}{\sqrt{x}+1}}+\sqrt{\frac{1-\sqrt{x}}{\sqrt{x}+1}}+1\right)-\frac{1}{2} x \log (x)-2 \text{sech}^{-1}\left(\sqrt{x}\right)}{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}",1,"(Sqrt[(1 - Sqrt[x])/(1 + Sqrt[x])]*(1 + Sqrt[x]) - 2*ArcSech[Sqrt[x]] + x*Log[1 + Sqrt[(1 - Sqrt[x])/(1 + Sqrt[x])] + Sqrt[(1 - Sqrt[x])/(1 + Sqrt[x])]*Sqrt[x]] - (x*Log[x])/2)/(2*x)","A",1
26,1,125,136,0.1164158,"\int \frac{\text{sech}^{-1}\left(\sqrt{x}\right)}{x^3} \, dx","Integrate[ArcSech[Sqrt[x]]/x^3,x]","\frac{1}{16} \left(-\frac{8 \text{sech}^{-1}\left(\sqrt{x}\right)}{x^2}+\frac{\sqrt{\frac{1-\sqrt{x}}{\sqrt{x}+1}} \left(3 x^{3/2}+3 x+2 \sqrt{x}+2\right)}{x^2}+3 \log \left(\sqrt{x} \sqrt{\frac{1-\sqrt{x}}{\sqrt{x}+1}}+\sqrt{\frac{1-\sqrt{x}}{\sqrt{x}+1}}+1\right)-\frac{3 \log (x)}{2}\right)","\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,"((Sqrt[(1 - Sqrt[x])/(1 + Sqrt[x])]*(2 + 2*Sqrt[x] + 3*x + 3*x^(3/2)))/x^2 - (8*ArcSech[Sqrt[x]])/x^2 + 3*Log[1 + Sqrt[(1 - Sqrt[x])/(1 + Sqrt[x])] + Sqrt[(1 - Sqrt[x])/(1 + Sqrt[x])]*Sqrt[x]] - (3*Log[x])/2)/16","A",1
27,1,140,172,0.1328457,"\int \frac{\text{sech}^{-1}\left(\sqrt{x}\right)}{x^4} \, dx","Integrate[ArcSech[Sqrt[x]]/x^4,x]","\frac{15 x^3 \log \left(\sqrt{x} \sqrt{\frac{1-\sqrt{x}}{\sqrt{x}+1}}+\sqrt{\frac{1-\sqrt{x}}{\sqrt{x}+1}}+1\right)-\frac{15}{2} x^3 \log (x)+\sqrt{\frac{1-\sqrt{x}}{\sqrt{x}+1}} \left(15 x^{5/2}+10 x^{3/2}+15 x^2+10 x+8 \sqrt{x}+8\right)-48 \text{sech}^{-1}\left(\sqrt{x}\right)}{144 x^3}","\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,"(Sqrt[(1 - Sqrt[x])/(1 + Sqrt[x])]*(8 + 8*Sqrt[x] + 10*x + 10*x^(3/2) + 15*x^2 + 15*x^(5/2)) - 48*ArcSech[Sqrt[x]] + 15*x^3*Log[1 + Sqrt[(1 - Sqrt[x])/(1 + Sqrt[x])] + Sqrt[(1 - Sqrt[x])/(1 + Sqrt[x])]*Sqrt[x]] - (15*x^3*Log[x])/2)/(144*x^3)","A",1
28,1,25,21,0.0249021,"\int \text{sech}^{-1}\left(\frac{1}{x}\right) \, dx","Integrate[ArcSech[x^(-1)],x]","x \text{sech}^{-1}\left(\frac{1}{x}\right)-\frac{x-1}{\sqrt{\frac{x-1}{x+1}}}","x \cosh ^{-1}(x)-\sqrt{x-1} \sqrt{x+1}",1,"-((-1 + x)/Sqrt[(-1 + x)/(1 + x)]) + x*ArcSech[x^(-1)]","A",1
29,1,219,61,0.9830815,"\int \frac{\text{sech}^{-1}\left(a x^n\right)}{x} \, dx","Integrate[ArcSech[a*x^n]/x,x]","\frac{\sqrt{\frac{1-a x^n}{a x^n+1}} \left(\sqrt{1-a^2 x^{2 n}} \left(-4 \text{Li}_2\left(\frac{1}{2}-\frac{1}{2} \sqrt{1-a^2 x^{2 n}}\right)+\log ^2\left(a^2 x^{2 n}\right)+2 \log ^2\left(\frac{1}{2} \left(\sqrt{1-a^2 x^{2 n}}+1\right)\right)-4 \log \left(\frac{1}{2} \left(\sqrt{1-a^2 x^{2 n}}+1\right)\right) \log \left(a^2 x^{2 n}\right)\right)+4 \sqrt{a^2 x^{2 n}-1} \left(2 n \log (x)-\log \left(a^2 x^{2 n}\right)\right) \tan ^{-1}\left(\sqrt{a^2 x^{2 n}-1}\right)\right)}{8 \left(n-a n x^n\right)}+\log (x) \text{sech}^{-1}\left(a x^n\right)","-\frac{\text{Li}_2\left(-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]*Log[x] + (Sqrt[(1 - a*x^n)/(1 + a*x^n)]*(4*Sqrt[-1 + a^2*x^(2*n)]*ArcTan[Sqrt[-1 + a^2*x^(2*n)]]*(2*n*Log[x] - Log[a^2*x^(2*n)]) + Sqrt[1 - a^2*x^(2*n)]*(Log[a^2*x^(2*n)]^2 - 4*Log[a^2*x^(2*n)]*Log[(1 + Sqrt[1 - a^2*x^(2*n)])/2] + 2*Log[(1 + Sqrt[1 - a^2*x^(2*n)])/2]^2 - 4*PolyLog[2, 1/2 - Sqrt[1 - a^2*x^(2*n)]/2])))/(8*(n - a*n*x^n))","B",1
30,1,49,54,0.0469708,"\int \frac{\text{sech}^{-1}\left(a x^5\right)}{x} \, dx","Integrate[ArcSech[a*x^5]/x,x]","\frac{1}{10} \left(\text{Li}_2\left(-e^{-2 \text{sech}^{-1}\left(a x^5\right)}\right)-\text{sech}^{-1}\left(a x^5\right) \left(\text{sech}^{-1}\left(a x^5\right)+2 \log \left(e^{-2 \text{sech}^{-1}\left(a x^5\right)}+1\right)\right)\right)","-\frac{1}{10} \text{Li}_2\left(-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]*(ArcSech[a*x^5] + 2*Log[1 + E^(-2*ArcSech[a*x^5])])) + PolyLog[2, -E^(-2*ArcSech[a*x^5])])/10","A",0
31,1,249,77,1.1733699,"\int \text{sech}^{-1}\left(c e^{a+b x}\right) \, dx","Integrate[ArcSech[c*E^(a + b*x)],x]","x \text{sech}^{-1}\left(c e^{a+b x}\right)-\frac{\sqrt{\frac{1-c e^{a+b x}}{c e^{a+b x}+1}} \sqrt{c e^{a+b x}+1} \left(4 \text{Li}_2\left(\frac{1}{2} \left(1-\sqrt{1-c^2 e^{2 (a+b x)}}\right)\right)-\log ^2\left(c^2 e^{2 (a+b x)}\right)-2 \log ^2\left(\frac{1}{2} \left(\sqrt{1-c^2 e^{2 (a+b x)}}+1\right)\right)+4 \log \left(\frac{1}{2} \left(\sqrt{1-c^2 e^{2 (a+b x)}}+1\right)\right) \log \left(c^2 e^{2 (a+b x)}\right)+\left(8 b x-4 \log \left(c^2 e^{2 (a+b x)}\right)\right) \tanh ^{-1}\left(\sqrt{1-c^2 e^{2 (a+b x)}}\right)\right)}{8 b \sqrt{1-c e^{a+b x}}}","-\frac{\text{Li}_2\left(-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,"x*ArcSech[c*E^(a + b*x)] - (Sqrt[(1 - c*E^(a + b*x))/(1 + c*E^(a + b*x))]*Sqrt[1 + c*E^(a + b*x)]*(ArcTanh[Sqrt[1 - c^2*E^(2*(a + b*x))]]*(8*b*x - 4*Log[c^2*E^(2*(a + b*x))]) - Log[c^2*E^(2*(a + b*x))]^2 + 4*Log[c^2*E^(2*(a + b*x))]*Log[(1 + Sqrt[1 - c^2*E^(2*(a + b*x))])/2] - 2*Log[(1 + Sqrt[1 - c^2*E^(2*(a + b*x))])/2]^2 + 4*PolyLog[2, (1 - Sqrt[1 - c^2*E^(2*(a + b*x))])/2]))/(8*b*Sqrt[1 - c*E^(a + b*x)])","B",1
32,1,65,64,0.0937582,"\int e^{\text{sech}^{-1}(a x)} x^4 \, dx","Integrate[E^ArcSech[a*x]*x^4,x]","\frac{15 a^4 x^4+4 \sqrt{\frac{1-a x}{a x+1}} (a x+1)^2 \left(3 a^3 x^3-3 a^2 x^2+2 a x-2\right)}{60 a^5}","-\frac{2 x e^{\text{sech}^{-1}(a x)}}{15 a^4}+\frac{x^2}{15 a^3}-\frac{x^3 e^{\text{sech}^{-1}(a x)}}{15 a^2}+\frac{1}{5} x^5 e^{\text{sech}^{-1}(a x)}+\frac{x^4}{20 a}",1,"(15*a^4*x^4 + 4*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2*(-2 + 2*a*x - 3*a^2*x^2 + 3*a^3*x^3))/(60*a^5)","A",0
