1,1,164,0,0.1236476,"\int x^4 \text{sech}^{-1}(a x)^2 \, dx","Int[x^4*ArcSech[a*x]^2,x]","\frac{3 i \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a x)}\right)}{20 a^5}-\frac{3 i \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a x)}\right)}{20 a^5}-\frac{x^3}{30 a^2}-\frac{x^3 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{10 a^2}-\frac{3 x}{20 a^4}-\frac{3 x \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{20 a^4}-\frac{3 \text{sech}^{-1}(a x) \tan ^{-1}\left(e^{\text{sech}^{-1}(a x)}\right)}{10 a^5}+\frac{1}{5} x^5 \text{sech}^{-1}(a x)^2","\frac{3 i \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a x)}\right)}{20 a^5}-\frac{3 i \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a x)}\right)}{20 a^5}-\frac{x^3}{30 a^2}-\frac{x^3 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{10 a^2}-\frac{3 x}{20 a^4}-\frac{3 x \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{20 a^4}-\frac{3 \text{sech}^{-1}(a x) \tan ^{-1}\left(e^{\text{sech}^{-1}(a x)}\right)}{10 a^5}+\frac{1}{5} x^5 \text{sech}^{-1}(a x)^2",1,"(-3*x)/(20*a^4) - x^3/(30*a^2) - (3*x*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x])/(20*a^4) - (x^3*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x])/(10*a^2) + (x^5*ArcSech[a*x]^2)/5 - (3*ArcSech[a*x]*ArcTan[E^ArcSech[a*x]])/(10*a^5) + (((3*I)/20)*PolyLog[2, (-I)*E^ArcSech[a*x]])/a^5 - (((3*I)/20)*PolyLog[2, I*E^ArcSech[a*x]])/a^5","A",9,6,10,0.6000,1,"{6285, 5418, 4185, 4180, 2279, 2391}"
2,1,104,0,0.0884237,"\int x^3 \text{sech}^{-1}(a x)^2 \, dx","Int[x^3*ArcSech[a*x]^2,x]","-\frac{x^2}{12 a^2}-\frac{x^2 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{6 a^2}-\frac{\log (x)}{3 a^4}-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{3 a^4}+\frac{1}{4} x^4 \text{sech}^{-1}(a x)^2","-\frac{x^2}{12 a^2}-\frac{x^2 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{6 a^2}-\frac{\log (x)}{3 a^4}-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{3 a^4}+\frac{1}{4} x^4 \text{sech}^{-1}(a x)^2",1,"-x^2/(12*a^2) - (Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x])/(3*a^4) - (x^2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x])/(6*a^2) + (x^4*ArcSech[a*x]^2)/4 - Log[x]/(3*a^4)","A",5,5,10,0.5000,1,"{6285, 5418, 4185, 4184, 3475}"
3,1,117,0,0.0970499,"\int x^2 \text{sech}^{-1}(a x)^2 \, dx","Int[x^2*ArcSech[a*x]^2,x]","\frac{i \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a x)}\right)}{3 a^3}-\frac{i \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a x)}\right)}{3 a^3}-\frac{x}{3 a^2}-\frac{x \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{3 a^2}-\frac{2 \text{sech}^{-1}(a x) \tan ^{-1}\left(e^{\text{sech}^{-1}(a x)}\right)}{3 a^3}+\frac{1}{3} x^3 \text{sech}^{-1}(a x)^2","\frac{i \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a x)}\right)}{3 a^3}-\frac{i \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a x)}\right)}{3 a^3}-\frac{x}{3 a^2}-\frac{x \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{3 a^2}-\frac{2 \text{sech}^{-1}(a x) \tan ^{-1}\left(e^{\text{sech}^{-1}(a x)}\right)}{3 a^3}+\frac{1}{3} x^3 \text{sech}^{-1}(a x)^2",1,"-x/(3*a^2) - (x*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x])/(3*a^2) + (x^3*ArcSech[a*x]^2)/3 - (2*ArcSech[a*x]*ArcTan[E^ArcSech[a*x]])/(3*a^3) + ((I/3)*PolyLog[2, (-I)*E^ArcSech[a*x]])/a^3 - ((I/3)*PolyLog[2, I*E^ArcSech[a*x]])/a^3","A",8,6,10,0.6000,1,"{6285, 5418, 4185, 4180, 2279, 2391}"
4,1,53,0,0.0567211,"\int x \text{sech}^{-1}(a x)^2 \, dx","Int[x*ArcSech[a*x]^2,x]","-\frac{\log (x)}{a^2}-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{a^2}+\frac{1}{2} x^2 \text{sech}^{-1}(a x)^2","-\frac{\log (x)}{a^2}-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{a^2}+\frac{1}{2} x^2 \text{sech}^{-1}(a x)^2",1,"-((Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x])/a^2) + (x^2*ArcSech[a*x]^2)/2 - Log[x]/a^2","A",4,4,8,0.5000,1,"{6285, 5418, 4184, 3475}"
5,1,63,0,0.0550174,"\int \text{sech}^{-1}(a x)^2 \, dx","Int[ArcSech[a*x]^2,x]","\frac{2 i \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a x)}\right)}{a}-\frac{2 i \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a x)}\right)}{a}+x \text{sech}^{-1}(a x)^2-\frac{4 \text{sech}^{-1}(a x) \tan ^{-1}\left(e^{\text{sech}^{-1}(a x)}\right)}{a}","\frac{2 i \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a x)}\right)}{a}-\frac{2 i \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a x)}\right)}{a}+x \text{sech}^{-1}(a x)^2-\frac{4 \text{sech}^{-1}(a x) \tan ^{-1}\left(e^{\text{sech}^{-1}(a x)}\right)}{a}",1,"x*ArcSech[a*x]^2 - (4*ArcSech[a*x]*ArcTan[E^ArcSech[a*x]])/a + ((2*I)*PolyLog[2, (-I)*E^ArcSech[a*x]])/a - ((2*I)*PolyLog[2, I*E^ArcSech[a*x]])/a","A",7,5,6,0.8333,1,"{6279, 5418, 4180, 2279, 2391}"
6,1,64,0,0.0915422,"\int \frac{\text{sech}^{-1}(a x)^2}{x} \, dx","Int[ArcSech[a*x]^2/x,x]","-\text{sech}^{-1}(a x) \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a x)}\right)+\frac{1}{2} \text{PolyLog}\left(3,-e^{2 \text{sech}^{-1}(a x)}\right)+\frac{1}{3} \text{sech}^{-1}(a x)^3-\text{sech}^{-1}(a x)^2 \log \left(e^{2 \text{sech}^{-1}(a x)}+1\right)","-\text{sech}^{-1}(a x) \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a x)}\right)+\frac{1}{2} \text{PolyLog}\left(3,-e^{2 \text{sech}^{-1}(a x)}\right)+\frac{1}{3} \text{sech}^{-1}(a x)^3-\text{sech}^{-1}(a x)^2 \log \left(e^{2 \text{sech}^{-1}(a x)}+1\right)",1,"ArcSech[a*x]^3/3 - ArcSech[a*x]^2*Log[1 + E^(2*ArcSech[a*x])] - ArcSech[a*x]*PolyLog[2, -E^(2*ArcSech[a*x])] + PolyLog[3, -E^(2*ArcSech[a*x])]/2","A",6,6,10,0.6000,1,"{6285, 3718, 2190, 2531, 2282, 6589}"
7,1,49,0,0.0483221,"\int \frac{\text{sech}^{-1}(a x)^2}{x^2} \, dx","Int[ArcSech[a*x]^2/x^2,x]","-\frac{\text{sech}^{-1}(a x)^2}{x}+\frac{2 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{x}-\frac{2}{x}","-\frac{\text{sech}^{-1}(a x)^2}{x}+\frac{2 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{x}-\frac{2}{x}",1,"-2/x + (2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x])/x - ArcSech[a*x]^2/x","A",4,3,10,0.3000,1,"{6285, 3296, 2638}"
8,1,90,0,0.0593064,"\int \frac{\text{sech}^{-1}(a x)^2}{x^3} \, dx","Int[ArcSech[a*x]^2/x^3,x]","-\frac{1}{4} a^2 \text{sech}^{-1}(a x)^2-\frac{(1-a x) (a x+1)}{4 x^2}-\frac{(1-a x) (a x+1) \text{sech}^{-1}(a x)^2}{2 x^2}+\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{2 x^2}","-\frac{1}{4} a^2 \text{sech}^{-1}(a x)^2-\frac{(1-a x) (a x+1)}{4 x^2}-\frac{(1-a x) (a x+1) \text{sech}^{-1}(a x)^2}{2 x^2}+\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{2 x^2}",1,"-((1 - a*x)*(1 + a*x))/(4*x^2) + (Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x])/(2*x^2) - (a^2*ArcSech[a*x]^2)/4 - ((1 - a*x)*(1 + a*x)*ArcSech[a*x]^2)/(2*x^2)","A",4,4,10,0.4000,1,"{6285, 5372, 3310, 30}"
9,1,102,0,0.084085,"\int \frac{\text{sech}^{-1}(a x)^2}{x^4} \, dx","Int[ArcSech[a*x]^2/x^4,x]","-\frac{4 a^2}{9 x}+\frac{4 a^2 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{9 x}-\frac{\text{sech}^{-1}(a x)^2}{3 x^3}+\frac{2 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{9 x^3}-\frac{2}{27 x^3}","-\frac{4 a^2}{9 x}+\frac{4 a^2 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{9 x}-\frac{\text{sech}^{-1}(a x)^2}{3 x^3}+\frac{2 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)}{9 x^3}-\frac{2}{27 x^3}",1,"-2/(27*x^3) - (4*a^2)/(9*x) + (2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x])/(9*x^3) + (4*a^2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x])/(9*x) - ArcSech[a*x]^2/(3*x^3)","A",5,5,10,0.5000,1,"{6285, 5373, 3310, 3296, 2638}"
10,1,297,0,0.2031943,"\int x^4 \text{sech}^{-1}(a x)^3 \, dx","Int[x^4*ArcSech[a*x]^3,x]","\frac{9 i \text{sech}^{-1}(a x) \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a x)}\right)}{20 a^5}-\frac{9 i \text{sech}^{-1}(a x) \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a x)}\right)}{20 a^5}-\frac{9 i \text{PolyLog}\left(3,-i e^{\text{sech}^{-1}(a x)}\right)}{20 a^5}+\frac{9 i \text{PolyLog}\left(3,i e^{\text{sech}^{-1}(a x)}\right)}{20 a^5}-\frac{3 x^3 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{20 a^2}-\frac{x^3 \text{sech}^{-1}(a x)}{10 a^2}+\frac{x \sqrt{\frac{1-a x}{a x+1}} (a x+1)}{20 a^4}+\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)}{a x}\right)}{2 a^5}-\frac{9 x \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{40 a^4}-\frac{9 x \text{sech}^{-1}(a x)}{20 a^4}-\frac{9 \text{sech}^{-1}(a x)^2 \tan ^{-1}\left(e^{\text{sech}^{-1}(a x)}\right)}{20 a^5}+\frac{1}{5} x^5 \text{sech}^{-1}(a x)^3","\frac{9 i \text{sech}^{-1}(a x) \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a x)}\right)}{20 a^5}-\frac{9 i \text{sech}^{-1}(a x) \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a x)}\right)}{20 a^5}-\frac{9 i \text{PolyLog}\left(3,-i e^{\text{sech}^{-1}(a x)}\right)}{20 a^5}+\frac{9 i \text{PolyLog}\left(3,i e^{\text{sech}^{-1}(a x)}\right)}{20 a^5}-\frac{3 x^3 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{20 a^2}-\frac{x^3 \text{sech}^{-1}(a x)}{10 a^2}+\frac{x \sqrt{\frac{1-a x}{a x+1}} (a x+1)}{20 a^4}+\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)}{a x}\right)}{2 a^5}-\frac{9 x \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{40 a^4}-\frac{9 x \text{sech}^{-1}(a x)}{20 a^4}-\frac{9 \text{sech}^{-1}(a x)^2 \tan ^{-1}\left(e^{\text{sech}^{-1}(a x)}\right)}{20 a^5}+\frac{1}{5} x^5 \text{sech}^{-1}(a x)^3",1,"(x*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x))/(20*a^4) - (9*x*ArcSech[a*x])/(20*a^4) - (x^3*ArcSech[a*x])/(10*a^2) - (9*x*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x]^2)/(40*a^4) - (3*x^3*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x]^2)/(20*a^2) + (x^5*ArcSech[a*x]^3)/5 - (9*ArcSech[a*x]^2*ArcTan[E^ArcSech[a*x]])/(20*a^5) + ArcTan[(Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x))/(a*x)]/(2*a^5) + (((9*I)/20)*ArcSech[a*x]*PolyLog[2, (-I)*E^ArcSech[a*x]])/a^5 - (((9*I)/20)*ArcSech[a*x]*PolyLog[2, I*E^ArcSech[a*x]])/a^5 - (((9*I)/20)*PolyLog[3, (-I)*E^ArcSech[a*x]])/a^5 + (((9*I)/20)*PolyLog[3, I*E^ArcSech[a*x]])/a^5","A",14,9,10,0.9000,1,"{6285, 5418, 4186, 3768, 3770, 4180, 2531, 2282, 6589}"
11,1,184,0,0.17673,"\int x^3 \text{sech}^{-1}(a x)^3 \, dx","Int[x^3*ArcSech[a*x]^3,x]","\frac{\text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a x)}\right)}{2 a^4}-\frac{x^2 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{4 a^2}-\frac{x^2 \text{sech}^{-1}(a x)}{4 a^2}+\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)}{4 a^4}-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{2 a^4}-\frac{\text{sech}^{-1}(a x)^2}{2 a^4}+\frac{\text{sech}^{-1}(a x) \log \left(e^{2 \text{sech}^{-1}(a x)}+1\right)}{a^4}+\frac{1}{4} x^4 \text{sech}^{-1}(a x)^3","\frac{\text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a x)}\right)}{2 a^4}-\frac{x^2 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{4 a^2}-\frac{x^2 \text{sech}^{-1}(a x)}{4 a^2}+\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)}{4 a^4}-\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{2 a^4}-\frac{\text{sech}^{-1}(a x)^2}{2 a^4}+\frac{\text{sech}^{-1}(a x) \log \left(e^{2 \text{sech}^{-1}(a x)}+1\right)}{a^4}+\frac{1}{4} x^4 \text{sech}^{-1}(a x)^3",1,"(Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x))/(4*a^4) - (x^2*ArcSech[a*x])/(4*a^2) - ArcSech[a*x]^2/(2*a^4) - (Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x]^2)/(2*a^4) - (x^2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x]^2)/(4*a^2) + (x^4*ArcSech[a*x]^3)/4 + (ArcSech[a*x]*Log[1 + E^(2*ArcSech[a*x])])/a^4 + PolyLog[2, -E^(2*ArcSech[a*x])]/(2*a^4)","A",10,10,10,1.000,1,"{6285, 5418, 4186, 3767, 8, 4184, 3718, 2190, 2279, 2391}"
12,1,198,0,0.140893,"\int x^2 \text{sech}^{-1}(a x)^3 \, dx","Int[x^2*ArcSech[a*x]^3,x]","\frac{i \text{sech}^{-1}(a x) \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a x)}\right)}{a^3}-\frac{i \text{sech}^{-1}(a x) \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a x)}\right)}{a^3}-\frac{i \text{PolyLog}\left(3,-i e^{\text{sech}^{-1}(a x)}\right)}{a^3}+\frac{i \text{PolyLog}\left(3,i e^{\text{sech}^{-1}(a x)}\right)}{a^3}+\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)}{a x}\right)}{a^3}-\frac{x \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{2 a^2}-\frac{x \text{sech}^{-1}(a x)}{a^2}-\frac{\text{sech}^{-1}(a x)^2 \tan ^{-1}\left(e^{\text{sech}^{-1}(a x)}\right)}{a^3}+\frac{1}{3} x^3 \text{sech}^{-1}(a x)^3","\frac{i \text{sech}^{-1}(a x) \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a x)}\right)}{a^3}-\frac{i \text{sech}^{-1}(a x) \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a x)}\right)}{a^3}-\frac{i \text{PolyLog}\left(3,-i e^{\text{sech}^{-1}(a x)}\right)}{a^3}+\frac{i \text{PolyLog}\left(3,i e^{\text{sech}^{-1}(a x)}\right)}{a^3}+\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1)}{a x}\right)}{a^3}-\frac{x \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{2 a^2}-\frac{x \text{sech}^{-1}(a x)}{a^2}-\frac{\text{sech}^{-1}(a x)^2 \tan ^{-1}\left(e^{\text{sech}^{-1}(a x)}\right)}{a^3}+\frac{1}{3} x^3 \text{sech}^{-1}(a x)^3",1,"-((x*ArcSech[a*x])/a^2) - (x*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x]^2)/(2*a^2) + (x^3*ArcSech[a*x]^3)/3 - (ArcSech[a*x]^2*ArcTan[E^ArcSech[a*x]])/a^3 + ArcTan[(Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x))/(a*x)]/a^3 + (I*ArcSech[a*x]*PolyLog[2, (-I)*E^ArcSech[a*x]])/a^3 - (I*ArcSech[a*x]*PolyLog[2, I*E^ArcSech[a*x]])/a^3 - (I*PolyLog[3, (-I)*E^ArcSech[a*x]])/a^3 + (I*PolyLog[3, I*E^ArcSech[a*x]])/a^3","A",11,8,10,0.8000,1,"{6285, 5418, 4186, 3770, 4180, 2531, 2282, 6589}"
13,1,102,0,0.1217615,"\int x \text{sech}^{-1}(a x)^3 \, dx","Int[x*ArcSech[a*x]^3,x]","\frac{3 \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a x)}\right)}{2 a^2}-\frac{3 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{2 a^2}-\frac{3 \text{sech}^{-1}(a x)^2}{2 a^2}+\frac{3 \text{sech}^{-1}(a x) \log \left(e^{2 \text{sech}^{-1}(a x)}+1\right)}{a^2}+\frac{1}{2} x^2 \text{sech}^{-1}(a x)^3","\frac{3 \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a x)}\right)}{2 a^2}-\frac{3 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{2 a^2}-\frac{3 \text{sech}^{-1}(a x)^2}{2 a^2}+\frac{3 \text{sech}^{-1}(a x) \log \left(e^{2 \text{sech}^{-1}(a x)}+1\right)}{a^2}+\frac{1}{2} x^2 \text{sech}^{-1}(a x)^3",1,"(-3*ArcSech[a*x]^2)/(2*a^2) - (3*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x]^2)/(2*a^2) + (x^2*ArcSech[a*x]^3)/2 + (3*ArcSech[a*x]*Log[1 + E^(2*ArcSech[a*x])])/a^2 + (3*PolyLog[2, -E^(2*ArcSech[a*x])])/(2*a^2)","A",7,7,8,0.8750,1,"{6285, 5418, 4184, 3718, 2190, 2279, 2391}"
14,1,111,0,0.0884604,"\int \text{sech}^{-1}(a x)^3 \, dx","Int[ArcSech[a*x]^3,x]","\frac{6 i \text{sech}^{-1}(a x) \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a x)}\right)}{a}-\frac{6 i \text{sech}^{-1}(a x) \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a x)}\right)}{a}-\frac{6 i \text{PolyLog}\left(3,-i e^{\text{sech}^{-1}(a x)}\right)}{a}+\frac{6 i \text{PolyLog}\left(3,i e^{\text{sech}^{-1}(a x)}\right)}{a}+x \text{sech}^{-1}(a x)^3-\frac{6 \text{sech}^{-1}(a x)^2 \tan ^{-1}\left(e^{\text{sech}^{-1}(a x)}\right)}{a}","\frac{6 i \text{sech}^{-1}(a x) \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(a x)}\right)}{a}-\frac{6 i \text{sech}^{-1}(a x) \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(a x)}\right)}{a}-\frac{6 i \text{PolyLog}\left(3,-i e^{\text{sech}^{-1}(a x)}\right)}{a}+\frac{6 i \text{PolyLog}\left(3,i e^{\text{sech}^{-1}(a x)}\right)}{a}+x \text{sech}^{-1}(a x)^3-\frac{6 \text{sech}^{-1}(a x)^2 \tan ^{-1}\left(e^{\text{sech}^{-1}(a x)}\right)}{a}",1,"x*ArcSech[a*x]^3 - (6*ArcSech[a*x]^2*ArcTan[E^ArcSech[a*x]])/a + ((6*I)*ArcSech[a*x]*PolyLog[2, (-I)*E^ArcSech[a*x]])/a - ((6*I)*ArcSech[a*x]*PolyLog[2, I*E^ArcSech[a*x]])/a - ((6*I)*PolyLog[3, (-I)*E^ArcSech[a*x]])/a + ((6*I)*PolyLog[3, I*E^ArcSech[a*x]])/a","A",9,6,6,1.000,1,"{6279, 5418, 4180, 2531, 2282, 6589}"
15,1,88,0,0.1075184,"\int \frac{\text{sech}^{-1}(a x)^3}{x} \, dx","Int[ArcSech[a*x]^3/x,x]","-\frac{3}{2} \text{sech}^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a x)}\right)+\frac{3}{2} \text{sech}^{-1}(a x) \text{PolyLog}\left(3,-e^{2 \text{sech}^{-1}(a x)}\right)-\frac{3}{4} \text{PolyLog}\left(4,-e^{2 \text{sech}^{-1}(a x)}\right)+\frac{1}{4} \text{sech}^{-1}(a x)^4-\text{sech}^{-1}(a x)^3 \log \left(e^{2 \text{sech}^{-1}(a x)}+1\right)","-\frac{3}{2} \text{sech}^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(a x)}\right)+\frac{3}{2} \text{sech}^{-1}(a x) \text{PolyLog}\left(3,-e^{2 \text{sech}^{-1}(a x)}\right)-\frac{3}{4} \text{PolyLog}\left(4,-e^{2 \text{sech}^{-1}(a x)}\right)+\frac{1}{4} \text{sech}^{-1}(a x)^4-\text{sech}^{-1}(a x)^3 \log \left(e^{2 \text{sech}^{-1}(a x)}+1\right)",1,"ArcSech[a*x]^4/4 - ArcSech[a*x]^3*Log[1 + E^(2*ArcSech[a*x])] - (3*ArcSech[a*x]^2*PolyLog[2, -E^(2*ArcSech[a*x])])/2 + (3*ArcSech[a*x]*PolyLog[3, -E^(2*ArcSech[a*x])])/2 - (3*PolyLog[4, -E^(2*ArcSech[a*x])])/4","A",7,7,10,0.7000,1,"{6285, 3718, 2190, 2531, 6609, 2282, 6589}"
16,1,83,0,0.0711182,"\int \frac{\text{sech}^{-1}(a x)^3}{x^2} \, dx","Int[ArcSech[a*x]^3/x^2,x]","\frac{6 \sqrt{\frac{1-a x}{a x+1}} (a x+1)}{x}-\frac{\text{sech}^{-1}(a x)^3}{x}+\frac{3 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{x}-\frac{6 \text{sech}^{-1}(a x)}{x}","\frac{6 \sqrt{\frac{1-a x}{a x+1}} (a x+1)}{x}-\frac{\text{sech}^{-1}(a x)^3}{x}+\frac{3 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{x}-\frac{6 \text{sech}^{-1}(a x)}{x}",1,"(6*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x))/x - (6*ArcSech[a*x])/x + (3*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x]^2)/x - ArcSech[a*x]^3/x","A",5,3,10,0.3000,1,"{6285, 3296, 2637}"
17,1,137,0,0.0862309,"\int \frac{\text{sech}^{-1}(a x)^3}{x^3} \, dx","Int[ArcSech[a*x]^3/x^3,x]","-\frac{1}{4} a^2 \text{sech}^{-1}(a x)^3-\frac{3}{8} a^2 \text{sech}^{-1}(a x)+\frac{3 \sqrt{\frac{1-a x}{a x+1}} (a x+1)}{8 x^2}-\frac{(1-a x) (a x+1) \text{sech}^{-1}(a x)^3}{2 x^2}+\frac{3 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{4 x^2}-\frac{3 (1-a x) (a x+1) \text{sech}^{-1}(a x)}{4 x^2}","-\frac{1}{4} a^2 \text{sech}^{-1}(a x)^3-\frac{3}{8} a^2 \text{sech}^{-1}(a x)+\frac{3 \sqrt{\frac{1-a x}{a x+1}} (a x+1)}{8 x^2}-\frac{(1-a x) (a x+1) \text{sech}^{-1}(a x)^3}{2 x^2}+\frac{3 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{4 x^2}-\frac{3 (1-a x) (a x+1) \text{sech}^{-1}(a x)}{4 x^2}",1,"(3*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x))/(8*x^2) - (3*a^2*ArcSech[a*x])/8 - (3*(1 - a*x)*(1 + a*x)*ArcSech[a*x])/(4*x^2) + (3*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x]^2)/(4*x^2) - (a^2*ArcSech[a*x]^3)/4 - ((1 - a*x)*(1 + a*x)*ArcSech[a*x]^3)/(2*x^2)","A",6,6,10,0.6000,1,"{6285, 5372, 3311, 30, 2635, 8}"
18,1,179,0,0.1250265,"\int \frac{\text{sech}^{-1}(a x)^3}{x^4} \, dx","Int[ArcSech[a*x]^3/x^4,x]","\frac{14 a^2 \sqrt{\frac{1-a x}{a x+1}} (a x+1)}{9 x}+\frac{2 a^2 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{3 x}-\frac{4 a^2 \text{sech}^{-1}(a x)}{3 x}+\frac{2 \left(\frac{1-a x}{a x+1}\right)^{3/2} (a x+1)^3}{27 x^3}+\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{3 x^3}-\frac{\text{sech}^{-1}(a x)^3}{3 x^3}-\frac{2 \text{sech}^{-1}(a x)}{9 x^3}","\frac{14 a^2 \sqrt{\frac{1-a x}{a x+1}} (a x+1)}{9 x}+\frac{2 a^2 \sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{3 x}-\frac{4 a^2 \text{sech}^{-1}(a x)}{3 x}+\frac{2 \left(\frac{1-a x}{a x+1}\right)^{3/2} (a x+1)^3}{27 x^3}+\frac{\sqrt{\frac{1-a x}{a x+1}} (a x+1) \text{sech}^{-1}(a x)^2}{3 x^3}-\frac{\text{sech}^{-1}(a x)^3}{3 x^3}-\frac{2 \text{sech}^{-1}(a x)}{9 x^3}",1,"(14*a^2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x))/(9*x) + (2*((1 - a*x)/(1 + a*x))^(3/2)*(1 + a*x)^3)/(27*x^3) - (2*ArcSech[a*x])/(9*x^3) - (4*a^2*ArcSech[a*x])/(3*x) + (Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x]^2)/(3*x^3) + (2*a^2*Sqrt[(1 - a*x)/(1 + a*x)]*(1 + a*x)*ArcSech[a*x]^2)/(3*x) - ArcSech[a*x]^3/(3*x^3)","A",8,6,10,0.6000,1,"{6285, 5373, 3311, 3296, 2637, 2633}"
19,1,142,0,0.0609944,"\int x^6 \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^6*(a + b*ArcSech[c*x]),x]","\frac{1}{7} x^7 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x^5 \sqrt{1-c x}}{42 c^2 \sqrt{\frac{1}{c x+1}}}-\frac{5 b x^3 \sqrt{1-c x}}{168 c^4 \sqrt{\frac{1}{c x+1}}}-\frac{5 b x \sqrt{1-c x}}{112 c^6 \sqrt{\frac{1}{c x+1}}}+\frac{5 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{112 c^7}","\frac{1}{7} x^7 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x^5 \sqrt{1-c x}}{42 c^2 \sqrt{\frac{1}{c x+1}}}-\frac{5 b x^3 \sqrt{1-c x}}{168 c^4 \sqrt{\frac{1}{c x+1}}}-\frac{5 b x \sqrt{1-c x}}{112 c^6 \sqrt{\frac{1}{c x+1}}}+\frac{5 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{112 c^7}",1,"(-5*b*x*Sqrt[1 - c*x])/(112*c^6*Sqrt[(1 + c*x)^(-1)]) - (5*b*x^3*Sqrt[1 - c*x])/(168*c^4*Sqrt[(1 + c*x)^(-1)]) - (b*x^5*Sqrt[1 - c*x])/(42*c^2*Sqrt[(1 + c*x)^(-1)]) + (x^7*(a + b*ArcSech[c*x]))/7 + (5*b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/(112*c^7)","A",8,6,12,0.5000,1,"{6283, 100, 12, 90, 41, 216}"