33,1,97,84,0.1331803,"\int e^{\text{sech}^{-1}(a x)} x^3 \, dx","Integrate[E^ArcSech[a*x]*x^3,x]","\frac{8 a^3 x^3-3 a \sqrt{\frac{1-a x}{a x+1}} \left(-2 a^3 x^4-2 a^2 x^3+a x^2+x\right)+3 i \log \left(2 \sqrt{\frac{1-a x}{a x+1}} (a x+1)-2 i a x\right)}{24 a^4}","\frac{\sqrt{\frac{1}{a x+1}} \sqrt{a x+1} \sin ^{-1}(a x)}{8 a^4}-\frac{x \sqrt{1-a x}}{8 a^3 \sqrt{\frac{1}{a x+1}}}+\frac{1}{4} x^4 e^{\text{sech}^{-1}(a x)}+\frac{x^3}{12 a}",1,"(8*a^3*x^3 - 3*a*Sqrt[(1 - a*x)/(1 + a*x)]*(x + a*x^2 - 2*a^2*x^3 - 2*a^3*x^4) + (3*I)*Log[(-2*I)*a*x + 2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)])/(24*a^4)","C",0
34,1,48,38,0.0627071,"\int e^{\text{sech}^{-1}(a x)} x^2 \, dx","Integrate[E^ArcSech[a*x]*x^2,x]","\frac{3 a^2 x^2+2 (a x-1) \sqrt{\frac{1-a x}{a x+1}} (a x+1)^2}{6 a^3}","-\frac{x e^{\text{sech}^{-1}(a x)}}{3 a^2}+\frac{1}{3} x^3 e^{\text{sech}^{-1}(a x)}+\frac{x^2}{6 a}",1,"(3*a^2*x^2 + 2*(-1 + a*x)*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2)/(6*a^3)","A",0
35,1,75,53,0.0792788,"\int e^{\text{sech}^{-1}(a x)} x \, dx","Integrate[E^ArcSech[a*x]*x,x]","\frac{2 a x+a x \sqrt{\frac{1-a x}{a x+1}} (a x+1)+i \log \left(2 \sqrt{\frac{1-a x}{a x+1}} (a x+1)-2 i a x\right)}{2 a^2}","\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,"(2*a*x + a*x*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x) + I*Log[(-2*I)*a*x + 2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)])/(2*a^2)","C",0
36,1,79,24,0.0435059,"\int e^{\text{sech}^{-1}(a x)} \, dx","Integrate[E^ArcSech[a*x],x]","\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)+2 \log (a x)-\log \left(a x \sqrt{\frac{1-a x}{a x+1}}+\sqrt{\frac{1-a x}{a x+1}}+1\right)}{a}","\frac{\log (x)}{a}+x e^{\text{sech}^{-1}(a x)}-\frac{\text{sech}^{-1}(a x)}{a}",1,"(Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x) + 2*Log[a*x] - Log[1 + Sqrt[(1 - a*x)/(1 + a*x)] + a*x*Sqrt[(1 - a*x)/(1 + a*x)]])/a","B",0
37,1,75,48,0.0465077,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x} \, dx","Integrate[E^ArcSech[a*x]/x,x]","\sqrt{\frac{1-a x}{a x+1}} \left(-\frac{1}{a x}-1\right)-\frac{1}{a x}-i \log \left(2 \sqrt{\frac{1-a x}{a x+1}} (a x+1)-2 i a x\right)","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)) + (-1 - 1/(a*x))*Sqrt[(1 - a*x)/(1 + a*x)] - I*Log[(-2*I)*a*x + 2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)]","C",0
38,1,93,35,0.0630993,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x^2} \, dx","Integrate[E^ArcSech[a*x]/x^2,x]","\frac{1}{2} \left(-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)}{a x^2}-\frac{1}{a x^2}-a \log (x)+a \log \left(a x \sqrt{\frac{1-a x}{a x+1}}+\sqrt{\frac{1-a x}{a x+1}}+1\right)\right)","a \tanh ^{-1}\left(\sqrt{\frac{1-a x}{a x+1}}\right)-\frac{e^{\text{sech}^{-1}(a x)}}{2 x}",1,"(-(1/(a*x^2)) - (Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x))/(a*x^2) - a*Log[x] + a*Log[1 + Sqrt[(1 - a*x)/(1 + a*x)] + a*x*Sqrt[(1 - a*x)/(1 + a*x)]])/2","B",0
39,1,43,55,0.0434681,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x^3} \, dx","Integrate[E^ArcSech[a*x]/x^3,x]","\frac{(a x-1) \sqrt{\frac{1-a x}{a x+1}} (a x+1)^2-1}{3 a x^3}","-\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 + (-1 + a*x)*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2)/(3*a*x^3)","A",1
40,1,110,132,0.0780149,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x^4} \, dx","Integrate[E^ArcSech[a*x]/x^4,x]","\frac{-a^4 x^4 \log (x)+a^4 x^4 \log \left(a x \sqrt{\frac{1-a x}{a x+1}}+\sqrt{\frac{1-a x}{a x+1}}+1\right)+\sqrt{\frac{1-a x}{a x+1}} \left(a^3 x^3+a^2 x^2-2 a x-2\right)-2}{8 a x^4}","\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{\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{a \sqrt{1-a x}}{8 x^2 \sqrt{\frac{1}{a x+1}}}",1,"(-2 + Sqrt[(1 - a*x)/(1 + a*x)]*(-2 - 2*a*x + a^2*x^2 + a^3*x^3) - a^4*x^4*Log[x] + a^4*x^4*Log[1 + Sqrt[(1 - a*x)/(1 + a*x)] + a*x*Sqrt[(1 - a*x)/(1 + a*x)]])/(8*a*x^4)","A",0
41,1,60,115,0.0694468,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x^5} \, dx","Integrate[E^ArcSech[a*x]/x^5,x]","\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)^2 \left(2 a^3 x^3-2 a^2 x^2+3 a x-3\right)-3}{15 a x^5}","\frac{2 a^3 \sqrt{1-a x}}{15 x \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{a \sqrt{1-a x}}{15 x^3 \sqrt{\frac{1}{a x+1}}}",1,"(-3 + Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2*(-3 + 3*a*x - 2*a^2*x^2 + 2*a^3*x^3))/(15*a*x^5)","A",0
42,1,129,163,0.1045682,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x^6} \, dx","Integrate[E^ArcSech[a*x]/x^6,x]","\frac{-3 a^6 x^6 \log (x)+3 a^6 x^6 \log \left(a x \sqrt{\frac{1-a x}{a x+1}}+\sqrt{\frac{1-a x}{a x+1}}+1\right)+\sqrt{\frac{1-a x}{a x+1}} \left(3 a^5 x^5+3 a^4 x^4+2 a^3 x^3+2 a^2 x^2-8 a x-8\right)-8}{48 a x^6}","\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^3 \sqrt{1-a x}}{16 x^2 \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 \sqrt{1-a x}}{24 x^4 \sqrt{\frac{1}{a x+1}}}",1,"(-8 + Sqrt[(1 - a*x)/(1 + a*x)]*(-8 - 8*a*x + 2*a^2*x^2 + 2*a^3*x^3 + 3*a^4*x^4 + 3*a^5*x^5) - 3*a^6*x^6*Log[x] + 3*a^6*x^6*Log[1 + Sqrt[(1 - a*x)/(1 + a*x)] + a*x*Sqrt[(1 - a*x)/(1 + a*x)]])/(48*a*x^6)","A",0
43,1,76,146,0.0890673,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x^7} \, dx","Integrate[E^ArcSech[a*x]/x^7,x]","\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)^2 \left(8 a^5 x^5-8 a^4 x^4+12 a^3 x^3-12 a^2 x^2+15 a x-15\right)-15}{105 a x^7}","\frac{8 a^5 \sqrt{1-a x}}{105 x \sqrt{\frac{1}{a x+1}}}+\frac{4 a^3 \sqrt{1-a x}}{105 x^3 \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{a \sqrt{1-a x}}{35 x^5 \sqrt{\frac{1}{a x+1}}}",1,"(-15 + Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2*(-15 + 15*a*x - 12*a^2*x^2 + 12*a^3*x^3 - 8*a^4*x^4 + 8*a^5*x^5))/(105*a*x^7)","A",0
44,1,145,194,0.1250858,"\int \frac{e^{\text{sech}^{-1}(a x)}}{x^8} \, dx","Integrate[E^ArcSech[a*x]/x^8,x]","\frac{-15 a^8 x^8 \log (x)+15 a^8 x^8 \log \left(a x \sqrt{\frac{1-a x}{a x+1}}+\sqrt{\frac{1-a x}{a x+1}}+1\right)+\sqrt{\frac{1-a x}{a x+1}} \left(15 a^7 x^7+15 a^6 x^6+10 a^5 x^5+10 a^4 x^4+8 a^3 x^3+8 a^2 x^2-48 a x-48\right)-48}{384 a x^8}","\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{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{\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{a \sqrt{1-a x}}{48 x^6 \sqrt{\frac{1}{a x+1}}}",1,"(-48 + Sqrt[(1 - a*x)/(1 + a*x)]*(-48 - 48*a*x + 8*a^2*x^2 + 8*a^3*x^3 + 10*a^4*x^4 + 10*a^5*x^5 + 15*a^6*x^6 + 15*a^7*x^7) - 15*a^8*x^8*Log[x] + 15*a^8*x^8*Log[1 + Sqrt[(1 - a*x)/(1 + a*x)] + a*x*Sqrt[(1 - a*x)/(1 + a*x)]])/(384*a*x^8)","A",0
45,1,111,111,0.1925695,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x^7 \, dx","Integrate[E^ArcSech[a*x^2]*x^7,x]","\frac{8 a^3 x^6-3 a \sqrt{\frac{1-a x^2}{a x^2+1}} \left(-2 a^3 x^8-2 a^2 x^6+a x^4+x^2\right)+3 i \log \left(2 \sqrt{\frac{1-a x^2}{a x^2+1}} \left(a x^2+1\right)-2 i a x^2\right)}{48 a^4}","\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^2 \sqrt{\frac{1}{a x^2+1}} \sqrt{a x^2+1} \sqrt{1-a^2 x^4}}{16 a^3}+\frac{x^6}{24 a}+\frac{1}{8} x^8 e^{\text{sech}^{-1}\left(a x^2\right)}",1,"(8*a^3*x^6 - 3*a*Sqrt[(1 - a*x^2)/(1 + a*x^2)]*(x^2 + a*x^4 - 2*a^2*x^6 - 2*a^3*x^8) + (3*I)*Log[(-2*I)*a*x^2 + 2*Sqrt[(1 - a*x^2)/(1 + a*x^2)]*(1 + a*x^2)])/(48*a^4)","C",0
46,1,139,115,0.3202076,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x^6 \, dx","Integrate[E^ArcSech[a*x^2]*x^6,x]","-\frac{2 i \sqrt{\frac{1-a x^2}{a x^2+1}} \sqrt{1-a^2 x^4} F\left(\left.i \sinh ^{-1}\left(\sqrt{-a} x\right)\right|-1\right)}{21 (-a)^{7/2} \left(a x^2-1\right)}+\frac{x \sqrt{\frac{1-a x^2}{a x^2+1}} \left(3 a^3 x^6+3 a^2 x^4-2 a x^2-2\right)}{21 a^3}+\frac{x^5}{5 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)}{21 a^{7/2}}-\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 x^5}{35 a}+\frac{1}{7} x^7 e^{\text{sech}^{-1}\left(a x^2\right)}",1,"x^5/(5*a) + (x*Sqrt[(1 - a*x^2)/(1 + a*x^2)]*(-2 - 2*a*x^2 + 3*a^2*x^4 + 3*a^3*x^6))/(21*a^3) - (((2*I)/21)*Sqrt[(1 - a*x^2)/(1 + a*x^2)]*Sqrt[1 - a^2*x^4]*EllipticF[I*ArcSinh[Sqrt[-a]*x], -1])/((-a)^(7/2)*(-1 + a*x^2))","C",0
47,1,56,58,0.0979548,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x^5 \, dx","Integrate[E^ArcSech[a*x^2]*x^5,x]","\frac{\left(a x^2-1\right) \sqrt{\frac{1-a x^2}{a x^2+1}} \left(a x^2+1\right)^2}{6 a^3}+\frac{x^4}{4 a}","-\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/(4*a) + ((-1 + a*x^2)*Sqrt[(1 - a*x^2)/(1 + a*x^2)]*(1 + a*x^2)^2)/(6*a^3)","A",0
48,1,140,112,0.4446133,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x^4 \, dx","Integrate[E^ArcSech[a*x^2]*x^4,x]","\frac{1}{15} \left(\frac{6 i \sqrt{\frac{1-a x^2}{a x^2+1}} \sqrt{1-a^2 x^4} \left(E\left(\left.i \sinh ^{-1}\left(\sqrt{-a} x\right)\right|-1\right)-F\left(\left.i \sinh ^{-1}\left(\sqrt{-a} x\right)\right|-1\right)\right)}{(-a)^{5/2} \left(a x^2-1\right)}+\frac{5 x^3}{a}+\frac{3 \sqrt{\frac{1-a x^2}{a x^2+1}} \left(a x^5+x^3\right)}{a}\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,"((5*x^3)/a + (3*Sqrt[(1 - a*x^2)/(1 + a*x^2)]*(x^3 + a*x^5))/a + ((6*I)*Sqrt[(1 - a*x^2)/(1 + a*x^2)]*Sqrt[1 - a^2*x^4]*(EllipticE[I*ArcSinh[Sqrt[-a]*x], -1] - EllipticF[I*ArcSinh[Sqrt[-a]*x], -1]))/((-a)^(5/2)*(-1 + a*x^2)))/15","C",0
49,1,92,63,0.1054772,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x^3 \, dx","Integrate[E^ArcSech[a*x^2]*x^3,x]","\frac{2 a x^2+i \log \left(2 \sqrt{\frac{1-a x^2}{a x^2+1}} \left(a x^2+1\right)-2 i a x^2\right)+a \sqrt{\frac{1-a x^2}{a x^2+1}} \left(a x^4+x^2\right)}{4 a^2}","\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,"(2*a*x^2 + a*Sqrt[(1 - a*x^2)/(1 + a*x^2)]*(x^2 + a*x^4) + I*Log[(-2*I)*a*x^2 + 2*Sqrt[(1 - a*x^2)/(1 + a*x^2)]*(1 + a*x^2)])/(4*a^2)","C",0
50,1,116,67,0.2001792,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x^2 \, dx","Integrate[E^ArcSech[a*x^2]*x^2,x]","-\frac{2 i \sqrt{\frac{1-a x^2}{a x^2+1}} \sqrt{1-a^2 x^4} F\left(\left.i \sinh ^{-1}\left(\sqrt{-a} x\right)\right|-1\right)}{3 (-a)^{3/2} \left(a x^2-1\right)}+\frac{\sqrt{\frac{1-a x^2}{a x^2+1}} \left(a x^3+x\right)}{3 a}+\frac{x}{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,"x/a + (Sqrt[(1 - a*x^2)/(1 + a*x^2)]*(x + a*x^3))/(3*a) - (((2*I)/3)*Sqrt[(1 - a*x^2)/(1 + a*x^2)]*Sqrt[1 - a^2*x^4]*EllipticF[I*ArcSinh[Sqrt[-a]*x], -1])/((-a)^(3/2)*(-1 + a*x^2))","C",0
51,1,100,68,0.0655294,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x \, dx","Integrate[E^ArcSech[a*x^2]*x,x]","\frac{\sqrt{\frac{1-a x^2}{a x^2+1}} \left(a x^2+1\right)+2 \log \left(a x^2\right)-\log \left(a x^2 \sqrt{\frac{1-a x^2}{a x^2+1}}+\sqrt{\frac{1-a x^2}{a x^2+1}}+1\right)}{2 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,"(Sqrt[(1 - a*x^2)/(1 + a*x^2)]*(1 + a*x^2) + 2*Log[a*x^2] - Log[1 + Sqrt[(1 - a*x^2)/(1 + a*x^2)] + a*x^2*Sqrt[(1 - a*x^2)/(1 + a*x^2)]])/(2*a)","A",0