20,1,109,0,0.0466268,"\int x^5 \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^5*(a + b*ArcSech[c*x]),x]","\frac{1}{6} x^6 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x^4 \sqrt{1-c x}}{30 c^2 \sqrt{\frac{1}{c x+1}}}-\frac{2 b x^2 \sqrt{1-c x}}{45 c^4 \sqrt{\frac{1}{c x+1}}}-\frac{4 b \sqrt{1-c x}}{45 c^6 \sqrt{\frac{1}{c x+1}}}","\frac{1}{6} x^6 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x^4 \sqrt{1-c x}}{30 c^2 \sqrt{\frac{1}{c x+1}}}-\frac{2 b x^2 \sqrt{1-c x}}{45 c^4 \sqrt{\frac{1}{c x+1}}}-\frac{4 b \sqrt{1-c x}}{45 c^6 \sqrt{\frac{1}{c x+1}}}",1,"(-4*b*Sqrt[1 - c*x])/(45*c^6*Sqrt[(1 + c*x)^(-1)]) - (2*b*x^2*Sqrt[1 - c*x])/(45*c^4*Sqrt[(1 + c*x)^(-1)]) - (b*x^4*Sqrt[1 - c*x])/(30*c^2*Sqrt[(1 + c*x)^(-1)]) + (x^6*(a + b*ArcSech[c*x]))/6","A",6,4,12,0.3333,1,"{6283, 100, 12, 74}"
21,1,110,0,0.0400105,"\int x^4 \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^4*(a + b*ArcSech[c*x]),x]","\frac{1}{5} x^5 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x^3 \sqrt{1-c x}}{20 c^2 \sqrt{\frac{1}{c x+1}}}-\frac{3 b x \sqrt{1-c x}}{40 c^4 \sqrt{\frac{1}{c x+1}}}+\frac{3 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{40 c^5}","\frac{1}{5} x^5 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x^3 \sqrt{1-c x}}{20 c^2 \sqrt{\frac{1}{c x+1}}}-\frac{3 b x \sqrt{1-c x}}{40 c^4 \sqrt{\frac{1}{c x+1}}}+\frac{3 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{40 c^5}",1,"(-3*b*x*Sqrt[1 - c*x])/(40*c^4*Sqrt[(1 + c*x)^(-1)]) - (b*x^3*Sqrt[1 - c*x])/(20*c^2*Sqrt[(1 + c*x)^(-1)]) + (x^5*(a + b*ArcSech[c*x]))/5 + (3*b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/(40*c^5)","A",6,6,12,0.5000,1,"{6283, 100, 12, 90, 41, 216}"
22,1,77,0,0.0307868,"\int x^3 \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^3*(a + b*ArcSech[c*x]),x]","\frac{1}{4} x^4 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x^2 \sqrt{1-c x}}{12 c^2 \sqrt{\frac{1}{c x+1}}}-\frac{b \sqrt{1-c x}}{6 c^4 \sqrt{\frac{1}{c x+1}}}","\frac{1}{4} x^4 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x^2 \sqrt{1-c x}}{12 c^2 \sqrt{\frac{1}{c x+1}}}-\frac{b \sqrt{1-c x}}{6 c^4 \sqrt{\frac{1}{c x+1}}}",1,"-(b*Sqrt[1 - c*x])/(6*c^4*Sqrt[(1 + c*x)^(-1)]) - (b*x^2*Sqrt[1 - c*x])/(12*c^2*Sqrt[(1 + c*x)^(-1)]) + (x^4*(a + b*ArcSech[c*x]))/4","A",4,4,12,0.3333,1,"{6283, 100, 12, 74}"
23,1,78,0,0.0274582,"\int x^2 \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^2*(a + b*ArcSech[c*x]),x]","\frac{1}{3} x^3 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x \sqrt{1-c x}}{6 c^2 \sqrt{\frac{1}{c x+1}}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{6 c^3}","\frac{1}{3} x^3 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x \sqrt{1-c x}}{6 c^2 \sqrt{\frac{1}{c x+1}}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{6 c^3}",1,"-(b*x*Sqrt[1 - c*x])/(6*c^2*Sqrt[(1 + c*x)^(-1)]) + (x^3*(a + b*ArcSech[c*x]))/3 + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/(6*c^3)","A",4,4,12,0.3333,1,"{6283, 90, 41, 216}"
24,1,45,0,0.0136379,"\int x \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x*(a + b*ArcSech[c*x]),x]","\frac{1}{2} x^2 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b \sqrt{1-c x}}{2 c^2 \sqrt{\frac{1}{c x+1}}}","\frac{1}{2} x^2 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b \sqrt{1-c x}}{2 c^2 \sqrt{\frac{1}{c x+1}}}",1,"-(b*Sqrt[1 - c*x])/(2*c^2*Sqrt[(1 + c*x)^(-1)]) + (x^2*(a + b*ArcSech[c*x]))/2","A",2,2,10,0.2000,1,"{6283, 74}"
25,1,40,0,0.0148849,"\int \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[a + b*ArcSech[c*x],x]","a x+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{c}+b x \text{sech}^{-1}(c x)","a x+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{c}+b x \text{sech}^{-1}(c x)",1,"a*x + b*x*ArcSech[c*x] + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/c","A",3,2,8,0.2500,1,"{6277, 216}"
26,1,56,0,0.0879521,"\int \frac{a+b \text{sech}^{-1}(c x)}{x} \, dx","Int[(a + b*ArcSech[c*x])/x,x]","-\frac{1}{2} b \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(c x)}\right)+\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{2 b}-\log \left(e^{2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)","\frac{1}{2} b \text{PolyLog}\left(2,-e^{-2 \text{sech}^{-1}(c x)}\right)-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{2 b}-\log \left(e^{-2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)",1,"(a + b*ArcSech[c*x])^2/(2*b) - (a + b*ArcSech[c*x])*Log[1 + E^(2*ArcSech[c*x])] - (b*PolyLog[2, -E^(2*ArcSech[c*x])])/2","A",6,6,12,0.5000,0,"{6281, 5660, 3718, 2190, 2279, 2391}"
27,1,40,0,0.0201413,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^2} \, dx","Int[(a + b*ArcSech[c*x])/x^2,x]","\frac{b \sqrt{1-c x}}{x \sqrt{\frac{1}{c x+1}}}-\frac{a+b \text{sech}^{-1}(c x)}{x}","\frac{b \sqrt{1-c x}}{x \sqrt{\frac{1}{c x+1}}}-\frac{a+b \text{sech}^{-1}(c x)}{x}",1,"(b*Sqrt[1 - c*x])/(x*Sqrt[(1 + c*x)^(-1)]) - (a + b*ArcSech[c*x])/x","A",2,2,12,0.1667,1,"{6283, 95}"
28,1,94,0,0.0399034,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^3} \, dx","Int[(a + b*ArcSech[c*x])/x^3,x]","-\frac{a+b \text{sech}^{-1}(c x)}{2 x^2}+\frac{1}{4} b c^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c x} \sqrt{c x+1}\right)+\frac{b \sqrt{1-c x}}{4 x^2 \sqrt{\frac{1}{c x+1}}}","-\frac{a+b \text{sech}^{-1}(c x)}{2 x^2}+\frac{1}{4} b c^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c x} \sqrt{c x+1}\right)+\frac{b \sqrt{1-c x}}{4 x^2 \sqrt{\frac{1}{c x+1}}}",1,"(b*Sqrt[1 - c*x])/(4*x^2*Sqrt[(1 + c*x)^(-1)]) - (a + b*ArcSech[c*x])/(2*x^2) + (b*c^2*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[1 - c*x]*Sqrt[1 + c*x]])/4","A",5,5,12,0.4167,1,"{6283, 103, 12, 92, 208}"
29,1,77,0,0.0332651,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^4} \, dx","Int[(a + b*ArcSech[c*x])/x^4,x]","-\frac{a+b \text{sech}^{-1}(c x)}{3 x^3}+\frac{2 b c^2 \sqrt{1-c x}}{9 x \sqrt{\frac{1}{c x+1}}}+\frac{b \sqrt{1-c x}}{9 x^3 \sqrt{\frac{1}{c x+1}}}","-\frac{a+b \text{sech}^{-1}(c x)}{3 x^3}+\frac{2 b c^2 \sqrt{1-c x}}{9 x \sqrt{\frac{1}{c x+1}}}+\frac{b \sqrt{1-c x}}{9 x^3 \sqrt{\frac{1}{c x+1}}}",1,"(b*Sqrt[1 - c*x])/(9*x^3*Sqrt[(1 + c*x)^(-1)]) + (2*b*c^2*Sqrt[1 - c*x])/(9*x*Sqrt[(1 + c*x)^(-1)]) - (a + b*ArcSech[c*x])/(3*x^3)","A",4,4,12,0.3333,1,"{6283, 103, 12, 95}"
30,1,126,0,0.054912,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^5} \, dx","Int[(a + b*ArcSech[c*x])/x^5,x]","-\frac{a+b \text{sech}^{-1}(c x)}{4 x^4}+\frac{3 b c^2 \sqrt{1-c x}}{32 x^2 \sqrt{\frac{1}{c x+1}}}+\frac{3}{32} b c^4 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c x} \sqrt{c x+1}\right)+\frac{b \sqrt{1-c x}}{16 x^4 \sqrt{\frac{1}{c x+1}}}","-\frac{a+b \text{sech}^{-1}(c x)}{4 x^4}+\frac{3 b c^2 \sqrt{1-c x}}{32 x^2 \sqrt{\frac{1}{c x+1}}}+\frac{3}{32} b c^4 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c x} \sqrt{c x+1}\right)+\frac{b \sqrt{1-c x}}{16 x^4 \sqrt{\frac{1}{c x+1}}}",1,"(b*Sqrt[1 - c*x])/(16*x^4*Sqrt[(1 + c*x)^(-1)]) + (3*b*c^2*Sqrt[1 - c*x])/(32*x^2*Sqrt[(1 + c*x)^(-1)]) - (a + b*ArcSech[c*x])/(4*x^4) + (3*b*c^4*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[1 - c*x]*Sqrt[1 + c*x]])/32","A",7,5,12,0.4167,1,"{6283, 103, 12, 92, 208}"
31,1,109,0,0.0503686,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^6} \, dx","Int[(a + b*ArcSech[c*x])/x^6,x]","-\frac{a+b \text{sech}^{-1}(c x)}{5 x^5}+\frac{4 b c^2 \sqrt{1-c x}}{75 x^3 \sqrt{\frac{1}{c x+1}}}+\frac{8 b c^4 \sqrt{1-c x}}{75 x \sqrt{\frac{1}{c x+1}}}+\frac{b \sqrt{1-c x}}{25 x^5 \sqrt{\frac{1}{c x+1}}}","-\frac{a+b \text{sech}^{-1}(c x)}{5 x^5}+\frac{4 b c^2 \sqrt{1-c x}}{75 x^3 \sqrt{\frac{1}{c x+1}}}+\frac{8 b c^4 \sqrt{1-c x}}{75 x \sqrt{\frac{1}{c x+1}}}+\frac{b \sqrt{1-c x}}{25 x^5 \sqrt{\frac{1}{c x+1}}}",1,"(b*Sqrt[1 - c*x])/(25*x^5*Sqrt[(1 + c*x)^(-1)]) + (4*b*c^2*Sqrt[1 - c*x])/(75*x^3*Sqrt[(1 + c*x)^(-1)]) + (8*b*c^4*Sqrt[1 - c*x])/(75*x*Sqrt[(1 + c*x)^(-1)]) - (a + b*ArcSech[c*x])/(5*x^5)","A",6,4,12,0.3333,1,"{6283, 103, 12, 95}"
32,1,158,0,0.0728699,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^7} \, dx","Int[(a + b*ArcSech[c*x])/x^7,x]","-\frac{a+b \text{sech}^{-1}(c x)}{6 x^6}+\frac{5 b c^4 \sqrt{1-c x}}{96 x^2 \sqrt{\frac{1}{c x+1}}}+\frac{5 b c^2 \sqrt{1-c x}}{144 x^4 \sqrt{\frac{1}{c x+1}}}+\frac{5}{96} b c^6 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c x} \sqrt{c x+1}\right)+\frac{b \sqrt{1-c x}}{36 x^6 \sqrt{\frac{1}{c x+1}}}","-\frac{a+b \text{sech}^{-1}(c x)}{6 x^6}+\frac{5 b c^4 \sqrt{1-c x}}{96 x^2 \sqrt{\frac{1}{c x+1}}}+\frac{5 b c^2 \sqrt{1-c x}}{144 x^4 \sqrt{\frac{1}{c x+1}}}+\frac{5}{96} b c^6 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c x} \sqrt{c x+1}\right)+\frac{b \sqrt{1-c x}}{36 x^6 \sqrt{\frac{1}{c x+1}}}",1,"(b*Sqrt[1 - c*x])/(36*x^6*Sqrt[(1 + c*x)^(-1)]) + (5*b*c^2*Sqrt[1 - c*x])/(144*x^4*Sqrt[(1 + c*x)^(-1)]) + (5*b*c^4*Sqrt[1 - c*x])/(96*x^2*Sqrt[(1 + c*x)^(-1)]) - (a + b*ArcSech[c*x])/(6*x^6) + (5*b*c^6*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[1 - c*x]*Sqrt[1 + c*x]])/96","A",9,5,12,0.4167,1,"{6283, 103, 12, 92, 208}"
33,1,124,0,0.1193947,"\int x^3 \left(a+b \text{sech}^{-1}(c x)\right)^2 \, dx","Int[x^3*(a + b*ArcSech[c*x])^2,x]","-\frac{b x^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{6 c^2}-\frac{b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{3 c^4}+\frac{1}{4} x^4 \left(a+b \text{sech}^{-1}(c x)\right)^2-\frac{b^2 x^2}{12 c^2}-\frac{b^2 \log (x)}{3 c^4}","-\frac{b x^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{6 c^2}-\frac{b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{3 c^4}+\frac{1}{4} x^4 \left(a+b \text{sech}^{-1}(c x)\right)^2-\frac{b^2 x^2}{12 c^2}-\frac{b^2 \log (x)}{3 c^4}",1,"-(b^2*x^2)/(12*c^2) - (b*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x]))/(3*c^4) - (b*x^2*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x]))/(6*c^2) + (x^4*(a + b*ArcSech[c*x])^2)/4 - (b^2*Log[x])/(3*c^4)","A",5,5,14,0.3571,1,"{6285, 5451, 4185, 4184, 3475}"
34,1,140,0,0.1228804,"\int x^2 \left(a+b \text{sech}^{-1}(c x)\right)^2 \, dx","Int[x^2*(a + b*ArcSech[c*x])^2,x]","\frac{i b^2 \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(c x)}\right)}{3 c^3}-\frac{i b^2 \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(c x)}\right)}{3 c^3}-\frac{b x \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{3 c^2}-\frac{2 b \tan ^{-1}\left(e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{3 c^3}+\frac{1}{3} x^3 \left(a+b \text{sech}^{-1}(c x)\right)^2-\frac{b^2 x}{3 c^2}","\frac{i b^2 \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(c x)}\right)}{3 c^3}-\frac{i b^2 \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(c x)}\right)}{3 c^3}-\frac{b x \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{3 c^2}-\frac{2 b \tan ^{-1}\left(e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{3 c^3}+\frac{1}{3} x^3 \left(a+b \text{sech}^{-1}(c x)\right)^2-\frac{b^2 x}{3 c^2}",1,"-(b^2*x)/(3*c^2) - (b*x*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x]))/(3*c^2) + (x^3*(a + b*ArcSech[c*x])^2)/3 - (2*b*(a + b*ArcSech[c*x])*ArcTan[E^ArcSech[c*x]])/(3*c^3) + ((I/3)*b^2*PolyLog[2, (-I)*E^ArcSech[c*x]])/c^3 - ((I/3)*b^2*PolyLog[2, I*E^ArcSech[c*x]])/c^3","A",8,6,14,0.4286,1,"{6285, 5451, 4185, 4180, 2279, 2391}"
35,1,65,0,0.0752577,"\int x \left(a+b \text{sech}^{-1}(c x)\right)^2 \, dx","Int[x*(a + b*ArcSech[c*x])^2,x]","-\frac{b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{c^2}+\frac{1}{2} x^2 \left(a+b \text{sech}^{-1}(c x)\right)^2-\frac{b^2 \log (x)}{c^2}","-\frac{b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{c^2}+\frac{1}{2} x^2 \left(a+b \text{sech}^{-1}(c x)\right)^2-\frac{b^2 \log (x)}{c^2}",1,"-((b*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x]))/c^2) + (x^2*(a + b*ArcSech[c*x])^2)/2 - (b^2*Log[x])/c^2","A",4,4,12,0.3333,1,"{6285, 5451, 4184, 3475}"
36,1,78,0,0.0702562,"\int \left(a+b \text{sech}^{-1}(c x)\right)^2 \, dx","Int[(a + b*ArcSech[c*x])^2,x]","\frac{2 i b^2 \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(c x)}\right)}{c}-\frac{2 i b^2 \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(c x)}\right)}{c}+x \left(a+b \text{sech}^{-1}(c x)\right)^2-\frac{4 b \tan ^{-1}\left(e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{c}","\frac{2 i b^2 \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(c x)}\right)}{c}-\frac{2 i b^2 \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(c x)}\right)}{c}+x \left(a+b \text{sech}^{-1}(c x)\right)^2-\frac{4 b \tan ^{-1}\left(e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{c}",1,"x*(a + b*ArcSech[c*x])^2 - (4*b*(a + b*ArcSech[c*x])*ArcTan[E^ArcSech[c*x]])/c + ((2*I)*b^2*PolyLog[2, (-I)*E^ArcSech[c*x]])/c - ((2*I)*b^2*PolyLog[2, I*E^ArcSech[c*x]])/c","A",7,5,10,0.5000,1,"{6279, 5451, 4180, 2279, 2391}"
37,1,83,0,0.1252813,"\int \frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{x} \, dx","Int[(a + b*ArcSech[c*x])^2/x,x]","-b \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,-e^{2 \text{sech}^{-1}(c x)}\right)+\frac{\left(a+b \text{sech}^{-1}(c x)\right)^3}{3 b}-\log \left(e^{2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)^2","-b \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,-e^{2 \text{sech}^{-1}(c x)}\right)+\frac{\left(a+b \text{sech}^{-1}(c x)\right)^3}{3 b}-\log \left(e^{2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)^2",1,"(a + b*ArcSech[c*x])^3/(3*b) - (a + b*ArcSech[c*x])^2*Log[1 + E^(2*ArcSech[c*x])] - b*(a + b*ArcSech[c*x])*PolyLog[2, -E^(2*ArcSech[c*x])] + (b^2*PolyLog[3, -E^(2*ArcSech[c*x])])/2","A",6,6,14,0.4286,1,"{6285, 3718, 2190, 2531, 2282, 6589}"
38,1,61,0,0.0699774,"\int \frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{x^2} \, dx","Int[(a + b*ArcSech[c*x])^2/x^2,x]","\frac{2 b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{x}-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{x}-\frac{2 b^2}{x}","\frac{2 b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{x}-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{x}-\frac{2 b^2}{x}",1,"(-2*b^2)/x + (2*b*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x]))/x - (a + b*ArcSech[c*x])^2/x","A",4,3,14,0.2143,1,"{6285, 3296, 2638}"
39,1,118,0,0.0847385,"\int \frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{x^3} \, dx","Int[(a + b*ArcSech[c*x])^2/x^3,x]","-\frac{1}{2} a b c^2 \text{sech}^{-1}(c x)+\frac{b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{2 x^2}-\frac{(1-c x) (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{2 x^2}-\frac{1}{4} b^2 c^2 \text{sech}^{-1}(c x)^2-\frac{b^2 (1-c x) (c x+1)}{4 x^2}","-\frac{1}{2} a b c^2 \text{sech}^{-1}(c x)+\frac{b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{2 x^2}-\frac{(1-c x) (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{2 x^2}-\frac{1}{4} b^2 c^2 \text{sech}^{-1}(c x)^2-\frac{b^2 (1-c x) (c x+1)}{4 x^2}",1,"-(b^2*(1 - c*x)*(1 + c*x))/(4*x^2) - (a*b*c^2*ArcSech[c*x])/2 - (b^2*c^2*ArcSech[c*x]^2)/4 + (b*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x]))/(2*x^2) - ((1 - c*x)*(1 + c*x)*(a + b*ArcSech[c*x])^2)/(2*x^2)","A",4,3,14,0.2143,1,"{6285, 5446, 3310}"
40,1,122,0,0.1018734,"\int \frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{x^4} \, dx","Int[(a + b*ArcSech[c*x])^2/x^4,x]","\frac{4 b c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{9 x}+\frac{2 b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{9 x^3}-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{3 x^3}-\frac{4 b^2 c^2}{9 x}-\frac{2 b^2}{27 x^3}","\frac{4 b c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{9 x}+\frac{2 b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{9 x^3}-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{3 x^3}-\frac{4 b^2 c^2}{9 x}-\frac{2 b^2}{27 x^3}",1,"(-2*b^2)/(27*x^3) - (4*b^2*c^2)/(9*x) + (2*b*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x]))/(9*x^3) + (4*b*c^2*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x]))/(9*x) - (a + b*ArcSech[c*x])^2/(3*x^3)","A",5,5,14,0.3571,1,"{6285, 5447, 3310, 3296, 2638}"
41,1,151,0,0.1196847,"\int \frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{x^5} \, dx","Int[(a + b*ArcSech[c*x])^2/x^5,x]","\frac{3 b c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{16 x^2}+\frac{3}{16} a b c^4 \text{sech}^{-1}(c x)-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{4 x^4}+\frac{b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{8 x^4}-\frac{3 b^2 c^2}{32 x^2}+\frac{3}{32} b^2 c^4 \text{sech}^{-1}(c x)^2-\frac{b^2}{32 x^4}","\frac{3 b c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{16 x^2}+\frac{3}{16} a b c^4 \text{sech}^{-1}(c x)-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{4 x^4}+\frac{b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{8 x^4}-\frac{3 b^2 c^2}{32 x^2}+\frac{3}{32} b^2 c^4 \text{sech}^{-1}(c x)^2-\frac{b^2}{32 x^4}",1,"-b^2/(32*x^4) - (3*b^2*c^2)/(32*x^2) + (3*a*b*c^4*ArcSech[c*x])/16 + (3*b^2*c^4*ArcSech[c*x]^2)/32 + (b*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x]))/(8*x^4) + (3*b*c^2*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x]))/(16*x^2) - (a + b*ArcSech[c*x])^2/(4*x^4)","A",5,3,14,0.2143,1,"{6285, 5447, 3310}"
42,1,223,0,0.2394059,"\int x^3 \left(a+b \text{sech}^{-1}(c x)\right)^3 \, dx","Int[x^3*(a + b*ArcSech[c*x])^3,x]","\frac{b^3 \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(c x)}\right)}{2 c^4}-\frac{b^2 x^2 \left(a+b \text{sech}^{-1}(c x)\right)}{4 c^2}+\frac{b^2 \log \left(e^{2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{c^4}-\frac{b x^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{4 c^2}-\frac{b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{2 c^4}-\frac{b \left(a+b \text{sech}^{-1}(c x)\right)^2}{2 c^4}+\frac{1}{4} x^4 \left(a+b \text{sech}^{-1}(c x)\right)^3+\frac{b^3 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{4 c^4}","\frac{b^3 \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(c x)}\right)}{2 c^4}-\frac{b^2 x^2 \left(a+b \text{sech}^{-1}(c x)\right)}{4 c^2}+\frac{b^2 \log \left(e^{2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{c^4}-\frac{b x^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{4 c^2}-\frac{b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{2 c^4}-\frac{b \left(a+b \text{sech}^{-1}(c x)\right)^2}{2 c^4}+\frac{1}{4} x^4 \left(a+b \text{sech}^{-1}(c x)\right)^3+\frac{b^3 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{4 c^4}",1,"(b^3*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x))/(4*c^4) - (b^2*x^2*(a + b*ArcSech[c*x]))/(4*c^2) - (b*(a + b*ArcSech[c*x])^2)/(2*c^4) - (b*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x])^2)/(2*c^4) - (b*x^2*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x])^2)/(4*c^2) + (x^4*(a + b*ArcSech[c*x])^3)/4 + (b^2*(a + b*ArcSech[c*x])*Log[1 + E^(2*ArcSech[c*x])])/c^4 + (b^3*PolyLog[2, -E^(2*ArcSech[c*x])])/(2*c^4)","A",10,10,14,0.7143,1,"{6285, 5451, 4186, 3767, 8, 4184, 3718, 2190, 2279, 2391}"
43,1,242,0,0.1953488,"\int x^2 \left(a+b \text{sech}^{-1}(c x)\right)^3 \, dx","Int[x^2*(a + b*ArcSech[c*x])^3,x]","\frac{i b^2 \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{c^3}-\frac{i b^2 \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{c^3}-\frac{i b^3 \text{PolyLog}\left(3,-i e^{\text{sech}^{-1}(c x)}\right)}{c^3}+\frac{i b^3 \text{PolyLog}\left(3,i e^{\text{sech}^{-1}(c x)}\right)}{c^3}-\frac{b^2 x \left(a+b \text{sech}^{-1}(c x)\right)}{c^2}-\frac{b x \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{2 c^2}-\frac{b \tan ^{-1}\left(e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)^2}{c^3}+\frac{1}{3} x^3 \left(a+b \text{sech}^{-1}(c x)\right)^3+\frac{b^3 \tan ^{-1}\left(\frac{\sqrt{\frac{1-c x}{c x+1}} (c x+1)}{c x}\right)}{c^3}","\frac{i b^2 \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{c^3}-\frac{i b^2 \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{c^3}-\frac{i b^3 \text{PolyLog}\left(3,-i e^{\text{sech}^{-1}(c x)}\right)}{c^3}+\frac{i b^3 \text{PolyLog}\left(3,i e^{\text{sech}^{-1}(c x)}\right)}{c^3}-\frac{b^2 x \left(a+b \text{sech}^{-1}(c x)\right)}{c^2}-\frac{b x \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{2 c^2}-\frac{b \tan ^{-1}\left(e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)^2}{c^3}+\frac{1}{3} x^3 \left(a+b \text{sech}^{-1}(c x)\right)^3+\frac{b^3 \tan ^{-1}\left(\frac{\sqrt{\frac{1-c x}{c x+1}} (c x+1)}{c x}\right)}{c^3}",1,"-((b^2*x*(a + b*ArcSech[c*x]))/c^2) - (b*x*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x])^2)/(2*c^2) + (x^3*(a + b*ArcSech[c*x])^3)/3 - (b*(a + b*ArcSech[c*x])^2*ArcTan[E^ArcSech[c*x]])/c^3 + (b^3*ArcTan[(Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x))/(c*x)])/c^3 + (I*b^2*(a + b*ArcSech[c*x])*PolyLog[2, (-I)*E^ArcSech[c*x]])/c^3 - (I*b^2*(a + b*ArcSech[c*x])*PolyLog[2, I*E^ArcSech[c*x]])/c^3 - (I*b^3*PolyLog[3, (-I)*E^ArcSech[c*x]])/c^3 + (I*b^3*PolyLog[3, I*E^ArcSech[c*x]])/c^3","A",11,8,14,0.5714,1,"{6285, 5451, 4186, 3770, 4180, 2531, 2282, 6589}"