52,1,135,147,0.2974877,"\int e^{\text{sech}^{-1}\left(a x^2\right)} \, dx","Integrate[E^ArcSech[a*x^2],x]","-\frac{2 i \sqrt{\frac{1-a x^2}{a x^2+1}} \sqrt{1-a^2 x^4} \left(E\left(\left.i \sinh ^{-1}\left(\sqrt{-a} x\right)\right|-1\right)-F\left(\left.i \sinh ^{-1}\left(\sqrt{-a} x\right)\right|-1\right)\right)}{\sqrt{-a} \left(a x^2-1\right)}+\sqrt{\frac{1-a x^2}{a x^2+1}} \left(-\frac{1}{a x}-x\right)-\frac{1}{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,"-(1/(a*x)) + (-(1/(a*x)) - x)*Sqrt[(1 - a*x^2)/(1 + a*x^2)] - ((2*I)*Sqrt[(1 - a*x^2)/(1 + a*x^2)]*Sqrt[1 - a^2*x^4]*(EllipticE[I*ArcSinh[Sqrt[-a]*x], -1] - EllipticF[I*ArcSinh[Sqrt[-a]*x], -1]))/(Sqrt[-a]*(-1 + a*x^2))","C",0
53,1,113,80,0.1491465,"\int \frac{e^{\text{sech}^{-1}\left(a x^2\right)}}{x} \, dx","Integrate[E^ArcSech[a*x^2]/x,x]","\frac{\sqrt{\frac{1-a x^2}{a x^2+1}} \left(a x^2+1\right) \tanh ^{-1}\left(\frac{a x^2}{\sqrt{a^2 x^4-1}}\right)}{2 \sqrt{a^2 x^4-1}}+\sqrt{\frac{1-a x^2}{a x^2+1}} \left(-\frac{1}{2 a x^2}-\frac{1}{2}\right)-\frac{1}{2 a x^2}","-\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*1/(a*x^2) + (-1/2 - 1/(2*a*x^2))*Sqrt[(1 - a*x^2)/(1 + a*x^2)] + (Sqrt[(1 - a*x^2)/(1 + a*x^2)]*(1 + a*x^2)*ArcTanh[(a*x^2)/Sqrt[-1 + a^2*x^4]])/(2*Sqrt[-1 + a^2*x^4])","A",0
54,1,123,115,0.1978023,"\int \frac{e^{\text{sech}^{-1}\left(a x^2\right)}}{x^2} \, dx","Integrate[E^ArcSech[a*x^2]/x^2,x]","\frac{2 i \sqrt{-a} \sqrt{\frac{1-a x^2}{a x^2+1}} \sqrt{1-a^2 x^4} F\left(\left.i \sinh ^{-1}\left(\sqrt{-a} x\right)\right|-1\right)}{3 a x^2-3}-\frac{1}{3 a x^3}-\frac{\sqrt{\frac{1-a x^2}{a x^2+1}} \left(a x^2+1\right)}{3 a x^3}","\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,"-1/3*1/(a*x^3) - (Sqrt[(1 - a*x^2)/(1 + a*x^2)]*(1 + a*x^2))/(3*a*x^3) + ((2*I)*Sqrt[-a]*Sqrt[(1 - a*x^2)/(1 + a*x^2)]*Sqrt[1 - a^2*x^4]*EllipticF[I*ArcSinh[Sqrt[-a]*x], -1])/(-3 + 3*a*x^2)","C",0
55,1,105,118,0.2682357,"\int \frac{e^{\text{sech}^{-1}\left(a x^2\right)}}{x^3} \, dx","Integrate[E^ArcSech[a*x^2]/x^3,x]","-\frac{-\frac{a^2 \sqrt{\frac{1-a x^2}{a x^2+1}} \left(a x^2+1\right) \tan ^{-1}\left(\sqrt{a^2 x^4-1}\right)}{\sqrt{a^2 x^4-1}}+\frac{\sqrt{\frac{1-a x^2}{a x^2+1}} \left(a x^2+1\right)}{x^4}+\frac{1}{x^4}}{4 a}","\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*(x^(-4) + (Sqrt[(1 - a*x^2)/(1 + a*x^2)]*(1 + a*x^2))/x^4 - (a^2*Sqrt[(1 - a*x^2)/(1 + a*x^2)]*(1 + a*x^2)*ArcTan[Sqrt[-1 + a^2*x^4]])/Sqrt[-1 + a^2*x^4])/a","A",0
56,1,159,109,2.5197308,"\int e^{\text{sech}^{-1}\left(a x^3\right)} x^m \, dx","Integrate[E^ArcSech[a*x^3]*x^m,x]","\frac{2^{\frac{m+1}{3}} x^{m+1} \left(a x^3\right)^{\frac{1}{3} (-m-1)} e^{\text{sech}^{-1}\left(a x^3\right)} \left(\frac{e^{\text{sech}^{-1}\left(a x^3\right)}}{e^{2 \text{sech}^{-1}\left(a x^3\right)}+1}\right)^{\frac{m+1}{3}} \left((m+10) \, _2F_1\left(1,\frac{2-m}{6};\frac{m+10}{6};-e^{2 \text{sech}^{-1}\left(a x^3\right)}\right)-(m+4) e^{2 \text{sech}^{-1}\left(a x^3\right)} \, _2F_1\left(1,\frac{8-m}{6};\frac{m+16}{6};-e^{2 \text{sech}^{-1}\left(a x^3\right)}\right)\right)}{(m+4) (m+10)}","-\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,"(2^((1 + m)/3)*E^ArcSech[a*x^3]*(E^ArcSech[a*x^3]/(1 + E^(2*ArcSech[a*x^3])))^((1 + m)/3)*x^(1 + m)*(a*x^3)^((-1 - m)/3)*((10 + m)*Hypergeometric2F1[1, (2 - m)/6, (10 + m)/6, -E^(2*ArcSech[a*x^3])] - E^(2*ArcSech[a*x^3])*(4 + m)*Hypergeometric2F1[1, (8 - m)/6, (16 + m)/6, -E^(2*ArcSech[a*x^3])]))/((4 + m)*(10 + m))","A",0
57,1,159,107,2.3907615,"\int e^{\text{sech}^{-1}\left(a x^2\right)} x^m \, dx","Integrate[E^ArcSech[a*x^2]*x^m,x]","\frac{2^{\frac{m+1}{2}} x^{m+1} \left(a x^2\right)^{\frac{1}{2} (-m-1)} e^{\text{sech}^{-1}\left(a x^2\right)} \left(\frac{e^{\text{sech}^{-1}\left(a x^2\right)}}{e^{2 \text{sech}^{-1}\left(a x^2\right)}+1}\right)^{\frac{m+1}{2}} \left((m+7) \, _2F_1\left(1,\frac{1-m}{4};\frac{m+7}{4};-e^{2 \text{sech}^{-1}\left(a x^2\right)}\right)-(m+3) e^{2 \text{sech}^{-1}\left(a x^2\right)} \, _2F_1\left(1,\frac{5-m}{4};\frac{m+11}{4};-e^{2 \text{sech}^{-1}\left(a x^2\right)}\right)\right)}{(m+3) (m+7)}","-\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^((1 + m)/2)*E^ArcSech[a*x^2]*(E^ArcSech[a*x^2]/(1 + E^(2*ArcSech[a*x^2])))^((1 + m)/2)*x^(1 + m)*(a*x^2)^((-1 - m)/2)*((7 + m)*Hypergeometric2F1[1, (1 - m)/4, (7 + m)/4, -E^(2*ArcSech[a*x^2])] - E^(2*ArcSech[a*x^2])*(3 + m)*Hypergeometric2F1[1, (5 - m)/4, (11 + m)/4, -E^(2*ArcSech[a*x^2])]))/((3 + m)*(7 + m))","A",0
58,1,145,91,0.3087025,"\int e^{\text{sech}^{-1}(a x)} x^m \, dx","Integrate[E^ArcSech[a*x]*x^m,x]","-\frac{2^{m+1} x^m (a x)^{-m} e^{2 \text{sech}^{-1}(a x)} \left(\frac{e^{\text{sech}^{-1}(a x)}}{e^{2 \text{sech}^{-1}(a x)}+1}\right)^m \left(e^{2 \text{sech}^{-1}(a x)}+1\right)^m \left((m+2) e^{2 \text{sech}^{-1}(a x)} \, _2F_1\left(\frac{m}{2}+2,m+2;\frac{m}{2}+3;-e^{2 \text{sech}^{-1}(a x)}\right)-(m+4) \, _2F_1\left(\frac{m}{2}+1,m+2;\frac{m}{2}+2;-e^{2 \text{sech}^{-1}(a x)}\right)\right)}{a (m+2) (m+4)}","\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+1} e^{\text{sech}^{-1}(a x)}}{m+1}+\frac{x^m}{a m (m+1)}",1,"-((2^(1 + m)*E^(2*ArcSech[a*x])*(E^ArcSech[a*x]/(1 + E^(2*ArcSech[a*x])))^m*(1 + E^(2*ArcSech[a*x]))^m*x^m*(-((4 + m)*Hypergeometric2F1[1 + m/2, 2 + m, 2 + m/2, -E^(2*ArcSech[a*x])]) + E^(2*ArcSech[a*x])*(2 + m)*Hypergeometric2F1[2 + m/2, 2 + m, 3 + m/2, -E^(2*ArcSech[a*x])]))/(a*(2 + m)*(4 + m)*(a*x)^m))","A",0