44,1,126,0,0.1565826,"\int x \left(a+b \text{sech}^{-1}(c x)\right)^3 \, dx","Int[x*(a + b*ArcSech[c*x])^3,x]","\frac{3 b^3 \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(c x)}\right)}{2 c^2}+\frac{3 b^2 \log \left(e^{2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{c^2}-\frac{3 b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{2 c^2}-\frac{3 b \left(a+b \text{sech}^{-1}(c x)\right)^2}{2 c^2}+\frac{1}{2} x^2 \left(a+b \text{sech}^{-1}(c x)\right)^3","\frac{3 b^3 \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(c x)}\right)}{2 c^2}+\frac{3 b^2 \log \left(e^{2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{c^2}-\frac{3 b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{2 c^2}-\frac{3 b \left(a+b \text{sech}^{-1}(c x)\right)^2}{2 c^2}+\frac{1}{2} x^2 \left(a+b \text{sech}^{-1}(c x)\right)^3",1,"(-3*b*(a + b*ArcSech[c*x])^2)/(2*c^2) - (3*b*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x])^2)/(2*c^2) + (x^2*(a + b*ArcSech[c*x])^3)/2 + (3*b^2*(a + b*ArcSech[c*x])*Log[1 + E^(2*ArcSech[c*x])])/c^2 + (3*b^3*PolyLog[2, -E^(2*ArcSech[c*x])])/(2*c^2)","A",7,7,12,0.5833,1,"{6285, 5451, 4184, 3718, 2190, 2279, 2391}"
45,1,140,0,0.1114168,"\int \left(a+b \text{sech}^{-1}(c x)\right)^3 \, dx","Int[(a + b*ArcSech[c*x])^3,x]","\frac{6 i b^2 \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{c}-\frac{6 i b^2 \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{c}-\frac{6 i b^3 \text{PolyLog}\left(3,-i e^{\text{sech}^{-1}(c x)}\right)}{c}+\frac{6 i b^3 \text{PolyLog}\left(3,i e^{\text{sech}^{-1}(c x)}\right)}{c}+x \left(a+b \text{sech}^{-1}(c x)\right)^3-\frac{6 b \tan ^{-1}\left(e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)^2}{c}","\frac{6 i b^2 \text{PolyLog}\left(2,-i e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{c}-\frac{6 i b^2 \text{PolyLog}\left(2,i e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{c}-\frac{6 i b^3 \text{PolyLog}\left(3,-i e^{\text{sech}^{-1}(c x)}\right)}{c}+\frac{6 i b^3 \text{PolyLog}\left(3,i e^{\text{sech}^{-1}(c x)}\right)}{c}+x \left(a+b \text{sech}^{-1}(c x)\right)^3-\frac{6 b \tan ^{-1}\left(e^{\text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)^2}{c}",1,"x*(a + b*ArcSech[c*x])^3 - (6*b*(a + b*ArcSech[c*x])^2*ArcTan[E^ArcSech[c*x]])/c + ((6*I)*b^2*(a + b*ArcSech[c*x])*PolyLog[2, (-I)*E^ArcSech[c*x]])/c - ((6*I)*b^2*(a + b*ArcSech[c*x])*PolyLog[2, I*E^ArcSech[c*x]])/c - ((6*I)*b^3*PolyLog[3, (-I)*E^ArcSech[c*x]])/c + ((6*I)*b^3*PolyLog[3, I*E^ArcSech[c*x]])/c","A",9,6,10,0.6000,1,"{6279, 5451, 4180, 2531, 2282, 6589}"
46,1,114,0,0.14476,"\int \frac{\left(a+b \text{sech}^{-1}(c x)\right)^3}{x} \, dx","Int[(a + b*ArcSech[c*x])^3/x,x]","\frac{3}{2} b^2 \text{PolyLog}\left(3,-e^{2 \text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)-\frac{3}{2} b \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)^2-\frac{3}{4} b^3 \text{PolyLog}\left(4,-e^{2 \text{sech}^{-1}(c x)}\right)+\frac{\left(a+b \text{sech}^{-1}(c x)\right)^4}{4 b}-\log \left(e^{2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)^3","\frac{3}{2} b^2 \text{PolyLog}\left(3,-e^{2 \text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)-\frac{3}{2} b \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(c x)}\right) \left(a+b \text{sech}^{-1}(c x)\right)^2-\frac{3}{4} b^3 \text{PolyLog}\left(4,-e^{2 \text{sech}^{-1}(c x)}\right)+\frac{\left(a+b \text{sech}^{-1}(c x)\right)^4}{4 b}-\log \left(e^{2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)^3",1,"(a + b*ArcSech[c*x])^4/(4*b) - (a + b*ArcSech[c*x])^3*Log[1 + E^(2*ArcSech[c*x])] - (3*b*(a + b*ArcSech[c*x])^2*PolyLog[2, -E^(2*ArcSech[c*x])])/2 + (3*b^2*(a + b*ArcSech[c*x])*PolyLog[3, -E^(2*ArcSech[c*x])])/2 - (3*b^3*PolyLog[4, -E^(2*ArcSech[c*x])])/4","A",7,7,14,0.5000,1,"{6285, 3718, 2190, 2531, 6609, 2282, 6589}"
47,1,102,0,0.1027113,"\int \frac{\left(a+b \text{sech}^{-1}(c x)\right)^3}{x^2} \, dx","Int[(a + b*ArcSech[c*x])^3/x^2,x]","-\frac{6 b^2 \left(a+b \text{sech}^{-1}(c x)\right)}{x}+\frac{3 b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{x}-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^3}{x}+\frac{6 b^3 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{x}","-\frac{6 b^2 \left(a+b \text{sech}^{-1}(c x)\right)}{x}+\frac{3 b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{x}-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^3}{x}+\frac{6 b^3 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{x}",1,"(6*b^3*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x))/x - (6*b^2*(a + b*ArcSech[c*x]))/x + (3*b*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x])^2)/x - (a + b*ArcSech[c*x])^3/x","A",5,3,14,0.2143,1,"{6285, 3296, 2637}"
48,1,163,0,0.1162225,"\int \frac{\left(a+b \text{sech}^{-1}(c x)\right)^3}{x^3} \, dx","Int[(a + b*ArcSech[c*x])^3/x^3,x]","-\frac{3 b^2 (1-c x) (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{4 x^2}-\frac{1}{4} c^2 \left(a+b \text{sech}^{-1}(c x)\right)^3+\frac{3 b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{4 x^2}-\frac{(1-c x) (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^3}{2 x^2}-\frac{3}{8} b^3 c^2 \text{sech}^{-1}(c x)+\frac{3 b^3 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{8 x^2}","-\frac{3 b^2 (1-c x) (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)}{4 x^2}-\frac{1}{4} c^2 \left(a+b \text{sech}^{-1}(c x)\right)^3+\frac{3 b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{4 x^2}-\frac{(1-c x) (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^3}{2 x^2}-\frac{3}{8} b^3 c^2 \text{sech}^{-1}(c x)+\frac{3 b^3 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{8 x^2}",1,"(3*b^3*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x))/(8*x^2) - (3*b^3*c^2*ArcSech[c*x])/8 - (3*b^2*(1 - c*x)*(1 + c*x)*(a + b*ArcSech[c*x]))/(4*x^2) + (3*b*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x])^2)/(4*x^2) - (c^2*(a + b*ArcSech[c*x])^3)/4 - ((1 - c*x)*(1 + c*x)*(a + b*ArcSech[c*x])^3)/(2*x^2)","A",6,6,14,0.4286,1,"{6285, 5446, 3311, 32, 2635, 8}"
49,1,213,0,0.1664017,"\int \frac{\left(a+b \text{sech}^{-1}(c x)\right)^3}{x^4} \, dx","Int[(a + b*ArcSech[c*x])^3/x^4,x]","-\frac{4 b^2 c^2 \left(a+b \text{sech}^{-1}(c x)\right)}{3 x}-\frac{2 b^2 \left(a+b \text{sech}^{-1}(c x)\right)}{9 x^3}+\frac{2 b c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{3 x}+\frac{b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{3 x^3}-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^3}{3 x^3}+\frac{14 b^3 c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{9 x}+\frac{2 b^3 \left(\frac{1-c x}{c x+1}\right)^{3/2} (c x+1)^3}{27 x^3}","-\frac{4 b^2 c^2 \left(a+b \text{sech}^{-1}(c x)\right)}{3 x}-\frac{2 b^2 \left(a+b \text{sech}^{-1}(c x)\right)}{9 x^3}+\frac{2 b c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{3 x}+\frac{b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{3 x^3}-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^3}{3 x^3}+\frac{14 b^3 c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{9 x}+\frac{2 b^3 \left(\frac{1-c x}{c x+1}\right)^{3/2} (c x+1)^3}{27 x^3}",1,"(14*b^3*c^2*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x))/(9*x) + (2*b^3*((1 - c*x)/(1 + c*x))^(3/2)*(1 + c*x)^3)/(27*x^3) - (2*b^2*(a + b*ArcSech[c*x]))/(9*x^3) - (4*b^2*c^2*(a + b*ArcSech[c*x]))/(3*x) + (b*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x])^2)/(3*x^3) + (2*b*c^2*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x])^2)/(3*x) - (a + b*ArcSech[c*x])^3/(3*x^3)","A",8,6,14,0.4286,1,"{6285, 5447, 3311, 3296, 2637, 2633}"
50,1,242,0,0.1962836,"\int \frac{\left(a+b \text{sech}^{-1}(c x)\right)^3}{x^5} \, dx","Int[(a + b*ArcSech[c*x])^3/x^5,x]","-\frac{9 b^2 c^2 \left(a+b \text{sech}^{-1}(c x)\right)}{32 x^2}-\frac{3 b^2 \left(a+b \text{sech}^{-1}(c x)\right)}{32 x^4}+\frac{9 b c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{32 x^2}+\frac{3}{32} c^4 \left(a+b \text{sech}^{-1}(c x)\right)^3-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^3}{4 x^4}+\frac{3 b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{16 x^4}+\frac{45 b^3 c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{256 x^2}+\frac{45}{256} b^3 c^4 \text{sech}^{-1}(c x)+\frac{3 b^3 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{128 x^4}","-\frac{9 b^2 c^2 \left(a+b \text{sech}^{-1}(c x)\right)}{32 x^2}-\frac{3 b^2 \left(a+b \text{sech}^{-1}(c x)\right)}{32 x^4}+\frac{9 b c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{32 x^2}+\frac{3}{32} c^4 \left(a+b \text{sech}^{-1}(c x)\right)^3-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^3}{4 x^4}+\frac{3 b \sqrt{\frac{1-c x}{c x+1}} (c x+1) \left(a+b \text{sech}^{-1}(c x)\right)^2}{16 x^4}+\frac{45 b^3 c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{256 x^2}+\frac{45}{256} b^3 c^4 \text{sech}^{-1}(c x)+\frac{3 b^3 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{128 x^4}",1,"(3*b^3*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x))/(128*x^4) + (45*b^3*c^2*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x))/(256*x^2) + (45*b^3*c^4*ArcSech[c*x])/256 - (3*b^2*(a + b*ArcSech[c*x]))/(32*x^4) - (9*b^2*c^2*(a + b*ArcSech[c*x]))/(32*x^2) + (3*b*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x])^2)/(16*x^4) + (9*b*c^2*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcSech[c*x])^2)/(32*x^2) + (3*c^4*(a + b*ArcSech[c*x])^3)/32 - (a + b*ArcSech[c*x])^3/(4*x^4)","A",10,6,14,0.4286,1,"{6285, 5447, 3311, 32, 2635, 8}"
51,0,0,0,0.016564,"\int \frac{x}{a+b \text{sech}^{-1}(c x)} \, dx","Int[x/(a + b*ArcSech[c*x]),x]","\int \frac{x}{a+b \text{sech}^{-1}(c x)} \, dx","\text{Int}\left(\frac{x}{a+b \text{sech}^{-1}(c x)},x\right)",0,"Defer[Int][x/(a + b*ArcSech[c*x]), x]","A",0,0,0,0,-1,"{}"
52,0,0,0,0.0071896,"\int \frac{1}{a+b \text{sech}^{-1}(c x)} \, dx","Int[(a + b*ArcSech[c*x])^(-1),x]","\int \frac{1}{a+b \text{sech}^{-1}(c x)} \, dx","\text{Int}\left(\frac{1}{a+b \text{sech}^{-1}(c x)},x\right)",0,"Defer[Int][(a + b*ArcSech[c*x])^(-1), x]","A",0,0,0,0,-1,"{}"
53,0,0,0,0.0271964,"\int \frac{1}{x \left(a+b \text{sech}^{-1}(c x)\right)} \, dx","Int[1/(x*(a + b*ArcSech[c*x])),x]","\int \frac{1}{x \left(a+b \text{sech}^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \text{sech}^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x*(a + b*ArcSech[c*x])), x]","A",0,0,0,0,-1,"{}"
54,1,46,0,0.1104013,"\int \frac{1}{x^2 \left(a+b \text{sech}^{-1}(c x)\right)} \, dx","Int[1/(x^2*(a + b*ArcSech[c*x])),x]","\frac{c \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{b}-\frac{c \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{b}","\frac{c \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{b}-\frac{c \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{b}",1,"(c*CoshIntegral[a/b + ArcSech[c*x]]*Sinh[a/b])/b - (c*Cosh[a/b]*SinhIntegral[a/b + ArcSech[c*x]])/b","A",4,4,14,0.2857,1,"{6285, 3303, 3298, 3301}"
55,1,63,0,0.1416057,"\int \frac{1}{x^3 \left(a+b \text{sech}^{-1}(c x)\right)} \, dx","Int[1/(x^3*(a + b*ArcSech[c*x])),x]","\frac{c^2 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \text{sech}^{-1}(c x)\right)}{2 b}-\frac{c^2 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \text{sech}^{-1}(c x)\right)}{2 b}","\frac{c^2 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \text{sech}^{-1}(c x)\right)}{2 b}-\frac{c^2 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \text{sech}^{-1}(c x)\right)}{2 b}",1,"(c^2*CoshIntegral[(2*a)/b + 2*ArcSech[c*x]]*Sinh[(2*a)/b])/(2*b) - (c^2*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSech[c*x]])/(2*b)","A",6,6,14,0.4286,1,"{6285, 5448, 12, 3303, 3298, 3301}"
56,1,117,0,0.2361693,"\int \frac{1}{x^4 \left(a+b \text{sech}^{-1}(c x)\right)} \, dx","Int[1/(x^4*(a + b*ArcSech[c*x])),x]","\frac{c^3 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{4 b}+\frac{c^3 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \text{sech}^{-1}(c x)\right)}{4 b}-\frac{c^3 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{4 b}-\frac{c^3 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \text{sech}^{-1}(c x)\right)}{4 b}","\frac{c^3 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{4 b}+\frac{c^3 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \text{sech}^{-1}(c x)\right)}{4 b}-\frac{c^3 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{4 b}-\frac{c^3 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \text{sech}^{-1}(c x)\right)}{4 b}",1,"(c^3*CoshIntegral[a/b + ArcSech[c*x]]*Sinh[a/b])/(4*b) + (c^3*CoshIntegral[(3*a)/b + 3*ArcSech[c*x]]*Sinh[(3*a)/b])/(4*b) - (c^3*Cosh[a/b]*SinhIntegral[a/b + ArcSech[c*x]])/(4*b) - (c^3*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSech[c*x]])/(4*b)","A",9,5,14,0.3571,1,"{6285, 5448, 3303, 3298, 3301}"
57,0,0,0,0.0156607,"\int \frac{x}{\left(a+b \text{sech}^{-1}(c x)\right)^2} \, dx","Int[x/(a + b*ArcSech[c*x])^2,x]","\int \frac{x}{\left(a+b \text{sech}^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x}{\left(a+b \text{sech}^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x/(a + b*ArcSech[c*x])^2, x]","A",0,0,0,0,-1,"{}"
58,0,0,0,0.0067468,"\int \frac{1}{\left(a+b \text{sech}^{-1}(c x)\right)^2} \, dx","Int[(a + b*ArcSech[c*x])^(-2),x]","\int \frac{1}{\left(a+b \text{sech}^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(a+b \text{sech}^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(a + b*ArcSech[c*x])^(-2), x]","A",0,0,0,0,-1,"{}"
59,0,0,0,0.0253484,"\int \frac{1}{x \left(a+b \text{sech}^{-1}(c x)\right)^2} \, dx","Int[1/(x*(a + b*ArcSech[c*x])^2),x]","\int \frac{1}{x \left(a+b \text{sech}^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \text{sech}^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(x*(a + b*ArcSech[c*x])^2), x]","A",0,0,0,0,-1,"{}"
60,1,86,0,0.1449173,"\int \frac{1}{x^2 \left(a+b \text{sech}^{-1}(c x)\right)^2} \, dx","Int[1/(x^2*(a + b*ArcSech[c*x])^2),x]","-\frac{c \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{b^2}+\frac{c \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{b^2}+\frac{\sqrt{\frac{1-c x}{c x+1}} (c x+1)}{b x \left(a+b \text{sech}^{-1}(c x)\right)}","-\frac{c \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{b^2}+\frac{c \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{b^2}+\frac{\sqrt{\frac{1-c x}{c x+1}} (c x+1)}{b x \left(a+b \text{sech}^{-1}(c x)\right)}",1,"(Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x))/(b*x*(a + b*ArcSech[c*x])) - (c*Cosh[a/b]*CoshIntegral[a/b + ArcSech[c*x]])/b^2 + (c*Sinh[a/b]*SinhIntegral[a/b + ArcSech[c*x]])/b^2","A",5,5,14,0.3571,1,"{6285, 3297, 3303, 3298, 3301}"
61,1,85,0,0.1645712,"\int \frac{1}{x^3 \left(a+b \text{sech}^{-1}(c x)\right)^2} \, dx","Int[1/(x^3*(a + b*ArcSech[c*x])^2),x]","-\frac{c^2 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \text{sech}^{-1}(c x)\right)}{b^2}+\frac{c^2 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \text{sech}^{-1}(c x)\right)}{b^2}+\frac{c^2 \sinh \left(2 \text{sech}^{-1}(c x)\right)}{2 b \left(a+b \text{sech}^{-1}(c x)\right)}","-\frac{c^2 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \text{sech}^{-1}(c x)\right)}{b^2}+\frac{c^2 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \text{sech}^{-1}(c x)\right)}{b^2}+\frac{c^2 \sinh \left(2 \text{sech}^{-1}(c x)\right)}{2 b \left(a+b \text{sech}^{-1}(c x)\right)}",1,"-((c^2*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSech[c*x]])/b^2) + (c^2*Sinh[2*ArcSech[c*x]])/(2*b*(a + b*ArcSech[c*x])) + (c^2*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSech[c*x]])/b^2","A",7,7,14,0.5000,1,"{6285, 5448, 12, 3297, 3303, 3298, 3301}"
62,1,190,0,0.2948621,"\int \frac{1}{x^4 \left(a+b \text{sech}^{-1}(c x)\right)^2} \, dx","Int[1/(x^4*(a + b*ArcSech[c*x])^2),x]","-\frac{c^3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{4 b^2}-\frac{3 c^3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \text{sech}^{-1}(c x)\right)}{4 b^2}+\frac{c^3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{4 b^2}+\frac{3 c^3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \text{sech}^{-1}(c x)\right)}{4 b^2}+\frac{c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{4 b x \left(a+b \text{sech}^{-1}(c x)\right)}+\frac{c^3 \sinh \left(3 \text{sech}^{-1}(c x)\right)}{4 b \left(a+b \text{sech}^{-1}(c x)\right)}","-\frac{c^3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{4 b^2}-\frac{3 c^3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \text{sech}^{-1}(c x)\right)}{4 b^2}+\frac{c^3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{4 b^2}+\frac{3 c^3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \text{sech}^{-1}(c x)\right)}{4 b^2}+\frac{c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{4 b x \left(a+b \text{sech}^{-1}(c x)\right)}+\frac{c^3 \sinh \left(3 \text{sech}^{-1}(c x)\right)}{4 b \left(a+b \text{sech}^{-1}(c x)\right)}",1,"(c^2*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x))/(4*b*x*(a + b*ArcSech[c*x])) - (c^3*Cosh[a/b]*CoshIntegral[a/b + ArcSech[c*x]])/(4*b^2) - (3*c^3*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSech[c*x]])/(4*b^2) + (c^3*Sinh[3*ArcSech[c*x]])/(4*b*(a + b*ArcSech[c*x])) + (c^3*Sinh[a/b]*SinhIntegral[a/b + ArcSech[c*x]])/(4*b^2) + (3*c^3*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSech[c*x]])/(4*b^2)","A",11,6,14,0.4286,1,"{6285, 5448, 3297, 3303, 3298, 3301}"
63,0,0,0,0.0158324,"\int \frac{x}{\left(a+b \text{sech}^{-1}(c x)\right)^3} \, dx","Int[x/(a + b*ArcSech[c*x])^3,x]","\int \frac{x}{\left(a+b \text{sech}^{-1}(c x)\right)^3} \, dx","\text{Int}\left(\frac{x}{\left(a+b \text{sech}^{-1}(c x)\right)^3},x\right)",0,"Defer[Int][x/(a + b*ArcSech[c*x])^3, x]","A",0,0,0,0,-1,"{}"
64,0,0,0,0.0059659,"\int \frac{1}{\left(a+b \text{sech}^{-1}(c x)\right)^3} \, dx","Int[(a + b*ArcSech[c*x])^(-3),x]","\int \frac{1}{\left(a+b \text{sech}^{-1}(c x)\right)^3} \, dx","\text{Int}\left(\frac{1}{\left(a+b \text{sech}^{-1}(c x)\right)^3},x\right)",0,"Defer[Int][(a + b*ArcSech[c*x])^(-3), x]","A",0,0,0,0,-1,"{}"
65,0,0,0,0.0248769,"\int \frac{1}{x \left(a+b \text{sech}^{-1}(c x)\right)^3} \, dx","Int[1/(x*(a + b*ArcSech[c*x])^3),x]","\int \frac{1}{x \left(a+b \text{sech}^{-1}(c x)\right)^3} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \text{sech}^{-1}(c x)\right)^3},x\right)",0,"Defer[Int][1/(x*(a + b*ArcSech[c*x])^3), x]","A",0,0,0,0,-1,"{}"
66,1,114,0,0.1756792,"\int \frac{1}{x^2 \left(a+b \text{sech}^{-1}(c x)\right)^3} \, dx","Int[1/(x^2*(a + b*ArcSech[c*x])^3),x]","\frac{c \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{2 b^3}-\frac{c \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{2 b^3}+\frac{1}{2 b^2 x \left(a+b \text{sech}^{-1}(c x)\right)}+\frac{\sqrt{\frac{1-c x}{c x+1}} (c x+1)}{2 b x \left(a+b \text{sech}^{-1}(c x)\right)^2}","\frac{c \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{2 b^3}-\frac{c \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{2 b^3}+\frac{1}{2 b^2 x \left(a+b \text{sech}^{-1}(c x)\right)}+\frac{\sqrt{\frac{1-c x}{c x+1}} (c x+1)}{2 b x \left(a+b \text{sech}^{-1}(c x)\right)^2}",1,"(Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x))/(2*b*x*(a + b*ArcSech[c*x])^2) + 1/(2*b^2*x*(a + b*ArcSech[c*x])) + (c*CoshIntegral[a/b + ArcSech[c*x]]*Sinh[a/b])/(2*b^3) - (c*Cosh[a/b]*SinhIntegral[a/b + ArcSech[c*x]])/(2*b^3)","A",6,5,14,0.3571,1,"{6285, 3297, 3303, 3298, 3301}"
67,1,112,0,0.2064644,"\int \frac{1}{x^3 \left(a+b \text{sech}^{-1}(c x)\right)^3} \, dx","Int[1/(x^3*(a + b*ArcSech[c*x])^3),x]","\frac{c^2 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \text{sech}^{-1}(c x)\right)}{b^3}-\frac{c^2 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \text{sech}^{-1}(c x)\right)}{b^3}+\frac{c^2 \cosh \left(2 \text{sech}^{-1}(c x)\right)}{2 b^2 \left(a+b \text{sech}^{-1}(c x)\right)}+\frac{c^2 \sinh \left(2 \text{sech}^{-1}(c x)\right)}{4 b \left(a+b \text{sech}^{-1}(c x)\right)^2}","\frac{c^2 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \text{sech}^{-1}(c x)\right)}{b^3}-\frac{c^2 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \text{sech}^{-1}(c x)\right)}{b^3}+\frac{c^2 \cosh \left(2 \text{sech}^{-1}(c x)\right)}{2 b^2 \left(a+b \text{sech}^{-1}(c x)\right)}+\frac{c^2 \sinh \left(2 \text{sech}^{-1}(c x)\right)}{4 b \left(a+b \text{sech}^{-1}(c x)\right)^2}",1,"(c^2*Cosh[2*ArcSech[c*x]])/(2*b^2*(a + b*ArcSech[c*x])) + (c^2*CoshIntegral[(2*a)/b + 2*ArcSech[c*x]]*Sinh[(2*a)/b])/b^3 + (c^2*Sinh[2*ArcSech[c*x]])/(4*b*(a + b*ArcSech[c*x])^2) - (c^2*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSech[c*x]])/b^3","A",8,7,14,0.5000,1,"{6285, 5448, 12, 3297, 3303, 3298, 3301}"