59,1,139,109,0.8360159,"\int e^{\text{sech}^{-1}\left(\frac{a}{x}\right)} x^m \, dx","Integrate[E^ArcSech[a/x]*x^m,x]","-\frac{a 2^{-m-1} x^m \left(\frac{a}{x}\right)^m e^{\text{sech}^{-1}\left(\frac{a}{x}\right)} \left(\frac{e^{\text{sech}^{-1}\left(\frac{a}{x}\right)}}{e^{2 \text{sech}^{-1}\left(\frac{a}{x}\right)}+1}\right)^{-m-1} \left(m e^{2 \text{sech}^{-1}\left(\frac{a}{x}\right)} \, _2F_1\left(1,\frac{m}{2}+2;2-\frac{m}{2};-e^{2 \text{sech}^{-1}\left(\frac{a}{x}\right)}\right)-(m-2) \, _2F_1\left(1,\frac{m}{2}+1;1-\frac{m}{2};-e^{2 \text{sech}^{-1}\left(\frac{a}{x}\right)}\right)\right)}{(m-2) m}","-\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,"-((2^(-1 - m)*a*E^ArcSech[a/x]*(E^ArcSech[a/x]/(1 + E^(2*ArcSech[a/x])))^(-1 - m)*(a/x)^m*x^m*(-((-2 + m)*Hypergeometric2F1[1, 1 + m/2, 1 - m/2, -E^(2*ArcSech[a/x])]) + E^(2*ArcSech[a/x])*m*Hypergeometric2F1[1, 2 + m/2, 2 - m/2, -E^(2*ArcSech[a/x])]))/((-2 + m)*m))","A",0
60,1,186,133,5.1707225,"\int e^{\text{sech}^{-1}\left(a x^p\right)} x^m \, dx","Integrate[E^ArcSech[a*x^p]*x^m,x]","\frac{2^{\frac{m+1}{p}} x^{m+1} \left(a x^p\right)^{-\frac{m+1}{p}} e^{\text{sech}^{-1}\left(a x^p\right)} \left(\frac{e^{\text{sech}^{-1}\left(a x^p\right)}}{e^{2 \text{sech}^{-1}\left(a x^p\right)}+1}\right)^{\frac{m+1}{p}} \left((m+3 p+1) \, _2F_1\left(1,1-\frac{m+p+1}{2 p};\frac{m+3 p+1}{2 p};-e^{2 \text{sech}^{-1}\left(a x^p\right)}\right)-(m+p+1) e^{2 \text{sech}^{-1}\left(a x^p\right)} \, _2F_1\left(1,-\frac{m-3 p+1}{2 p};\frac{m+5 p+1}{2 p};-e^{2 \text{sech}^{-1}\left(a x^p\right)}\right)\right)}{(m+p+1) (m+3 p+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,"(2^((1 + m)/p)*E^ArcSech[a*x^p]*(E^ArcSech[a*x^p]/(1 + E^(2*ArcSech[a*x^p])))^((1 + m)/p)*x^(1 + m)*(-(E^(2*ArcSech[a*x^p])*(1 + m + p)*Hypergeometric2F1[1, -1/2*(1 + m - 3*p)/p, (1 + m + 5*p)/(2*p), -E^(2*ArcSech[a*x^p])]) + (1 + m + 3*p)*Hypergeometric2F1[1, 1 - (1 + m + p)/(2*p), (1 + m + 3*p)/(2*p), -E^(2*ArcSech[a*x^p])]))/((1 + m + p)*(1 + m + 3*p)*(a*x^p)^((1 + m)/p))","A",0
61,1,159,119,0.308871,"\int e^{\text{sech}^{-1}\left(a x^p\right)} x \, dx","Integrate[E^ArcSech[a*x^p]*x,x]","\frac{x^{2-p} \left(\frac{a^2 p x^{2 p} \sqrt{\frac{1-a x^p}{a x^p+1}} \sqrt{1-a^2 x^{2 p}} \, _2F_1\left(\frac{1}{2},\frac{1}{2}+\frac{1}{p};\frac{3}{2}+\frac{1}{p};a^2 x^{2 p}\right)}{(p+2) \left(a x^p-1\right)}-a x^p \sqrt{\frac{1-a x^p}{a x^p+1}}-\sqrt{\frac{1-a x^p}{a x^p+1}}-1\right)}{a (p-2)}","\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,"(x^(2 - p)*(-1 - Sqrt[(1 - a*x^p)/(1 + a*x^p)] - a*x^p*Sqrt[(1 - a*x^p)/(1 + a*x^p)] + (a^2*p*x^(2*p)*Sqrt[(1 - a*x^p)/(1 + a*x^p)]*Sqrt[1 - a^2*x^(2*p)]*Hypergeometric2F1[1/2, 1/2 + p^(-1), 3/2 + p^(-1), a^2*x^(2*p)])/((2 + p)*(-1 + a*x^p))))/(a*(-2 + p))","A",0
62,1,139,105,0.41096,"\int e^{\text{sech}^{-1}\left(a x^p\right)} \, dx","Integrate[E^ArcSech[a*x^p],x]","\frac{x \left(-\frac{a^2 p x^p \sqrt{\frac{1-a x^p}{a x^p+1}} \sqrt{1-a^2 x^{2 p}} \, _2F_1\left(\frac{1}{2},\frac{p+1}{2 p};\frac{1}{2} \left(3+\frac{1}{p}\right);a^2 x^{2 p}\right)}{(p+1) \left(a x^p-1\right)}+\left(a+x^{-p}\right) \sqrt{\frac{1-a x^p}{a x^p+1}}+x^{-p}\right)}{a-a p}","\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,"(x*(x^(-p) + (a + x^(-p))*Sqrt[(1 - a*x^p)/(1 + a*x^p)] - (a^2*p*x^p*Sqrt[(1 - a*x^p)/(1 + a*x^p)]*Sqrt[1 - a^2*x^(2*p)]*Hypergeometric2F1[1/2, (1 + p)/(2*p), (3 + p^(-1))/2, a^2*x^(2*p)])/((1 + p)*(-1 + a*x^p))))/(a - a*p)","A",0
63,1,96,87,0.1566362,"\int \frac{e^{\text{sech}^{-1}\left(a x^p\right)}}{x} \, dx","Integrate[E^ArcSech[a*x^p]/x,x]","-\frac{i \left(a \log \left(2 \sqrt{\frac{1-a x^p}{a x^p+1}} \left(a x^p+1\right)-2 i a x^p\right)-i \left(a+x^{-p}\right) \sqrt{\frac{1-a x^p}{a x^p+1}}-i x^{-p}\right)}{a p}","-\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}-\frac{x^{-p} \sqrt{1-a x^p}}{a p \sqrt{\frac{1}{a x^p+1}}}",1,"((-I)*((-I)/x^p - I*(a + x^(-p))*Sqrt[(1 - a*x^p)/(1 + a*x^p)] + a*Log[(-2*I)*a*x^p + 2*Sqrt[(1 - a*x^p)/(1 + a*x^p)]*(1 + a*x^p)]))/(a*p)","C",0
64,1,156,107,0.2842997,"\int \frac{e^{\text{sech}^{-1}\left(a x^p\right)}}{x^2} \, dx","Integrate[E^ArcSech[a*x^p]/x^2,x]","x^{-p-1} \left(\frac{a p x^{2 p} \sqrt{\frac{1-a x^p}{a x^p+1}} \sqrt{1-a^2 x^{2 p}} \, _2F_1\left(\frac{1}{2},\frac{p-1}{2 p};\frac{3}{2}-\frac{1}{2 p};a^2 x^{2 p}\right)}{(p-1) (p+1) \left(a x^p-1\right)}-\frac{\sqrt{\frac{1-a x^p}{a x^p+1}} \left(a x^p+1\right)}{a (p+1)}-\frac{1}{a p+a}\right)","\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,"x^(-1 - p)*(-(a + a*p)^(-1) - (Sqrt[(1 - a*x^p)/(1 + a*x^p)]*(1 + a*x^p))/(a*(1 + p)) + (a*p*x^(2*p)*Sqrt[(1 - a*x^p)/(1 + a*x^p)]*Sqrt[1 - a^2*x^(2*p)]*Hypergeometric2F1[1/2, (-1 + p)/(2*p), 3/2 - 1/(2*p), a^2*x^(2*p)])/((-1 + p)*(1 + p)*(-1 + a*x^p)))","A",0
65,1,105,203,0.155627,"\int e^{2 \text{sech}^{-1}(a x)} x^4 \, dx","Integrate[E^(2*ArcSech[a*x])*x^4,x]","\frac{-12 a^5 x^5+40 a^3 x^3-15 a \sqrt{\frac{1-a x}{a x+1}} \left(-2 a^3 x^4-2 a^2 x^3+a x^2+x\right)+15 i \log \left(2 \sqrt{\frac{1-a x}{a x+1}} (a x+1)-2 i a x\right)}{60 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,"(40*a^3*x^3 - 12*a^5*x^5 - 15*a*Sqrt[(1 - a*x)/(1 + a*x)]*(x + a*x^2 - 2*a^2*x^3 - 2*a^3*x^4) + (15*I)*Log[(-2*I)*a*x + 2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)])/(60*a^5)","C",0
66,1,52,117,0.0703599,"\int e^{2 \text{sech}^{-1}(a x)} x^3 \, dx","Integrate[E^(2*ArcSech[a*x])*x^3,x]","\frac{2 (a x-1) \sqrt{\frac{1-a x}{a x+1}} (a x+1)^2}{3 a^4}+\frac{x^2}{a^2}-\frac{x^4}{4}","\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^2/a^2 - x^4/4 + (2*(-1 + a*x)*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2)/(3*a^4)","A",1
67,1,86,169,0.0756258,"\int e^{2 \text{sech}^{-1}(a x)} x^2 \, dx","Integrate[E^(2*ArcSech[a*x])*x^2,x]","\frac{i \log \left(2 \sqrt{\frac{1-a x}{a x+1}} (a x+1)-2 i a x\right)}{a^3}+\sqrt{\frac{1-a x}{a x+1}} \left(\frac{x}{a^2}+\frac{x^2}{a}\right)+\frac{2 x}{a^2}-\frac{x^3}{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,"(2*x)/a^2 - x^3/3 + Sqrt[(1 - a*x)/(1 + a*x)]*(x/a^2 + x^2/a) + (I*Log[(-2*I)*a*x + 2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)])/a^3","C",0
68,1,89,85,0.061847,"\int e^{2 \text{sech}^{-1}(a x)} x \, dx","Integrate[E^(2*ArcSech[a*x])*x,x]","\frac{-a^2 x^2+4 \sqrt{\frac{1-a x}{a x+1}} (a x+1)-4 \log \left(a x \sqrt{\frac{1-a x}{a x+1}}+\sqrt{\frac{1-a x}{a x+1}}+1\right)+8 \log (x)}{2 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,"(-(a^2*x^2) + 4*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x) + 8*Log[x] - 4*Log[1 + Sqrt[(1 - a*x)/(1 + a*x)] + a*x*Sqrt[(1 - a*x)/(1 + a*x)]])/(2*a^2)","A",0
69,1,75,57,0.0993891,"\int e^{2 \text{sech}^{-1}(a x)} \, dx","Integrate[E^(2*ArcSech[a*x]),x]","-\frac{a^2 x^2+2 \sqrt{\frac{1-a x}{a x+1}} (a x+1)+2 a x \tan ^{-1}\left(\frac{a x}{\sqrt{\frac{1-a x}{a x+1}} (a x+1)}\right)+2}{a^2 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,"-((2 + a^2*x^2 + 2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x) + 2*a*x*ArcTan[(a*x)/(Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x))])/(a^2*x))","A",0
70,1,86,86,0.0602017,"\int \frac{e^{2 \text{sech}^{-1}(a x)}}{x} \, dx","Integrate[E^(2*ArcSech[a*x])/x,x]","-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)}{a^2 x^2}-\frac{1}{a^2 x^2}+\log \left(a x \sqrt{\frac{1-a x}{a x+1}}+\sqrt{\frac{1-a x}{a x+1}}+1\right)-2 \log (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)",1,"-(1/(a^2*x^2)) - (Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x))/(a^2*x^2) - 2*Log[x] + Log[1 + Sqrt[(1 - a*x)/(1 + a*x)] + a*x*Sqrt[(1 - a*x)/(1 + a*x)]]","A",0
71,1,52,57,0.0632989,"\int \frac{e^{2 \text{sech}^{-1}(a x)}}{x^2} \, dx","Integrate[E^(2*ArcSech[a*x])/x^2,x]","\frac{3 a^2 x^2+2 (a x-1) \sqrt{\frac{1-a x}{a x+1}} (a x+1)^2-2}{3 a^2 x^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,"(-2 + 3*a^2*x^2 + 2*(-1 + a*x)*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2)/(3*a^2*x^3)","A",1
72,1,121,147,0.126181,"\int \frac{e^{2 \text{sech}^{-1}(a x)}}{x^3} \, dx","Integrate[E^(2*ArcSech[a*x])/x^3,x]","\frac{a^4 (-\log (x))+a^4 \log \left(a x \sqrt{\frac{1-a x}{a x+1}}+\sqrt{\frac{1-a x}{a x+1}}+1\right)+\frac{(a x+1) \left(a^2 x^2 \sqrt{\frac{1-a x}{a x+1}}+2 a x-2 \sqrt{\frac{1-a x}{a x+1}}-2\right)}{x^4}}{4 a^2}","\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,"(((1 + a*x)*(-2 + 2*a*x - 2*Sqrt[(1 - a*x)/(1 + a*x)] + a^2*x^2*Sqrt[(1 - a*x)/(1 + a*x)]))/x^4 - a^4*Log[x] + a^4*Log[1 + Sqrt[(1 - a*x)/(1 + a*x)] + a*x*Sqrt[(1 - a*x)/(1 + a*x)]])/(4*a^2)","A",0
73,1,69,183,0.0838711,"\int \frac{e^{2 \text{sech}^{-1}(a x)}}{x^4} \, dx","Integrate[E^(2*ArcSech[a*x])/x^4,x]","\frac{5 a^2 x^2+2 \sqrt{\frac{1-a x}{a x+1}} (a x+1)^2 \left(2 a^3 x^3-2 a^2 x^2+3 a x-3\right)-6}{15 a^2 x^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,"(-6 + 5*a^2*x^2 + 2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2*(-3 + 3*a*x - 2*a^2*x^2 + 2*a^3*x^3))/(15*a^2*x^5)","A",0
74,1,137,267,0.1472216,"\int \frac{e^{2 \text{sech}^{-1}(a x)}}{x^5} \, dx","Integrate[E^(2*ArcSech[a*x])/x^5,x]","\frac{-3 a^6 x^6 \log (x)+3 a^6 x^6 \log \left(a x \sqrt{\frac{1-a x}{a x+1}}+\sqrt{\frac{1-a x}{a x+1}}+1\right)+6 a^2 x^2+\sqrt{\frac{1-a x}{a x+1}} \left(3 a^5 x^5+3 a^4 x^4+2 a^3 x^3+2 a^2 x^2-8 a x-8\right)-8}{24 a^2 x^6}","\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,"(-8 + 6*a^2*x^2 + Sqrt[(1 - a*x)/(1 + a*x)]*(-8 - 8*a*x + 2*a^2*x^2 + 2*a^3*x^3 + 3*a^4*x^4 + 3*a^5*x^5) - 3*a^6*x^6*Log[x] + 3*a^6*x^6*Log[1 + Sqrt[(1 - a*x)/(1 + a*x)] + a*x*Sqrt[(1 - a*x)/(1 + a*x)]])/(24*a^2*x^6)","A",0
75,1,85,301,0.1028728,"\int \frac{e^{2 \text{sech}^{-1}(a x)}}{x^6} \, dx","Integrate[E^(2*ArcSech[a*x])/x^6,x]","\frac{21 a^2 x^2+2 \sqrt{\frac{1-a x}{a x+1}} (a x+1)^2 \left(8 a^5 x^5-8 a^4 x^4+12 a^3 x^3-12 a^2 x^2+15 a x-15\right)-30}{105 a^2 x^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,"(-30 + 21*a^2*x^2 + 2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2*(-15 + 15*a*x - 12*a^2*x^2 + 12*a^3*x^3 - 8*a^4*x^4 + 8*a^5*x^5))/(105*a^2*x^7)","A",0
76,1,65,147,0.0962073,"\int e^{-\text{sech}^{-1}(a x)} x^4 \, dx","Integrate[x^4/E^ArcSech[a*x],x]","\frac{15 a^4 x^4-4 \sqrt{\frac{1-a x}{a x+1}} (a x+1)^2 \left(3 a^3 x^3-3 a^2 x^2+2 a x-2\right)}{60 a^5}","-\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,"(15*a^4*x^4 - 4*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2*(-2 + 2*a*x - 3*a^2*x^2 + 3*a^3*x^3))/(60*a^5)","A",1