68,1,240,0,0.3711143,"\int \frac{1}{x^4 \left(a+b \text{sech}^{-1}(c x)\right)^3} \, dx","Int[1/(x^4*(a + b*ArcSech[c*x])^3),x]","\frac{c^3 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{8 b^3}+\frac{9 c^3 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \text{sech}^{-1}(c x)\right)}{8 b^3}-\frac{c^3 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{8 b^3}-\frac{9 c^3 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \text{sech}^{-1}(c x)\right)}{8 b^3}+\frac{c^2}{8 b^2 x \left(a+b \text{sech}^{-1}(c x)\right)}+\frac{3 c^3 \cosh \left(3 \text{sech}^{-1}(c x)\right)}{8 b^2 \left(a+b \text{sech}^{-1}(c x)\right)}+\frac{c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{8 b x \left(a+b \text{sech}^{-1}(c x)\right)^2}+\frac{c^3 \sinh \left(3 \text{sech}^{-1}(c x)\right)}{8 b \left(a+b \text{sech}^{-1}(c x)\right)^2}","\frac{c^3 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{8 b^3}+\frac{9 c^3 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \text{sech}^{-1}(c x)\right)}{8 b^3}-\frac{c^3 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{sech}^{-1}(c x)\right)}{8 b^3}-\frac{9 c^3 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \text{sech}^{-1}(c x)\right)}{8 b^3}+\frac{c^2}{8 b^2 x \left(a+b \text{sech}^{-1}(c x)\right)}+\frac{3 c^3 \cosh \left(3 \text{sech}^{-1}(c x)\right)}{8 b^2 \left(a+b \text{sech}^{-1}(c x)\right)}+\frac{c^2 \sqrt{\frac{1-c x}{c x+1}} (c x+1)}{8 b x \left(a+b \text{sech}^{-1}(c x)\right)^2}+\frac{c^3 \sinh \left(3 \text{sech}^{-1}(c x)\right)}{8 b \left(a+b \text{sech}^{-1}(c x)\right)^2}",1,"(c^2*Sqrt[(1 - c*x)/(1 + c*x)]*(1 + c*x))/(8*b*x*(a + b*ArcSech[c*x])^2) + c^2/(8*b^2*x*(a + b*ArcSech[c*x])) + (3*c^3*Cosh[3*ArcSech[c*x]])/(8*b^2*(a + b*ArcSech[c*x])) + (c^3*CoshIntegral[a/b + ArcSech[c*x]]*Sinh[a/b])/(8*b^3) + (9*c^3*CoshIntegral[(3*a)/b + 3*ArcSech[c*x]]*Sinh[(3*a)/b])/(8*b^3) + (c^3*Sinh[3*ArcSech[c*x]])/(8*b*(a + b*ArcSech[c*x])^2) - (c^3*Cosh[a/b]*SinhIntegral[a/b + ArcSech[c*x]])/(8*b^3) - (9*c^3*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSech[c*x]])/(8*b^3)","A",13,6,14,0.4286,1,"{6285, 5448, 3297, 3303, 3298, 3301}"
69,0,0,0,0.0237076,"\int (d x)^m \left(a+b \text{sech}^{-1}(c x)\right)^3 \, dx","Int[(d*x)^m*(a + b*ArcSech[c*x])^3,x]","\int (d x)^m \left(a+b \text{sech}^{-1}(c x)\right)^3 \, dx","\text{Int}\left((d x)^m \left(a+b \text{sech}^{-1}(c x)\right)^3,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcSech[c*x])^3, x]","A",0,0,0,0,-1,"{}"
70,0,0,0,0.0255439,"\int (d x)^m \left(a+b \text{sech}^{-1}(c x)\right)^2 \, dx","Int[(d*x)^m*(a + b*ArcSech[c*x])^2,x]","\int (d x)^m \left(a+b \text{sech}^{-1}(c x)\right)^2 \, dx","\text{Int}\left((d x)^m \left(a+b \text{sech}^{-1}(c x)\right)^2,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcSech[c*x])^2, x]","A",0,0,0,0,-1,"{}"
71,1,87,0,0.0371767,"\int (d x)^m \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[(d*x)^m*(a + b*ArcSech[c*x]),x]","\frac{(d x)^{m+1} \left(a+b \text{sech}^{-1}(c x)\right)}{d (m+1)}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} (d x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right)}{d (m+1)^2}","\frac{(d x)^{m+1} \left(a+b \text{sech}^{-1}(c x)\right)}{d (m+1)}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} (d x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right)}{d (m+1)^2}",1,"((d*x)^(1 + m)*(a + b*ArcSech[c*x]))/(d*(1 + m)) + (b*(d*x)^(1 + m)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(d*(1 + m)^2)","A",3,3,14,0.2143,1,"{6283, 125, 364}"
72,0,0,0,0.0279905,"\int \frac{(d x)^m}{a+b \text{sech}^{-1}(c x)} \, dx","Int[(d*x)^m/(a + b*ArcSech[c*x]),x]","\int \frac{(d x)^m}{a+b \text{sech}^{-1}(c x)} \, dx","\text{Int}\left(\frac{(d x)^m}{a+b \text{sech}^{-1}(c x)},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcSech[c*x]), x]","A",0,0,0,0,-1,"{}"
73,0,0,0,0.0273039,"\int \frac{(d x)^m}{\left(a+b \text{sech}^{-1}(c x)\right)^2} \, dx","Int[(d*x)^m/(a + b*ArcSech[c*x])^2,x]","\int \frac{(d x)^m}{\left(a+b \text{sech}^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{(d x)^m}{\left(a+b \text{sech}^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcSech[c*x])^2, x]","A",0,0,0,0,-1,"{}"
74,1,264,0,0.3622041,"\int (d+e x)^3 \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[(d + e*x)^3*(a + b*ArcSech[c*x]),x]","\frac{(d+e x)^4 \left(a+b \text{sech}^{-1}(c x)\right)}{4 e}-\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(9 c^2 d^2+e^2\right)}{6 c^4}+\frac{b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(2 c^2 d^2+e^2\right) \sin ^{-1}(c x)}{2 c^3}-\frac{b d^4 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{4 e}-\frac{b d e^2 x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{2 c^2}-\frac{b e^3 x^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{12 c^2}","\frac{(d+e x)^4 \left(a+b \text{sech}^{-1}(c x)\right)}{4 e}-\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(9 c^2 d^2+e^2\right)}{6 c^4}+\frac{b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(2 c^2 d^2+e^2\right) \sin ^{-1}(c x)}{2 c^3}-\frac{b d^4 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{4 e}-\frac{b d e^2 x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{2 c^2}-\frac{b e^3 x^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{12 c^2}",1,"-(b*e*(9*c^2*d^2 + e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(6*c^4) - (b*d*e^2*x*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(2*c^2) - (b*e^3*x^2*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(12*c^2) + ((d + e*x)^4*(a + b*ArcSech[c*x]))/(4*e) + (b*d*(2*c^2*d^2 + e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/(2*c^3) - (b*d^4*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[1 - c^2*x^2]])/(4*e)","A",9,7,16,0.4375,1,"{6288, 1809, 844, 216, 266, 63, 208}"
75,1,201,0,0.2173728,"\int (d+e x)^2 \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[(d + e*x)^2*(a + b*ArcSech[c*x]),x]","\frac{(d+e x)^3 \left(a+b \text{sech}^{-1}(c x)\right)}{3 e}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(6 c^2 d^2+e^2\right) \sin ^{-1}(c x)}{6 c^3}-\frac{b d^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{3 e}-\frac{b d e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{c^2}-\frac{b e^2 x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{6 c^2}","\frac{(d+e x)^3 \left(a+b \text{sech}^{-1}(c x)\right)}{3 e}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(6 c^2 d^2+e^2\right) \sin ^{-1}(c x)}{6 c^3}-\frac{b d^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{3 e}-\frac{b d e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{c^2}-\frac{b e^2 x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{6 c^2}",1,"-((b*d*e*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/c^2) - (b*e^2*x*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(6*c^2) + ((d + e*x)^3*(a + b*ArcSech[c*x]))/(3*e) + (b*(6*c^2*d^2 + e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/(6*c^3) - (b*d^3*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[1 - c^2*x^2]])/(3*e)","A",8,7,16,0.4375,1,"{6288, 1809, 844, 216, 266, 63, 208}"
76,1,142,0,0.1178314,"\int (d+e x) \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[(d + e*x)*(a + b*ArcSech[c*x]),x]","\frac{(d+e x)^2 \left(a+b \text{sech}^{-1}(c x)\right)}{2 e}-\frac{b d^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{2 e}-\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{2 c^2}+\frac{b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{c}","\frac{(d+e x)^2 \left(a+b \text{sech}^{-1}(c x)\right)}{2 e}-\frac{b d^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{2 e}-\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{2 c^2}+\frac{b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{c}",1,"-(b*e*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(2*c^2) + ((d + e*x)^2*(a + b*ArcSech[c*x]))/(2*e) + (b*d*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/c - (b*d^2*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[1 - c^2*x^2]])/(2*e)","A",7,7,14,0.5000,1,"{6288, 1809, 844, 216, 266, 63, 208}"
77,1,40,0,0.0151617,"\int \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[a + b*ArcSech[c*x],x]","a x+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{c}+b x \text{sech}^{-1}(c x)","a x+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{c}+b x \text{sech}^{-1}(c x)",1,"a*x + b*x*ArcSech[c*x] + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/c","A",3,2,8,0.2500,1,"{6277, 216}"
78,1,229,0,0.933496,"\int \frac{a+b \text{sech}^{-1}(c x)}{d+e x} \, dx","Int[(a + b*ArcSech[c*x])/(d + e*x),x]","-\frac{b \text{PolyLog}\left(2,-\frac{\left(e-\sqrt{e^2-c^2 d^2}\right) e^{-\text{sech}^{-1}(c x)}}{c d}\right)}{e}-\frac{b \text{PolyLog}\left(2,-\frac{\left(\sqrt{e^2-c^2 d^2}+e\right) e^{-\text{sech}^{-1}(c x)}}{c d}\right)}{e}+\frac{b \text{PolyLog}\left(2,-e^{-2 \text{sech}^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\left(e-\sqrt{e^2-c^2 d^2}\right) e^{-\text{sech}^{-1}(c x)}}{c d}+1\right)}{e}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\left(\sqrt{e^2-c^2 d^2}+e\right) e^{-\text{sech}^{-1}(c x)}}{c d}+1\right)}{e}-\frac{\log \left(e^{-2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{e}","-\frac{b \text{PolyLog}\left(2,-\frac{\left(e-\sqrt{e^2-c^2 d^2}\right) e^{-\text{sech}^{-1}(c x)}}{c d}\right)}{e}-\frac{b \text{PolyLog}\left(2,-\frac{\left(\sqrt{e^2-c^2 d^2}+e\right) e^{-\text{sech}^{-1}(c x)}}{c d}\right)}{e}+\frac{b \text{PolyLog}\left(2,-e^{-2 \text{sech}^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\left(e-\sqrt{e^2-c^2 d^2}\right) e^{-\text{sech}^{-1}(c x)}}{c d}+1\right)}{e}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\left(\sqrt{e^2-c^2 d^2}+e\right) e^{-\text{sech}^{-1}(c x)}}{c d}+1\right)}{e}-\frac{\log \left(e^{-2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{e}",1,"-(((a + b*ArcSech[c*x])*Log[1 + E^(-2*ArcSech[c*x])])/e) + ((a + b*ArcSech[c*x])*Log[1 + (e - Sqrt[-(c^2*d^2) + e^2])/(c*d*E^ArcSech[c*x])])/e + ((a + b*ArcSech[c*x])*Log[1 + (e + Sqrt[-(c^2*d^2) + e^2])/(c*d*E^ArcSech[c*x])])/e + (b*PolyLog[2, -E^(-2*ArcSech[c*x])])/(2*e) - (b*PolyLog[2, -((e - Sqrt[-(c^2*d^2) + e^2])/(c*d*E^ArcSech[c*x]))])/e - (b*PolyLog[2, -((e + Sqrt[-(c^2*d^2) + e^2])/(c*d*E^ArcSech[c*x]))])/e","A",4,2,16,0.1250,1,"{6287, 2518}"
79,1,147,0,0.1190073,"\int \frac{a+b \text{sech}^{-1}(c x)}{(d+e x)^2} \, dx","Int[(a + b*ArcSech[c*x])/(d + e*x)^2,x]","-\frac{a+b \text{sech}^{-1}(c x)}{e (d+e x)}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{d \sqrt{c^2 d^2-e^2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d e}","-\frac{a+b \text{sech}^{-1}(c x)}{e (d+e x)}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{d \sqrt{c^2 d^2-e^2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d e}",1,"-((a + b*ArcSech[c*x])/(e*(d + e*x))) + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(d*Sqrt[c^2*d^2 - e^2]) + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[1 - c^2*x^2]])/(d*e)","A",8,7,16,0.4375,1,"{6288, 961, 266, 63, 208, 725, 204}"
80,1,306,0,0.1932465,"\int \frac{a+b \text{sech}^{-1}(c x)}{(d+e x)^3} \, dx","Int[(a + b*ArcSech[c*x])/(d + e*x)^3,x]","-\frac{a+b \text{sech}^{-1}(c x)}{2 e (d+e x)^2}+\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{2 d \left(c^2 d^2-e^2\right) (d+e x)}+\frac{b c^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{2 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{2 d^2 \sqrt{c^2 d^2-e^2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{2 d^2 e}","-\frac{a+b \text{sech}^{-1}(c x)}{2 e (d+e x)^2}+\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{2 d \left(c^2 d^2-e^2\right) (d+e x)}+\frac{b c^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{2 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{2 d^2 \sqrt{c^2 d^2-e^2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{2 d^2 e}",1,"(b*e*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(2*d*(c^2*d^2 - e^2)*(d + e*x)) - (a + b*ArcSech[c*x])/(2*e*(d + e*x)^2) + (b*c^2*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(2*(c^2*d^2 - e^2)^(3/2)) + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(2*d^2*Sqrt[c^2*d^2 - e^2]) + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[1 - c^2*x^2]])/(2*d^2*e)","A",11,8,16,0.5000,1,"{6288, 961, 266, 63, 208, 731, 725, 204}"
81,1,343,0,0.6212923,"\int (d+e x)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[(d + e*x)^(3/2)*(a + b*ArcSech[c*x]),x]","\frac{2 (d+e x)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 e}-\frac{4 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(2 c^2 d^2+e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^3 \sqrt{d+e x}}-\frac{4 b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x}}{15 c^2}-\frac{4 b d^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 e \sqrt{d+e x}}-\frac{28 b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c \sqrt{\frac{c (d+e x)}{c d+e}}}","\frac{2 (d+e x)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 e}-\frac{4 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(2 c^2 d^2+e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^3 \sqrt{d+e x}}-\frac{4 b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x}}{15 c^2}-\frac{4 b d^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 e \sqrt{d+e x}}-\frac{28 b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c \sqrt{\frac{c (d+e x)}{c d+e}}}",1,"(-4*b*e*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2])/(15*c^2) + (2*(d + e*x)^(5/2)*(a + b*ArcSech[c*x]))/(5*e) - (28*b*d*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*c*Sqrt[(c*(d + e*x))/(c*d + e)]) - (4*b*(2*c^2*d^2 + e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[(c*(d + e*x))/(c*d + e)]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*c^3*Sqrt[d + e*x]) - (4*b*d^3*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[(c*(d + e*x))/(c*d + e)]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(5*e*Sqrt[d + e*x])","A",21,12,18,0.6667,1,"{6288, 958, 719, 419, 932, 168, 538, 537, 844, 424, 931, 1584}"
82,1,279,0,0.3722026,"\int \sqrt{d+e x} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[Sqrt[d + e*x]*(a + b*ArcSech[c*x]),x]","\frac{2 (d+e x)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 e}-\frac{4 b d^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 e \sqrt{d+e x}}-\frac{4 b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c \sqrt{d+e x}}-\frac{4 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c \sqrt{\frac{c (d+e x)}{c d+e}}}","\frac{2 (d+e x)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 e}-\frac{4 b d^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 e \sqrt{d+e x}}-\frac{4 b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c \sqrt{d+e x}}-\frac{4 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c \sqrt{\frac{c (d+e x)}{c d+e}}}",1,"(2*(d + e*x)^(3/2)*(a + b*ArcSech[c*x]))/(3*e) - (4*b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c*Sqrt[(c*(d + e*x))/(c*d + e)]) - (4*b*d*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[(c*(d + e*x))/(c*d + e)]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c*Sqrt[d + e*x]) - (4*b*d^2*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[(c*(d + e*x))/(c*d + e)]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*e*Sqrt[d + e*x])","A",14,10,18,0.5556,1,"{6288, 958, 719, 419, 932, 168, 538, 537, 844, 424}"
83,1,187,0,0.2465466,"\int \frac{a+b \text{sech}^{-1}(c x)}{\sqrt{d+e x}} \, dx","Int[(a + b*ArcSech[c*x])/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(a+b \text{sech}^{-1}(c x)\right)}{e}-\frac{4 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c \sqrt{d+e x}}-\frac{4 b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{e \sqrt{d+e x}}","\frac{2 \sqrt{d+e x} \left(a+b \text{sech}^{-1}(c x)\right)}{e}-\frac{4 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c \sqrt{d+e x}}-\frac{4 b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{e \sqrt{d+e x}}",1,"(2*Sqrt[d + e*x]*(a + b*ArcSech[c*x]))/e - (4*b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[(c*(d + e*x))/(c*d + e)]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(c*Sqrt[d + e*x]) - (4*b*d*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[(c*(d + e*x))/(c*d + e)]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(e*Sqrt[d + e*x])","A",8,8,18,0.4444,1,"{6288, 944, 719, 419, 932, 168, 538, 537}"
84,1,105,0,0.1777254,"\int \frac{a+b \text{sech}^{-1}(c x)}{(d+e x)^{3/2}} \, dx","Int[(a + b*ArcSech[c*x])/(d + e*x)^(3/2),x]","\frac{4 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{e \sqrt{d+e x}}-\frac{2 \left(a+b \text{sech}^{-1}(c x)\right)}{e \sqrt{d+e x}}","\frac{4 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{e \sqrt{d+e x}}-\frac{2 \left(a+b \text{sech}^{-1}(c x)\right)}{e \sqrt{d+e x}}",1,"(-2*(a + b*ArcSech[c*x]))/(e*Sqrt[d + e*x]) + (4*b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[(c*(d + e*x))/(c*d + e)]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(e*Sqrt[d + e*x])","A",5,5,18,0.2778,1,"{6288, 932, 168, 538, 537}"
85,1,278,0,0.3125299,"\int \frac{a+b \text{sech}^{-1}(c x)}{(d+e x)^{5/2}} \, dx","Int[(a + b*ArcSech[c*x])/(d + e*x)^(5/2),x]","-\frac{2 \left(a+b \text{sech}^{-1}(c x)\right)}{3 e (d+e x)^{3/2}}+\frac{4 b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{3 d \left(c^2 d^2-e^2\right) \sqrt{d+e x}}-\frac{4 b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 d \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{4 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 d e \sqrt{d+e x}}","-\frac{2 \left(a+b \text{sech}^{-1}(c x)\right)}{3 e (d+e x)^{3/2}}+\frac{4 b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{3 d \left(c^2 d^2-e^2\right) \sqrt{d+e x}}-\frac{4 b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 d \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{4 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 d e \sqrt{d+e x}}",1,"(4*b*e*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(3*d*(c^2*d^2 - e^2)*Sqrt[d + e*x]) - (2*(a + b*ArcSech[c*x]))/(3*e*(d + e*x)^(3/2)) - (4*b*c*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*d*(c^2*d^2 - e^2)*Sqrt[(c*(d + e*x))/(c*d + e)]) + (4*b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[(c*(d + e*x))/(c*d + e)]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*d*e*Sqrt[d + e*x])","A",11,10,18,0.5556,1,"{6288, 958, 745, 21, 719, 424, 932, 168, 538, 537}"
86,1,609,0,0.5941173,"\int \frac{a+b \text{sech}^{-1}(c x)}{(d+e x)^{7/2}} \, dx","Int[(a + b*ArcSech[c*x])/(d + e*x)^(7/2),x]","-\frac{2 \left(a+b \text{sech}^{-1}(c x)\right)}{5 e (d+e x)^{5/2}}+\frac{16 b c^2 e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{15 \left(c^2 d^2-e^2\right)^2 \sqrt{d+e x}}+\frac{4 b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{5 d^2 \left(c^2 d^2-e^2\right) \sqrt{d+e x}}+\frac{4 b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{15 d \left(c^2 d^2-e^2\right) (d+e x)^{3/2}}+\frac{4 b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 d \left(c^2 d^2-e^2\right) \sqrt{d+e x}}-\frac{16 b c^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 \left(c^2 d^2-e^2\right)^2 \sqrt{\frac{c (d+e x)}{c d+e}}}-\frac{4 b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 d^2 \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{4 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 d^2 e \sqrt{d+e x}}","-\frac{2 \left(a+b \text{sech}^{-1}(c x)\right)}{5 e (d+e x)^{5/2}}+\frac{16 b c^2 e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{15 \left(c^2 d^2-e^2\right)^2 \sqrt{d+e x}}+\frac{4 b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{5 d^2 \left(c^2 d^2-e^2\right) \sqrt{d+e x}}+\frac{4 b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{15 d \left(c^2 d^2-e^2\right) (d+e x)^{3/2}}+\frac{4 b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 d \left(c^2 d^2-e^2\right) \sqrt{d+e x}}-\frac{16 b c^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 \left(c^2 d^2-e^2\right)^2 \sqrt{\frac{c (d+e x)}{c d+e}}}-\frac{4 b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 d^2 \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{4 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 d^2 e \sqrt{d+e x}}",1,"(4*b*e*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(15*d*(c^2*d^2 - e^2)*(d + e*x)^(3/2)) + (16*b*c^2*e*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(15*(c^2*d^2 - e^2)^2*Sqrt[d + e*x]) + (4*b*e*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(5*d^2*(c^2*d^2 - e^2)*Sqrt[d + e*x]) - (2*(a + b*ArcSech[c*x]))/(5*e*(d + e*x)^(5/2)) - (16*b*c^3*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*(c^2*d^2 - e^2)^2*Sqrt[(c*(d + e*x))/(c*d + e)]) - (4*b*c*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(5*d^2*(c^2*d^2 - e^2)*Sqrt[(c*(d + e*x))/(c*d + e)]) + (4*b*c*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[(c*(d + e*x))/(c*d + e)]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*d*(c^2*d^2 - e^2)*Sqrt[d + e*x]) + (4*b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[(c*(d + e*x))/(c*d + e)]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(5*d^2*e*Sqrt[d + e*x])","A",18,13,18,0.7222,1,"{6288, 958, 745, 835, 844, 719, 424, 419, 21, 932, 168, 538, 537}"
87,0,0,0,0.0481412,"\int (d+e x)^m \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[(d + e*x)^m*(a + b*ArcSech[c*x]),x]","\int (d+e x)^m \left(a+b \text{sech}^{-1}(c x)\right) \, dx","\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \text{Int}\left(\frac{(d+e x)^{m+1}}{x \sqrt{1-c^2 x^2}},x\right)}{e (m+1)}+\frac{(d+e x)^{m+1} \left(a+b \text{sech}^{-1}(c x)\right)}{e (m+1)}",0,"((d + e*x)^(1 + m)*(a + b*ArcSech[c*x]))/(e*(1 + m)) + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Defer[Int][(d + e*x)^(1 + m)/(x*Sqrt[1 - c^2*x^2]), x])/(e*(1 + m))","A",0,0,0,0,-1,"{}"
88,1,229,0,0.127182,"\int x^4 \left(d+e x^2\right) \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^4*(d + e*x^2)*(a + b*ArcSech[c*x]),x]","\frac{1}{5} d x^5 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{7} e x^7 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(42 c^2 d+25 e\right)}{840 c^4}-\frac{b x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(42 c^2 d+25 e\right)}{560 c^6}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(42 c^2 d+25 e\right) \sin ^{-1}(c x)}{560 c^7}-\frac{b e x^5 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{42 c^2}","\frac{1}{5} d x^5 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{7} e x^7 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(42 c^2 d+25 e\right)}{840 c^4}-\frac{b x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(42 c^2 d+25 e\right)}{560 c^6}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(42 c^2 d+25 e\right) \sin ^{-1}(c x)}{560 c^7}-\frac{b e x^5 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{42 c^2}",1,"-(b*(42*c^2*d + 25*e)*x*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(560*c^6) - (b*(42*c^2*d + 25*e)*x^3*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(840*c^4) - (b*e*x^5*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(42*c^2) + (d*x^5*(a + b*ArcSech[c*x]))/5 + (e*x^7*(a + b*ArcSech[c*x]))/7 + (b*(42*c^2*d + 25*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/(560*c^7)","A",6,6,19,0.3158,1,"{14, 6301, 12, 459, 321, 216}"
89,1,174,0,0.1029857,"\int x^2 \left(d+e x^2\right) \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)*(a + b*ArcSech[c*x]),x]","\frac{1}{3} d x^3 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{5} e x^5 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(20 c^2 d+9 e\right)}{120 c^4}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(20 c^2 d+9 e\right) \sin ^{-1}(c x)}{120 c^5}-\frac{b e x^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{20 c^2}","\frac{1}{3} d x^3 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{5} e x^5 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(20 c^2 d+9 e\right)}{120 c^4}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(20 c^2 d+9 e\right) \sin ^{-1}(c x)}{120 c^5}-\frac{b e x^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{20 c^2}",1,"-(b*(20*c^2*d + 9*e)*x*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(120*c^4) - (b*e*x^3*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(20*c^2) + (d*x^3*(a + b*ArcSech[c*x]))/3 + (e*x^5*(a + b*ArcSech[c*x]))/5 + (b*(20*c^2*d + 9*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/(120*c^5)","A",5,6,19,0.3158,1,"{14, 6301, 12, 459, 321, 216}"
90,1,112,0,0.0508121,"\int \left(d+e x^2\right) \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[(d + e*x^2)*(a + b*ArcSech[c*x]),x]","d x \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{3} e x^3 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(6 c^2 d+e\right) \sin ^{-1}(c x)}{6 c^3}-\frac{b e x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{6 c^2}","d x \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{3} e x^3 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(6 c^2 d+e\right) \sin ^{-1}(c x)}{6 c^3}-\frac{b e x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{6 c^2}",1,"-(b*e*x*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(6*c^2) + d*x*(a + b*ArcSech[c*x]) + (e*x^3*(a + b*ArcSech[c*x]))/3 + (b*(6*c^2*d + e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/(6*c^3)","A",4,4,16,0.2500,1,"{6291, 12, 388, 216}"
91,1,96,0,0.0658553,"\int \frac{\left(d+e x^2\right) \left(a+b \text{sech}^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)*(a + b*ArcSech[c*x]))/x^2,x]","-\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{x}+e x \left(a+b \text{sech}^{-1}(c x)\right)+\frac{b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{x}+\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{c}","-\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{x}+e x \left(a+b \text{sech}^{-1}(c x)\right)+\frac{b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{x}+\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{c}",1,"(b*d*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/x - (d*(a + b*ArcSech[c*x]))/x + e*x*(a + b*ArcSech[c*x]) + (b*e*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/c","A",3,4,19,0.2105,1,"{14, 6301, 451, 216}"
92,1,126,0,0.0792224,"\int \frac{\left(d+e x^2\right) \left(a+b \text{sech}^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)*(a + b*ArcSech[c*x]))/x^4,x]","-\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{3 x^3}-\frac{e \left(a+b \text{sech}^{-1}(c x)\right)}{x}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(2 c^2 d+9 e\right)}{9 x}+\frac{b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{9 x^3}","-\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{3 x^3}-\frac{e \left(a+b \text{sech}^{-1}(c x)\right)}{x}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(2 c^2 d+9 e\right)}{9 x}+\frac{b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{9 x^3}",1,"(b*d*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(9*x^3) + (b*(2*c^2*d + 9*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(9*x) - (d*(a + b*ArcSech[c*x]))/(3*x^3) - (e*(a + b*ArcSech[c*x]))/x","A",4,5,19,0.2632,1,"{14, 6301, 12, 453, 264}"
93,1,183,0,0.0994742,"\int \frac{\left(d+e x^2\right) \left(a+b \text{sech}^{-1}(c x)\right)}{x^6} \, dx","Int[((d + e*x^2)*(a + b*ArcSech[c*x]))/x^6,x]","-\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{5 x^5}-\frac{e \left(a+b \text{sech}^{-1}(c x)\right)}{3 x^3}+\frac{2 b c^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(12 c^2 d+25 e\right)}{225 x}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(12 c^2 d+25 e\right)}{225 x^3}+\frac{b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{25 x^5}","-\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{5 x^5}-\frac{e \left(a+b \text{sech}^{-1}(c x)\right)}{3 x^3}+\frac{2 b c^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(12 c^2 d+25 e\right)}{225 x}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(12 c^2 d+25 e\right)}{225 x^3}+\frac{b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{25 x^5}",1,"(b*d*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(25*x^5) + (b*(12*c^2*d + 25*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(225*x^3) + (2*b*c^2*(12*c^2*d + 25*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(225*x) - (d*(a + b*ArcSech[c*x]))/(5*x^5) - (e*(a + b*ArcSech[c*x]))/(3*x^3)","A",5,6,19,0.3158,1,"{14, 6301, 12, 453, 271, 264}"
94,1,238,0,0.1215738,"\int \frac{\left(d+e x^2\right) \left(a+b \text{sech}^{-1}(c x)\right)}{x^8} \, dx","Int[((d + e*x^2)*(a + b*ArcSech[c*x]))/x^8,x]","-\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{7 x^7}-\frac{e \left(a+b \text{sech}^{-1}(c x)\right)}{5 x^5}+\frac{8 b c^4 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(30 c^2 d+49 e\right)}{3675 x}+\frac{4 b c^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(30 c^2 d+49 e\right)}{3675 x^3}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(30 c^2 d+49 e\right)}{1225 x^5}+\frac{b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{49 x^7}","-\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{7 x^7}-\frac{e \left(a+b \text{sech}^{-1}(c x)\right)}{5 x^5}+\frac{8 b c^4 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(30 c^2 d+49 e\right)}{3675 x}+\frac{4 b c^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(30 c^2 d+49 e\right)}{3675 x^3}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(30 c^2 d+49 e\right)}{1225 x^5}+\frac{b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{49 x^7}",1,"(b*d*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(49*x^7) + (b*(30*c^2*d + 49*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(1225*x^5) + (4*b*c^2*(30*c^2*d + 49*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(3675*x^3) + (8*b*c^4*(30*c^2*d + 49*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(3675*x) - (d*(a + b*ArcSech[c*x]))/(7*x^7) - (e*(a + b*ArcSech[c*x]))/(5*x^5)","A",6,6,19,0.3158,1,"{14, 6301, 12, 453, 271, 264}"
95,1,232,0,0.1638303,"\int x^5 \left(d+e x^2\right) \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^5*(d + e*x^2)*(a + b*ArcSech[c*x]),x]","\frac{1}{6} d x^6 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{8} e x^8 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{5/2} \left(4 c^2 d+9 e\right)}{120 c^8}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2} \left(8 c^2 d+9 e\right)}{72 c^8}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(4 c^2 d+3 e\right)}{24 c^8}+\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{7/2}}{56 c^8}","\frac{1}{6} d x^6 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{8} e x^8 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{5/2} \left(4 c^2 d+9 e\right)}{120 c^8}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2} \left(8 c^2 d+9 e\right)}{72 c^8}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(4 c^2 d+3 e\right)}{24 c^8}+\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{7/2}}{56 c^8}",1,"-(b*(4*c^2*d + 3*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(24*c^8) + (b*(8*c^2*d + 9*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*(1 - c^2*x^2)^(3/2))/(72*c^8) - (b*(4*c^2*d + 9*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*(1 - c^2*x^2)^(5/2))/(120*c^8) + (b*e*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*(1 - c^2*x^2)^(7/2))/(56*c^8) + (d*x^6*(a + b*ArcSech[c*x]))/6 + (e*x^8*(a + b*ArcSech[c*x]))/8","A",5,5,19,0.2632,1,"{14, 6301, 12, 446, 77}"
96,1,180,0,0.1349287,"\int x^3 \left(d+e x^2\right) \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)*(a + b*ArcSech[c*x]),x]","\frac{1}{4} d x^4 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{6} e x^6 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2} \left(3 c^2 d+4 e\right)}{36 c^6}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(3 c^2 d+2 e\right)}{12 c^6}-\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{5/2}}{30 c^6}","\frac{1}{4} d x^4 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{6} e x^6 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2} \left(3 c^2 d+4 e\right)}{36 c^6}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(3 c^2 d+2 e\right)}{12 c^6}-\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{5/2}}{30 c^6}",1,"-(b*(3*c^2*d + 2*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(12*c^6) + (b*(3*c^2*d + 4*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*(1 - c^2*x^2)^(3/2))/(36*c^6) - (b*e*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*(1 - c^2*x^2)^(5/2))/(30*c^6) + (d*x^4*(a + b*ArcSech[c*x]))/4 + (e*x^6*(a + b*ArcSech[c*x]))/6","A",5,5,19,0.2632,1,"{14, 6301, 12, 446, 77}"
97,1,164,0,0.1931805,"\int x \left(d+e x^2\right) \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)*(a + b*ArcSech[c*x]),x]","\frac{\left(d+e x^2\right)^2 \left(a+b \text{sech}^{-1}(c x)\right)}{4 e}-\frac{b d^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{4 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(2 c^2 d+e\right)}{4 c^4}+\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2}}{12 c^4}","\frac{\left(d+e x^2\right)^2 \left(a+b \text{sech}^{-1}(c x)\right)}{4 e}-\frac{b d^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{4 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(2 c^2 d+e\right)}{4 c^4}+\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2}}{12 c^4}",1,"-(b*(2*c^2*d + e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(4*c^4) + (b*e*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*(1 - c^2*x^2)^(3/2))/(12*c^4) + ((d + e*x^2)^2*(a + b*ArcSech[c*x]))/(4*e) - (b*d^2*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[1 - c^2*x^2]])/(4*e)","A",7,6,17,0.3529,1,"{6299, 517, 446, 88, 63, 208}"
98,1,296,0,0.875166,"\int \frac{\left(d+e x^2\right) \left(a+b \text{sech}^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)*(a + b*ArcSech[c*x]))/x,x]","\frac{i b d \sqrt{1-\frac{1}{c^2 x^2}} \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-d \log \left(\frac{1}{x}\right) \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{2} e x^2 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{i b d \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x)^2}{2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{b d \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b d \sqrt{1-\frac{1}{c^2 x^2}} \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{b e x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}{2 c}","\frac{i b d \sqrt{1-\frac{1}{c^2 x^2}} \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-d \log \left(\frac{1}{x}\right) \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{2} e x^2 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{i b d \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x)^2}{2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{b d \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b d \sqrt{1-\frac{1}{c^2 x^2}} \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{b e x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}{2 c}",1,"-(b*e*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x)/(2*c) + ((I/2)*b*d*Sqrt[1 - 1/(c^2*x^2)]*ArcCsc[c*x]^2)/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) + (e*x^2*(a + b*ArcSech[c*x]))/2 - (b*d*Sqrt[1 - 1/(c^2*x^2)]*ArcCsc[c*x]*Log[1 - E^((2*I)*ArcCsc[c*x])])/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) + (b*d*Sqrt[1 - 1/(c^2*x^2)]*ArcCsc[c*x]*Log[x^(-1)])/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) - d*(a + b*ArcSech[c*x])*Log[x^(-1)] + ((I/2)*b*d*Sqrt[1 - 1/(c^2*x^2)]*PolyLog[2, E^((2*I)*ArcCsc[c*x])])/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)])","A",12,12,19,0.6316,1,"{6303, 14, 5790, 6742, 95, 2328, 2326, 4625, 3717, 2190, 2279, 2391}"
99,1,309,0,0.7800077,"\int \frac{\left(d+e x^2\right) \left(a+b \text{sech}^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)*(a + b*ArcSech[c*x]))/x^3,x]","\frac{i b e \sqrt{1-\frac{1}{c^2 x^2}} \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{2 x^2}-e \log \left(\frac{1}{x}\right) \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{4} b c^2 d \text{sech}^{-1}(c x)+\frac{i b e \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x)^2}{2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{b e \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b e \sqrt{1-\frac{1}{c^2 x^2}} \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b c d \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}{4 x}","\frac{i b e \sqrt{1-\frac{1}{c^2 x^2}} \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{2 x^2}-e \log \left(\frac{1}{x}\right) \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{4} b c^2 d \text{sech}^{-1}(c x)+\frac{i b e \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x)^2}{2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{b e \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b e \sqrt{1-\frac{1}{c^2 x^2}} \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b c d \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}{4 x}",1,"(b*c*d*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)])/(4*x) + ((I/2)*b*e*Sqrt[1 - 1/(c^2*x^2)]*ArcCsc[c*x]^2)/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) + (b*c^2*d*ArcSech[c*x])/4 - (d*(a + b*ArcSech[c*x]))/(2*x^2) - (b*e*Sqrt[1 - 1/(c^2*x^2)]*ArcCsc[c*x]*Log[1 - E^((2*I)*ArcCsc[c*x])])/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) + (b*e*Sqrt[1 - 1/(c^2*x^2)]*ArcCsc[c*x]*Log[x^(-1)])/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) - e*(a + b*ArcSech[c*x])*Log[x^(-1)] + ((I/2)*b*e*Sqrt[1 - 1/(c^2*x^2)]*PolyLog[2, E^((2*I)*ArcCsc[c*x])])/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)])","A",14,14,19,0.7368,1,"{6303, 14, 5790, 12, 6742, 90, 52, 2328, 2326, 4625, 3717, 2190, 2279, 2391}"
100,1,275,0,0.2345843,"\int x^2 \left(d+e x^2\right)^2 \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)^2*(a + b*ArcSech[c*x]),x]","\frac{1}{3} d^2 x^3 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{2}{5} d e x^5 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{7} e^2 x^7 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(280 c^4 d^2+252 c^2 d e+75 e^2\right)}{1680 c^6}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(280 c^4 d^2+252 c^2 d e+75 e^2\right) \sin ^{-1}(c x)}{1680 c^7}-\frac{b e x^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(84 c^2 d+25 e\right)}{840 c^4}-\frac{b e^2 x^5 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{42 c^2}","\frac{1}{3} d^2 x^3 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{2}{5} d e x^5 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{7} e^2 x^7 \left(a+b \text{sech}^{-1}(c x)\right)-\frac{b x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(280 c^4 d^2+252 c^2 d e+75 e^2\right)}{1680 c^6}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(280 c^4 d^2+252 c^2 d e+75 e^2\right) \sin ^{-1}(c x)}{1680 c^7}-\frac{b e x^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(84 c^2 d+25 e\right)}{840 c^4}-\frac{b e^2 x^5 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{42 c^2}",1,"-(b*(280*c^4*d^2 + 252*c^2*d*e + 75*e^2)*x*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(1680*c^6) - (b*e*(84*c^2*d + 25*e)*x^3*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(840*c^4) - (b*e^2*x^5*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(42*c^2) + (d^2*x^3*(a + b*ArcSech[c*x]))/3 + (2*d*e*x^5*(a + b*ArcSech[c*x]))/5 + (e^2*x^7*(a + b*ArcSech[c*x]))/7 + (b*(280*c^4*d^2 + 252*c^2*d*e + 75*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/(1680*c^7)","A",6,7,21,0.3333,1,"{270, 6301, 12, 1267, 459, 321, 216}"
101,1,204,0,0.1268563,"\int \left(d+e x^2\right)^2 \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^2*(a + b*ArcSech[c*x]),x]","d^2 x \left(a+b \text{sech}^{-1}(c x)\right)+\frac{2}{3} d e x^3 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(120 c^4 d^2+40 c^2 d e+9 e^2\right) \sin ^{-1}(c x)}{120 c^5}-\frac{b e x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(40 c^2 d+9 e\right)}{120 c^4}-\frac{b e^2 x^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{20 c^2}","d^2 x \left(a+b \text{sech}^{-1}(c x)\right)+\frac{2}{3} d e x^3 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(120 c^4 d^2+40 c^2 d e+9 e^2\right) \sin ^{-1}(c x)}{120 c^5}-\frac{b e x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(40 c^2 d+9 e\right)}{120 c^4}-\frac{b e^2 x^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{20 c^2}",1,"-(b*e*(40*c^2*d + 9*e)*x*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(120*c^4) - (b*e^2*x^3*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(20*c^2) + d^2*x*(a + b*ArcSech[c*x]) + (2*d*e*x^3*(a + b*ArcSech[c*x]))/3 + (e^2*x^5*(a + b*ArcSech[c*x]))/5 + (b*(120*c^4*d^2 + 40*c^2*d*e + 9*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/(120*c^5)","A",5,6,18,0.3333,1,"{194, 6291, 12, 1159, 388, 216}"