77,1,97,163,0.1285901,"\int e^{-\text{sech}^{-1}(a x)} x^3 \, dx","Integrate[x^3/E^ArcSech[a*x],x]","\frac{8 a^3 x^3+3 a \sqrt{\frac{1-a x}{a x+1}} \left(-2 a^3 x^4-2 a^2 x^3+a x^2+x\right)-3 i \log \left(2 \sqrt{\frac{1-a x}{a x+1}} (a x+1)-2 i a x\right)}{24 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,"(8*a^3*x^3 + 3*a*Sqrt[(1 - a*x)/(1 + a*x)]*(x + a*x^2 - 2*a^2*x^3 - 2*a^3*x^4) - (3*I)*Log[(-2*I)*a*x + 2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)])/(24*a^4)","C",0
78,1,48,75,0.0602973,"\int e^{-\text{sech}^{-1}(a x)} x^2 \, dx","Integrate[x^2/E^ArcSech[a*x],x]","\frac{3 a^2 x^2-2 (a x-1) \sqrt{\frac{1-a x}{a x+1}} (a x+1)^2}{6 a^3}","-\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,"(3*a^2*x^2 - 2*(-1 + a*x)*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2)/(6*a^3)","A",1
79,1,75,94,0.0685338,"\int e^{-\text{sech}^{-1}(a x)} x \, dx","Integrate[x/E^ArcSech[a*x],x]","-\frac{-2 a x+a x \sqrt{\frac{1-a x}{a x+1}} (a x+1)+i \log \left(2 \sqrt{\frac{1-a x}{a x+1}} (a x+1)-2 i a x\right)}{2 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,"-1/2*(-2*a*x + a*x*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x) + I*Log[(-2*I)*a*x + 2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)])/a^2","C",0
80,1,72,65,0.032278,"\int e^{-\text{sech}^{-1}(a x)} \, dx","Integrate[E^(-ArcSech[a*x]),x]","\frac{\log \left(a x \sqrt{\frac{1-a x}{a x+1}}+\sqrt{\frac{1-a x}{a x+1}}+1\right)-\sqrt{\frac{1-a x}{a x+1}} (a x+1)}{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)) + Log[1 + Sqrt[(1 - a*x)/(1 + a*x)] + a*x*Sqrt[(1 - a*x)/(1 + a*x)]])/a","A",0
81,1,74,46,0.0376086,"\int \frac{e^{-\text{sech}^{-1}(a x)}}{x} \, dx","Integrate[1/(E^ArcSech[a*x]*x),x]","\sqrt{\frac{1-a x}{a x+1}} \left(\frac{1}{a x}+1\right)-\frac{1}{a x}+i \log \left(2 \sqrt{\frac{1-a x}{a x+1}} (a x+1)-2 i a x\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,"-(1/(a*x)) + (1 + 1/(a*x))*Sqrt[(1 - a*x)/(1 + a*x)] + I*Log[(-2*I)*a*x + 2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)]","C",0
82,1,92,72,0.0602753,"\int \frac{e^{-\text{sech}^{-1}(a x)}}{x^2} \, dx","Integrate[1/(E^ArcSech[a*x]*x^2),x]","\frac{1}{2} \left(\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)}{a x^2}-\frac{1}{a x^2}+a \log (x)-a \log \left(a x \sqrt{\frac{1-a x}{a x+1}}+\sqrt{\frac{1-a x}{a x+1}}+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,"(-(1/(a*x^2)) + (Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x))/(a*x^2) + a*Log[x] - a*Log[1 + Sqrt[(1 - a*x)/(1 + a*x)] + a*x*Sqrt[(1 - a*x)/(1 + a*x)]])/2","A",0
83,1,43,116,0.0562605,"\int \frac{e^{-\text{sech}^{-1}(a x)}}{x^3} \, dx","Integrate[1/(E^ArcSech[a*x]*x^3),x]","-\frac{(a x-1) \sqrt{\frac{1-a x}{a x+1}} (a x+1)^2+1}{3 a x^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,"-1/3*(1 + (-1 + a*x)*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2)/(a*x^3)","A",0
84,1,110,200,0.1085283,"\int \frac{e^{-\text{sech}^{-1}(a x)}}{x^4} \, dx","Integrate[1/(E^ArcSech[a*x]*x^4),x]","-\frac{-a^4 x^4 \log (x)+a^4 x^4 \log \left(a x \sqrt{\frac{1-a x}{a x+1}}+\sqrt{\frac{1-a x}{a x+1}}+1\right)+\sqrt{\frac{1-a x}{a x+1}} \left(a^3 x^3+a^2 x^2-2 a x-2\right)+2}{8 a x^4}","\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,"-1/8*(2 + Sqrt[(1 - a*x)/(1 + a*x)]*(-2 - 2*a*x + a^2*x^2 + a^3*x^3) - a^4*x^4*Log[x] + a^4*x^4*Log[1 + Sqrt[(1 - a*x)/(1 + a*x)] + a*x*Sqrt[(1 - a*x)/(1 + a*x)]])/(a*x^4)","A",0
85,1,60,233,0.0741031,"\int \frac{e^{-\text{sech}^{-1}(a x)}}{x^5} \, dx","Integrate[1/(E^ArcSech[a*x]*x^5),x]","-\frac{\sqrt{\frac{1-a x}{a x+1}} \left(2 a^3 x^3-2 a^2 x^2+3 a x-3\right) (a x+1)^2+3}{15 a x^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,"-1/15*(3 + Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2*(-3 + 3*a*x - 2*a^2*x^2 + 2*a^3*x^3))/(a*x^5)","A",0
86,1,129,320,0.1408752,"\int \frac{e^{-\text{sech}^{-1}(a x)}}{x^6} \, dx","Integrate[1/(E^ArcSech[a*x]*x^6),x]","-\frac{-3 a^6 x^6 \log (x)+3 a^6 x^6 \log \left(a x \sqrt{\frac{1-a x}{a x+1}}+\sqrt{\frac{1-a x}{a x+1}}+1\right)+\sqrt{\frac{1-a x}{a x+1}} \left(3 a^5 x^5+3 a^4 x^4+2 a^3 x^3+2 a^2 x^2-8 a x-8\right)+8}{48 a x^6}","\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,"-1/48*(8 + Sqrt[(1 - a*x)/(1 + a*x)]*(-8 - 8*a*x + 2*a^2*x^2 + 2*a^3*x^3 + 3*a^4*x^4 + 3*a^5*x^5) - 3*a^6*x^6*Log[x] + 3*a^6*x^6*Log[1 + Sqrt[(1 - a*x)/(1 + a*x)] + a*x*Sqrt[(1 - a*x)/(1 + a*x)]])/(a*x^6)","A",0
87,1,76,353,0.1011333,"\int \frac{e^{-\text{sech}^{-1}(a x)}}{x^7} \, dx","Integrate[1/(E^ArcSech[a*x]*x^7),x]","-\frac{\sqrt{\frac{1-a x}{a x+1}} \left(8 a^5 x^5-8 a^4 x^4+12 a^3 x^3-12 a^2 x^2+15 a x-15\right) (a x+1)^2+15}{105 a x^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,"-1/105*(15 + Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)^2*(-15 + 15*a*x - 12*a^2*x^2 + 12*a^3*x^3 - 8*a^4*x^4 + 8*a^5*x^5))/(a*x^7)","A",0
88,0,0,89,0.6741963,"\int \frac{e^{\text{sech}^{-1}(c x)} (d x)^m}{1-c^2 x^2} \, dx","Integrate[(E^ArcSech[c*x]*(d*x)^m)/(1 - c^2*x^2),x]","\int \frac{e^{\text{sech}^{-1}(c x)} (d x)^m}{1-c^2 x^2} \, dx","\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,"Integrate[(E^ArcSech[c*x]*(d*x)^m)/(1 - c^2*x^2), x]","F",-1
89,1,69,88,0.2013951,"\int \frac{e^{\text{sech}^{-1}(c x)} x^4}{1-c^2 x^2} \, dx","Integrate[(E^ArcSech[c*x]*x^4)/(1 - c^2*x^2),x]","-\frac{3 c^2 x^2+3 \log \left(1-c^2 x^2\right)+2 \sqrt{\frac{1-c x}{c x+1}} \left(c^3 x^3+c^2 x^2+2 c x+2\right)}{6 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}",1,"-1/6*(3*c^2*x^2 + 2*Sqrt[(1 - c*x)/(1 + c*x)]*(2 + 2*c*x + c^2*x^2 + c^3*x^3) + 3*Log[1 - c^2*x^2])/c^5","A",0