102,1,177,0,0.1315604,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \text{sech}^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSech[c*x]))/x^2,x]","-\frac{d^2 \left(a+b \text{sech}^{-1}(c x)\right)}{x}+2 d e x \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{3} e^2 x^3 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{b d^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{x}+\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(12 c^2 d+e\right) \sin ^{-1}(c x)}{6 c^3}-\frac{b e^2 x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{6 c^2}","-\frac{d^2 \left(a+b \text{sech}^{-1}(c x)\right)}{x}+2 d e x \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{3} e^2 x^3 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{b d^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{x}+\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(12 c^2 d+e\right) \sin ^{-1}(c x)}{6 c^3}-\frac{b e^2 x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{6 c^2}",1,"(b*d^2*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/x - (b*e^2*x*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(6*c^2) - (d^2*(a + b*ArcSech[c*x]))/x + 2*d*e*x*(a + b*ArcSech[c*x]) + (e^2*x^3*(a + b*ArcSech[c*x]))/3 + (b*e*(12*c^2*d + e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/(6*c^3)","A",5,6,21,0.2857,1,"{270, 6301, 12, 1265, 388, 216}"
103,1,176,0,0.1389949,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \text{sech}^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSech[c*x]))/x^4,x]","-\frac{d^2 \left(a+b \text{sech}^{-1}(c x)\right)}{3 x^3}-\frac{2 d e \left(a+b \text{sech}^{-1}(c x)\right)}{x}+e^2 x \left(a+b \text{sech}^{-1}(c x)\right)+\frac{b d^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{9 x^3}+\frac{2 b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(c^2 d+9 e\right)}{9 x}+\frac{b e^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{c}","-\frac{d^2 \left(a+b \text{sech}^{-1}(c x)\right)}{3 x^3}-\frac{2 d e \left(a+b \text{sech}^{-1}(c x)\right)}{x}+e^2 x \left(a+b \text{sech}^{-1}(c x)\right)+\frac{b d^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{9 x^3}+\frac{2 b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(c^2 d+9 e\right)}{9 x}+\frac{b e^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sin ^{-1}(c x)}{c}",1,"(b*d^2*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(9*x^3) + (2*b*d*(c^2*d + 9*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(9*x) - (d^2*(a + b*ArcSech[c*x]))/(3*x^3) - (2*d*e*(a + b*ArcSech[c*x]))/x + e^2*x*(a + b*ArcSech[c*x]) + (b*e^2*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcSin[c*x])/c","A",5,6,21,0.2857,1,"{270, 6301, 12, 1265, 451, 216}"
104,1,213,0,0.1667137,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \text{sech}^{-1}(c x)\right)}{x^6} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSech[c*x]))/x^6,x]","-\frac{d^2 \left(a+b \text{sech}^{-1}(c x)\right)}{5 x^5}-\frac{2 d e \left(a+b \text{sech}^{-1}(c x)\right)}{3 x^3}-\frac{e^2 \left(a+b \text{sech}^{-1}(c x)\right)}{x}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(24 c^4 d^2+100 c^2 d e+225 e^2\right)}{225 x}+\frac{b d^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{25 x^5}+\frac{2 b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(6 c^2 d+25 e\right)}{225 x^3}","-\frac{d^2 \left(a+b \text{sech}^{-1}(c x)\right)}{5 x^5}-\frac{2 d e \left(a+b \text{sech}^{-1}(c x)\right)}{3 x^3}-\frac{e^2 \left(a+b \text{sech}^{-1}(c x)\right)}{x}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(24 c^4 d^2+100 c^2 d e+225 e^2\right)}{225 x}+\frac{b d^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{25 x^5}+\frac{2 b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(6 c^2 d+25 e\right)}{225 x^3}",1,"(b*d^2*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(25*x^5) + (2*b*d*(6*c^2*d + 25*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(225*x^3) + (b*(24*c^4*d^2 + 100*c^2*d*e + 225*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(225*x) - (d^2*(a + b*ArcSech[c*x]))/(5*x^5) - (2*d*e*(a + b*ArcSech[c*x]))/(3*x^3) - (e^2*(a + b*ArcSech[c*x]))/x","A",5,6,21,0.2857,1,"{270, 6301, 12, 1265, 453, 264}"
105,1,281,0,0.200737,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \text{sech}^{-1}(c x)\right)}{x^8} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSech[c*x]))/x^8,x]","-\frac{d^2 \left(a+b \text{sech}^{-1}(c x)\right)}{7 x^7}-\frac{2 d e \left(a+b \text{sech}^{-1}(c x)\right)}{5 x^5}-\frac{e^2 \left(a+b \text{sech}^{-1}(c x)\right)}{3 x^3}+\frac{2 b c^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(360 c^4 d^2+1176 c^2 d e+1225 e^2\right)}{11025 x}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(360 c^4 d^2+1176 c^2 d e+1225 e^2\right)}{11025 x^3}+\frac{b d^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{49 x^7}+\frac{2 b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(15 c^2 d+49 e\right)}{1225 x^5}","-\frac{d^2 \left(a+b \text{sech}^{-1}(c x)\right)}{7 x^7}-\frac{2 d e \left(a+b \text{sech}^{-1}(c x)\right)}{5 x^5}-\frac{e^2 \left(a+b \text{sech}^{-1}(c x)\right)}{3 x^3}+\frac{2 b c^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(360 c^4 d^2+1176 c^2 d e+1225 e^2\right)}{11025 x}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(360 c^4 d^2+1176 c^2 d e+1225 e^2\right)}{11025 x^3}+\frac{b d^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{49 x^7}+\frac{2 b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(15 c^2 d+49 e\right)}{1225 x^5}",1,"(b*d^2*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(49*x^7) + (2*b*d*(15*c^2*d + 49*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(1225*x^5) + (b*(360*c^4*d^2 + 1176*c^2*d*e + 1225*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(11025*x^3) + (2*b*c^2*(360*c^4*d^2 + 1176*c^2*d*e + 1225*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(11025*x) - (d^2*(a + b*ArcSech[c*x]))/(7*x^7) - (2*d*e*(a + b*ArcSech[c*x]))/(5*x^5) - (e^2*(a + b*ArcSech[c*x]))/(3*x^3)","A",6,7,21,0.3333,1,"{270, 6301, 12, 1265, 453, 271, 264}"
106,1,278,0,0.237377,"\int x^3 \left(d+e x^2\right)^2 \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)^2*(a + b*ArcSech[c*x]),x]","\frac{1}{4} d^2 x^4 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{3} d e x^6 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{8} e^2 x^8 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2} \left(6 c^4 d^2+16 c^2 d e+9 e^2\right)}{72 c^8}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(6 c^4 d^2+8 c^2 d e+3 e^2\right)}{24 c^8}-\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{5/2} \left(8 c^2 d+9 e\right)}{120 c^8}+\frac{b e^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{7/2}}{56 c^8}","\frac{1}{4} d^2 x^4 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{3} d e x^6 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{8} e^2 x^8 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2} \left(6 c^4 d^2+16 c^2 d e+9 e^2\right)}{72 c^8}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(6 c^4 d^2+8 c^2 d e+3 e^2\right)}{24 c^8}-\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{5/2} \left(8 c^2 d+9 e\right)}{120 c^8}+\frac{b e^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{7/2}}{56 c^8}",1,"-(b*(6*c^4*d^2 + 8*c^2*d*e + 3*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(24*c^8) + (b*(6*c^4*d^2 + 16*c^2*d*e + 9*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*(1 - c^2*x^2)^(3/2))/(72*c^8) - (b*e*(8*c^2*d + 9*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*(1 - c^2*x^2)^(5/2))/(120*c^8) + (b*e^2*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*(1 - c^2*x^2)^(7/2))/(56*c^8) + (d^2*x^4*(a + b*ArcSech[c*x]))/4 + (d*e*x^6*(a + b*ArcSech[c*x]))/3 + (e^2*x^8*(a + b*ArcSech[c*x]))/8","A",5,6,21,0.2857,1,"{266, 43, 6301, 12, 1251, 771}"
107,1,230,0,0.252243,"\int x \left(d+e x^2\right)^2 \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)^2*(a + b*ArcSech[c*x]),x]","\frac{\left(d+e x^2\right)^3 \left(a+b \text{sech}^{-1}(c x)\right)}{6 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(3 c^4 d^2+3 c^2 d e+e^2\right)}{6 c^6}-\frac{b d^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{6 e}+\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2} \left(3 c^2 d+2 e\right)}{18 c^6}-\frac{b e^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{5/2}}{30 c^6}","\frac{\left(d+e x^2\right)^3 \left(a+b \text{sech}^{-1}(c x)\right)}{6 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(3 c^4 d^2+3 c^2 d e+e^2\right)}{6 c^6}-\frac{b d^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{6 e}+\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2} \left(3 c^2 d+2 e\right)}{18 c^6}-\frac{b e^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(1-c^2 x^2\right)^{5/2}}{30 c^6}",1,"-(b*(3*c^4*d^2 + 3*c^2*d*e + e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(6*c^6) + (b*e*(3*c^2*d + 2*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*(1 - c^2*x^2)^(3/2))/(18*c^6) - (b*e^2*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*(1 - c^2*x^2)^(5/2))/(30*c^6) + ((d + e*x^2)^3*(a + b*ArcSech[c*x]))/(6*e) - (b*d^3*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[1 - c^2*x^2]])/(6*e)","A",7,6,19,0.3158,1,"{6299, 517, 446, 88, 63, 208}"
108,1,370,0,1.0977586,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \text{sech}^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSech[c*x]))/x,x]","\frac{i b d^2 \sqrt{1-\frac{1}{c^2 x^2}} \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-d^2 \log \left(\frac{1}{x}\right) \left(a+b \text{sech}^{-1}(c x)\right)+d e x^2 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{4} e^2 x^4 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{i b d^2 \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x)^2}{2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{b d^2 \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b d^2 \sqrt{1-\frac{1}{c^2 x^2}} \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{b e x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \left(6 c^2 d+e\right)}{6 c^3}-\frac{b e^2 x^3 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}{12 c}","\frac{i b d^2 \sqrt{1-\frac{1}{c^2 x^2}} \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-d^2 \log \left(\frac{1}{x}\right) \left(a+b \text{sech}^{-1}(c x)\right)+d e x^2 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{4} e^2 x^4 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{i b d^2 \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x)^2}{2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{b d^2 \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b d^2 \sqrt{1-\frac{1}{c^2 x^2}} \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{b e x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \left(6 c^2 d+e\right)}{6 c^3}-\frac{b e^2 x^3 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}{12 c}",1,"-(b*e*(6*c^2*d + e)*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x)/(6*c^3) - (b*e^2*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x^3)/(12*c) + ((I/2)*b*d^2*Sqrt[1 - 1/(c^2*x^2)]*ArcCsc[c*x]^2)/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) + d*e*x^2*(a + b*ArcSech[c*x]) + (e^2*x^4*(a + b*ArcSech[c*x]))/4 - (b*d^2*Sqrt[1 - 1/(c^2*x^2)]*ArcCsc[c*x]*Log[1 - E^((2*I)*ArcCsc[c*x])])/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) + (b*d^2*Sqrt[1 - 1/(c^2*x^2)]*ArcCsc[c*x]*Log[x^(-1)])/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) - d^2*(a + b*ArcSech[c*x])*Log[x^(-1)] + ((I/2)*b*d^2*Sqrt[1 - 1/(c^2*x^2)]*PolyLog[2, E^((2*I)*ArcCsc[c*x])])/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)])","A",13,14,21,0.6667,1,"{6303, 266, 43, 5790, 6742, 454, 95, 2328, 2326, 4625, 3717, 2190, 2279, 2391}"
109,1,373,0,1.047492,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \text{sech}^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSech[c*x]))/x^3,x]","\frac{i b d e \sqrt{1-\frac{1}{c^2 x^2}} \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{d^2 \left(a+b \text{sech}^{-1}(c x)\right)}{2 x^2}-2 d e \log \left(\frac{1}{x}\right) \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{2} e^2 x^2 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{4} b c^2 d^2 \text{sech}^{-1}(c x)+\frac{i b d e \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x)^2}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{2 b d e \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{2 b d e \sqrt{1-\frac{1}{c^2 x^2}} \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b c d^2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}{4 x}-\frac{b e^2 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}{2 c}","\frac{i b d e \sqrt{1-\frac{1}{c^2 x^2}} \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{d^2 \left(a+b \text{sech}^{-1}(c x)\right)}{2 x^2}-2 d e \log \left(\frac{1}{x}\right) \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{2} e^2 x^2 \left(a+b \text{sech}^{-1}(c x)\right)+\frac{1}{4} b c^2 d^2 \text{sech}^{-1}(c x)+\frac{i b d e \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x)^2}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{2 b d e \sqrt{1-\frac{1}{c^2 x^2}} \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{2 b d e \sqrt{1-\frac{1}{c^2 x^2}} \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)}{\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b c d^2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}{4 x}-\frac{b e^2 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}{2 c}",1,"(b*c*d^2*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)])/(4*x) - (b*e^2*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x)/(2*c) + (I*b*d*e*Sqrt[1 - 1/(c^2*x^2)]*ArcCsc[c*x]^2)/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) + (b*c^2*d^2*ArcSech[c*x])/4 - (d^2*(a + b*ArcSech[c*x]))/(2*x^2) + (e^2*x^2*(a + b*ArcSech[c*x]))/2 - (2*b*d*e*Sqrt[1 - 1/(c^2*x^2)]*ArcCsc[c*x]*Log[1 - E^((2*I)*ArcCsc[c*x])])/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) + (2*b*d*e*Sqrt[1 - 1/(c^2*x^2)]*ArcCsc[c*x]*Log[x^(-1)])/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) - 2*d*e*(a + b*ArcSech[c*x])*Log[x^(-1)] + (I*b*d*e*Sqrt[1 - 1/(c^2*x^2)]*PolyLog[2, E^((2*I)*ArcCsc[c*x])])/(Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)])","A",15,16,21,0.7619,1,"{6303, 266, 43, 5790, 12, 6742, 95, 90, 52, 2328, 2326, 4625, 3717, 2190, 2279, 2391}"
110,1,519,0,1.2733032,"\int \frac{x^2 \left(a+b \text{sech}^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x^2*(a + b*ArcSech[c*x]))/(d + e*x^2),x]","-\frac{b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}+\frac{b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}-\frac{b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 e^{3/2}}+\frac{x \left(a+b \text{sech}^{-1}(c x)\right)}{e}-\frac{b \tan ^{-1}\left(\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}\right)}{c e}","-\frac{b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}+\frac{b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}-\frac{b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 e^{3/2}}+\frac{x \left(a+b \text{sech}^{-1}(c x)\right)}{e}-\frac{b \tan ^{-1}\left(\sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}\right)}{c e}",1,"(x*(a + b*ArcSech[c*x]))/e - (b*ArcTan[Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]])/(c*e) + (Sqrt[-d]*(a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^(3/2)) - (Sqrt[-d]*(a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^(3/2)) + (Sqrt[-d]*(a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^(3/2)) - (Sqrt[-d]*(a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^(3/2)) - (b*Sqrt[-d]*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(2*e^(3/2)) + (b*Sqrt[-d]*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^(3/2)) - (b*Sqrt[-d]*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(2*e^(3/2)) + (b*Sqrt[-d]*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^(3/2))","A",24,11,21,0.5238,1,"{6303, 5792, 5662, 92, 205, 5707, 5800, 5562, 2190, 2279, 2391}"
111,1,441,0,1.2288866,"\int \frac{x \left(a+b \text{sech}^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x*(a + b*ArcSech[c*x]))/(d + e*x^2),x]","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}-\frac{b \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 e}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 e}-\frac{\log \left(e^{2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{e}","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,-e^{-2 \text{sech}^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 e}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 e}-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{b e}-\frac{\log \left(e^{-2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{e}",1,"((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e) + ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e) + ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e) + ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e) - ((a + b*ArcSech[c*x])*Log[1 + E^(2*ArcSech[c*x])])/e + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(2*e) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e) + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(2*e) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e) - (b*PolyLog[2, -E^(2*ArcSech[c*x])])/(2*e)","A",26,9,19,0.4737,0,"{6303, 5792, 5660, 3718, 2190, 2279, 2391, 5800, 5562}"
112,1,469,0,0.966431,"\int \frac{a+b \text{sech}^{-1}(c x)}{d+e x^2} \, dx","Int[(a + b*ArcSech[c*x])/(d + e*x^2),x]","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 \sqrt{-d} \sqrt{e}}","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 \sqrt{-d} \sqrt{e}}",1,"((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) + ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(2*Sqrt[-d]*Sqrt[e]) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(2*Sqrt[-d]*Sqrt[e]) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e])","A",19,7,18,0.3889,1,"{6293, 5707, 5800, 5562, 2190, 2279, 2391}"
113,1,417,0,0.9892922,"\int \frac{a+b \text{sech}^{-1}(c x)}{x \left(d+e x^2\right)} \, dx","Int[(a + b*ArcSech[c*x])/(x*(d + e*x^2)),x]","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 d}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 d}+\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{2 b d}","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 d}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 d}+\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{2 b d}",1,"(a + b*ArcSech[c*x])^2/(2*b*d) - ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d) - ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d) - ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d) - ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(2*d) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(2*d) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d)","A",19,7,21,0.3333,1,"{6303, 5792, 5800, 5562, 2190, 2279, 2391}"
114,1,523,0,1.2610262,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^2 \left(d+e x^2\right)} \, dx","Int[(a + b*ArcSech[c*x])/(x^2*(d + e*x^2)),x]","-\frac{b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}+\frac{b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}-\frac{b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}+\frac{b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 (-d)^{3/2}}-\frac{a}{d x}+\frac{b c \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}{d}-\frac{b \text{sech}^{-1}(c x)}{d x}","-\frac{b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}+\frac{b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}-\frac{b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}+\frac{b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 (-d)^{3/2}}-\frac{a}{d x}+\frac{b c \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}{d}-\frac{b \text{sech}^{-1}(c x)}{d x}",1,"(b*c*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)])/d - a/(d*x) - (b*ArcSech[c*x])/(d*x) + (Sqrt[e]*(a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) - (Sqrt[e]*(a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) + (Sqrt[e]*(a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) - (Sqrt[e]*(a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) - (b*Sqrt[e]*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(2*(-d)^(3/2)) + (b*Sqrt[e]*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) - (b*Sqrt[e]*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(2*(-d)^(3/2)) + (b*Sqrt[e]*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*(-d)^(3/2))","A",24,10,21,0.4762,1,"{6303, 5792, 5654, 74, 5707, 5800, 5562, 2190, 2279, 2391}"