90,1,110,75,0.1609411,"\int \frac{e^{\text{sech}^{-1}(c x)} x^3}{1-c^2 x^2} \, dx","Integrate[(E^ArcSech[c*x]*x^3)/(1 - c^2*x^2),x]","-\frac{c^2 x^2 \sqrt{\frac{1-c x}{c x+1}}+2 c x+c x \sqrt{\frac{1-c x}{c x+1}}+\log (1-c x)-\log (c x+1)-i \log \left(2 \sqrt{\frac{1-c x}{c x+1}} (c x+1)-2 i c x\right)}{2 c^4}","\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}",1,"-1/2*(2*c*x + c*x*Sqrt[(1 - c*x)/(1 + c*x)] + c^2*x^2*Sqrt[(1 - c*x)/(1 + c*x)] + Log[1 - c*x] - Log[1 + c*x] - I*Log[(-2*I)*c*x + 2*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)])/c^4","C",0
91,1,44,45,0.0922832,"\int \frac{e^{\text{sech}^{-1}(c x)} x^2}{1-c^2 x^2} \, dx","Integrate[(E^ArcSech[c*x]*x^2)/(1 - c^2*x^2),x]","-\frac{\log \left(1-c^2 x^2\right)+2 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{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}",1,"-1/2*(2*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x) + Log[1 - c^2*x^2])/c^3","A",1
92,1,68,37,0.0504694,"\int \frac{e^{\text{sech}^{-1}(c x)} x}{1-c^2 x^2} \, dx","Integrate[(E^ArcSech[c*x]*x)/(1 - c^2*x^2),x]","-\frac{\log (1-c x)}{2 c^2}+\frac{\log (c x+1)}{2 c^2}+\frac{i \log \left(2 \sqrt{\frac{1-c x}{c x+1}} (c x+1)-2 i c x\right)}{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,"-1/2*Log[1 - c*x]/c^2 + Log[1 + c*x]/(2*c^2) + (I*Log[(-2*I)*c*x + 2*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)])/c^2","C",0
93,1,73,71,0.042741,"\int \frac{e^{\text{sech}^{-1}(c x)}}{1-c^2 x^2} \, dx","Integrate[E^ArcSech[c*x]/(1 - c^2*x^2),x]","-\frac{\log \left(1-c^2 x^2\right)}{2 c}+\frac{2 \log (x)}{c}-\frac{\log \left(c x \sqrt{\frac{1-c x}{c x+1}}+\sqrt{\frac{1-c x}{c x+1}}+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,"(2*Log[x])/c - Log[1 - c^2*x^2]/(2*c) - Log[1 + Sqrt[(1 - c*x)/(1 + c*x)] + c*x*Sqrt[(1 - c*x)/(1 + c*x)]]/c","A",0
94,1,59,42,0.1666144,"\int \frac{e^{\text{sech}^{-1}(c x)}}{x \left(1-c^2 x^2\right)} \, dx","Integrate[E^ArcSech[c*x]/(x*(1 - c^2*x^2)),x]","-\sqrt{\frac{1-c x}{c x+1}} \left(\frac{1}{c x}+1\right)-\frac{1}{c x}-\frac{1}{2} \log (1-c x)+\frac{1}{2} \log (c x+1)","-\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)) - (1 + 1/(c*x))*Sqrt[(1 - c*x)/(1 + c*x)] - Log[1 - c*x]/2 + Log[1 + c*x]/2","A",0
95,1,108,108,0.159424,"\int \frac{e^{\text{sech}^{-1}(c x)}}{x^2 \left(1-c^2 x^2\right)} \, dx","Integrate[E^ArcSech[c*x]/(x^2*(1 - c^2*x^2)),x]","\frac{1}{2} \left(-c \log \left(1-c^2 x^2\right)-\frac{\sqrt{\frac{1-c x}{c x+1}} (c x+1)}{c x^2}-\frac{1}{c x^2}+3 c \log (x)-c \log \left(c x \sqrt{\frac{1-c x}{c x+1}}+\sqrt{\frac{1-c x}{c x+1}}+1\right)\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/(c*x^2)) - (Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x))/(c*x^2) + 3*c*Log[x] - c*Log[1 - c^2*x^2] - c*Log[1 + Sqrt[(1 - c*x)/(1 + c*x)] + c*x*Sqrt[(1 - c*x)/(1 + c*x)]])/2","A",0
96,1,90,85,0.2644074,"\int \frac{e^{\text{sech}^{-1}(c x)}}{x^3 \left(1-c^2 x^2\right)} \, dx","Integrate[E^ArcSech[c*x]/(x^3*(1 - c^2*x^2)),x]","-\frac{3 c^3 x^3 \log (1-c x)-3 c^3 x^3 \log (c x+1)+6 c^2 x^2+2 \sqrt{\frac{1-c x}{c x+1}} \left(2 c^3 x^3+2 c^2 x^2+c x+1\right)+2}{6 c x^3}","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,"-1/6*(2 + 6*c^2*x^2 + 2*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x + 2*c^2*x^2 + 2*c^3*x^3) + 3*c^3*x^3*Log[1 - c*x] - 3*c^3*x^3*Log[1 + c*x])/(c*x^3)","A",0
97,1,28,12,0.2751797,"\int \frac{x \left(-1+a e^{\text{sech}^{-1}(a x)} x\right)}{1-a^2 x^2} \, dx","Integrate[(x*(-1 + a*E^ArcSech[a*x]*x))/(1 - a^2*x^2),x]","-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)}{a^2}","-\frac{x e^{\text{sech}^{-1}(a x)}}{a}",1,"-((Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x))/a^2)","B",0
98,1,52,61,0.0606932,"\int \frac{\text{sech}^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx","Integrate[ArcSech[a + b*x]/((a*d)/b + d*x),x]","\frac{\text{Li}_2\left(-e^{-2 \text{sech}^{-1}(a+b x)}\right)-\text{sech}^{-1}(a+b x) \left(\text{sech}^{-1}(a+b x)+2 \log \left(e^{-2 \text{sech}^{-1}(a+b x)}+1\right)\right)}{2 d}","-\frac{\text{Li}_2\left(-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]*(ArcSech[a + b*x] + 2*Log[1 + E^(-2*ArcSech[a + b*x])])) + PolyLog[2, -E^(-2*ArcSech[a + b*x])])/(2*d)","A",0
99,1,84,57,0.2132655,"\int x^3 \text{sech}^{-1}\left(a+b x^4\right) \, dx","Integrate[x^3*ArcSech[a + b*x^4],x]","\frac{\frac{\sqrt{1-\left(a+b x^4\right)^2} \sin ^{-1}\left(a+b x^4\right)}{\sqrt{-\frac{a+b x^4-1}{a+b x^4+1}} \left(a+b x^4+1\right)}+\left(a+b x^4\right) \text{sech}^{-1}\left(a+b x^4\right)}{4 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] + (Sqrt[1 - (a + b*x^4)^2]*ArcSin[a + b*x^4])/(Sqrt[-((-1 + a + b*x^4)/(1 + a + b*x^4))]*(1 + a + b*x^4)))/(4*b)","A",1
100,1,84,58,0.2641365,"\int x^{-1+n} \text{sech}^{-1}\left(a+b x^n\right) \, dx","Integrate[x^(-1 + n)*ArcSech[a + b*x^n],x]","\frac{\frac{\sqrt{1-\left(a+b x^n\right)^2} \sin ^{-1}\left(a+b x^n\right)}{\sqrt{-\frac{a+b x^n-1}{a+b x^n+1}} \left(a+b x^n+1\right)}+\left(a+b x^n\right) \text{sech}^{-1}\left(a+b x^n\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] + (Sqrt[1 - (a + b*x^n)^2]*ArcSin[a + b*x^n])/(Sqrt[-((-1 + a + b*x^n)/(1 + a + b*x^n))]*(1 + a + b*x^n)))/(b*n)","A",1