115,1,611,0,1.5479411,"\int \frac{x^5 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^5*(a + b*ArcSech[c*x]))/(d + e*x^2)^2,x]","-\frac{b d \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}-\frac{b d \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}-\frac{b d \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}-\frac{b d \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}+\frac{b d \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(c x)}\right)}{e^3}-\frac{d \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}-\frac{d \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{e^3}-\frac{d \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}-\frac{d \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{e^3}+\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{2 e^2 \left(\frac{d}{x^2}+e\right)}+\frac{2 d \log \left(e^{2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{e^3}+\frac{x^2 \left(a+b \text{sech}^{-1}(c x)\right)}{2 e^2}-\frac{b d \sqrt{\frac{1}{c^2 x^2}-1} \tanh ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}-1}}\right)}{2 e^{5/2} \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \sqrt{c^2 d+e}}-\frac{b x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}{2 c e^2}","-\frac{b d \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}-\frac{b d \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}-\frac{b d \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}-\frac{b d \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}-\frac{b d \text{PolyLog}\left(2,-e^{-2 \text{sech}^{-1}(c x)}\right)}{e^3}-\frac{d \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}-\frac{d \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{e^3}-\frac{d \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}-\frac{d \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{e^3}+\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{2 e^2 \left(\frac{d}{x^2}+e\right)}+\frac{2 d \left(a+b \text{sech}^{-1}(c x)\right)^2}{b e^3}+\frac{2 d \log \left(e^{-2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{e^3}+\frac{x^2 \left(a+b \text{sech}^{-1}(c x)\right)}{2 e^2}-\frac{b d \sqrt{\frac{1}{c^2 x^2}-1} \tanh ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}-1}}\right)}{2 e^{5/2} \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \sqrt{c^2 d+e}}-\frac{b x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}{2 c e^2}",1,"-(b*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x)/(2*c*e^2) + (d*(a + b*ArcSech[c*x]))/(2*e^2*(e + d/x^2)) + (x^2*(a + b*ArcSech[c*x]))/(2*e^2) - (b*d*Sqrt[-1 + 1/(c^2*x^2)]*ArcTanh[Sqrt[c^2*d + e]/(c*Sqrt[e]*Sqrt[-1 + 1/(c^2*x^2)]*x)])/(2*e^(5/2)*Sqrt[c^2*d + e]*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) - (d*(a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/e^3 - (d*(a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/e^3 - (d*(a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/e^3 - (d*(a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/e^3 + (2*d*(a + b*ArcSech[c*x])*Log[1 + E^(2*ArcSech[c*x])])/e^3 - (b*d*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/e^3 - (b*d*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/e^3 - (b*d*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/e^3 - (b*d*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/e^3 + (b*d*PolyLog[2, -E^(2*ArcSech[c*x])])/e^3","A",32,15,21,0.7143,0,"{6303, 5792, 5662, 95, 5660, 3718, 2190, 2279, 2391, 5788, 519, 377, 208, 5800, 5562}"
116,1,562,0,1.4633122,"\int \frac{x^3 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^3*(a + b*ArcSech[c*x]))/(d + e*x^2)^2,x]","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}-\frac{b \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(c x)}\right)}{2 e^2}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 e^2}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 e^2}-\frac{a+b \text{sech}^{-1}(c x)}{2 e \left(\frac{d}{x^2}+e\right)}-\frac{\log \left(e^{2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{e^2}+\frac{b \sqrt{\frac{1}{c^2 x^2}-1} \tanh ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}-1}}\right)}{2 e^{3/2} \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \sqrt{c^2 d+e}}","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,-e^{-2 \text{sech}^{-1}(c x)}\right)}{2 e^2}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 e^2}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 e^2}-\frac{a+b \text{sech}^{-1}(c x)}{2 e \left(\frac{d}{x^2}+e\right)}-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{b e^2}-\frac{\log \left(e^{-2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{e^2}+\frac{b \sqrt{\frac{1}{c^2 x^2}-1} \tanh ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}-1}}\right)}{2 e^{3/2} \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \sqrt{c^2 d+e}}",1,"-(a + b*ArcSech[c*x])/(2*e*(e + d/x^2)) + (b*Sqrt[-1 + 1/(c^2*x^2)]*ArcTanh[Sqrt[c^2*d + e]/(c*Sqrt[e]*Sqrt[-1 + 1/(c^2*x^2)]*x)])/(2*e^(3/2)*Sqrt[c^2*d + e]*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) + ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^2) + ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^2) + ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^2) + ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^2) - ((a + b*ArcSech[c*x])*Log[1 + E^(2*ArcSech[c*x])])/e^2 + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(2*e^2) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^2) + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(2*e^2) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^2) - (b*PolyLog[2, -E^(2*ArcSech[c*x])])/(2*e^2)","A",30,13,21,0.6190,0,"{6303, 5792, 5660, 3718, 2190, 2279, 2391, 5788, 519, 377, 208, 5800, 5562}"
117,1,147,0,0.2446746,"\int \frac{x \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x*(a + b*ArcSech[c*x]))/(d + e*x^2)^2,x]","-\frac{a+b \text{sech}^{-1}(c x)}{2 e \left(d+e x^2\right)}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{2 d e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{\sqrt{c^2 d+e}}\right)}{2 d \sqrt{e} \sqrt{c^2 d+e}}","-\frac{a+b \text{sech}^{-1}(c x)}{2 e \left(d+e x^2\right)}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{2 d e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{\sqrt{c^2 d+e}}\right)}{2 d \sqrt{e} \sqrt{c^2 d+e}}",1,"-(a + b*ArcSech[c*x])/(2*e*(d + e*x^2)) + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[1 - c^2*x^2]])/(2*d*e) - (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[(Sqrt[e]*Sqrt[1 - c^2*x^2])/Sqrt[c^2*d + e]])/(2*d*Sqrt[e]*Sqrt[c^2*d + e])","A",8,6,19,0.3158,1,"{6299, 517, 446, 86, 63, 208}"
118,1,542,0,1.3628793,"\int \frac{a+b \text{sech}^{-1}(c x)}{x \left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcSech[c*x])/(x*(d + e*x^2)^2),x]","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 d^2}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 d^2}-\frac{e \left(a+b \text{sech}^{-1}(c x)\right)}{2 d^2 \left(\frac{d}{x^2}+e\right)}+\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{2 b d^2}+\frac{b \sqrt{e} \sqrt{\frac{1}{c^2 x^2}-1} \tanh ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}-1}}\right)}{2 d^2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \sqrt{c^2 d+e}}","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 d^2}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 d^2}-\frac{e \left(a+b \text{sech}^{-1}(c x)\right)}{2 d^2 \left(\frac{d}{x^2}+e\right)}+\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{2 b d^2}+\frac{b \sqrt{e} \sqrt{\frac{1}{c^2 x^2}-1} \tanh ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}-1}}\right)}{2 d^2 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \sqrt{c^2 d+e}}",1,"-(e*(a + b*ArcSech[c*x]))/(2*d^2*(e + d/x^2)) + (a + b*ArcSech[c*x])^2/(2*b*d^2) + (b*Sqrt[e]*Sqrt[-1 + 1/(c^2*x^2)]*ArcTanh[Sqrt[c^2*d + e]/(c*Sqrt[e]*Sqrt[-1 + 1/(c^2*x^2)]*x)])/(2*d^2*Sqrt[c^2*d + e]*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) - ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d^2) - ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d^2) - ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d^2) - ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d^2) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(2*d^2) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d^2) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(2*d^2) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d^2)","A",25,11,21,0.5238,1,"{6303, 5792, 5788, 519, 377, 208, 5800, 5562, 2190, 2279, 2391}"
119,1,840,0,3.0878631,"\int \frac{x^4 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^4*(a + b*ArcSech[c*x]))/(d + e*x^2)^2,x]","\frac{x \left(a+b \text{sech}^{-1}(c x)\right)}{e^2}+\frac{3 \sqrt{-d} \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{4 e^{5/2}}-\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{4 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{4 e^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{b d \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{2 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}} e^2}+\frac{b d \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{2 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}} e^2}-\frac{b \tan ^{-1}\left(\sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}}\right)}{c e^2}-\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 e^{5/2}}+\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 e^{5/2}}-\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 e^{5/2}}+\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 e^{5/2}}","\frac{x \left(a+b \text{sech}^{-1}(c x)\right)}{e^2}+\frac{3 \sqrt{-d} \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right) \left(a+b \text{sech}^{-1}(c x)\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{4 e^{5/2}}-\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{4 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{4 e^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{b d \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{2 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}} e^2}+\frac{b d \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{2 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}} e^2}-\frac{b \tan ^{-1}\left(\sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}}\right)}{c e^2}-\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 e^{5/2}}+\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 e^{5/2}}-\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 e^{5/2}}+\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 e^{5/2}}",1,"-(d*(a + b*ArcSech[c*x]))/(4*e^2*(Sqrt[-d]*Sqrt[e] - d/x)) + (d*(a + b*ArcSech[c*x]))/(4*e^2*(Sqrt[-d]*Sqrt[e] + d/x)) + (x*(a + b*ArcSech[c*x]))/e^2 + (b*d*ArcTan[(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(2*Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*e^2) + (b*d*ArcTan[(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(2*Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*e^2) - (b*ArcTan[Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]])/(c*e^2) + (3*Sqrt[-d]*(a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*e^(5/2)) - (3*Sqrt[-d]*(a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*e^(5/2)) + (3*Sqrt[-d]*(a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*e^(5/2)) - (3*Sqrt[-d]*(a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*e^(5/2)) - (3*b*Sqrt[-d]*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(4*e^(5/2)) + (3*b*Sqrt[-d]*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*e^(5/2)) - (3*b*Sqrt[-d]*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(4*e^(5/2)) + (3*b*Sqrt[-d]*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*e^(5/2))","A",50,13,21,0.6190,1,"{6303, 5792, 5662, 92, 205, 5707, 5802, 93, 5800, 5562, 2190, 2279, 2391}"
120,1,786,0,1.5743687,"\int \frac{x^2 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^2*(a + b*ArcSech[c*x]))/(d + e*x^2)^2,x]","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{4 \sqrt{-d} e^{3/2}}+\frac{a+b \text{sech}^{-1}(c x)}{4 e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \text{sech}^{-1}(c x)}{4 e \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}-\frac{b \tan ^{-1}\left(\frac{\sqrt{\frac{1}{c x}+1} \sqrt{c d-\sqrt{-d} \sqrt{e}}}{\sqrt{\frac{1}{c x}-1} \sqrt{c d+\sqrt{-d} \sqrt{e}}}\right)}{2 e \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}-\frac{b \tan ^{-1}\left(\frac{\sqrt{\frac{1}{c x}+1} \sqrt{c d+\sqrt{-d} \sqrt{e}}}{\sqrt{\frac{1}{c x}-1} \sqrt{c d-\sqrt{-d} \sqrt{e}}}\right)}{2 e \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{4 \sqrt{-d} e^{3/2}}+\frac{a+b \text{sech}^{-1}(c x)}{4 e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \text{sech}^{-1}(c x)}{4 e \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}-\frac{b \tan ^{-1}\left(\frac{\sqrt{\frac{1}{c x}+1} \sqrt{c d-\sqrt{-d} \sqrt{e}}}{\sqrt{\frac{1}{c x}-1} \sqrt{c d+\sqrt{-d} \sqrt{e}}}\right)}{2 e \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}-\frac{b \tan ^{-1}\left(\frac{\sqrt{\frac{1}{c x}+1} \sqrt{c d+\sqrt{-d} \sqrt{e}}}{\sqrt{\frac{1}{c x}-1} \sqrt{c d-\sqrt{-d} \sqrt{e}}}\right)}{2 e \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}",1,"(a + b*ArcSech[c*x])/(4*e*(Sqrt[-d]*Sqrt[e] - d/x)) - (a + b*ArcSech[c*x])/(4*e*(Sqrt[-d]*Sqrt[e] + d/x)) - (b*ArcTan[(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(2*Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*e) - (b*ArcTan[(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(2*Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*e) + ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) - ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) + ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) - ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(4*Sqrt[-d]*e^(3/2)) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(4*Sqrt[-d]*e^(3/2)) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2))","A",27,10,21,0.4762,1,"{6303, 5707, 5802, 93, 205, 5800, 5562, 2190, 2279, 2391}"
121,1,786,0,2.8359078,"\int \frac{a+b \text{sech}^{-1}(c x)}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcSech[c*x])/(d + e*x^2)^2,x]","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{a+b \text{sech}^{-1}(c x)}{4 d \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{a+b \text{sech}^{-1}(c x)}{4 d \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}+\frac{b \tan ^{-1}\left(\frac{\sqrt{\frac{1}{c x}+1} \sqrt{c d-\sqrt{-d} \sqrt{e}}}{\sqrt{\frac{1}{c x}-1} \sqrt{c d+\sqrt{-d} \sqrt{e}}}\right)}{2 d \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}+\frac{b \tan ^{-1}\left(\frac{\sqrt{\frac{1}{c x}+1} \sqrt{c d+\sqrt{-d} \sqrt{e}}}{\sqrt{\frac{1}{c x}-1} \sqrt{c d-\sqrt{-d} \sqrt{e}}}\right)}{2 d \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{a+b \text{sech}^{-1}(c x)}{4 d \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{a+b \text{sech}^{-1}(c x)}{4 d \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}+\frac{b \tan ^{-1}\left(\frac{\sqrt{\frac{1}{c x}+1} \sqrt{c d-\sqrt{-d} \sqrt{e}}}{\sqrt{\frac{1}{c x}-1} \sqrt{c d+\sqrt{-d} \sqrt{e}}}\right)}{2 d \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}+\frac{b \tan ^{-1}\left(\frac{\sqrt{\frac{1}{c x}+1} \sqrt{c d+\sqrt{-d} \sqrt{e}}}{\sqrt{\frac{1}{c x}-1} \sqrt{c d-\sqrt{-d} \sqrt{e}}}\right)}{2 d \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}",1,"-(a + b*ArcSech[c*x])/(4*d*(Sqrt[-d]*Sqrt[e] - d/x)) + (a + b*ArcSech[c*x])/(4*d*(Sqrt[-d]*Sqrt[e] + d/x)) + (b*ArcTan[(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(2*d*Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[c*d + Sqrt[-d]*Sqrt[e]]) + (b*ArcTan[(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(2*d*Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[c*d + Sqrt[-d]*Sqrt[e]]) - ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) + ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) - ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) + ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(4*(-d)^(3/2)*Sqrt[e]) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(4*(-d)^(3/2)*Sqrt[e]) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e])","A",47,11,18,0.6111,1,"{6293, 5792, 5707, 5802, 93, 205, 5800, 5562, 2190, 2279, 2391}"
122,1,844,0,2.952631,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^2 \left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcSech[c*x])/(x^2*(d + e*x^2)^2),x]","-\frac{a}{d^2 x}-\frac{b \text{sech}^{-1}(c x)}{d^2 x}+\frac{e \left(a+b \text{sech}^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{e \left(a+b \text{sech}^{-1}(c x)\right)}{4 d^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}-\frac{b e \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{2 d^2 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}-\frac{b e \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{2 d^2 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}-\frac{3 \sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{4 (-d)^{5/2}}+\frac{3 b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{3 b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}+\frac{3 b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{3 b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}+\frac{b c \sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}}}{d^2}","-\frac{a}{d^2 x}-\frac{b \text{sech}^{-1}(c x)}{d^2 x}+\frac{e \left(a+b \text{sech}^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{e \left(a+b \text{sech}^{-1}(c x)\right)}{4 d^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}-\frac{b e \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{2 d^2 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}-\frac{b e \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{2 d^2 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}-\frac{3 \sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{4 (-d)^{5/2}}+\frac{3 b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{3 b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}+\frac{3 b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{3 b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}+\frac{b c \sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}}}{d^2}",1,"(b*c*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)])/d^2 - a/(d^2*x) - (b*ArcSech[c*x])/(d^2*x) + (e*(a + b*ArcSech[c*x]))/(4*d^2*(Sqrt[-d]*Sqrt[e] - d/x)) - (e*(a + b*ArcSech[c*x]))/(4*d^2*(Sqrt[-d]*Sqrt[e] + d/x)) - (b*e*ArcTan[(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(2*d^2*Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[c*d + Sqrt[-d]*Sqrt[e]]) - (b*e*ArcTan[(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(2*d^2*Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[c*d + Sqrt[-d]*Sqrt[e]]) - (3*Sqrt[e]*(a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) + (3*Sqrt[e]*(a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) - (3*Sqrt[e]*(a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) + (3*Sqrt[e]*(a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) + (3*b*Sqrt[e]*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(4*(-d)^(5/2)) - (3*b*Sqrt[e]*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) + (3*b*Sqrt[e]*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(4*(-d)^(5/2)) - (3*b*Sqrt[e]*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*(-d)^(5/2))","A",50,13,21,0.6190,1,"{6303, 5792, 5654, 74, 5707, 5802, 93, 205, 5800, 5562, 2190, 2279, 2391}"
123,1,760,0,1.7093531,"\int \frac{x^5 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^5*(a + b*ArcSech[c*x]))/(d + e*x^2)^3,x]","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}-\frac{b \text{PolyLog}\left(2,-e^{2 \text{sech}^{-1}(c x)}\right)}{2 e^3}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 e^3}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 e^3}-\frac{a+b \text{sech}^{-1}(c x)}{2 e^2 \left(\frac{d}{x^2}+e\right)}-\frac{a+b \text{sech}^{-1}(c x)}{4 e \left(\frac{d}{x^2}+e\right)^2}-\frac{\log \left(e^{2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{e^3}+\frac{b d \left(c^2-\frac{1}{x^2}\right)}{8 c e^2 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \left(c^2 d+e\right) \left(\frac{d}{x^2}+e\right)}+\frac{b \sqrt{\frac{1}{c^2 x^2}-1} \left(c^2 d+2 e\right) \tanh ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}-1}}\right)}{8 e^{5/2} \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \left(c^2 d+e\right)^{3/2}}+\frac{b \sqrt{\frac{1}{c^2 x^2}-1} \tanh ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}-1}}\right)}{2 e^{5/2} \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \sqrt{c^2 d+e}}","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,-e^{-2 \text{sech}^{-1}(c x)}\right)}{2 e^3}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 e^3}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 e^3}-\frac{a+b \text{sech}^{-1}(c x)}{2 e^2 \left(\frac{d}{x^2}+e\right)}-\frac{a+b \text{sech}^{-1}(c x)}{4 e \left(\frac{d}{x^2}+e\right)^2}-\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{b e^3}-\frac{\log \left(e^{-2 \text{sech}^{-1}(c x)}+1\right) \left(a+b \text{sech}^{-1}(c x)\right)}{e^3}+\frac{b d \left(c^2-\frac{1}{x^2}\right)}{8 c e^2 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \left(c^2 d+e\right) \left(\frac{d}{x^2}+e\right)}+\frac{b \sqrt{\frac{1}{c^2 x^2}-1} \left(c^2 d+2 e\right) \tanh ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}-1}}\right)}{8 e^{5/2} \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \left(c^2 d+e\right)^{3/2}}+\frac{b \sqrt{\frac{1}{c^2 x^2}-1} \tanh ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}-1}}\right)}{2 e^{5/2} \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \sqrt{c^2 d+e}}",1,"(b*d*(c^2 - x^(-2)))/(8*c*e^2*(c^2*d + e)*(e + d/x^2)*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x) - (a + b*ArcSech[c*x])/(4*e*(e + d/x^2)^2) - (a + b*ArcSech[c*x])/(2*e^2*(e + d/x^2)) + (b*Sqrt[-1 + 1/(c^2*x^2)]*ArcTanh[Sqrt[c^2*d + e]/(c*Sqrt[e]*Sqrt[-1 + 1/(c^2*x^2)]*x)])/(2*e^(5/2)*Sqrt[c^2*d + e]*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) + (b*(c^2*d + 2*e)*Sqrt[-1 + 1/(c^2*x^2)]*ArcTanh[Sqrt[c^2*d + e]/(c*Sqrt[e]*Sqrt[-1 + 1/(c^2*x^2)]*x)])/(8*e^(5/2)*(c^2*d + e)^(3/2)*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) + ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^3) + ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^3) + ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^3) + ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^3) - ((a + b*ArcSech[c*x])*Log[1 + E^(2*ArcSech[c*x])])/e^3 + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(2*e^3) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^3) + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(2*e^3) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^3) - (b*PolyLog[2, -E^(2*ArcSech[c*x])])/(2*e^3)","A",35,14,21,0.6667,0,"{6303, 5792, 5660, 3718, 2190, 2279, 2391, 5788, 519, 382, 377, 208, 5800, 5562}"
124,1,173,0,0.1892578,"\int \frac{x^3 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^3*(a + b*ArcSech[c*x]))/(d + e*x^2)^3,x]","\frac{x^4 \left(a+b \text{sech}^{-1}(c x)\right)}{4 d \left(d+e x^2\right)^2}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+2 e\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{\sqrt{c^2 d+e}}\right)}{8 d e^{3/2} \left(c^2 d+e\right)^{3/2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{8 e \left(c^2 d+e\right) \left(d+e x^2\right)}","\frac{x^4 \left(a+b \text{sech}^{-1}(c x)\right)}{4 d \left(d+e x^2\right)^2}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+2 e\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{\sqrt{c^2 d+e}}\right)}{8 d e^{3/2} \left(c^2 d+e\right)^{3/2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{8 e \left(c^2 d+e\right) \left(d+e x^2\right)}",1,"(b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(8*e*(c^2*d + e)*(d + e*x^2)) + (x^4*(a + b*ArcSech[c*x]))/(4*d*(d + e*x^2)^2) - (b*(c^2*d + 2*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[(Sqrt[e]*Sqrt[1 - c^2*x^2])/Sqrt[c^2*d + e]])/(8*d*e^(3/2)*(c^2*d + e)^(3/2))","A",6,7,21,0.3333,1,"{264, 6301, 12, 446, 78, 63, 208}"
125,1,217,0,0.2926658,"\int \frac{x \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x*(a + b*ArcSech[c*x]))/(d + e*x^2)^3,x]","-\frac{a+b \text{sech}^{-1}(c x)}{4 e \left(d+e x^2\right)^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{4 d^2 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(3 c^2 d+2 e\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{\sqrt{c^2 d+e}}\right)}{8 d^2 \sqrt{e} \left(c^2 d+e\right)^{3/2}}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{8 d \left(c^2 d+e\right) \left(d+e x^2\right)}","-\frac{a+b \text{sech}^{-1}(c x)}{4 e \left(d+e x^2\right)^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{4 d^2 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(3 c^2 d+2 e\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{\sqrt{c^2 d+e}}\right)}{8 d^2 \sqrt{e} \left(c^2 d+e\right)^{3/2}}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{8 d \left(c^2 d+e\right) \left(d+e x^2\right)}",1,"-(b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(8*d*(c^2*d + e)*(d + e*x^2)) - (a + b*ArcSech[c*x])/(4*e*(d + e*x^2)^2) + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[1 - c^2*x^2]])/(4*d^2*e) - (b*(3*c^2*d + 2*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[(Sqrt[e]*Sqrt[1 - c^2*x^2])/Sqrt[c^2*d + e]])/(8*d^2*Sqrt[e]*(c^2*d + e)^(3/2))","A",9,7,19,0.3684,1,"{6299, 517, 446, 103, 156, 63, 208}"
126,1,741,0,1.5421142,"\int \frac{a+b \text{sech}^{-1}(c x)}{x \left(d+e x^2\right)^3} \, dx","Int[(a + b*ArcSech[c*x])/(x*(d + e*x^2)^3),x]","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 d^3}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 d^3}+\frac{e^2 \left(a+b \text{sech}^{-1}(c x)\right)}{4 d^3 \left(\frac{d}{x^2}+e\right)^2}-\frac{e \left(a+b \text{sech}^{-1}(c x)\right)}{d^3 \left(\frac{d}{x^2}+e\right)}+\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{2 b d^3}-\frac{b e \left(c^2-\frac{1}{x^2}\right)}{8 c d^2 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \left(c^2 d+e\right) \left(\frac{d}{x^2}+e\right)}-\frac{b \sqrt{e} \sqrt{\frac{1}{c^2 x^2}-1} \left(c^2 d+2 e\right) \tanh ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}-1}}\right)}{8 d^3 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \left(c^2 d+e\right)^{3/2}}+\frac{b \sqrt{e} \sqrt{\frac{1}{c^2 x^2}-1} \tanh ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}-1}}\right)}{d^3 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \sqrt{c^2 d+e}}","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}+1\right)}{2 d^3}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}+1\right)}{2 d^3}+\frac{e^2 \left(a+b \text{sech}^{-1}(c x)\right)}{4 d^3 \left(\frac{d}{x^2}+e\right)^2}-\frac{e \left(a+b \text{sech}^{-1}(c x)\right)}{d^3 \left(\frac{d}{x^2}+e\right)}+\frac{\left(a+b \text{sech}^{-1}(c x)\right)^2}{2 b d^3}-\frac{b e \left(c^2-\frac{1}{x^2}\right)}{8 c d^2 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \left(c^2 d+e\right) \left(\frac{d}{x^2}+e\right)}-\frac{b \sqrt{e} \sqrt{\frac{1}{c^2 x^2}-1} \left(c^2 d+2 e\right) \tanh ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}-1}}\right)}{8 d^3 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \left(c^2 d+e\right)^{3/2}}+\frac{b \sqrt{e} \sqrt{\frac{1}{c^2 x^2}-1} \tanh ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}-1}}\right)}{d^3 \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1} \sqrt{c^2 d+e}}",1,"-(b*e*(c^2 - x^(-2)))/(8*c*d^2*(c^2*d + e)*(e + d/x^2)*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x) + (e^2*(a + b*ArcSech[c*x]))/(4*d^3*(e + d/x^2)^2) - (e*(a + b*ArcSech[c*x]))/(d^3*(e + d/x^2)) + (a + b*ArcSech[c*x])^2/(2*b*d^3) + (b*Sqrt[e]*Sqrt[-1 + 1/(c^2*x^2)]*ArcTanh[Sqrt[c^2*d + e]/(c*Sqrt[e]*Sqrt[-1 + 1/(c^2*x^2)]*x)])/(d^3*Sqrt[c^2*d + e]*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) - (b*Sqrt[e]*(c^2*d + 2*e)*Sqrt[-1 + 1/(c^2*x^2)]*ArcTanh[Sqrt[c^2*d + e]/(c*Sqrt[e]*Sqrt[-1 + 1/(c^2*x^2)]*x)])/(8*d^3*(c^2*d + e)^(3/2)*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]) - ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d^3) - ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d^3) - ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d^3) - ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d^3) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(2*d^3) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d^3) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(2*d^3) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d^3)","A",30,12,21,0.5714,1,"{6303, 5792, 5788, 519, 382, 377, 208, 5800, 5562, 2190, 2279, 2391}"
127,1,1272,0,2.263345,"\int \frac{x^4 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^4*(a + b*ArcSech[c*x]))/(d + e*x^2)^3,x]","\frac{b \sqrt{-d} \sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}} c}{16 e^{3/2} \left(d c^2+e\right) \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{b \sqrt{-d} \sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}} c}{16 e^{3/2} \left(d c^2+e\right) \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{3 \left(a+b \text{sech}^{-1}(c x)\right)}{16 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{3 \left(a+b \text{sech}^{-1}(c x)\right)}{16 e^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{-d} \left(a+b \text{sech}^{-1}(c x)\right)}{16 e^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{-d} \left(a+b \text{sech}^{-1}(c x)\right)}{16 e^{3/2} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}-\frac{b d \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 \left(c d-\sqrt{-d} \sqrt{e}\right)^{3/2} \left(c d+\sqrt{-d} \sqrt{e}\right)^{3/2} e}-\frac{3 b \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}} e^2}-\frac{b d \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 \left(c d-\sqrt{-d} \sqrt{e}\right)^{3/2} \left(c d+\sqrt{-d} \sqrt{e}\right)^{3/2} e}-\frac{3 b \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}} e^2}+\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}","\frac{b \sqrt{-d} \sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}} c}{16 e^{3/2} \left(d c^2+e\right) \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{b \sqrt{-d} \sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}} c}{16 e^{3/2} \left(d c^2+e\right) \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{3 \left(a+b \text{sech}^{-1}(c x)\right)}{16 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{3 \left(a+b \text{sech}^{-1}(c x)\right)}{16 e^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{-d} \left(a+b \text{sech}^{-1}(c x)\right)}{16 e^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{-d} \left(a+b \text{sech}^{-1}(c x)\right)}{16 e^{3/2} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}-\frac{b d \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 \left(c d-\sqrt{-d} \sqrt{e}\right)^{3/2} \left(c d+\sqrt{-d} \sqrt{e}\right)^{3/2} e}-\frac{3 b \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}} e^2}-\frac{b d \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 \left(c d-\sqrt{-d} \sqrt{e}\right)^{3/2} \left(c d+\sqrt{-d} \sqrt{e}\right)^{3/2} e}-\frac{3 b \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}} e^2}+\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}",1,"(b*c*Sqrt[-d]*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)])/(16*e^(3/2)*(c^2*d + e)*(Sqrt[-d]*Sqrt[e] - d/x)) + (b*c*Sqrt[-d]*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)])/(16*e^(3/2)*(c^2*d + e)*(Sqrt[-d]*Sqrt[e] + d/x)) + (Sqrt[-d]*(a + b*ArcSech[c*x]))/(16*e^(3/2)*(Sqrt[-d]*Sqrt[e] - d/x)^2) + (3*(a + b*ArcSech[c*x]))/(16*e^2*(Sqrt[-d]*Sqrt[e] - d/x)) - (Sqrt[-d]*(a + b*ArcSech[c*x]))/(16*e^(3/2)*(Sqrt[-d]*Sqrt[e] + d/x)^2) - (3*(a + b*ArcSech[c*x]))/(16*e^2*(Sqrt[-d]*Sqrt[e] + d/x)) - (3*b*ArcTan[(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(8*Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*e^2) - (b*d*ArcTan[(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(8*(c*d - Sqrt[-d]*Sqrt[e])^(3/2)*(c*d + Sqrt[-d]*Sqrt[e])^(3/2)*e) - (3*b*ArcTan[(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(8*Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*e^2) - (b*d*ArcTan[(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(8*(c*d - Sqrt[-d]*Sqrt[e])^(3/2)*(c*d + Sqrt[-d]*Sqrt[e])^(3/2)*e) + (3*(a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) - (3*(a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) + (3*(a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) - (3*(a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) - (3*b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(16*Sqrt[-d]*e^(5/2)) + (3*b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) - (3*b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(16*Sqrt[-d]*e^(5/2)) + (3*b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2))","A",35,11,21,0.5238,1,"{6303, 5707, 5802, 96, 93, 205, 5800, 5562, 2190, 2279, 2391}"
128,1,1276,0,4.0401462,"\int \frac{x^2 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^2*(a + b*ArcSech[c*x]))/(d + e*x^2)^3,x]","\frac{b \sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}} c}{16 \sqrt{-d} \sqrt{e} \left(d c^2+e\right) \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{b \sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}} c}{16 \sqrt{-d} \sqrt{e} \left(d c^2+e\right) \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{a+b \text{sech}^{-1}(c x)}{16 d e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \text{sech}^{-1}(c x)}{16 d e \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{a+b \text{sech}^{-1}(c x)}{16 \sqrt{-d} \sqrt{e} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{a+b \text{sech}^{-1}(c x)}{16 \sqrt{-d} \sqrt{e} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}-\frac{b \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 d \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}} e}+\frac{b \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 \left(c d-\sqrt{-d} \sqrt{e}\right)^{3/2} \left(c d+\sqrt{-d} \sqrt{e}\right)^{3/2}}-\frac{b \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 d \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}} e}+\frac{b \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 \left(c d-\sqrt{-d} \sqrt{e}\right)^{3/2} \left(c d+\sqrt{-d} \sqrt{e}\right)^{3/2}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}","\frac{b \sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}} c}{16 \sqrt{-d} \sqrt{e} \left(d c^2+e\right) \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{b \sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}} c}{16 \sqrt{-d} \sqrt{e} \left(d c^2+e\right) \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{a+b \text{sech}^{-1}(c x)}{16 d e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \text{sech}^{-1}(c x)}{16 d e \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{a+b \text{sech}^{-1}(c x)}{16 \sqrt{-d} \sqrt{e} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{a+b \text{sech}^{-1}(c x)}{16 \sqrt{-d} \sqrt{e} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}-\frac{b \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 d \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}} e}+\frac{b \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 \left(c d-\sqrt{-d} \sqrt{e}\right)^{3/2} \left(c d+\sqrt{-d} \sqrt{e}\right)^{3/2}}-\frac{b \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 d \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}} e}+\frac{b \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 \left(c d-\sqrt{-d} \sqrt{e}\right)^{3/2} \left(c d+\sqrt{-d} \sqrt{e}\right)^{3/2}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}",1,"(b*c*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)])/(16*Sqrt[-d]*Sqrt[e]*(c^2*d + e)*(Sqrt[-d]*Sqrt[e] - d/x)) + (b*c*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)])/(16*Sqrt[-d]*Sqrt[e]*(c^2*d + e)*(Sqrt[-d]*Sqrt[e] + d/x)) + (a + b*ArcSech[c*x])/(16*Sqrt[-d]*Sqrt[e]*(Sqrt[-d]*Sqrt[e] - d/x)^2) + (a + b*ArcSech[c*x])/(16*d*e*(Sqrt[-d]*Sqrt[e] - d/x)) - (a + b*ArcSech[c*x])/(16*Sqrt[-d]*Sqrt[e]*(Sqrt[-d]*Sqrt[e] + d/x)^2) - (a + b*ArcSech[c*x])/(16*d*e*(Sqrt[-d]*Sqrt[e] + d/x)) + (b*ArcTan[(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(8*(c*d - Sqrt[-d]*Sqrt[e])^(3/2)*(c*d + Sqrt[-d]*Sqrt[e])^(3/2)) - (b*ArcTan[(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(8*d*Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*e) + (b*ArcTan[(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(8*(c*d - Sqrt[-d]*Sqrt[e])^(3/2)*(c*d + Sqrt[-d]*Sqrt[e])^(3/2)) - (b*ArcTan[(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(8*d*Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*e) - ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) + ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) - ((a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) + ((a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(16*(-d)^(3/2)*e^(3/2)) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(16*(-d)^(3/2)*e^(3/2)) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2))","A",63,12,21,0.5714,1,"{6303, 5792, 5707, 5802, 96, 93, 205, 5800, 5562, 2190, 2279, 2391}"
129,1,1272,0,4.9095724,"\int \frac{a+b \text{sech}^{-1}(c x)}{\left(d+e x^2\right)^3} \, dx","Int[(a + b*ArcSech[c*x])/(d + e*x^2)^3,x]","\frac{b \sqrt{e} \sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{b \sqrt{e} \sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}-\frac{5 \left(a+b \text{sech}^{-1}(c x)\right)}{16 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{5 \left(a+b \text{sech}^{-1}(c x)\right)}{16 d^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right)}{16 (-d)^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right)}{16 (-d)^{3/2} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}-\frac{b e \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 d \left(c d-\sqrt{-d} \sqrt{e}\right)^{3/2} \left(c d+\sqrt{-d} \sqrt{e}\right)^{3/2}}+\frac{5 b \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 d^2 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}-\frac{b e \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 d \left(c d-\sqrt{-d} \sqrt{e}\right)^{3/2} \left(c d+\sqrt{-d} \sqrt{e}\right)^{3/2}}+\frac{5 b \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 d^2 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}+\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}","\frac{b \sqrt{e} \sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{b \sqrt{e} \sqrt{\frac{1}{c x}-1} \sqrt{1+\frac{1}{c x}} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}-\frac{5 \left(a+b \text{sech}^{-1}(c x)\right)}{16 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{5 \left(a+b \text{sech}^{-1}(c x)\right)}{16 d^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right)}{16 (-d)^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{e} \left(a+b \text{sech}^{-1}(c x)\right)}{16 (-d)^{3/2} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}-\frac{b e \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 d \left(c d-\sqrt{-d} \sqrt{e}\right)^{3/2} \left(c d+\sqrt{-d} \sqrt{e}\right)^{3/2}}+\frac{5 b \tan ^{-1}\left(\frac{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 d^2 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}-\frac{b e \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 d \left(c d-\sqrt{-d} \sqrt{e}\right)^{3/2} \left(c d+\sqrt{-d} \sqrt{e}\right)^{3/2}}+\frac{5 b \tan ^{-1}\left(\frac{\sqrt{c d+\sqrt{-d} \sqrt{e}} \sqrt{1+\frac{1}{c x}}}{\sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{\frac{1}{c x}-1}}\right)}{8 d^2 \sqrt{c d-\sqrt{-d} \sqrt{e}} \sqrt{c d+\sqrt{-d} \sqrt{e}}}+\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \text{sech}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{sech}^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{sech}^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}",1,"(b*c*Sqrt[e]*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)])/(16*(-d)^(3/2)*(c^2*d + e)*(Sqrt[-d]*Sqrt[e] - d/x)) + (b*c*Sqrt[e]*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)])/(16*(-d)^(3/2)*(c^2*d + e)*(Sqrt[-d]*Sqrt[e] + d/x)) + (Sqrt[e]*(a + b*ArcSech[c*x]))/(16*(-d)^(3/2)*(Sqrt[-d]*Sqrt[e] - d/x)^2) - (5*(a + b*ArcSech[c*x]))/(16*d^2*(Sqrt[-d]*Sqrt[e] - d/x)) - (Sqrt[e]*(a + b*ArcSech[c*x]))/(16*(-d)^(3/2)*(Sqrt[-d]*Sqrt[e] + d/x)^2) + (5*(a + b*ArcSech[c*x]))/(16*d^2*(Sqrt[-d]*Sqrt[e] + d/x)) + (5*b*ArcTan[(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(8*d^2*Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[c*d + Sqrt[-d]*Sqrt[e]]) - (b*e*ArcTan[(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(8*d*(c*d - Sqrt[-d]*Sqrt[e])^(3/2)*(c*d + Sqrt[-d]*Sqrt[e])^(3/2)) + (5*b*ArcTan[(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(8*d^2*Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[c*d + Sqrt[-d]*Sqrt[e]]) - (b*e*ArcTan[(Sqrt[c*d + Sqrt[-d]*Sqrt[e]]*Sqrt[1 + 1/(c*x)])/(Sqrt[c*d - Sqrt[-d]*Sqrt[e]]*Sqrt[-1 + 1/(c*x)])])/(8*d*(c*d - Sqrt[-d]*Sqrt[e])^(3/2)*(c*d + Sqrt[-d]*Sqrt[e])^(3/2)) + (3*(a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*(a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) + (3*(a + b*ArcSech[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*(a + b*ArcSech[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e]))])/(16*(-d)^(5/2)*Sqrt[e]) + (3*b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*b*PolyLog[2, -((c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e]))])/(16*(-d)^(5/2)*Sqrt[e]) + (3*b*PolyLog[2, (c*Sqrt[-d]*E^ArcSech[c*x])/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e])","A",81,12,18,0.6667,1,"{6293, 5792, 5707, 5802, 96, 93, 205, 5800, 5562, 2190, 2279, 2391}"
130,1,447,0,1.3954717,"\int x^5 \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^5*Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]),x]","\frac{d^2 \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 e^3}-\frac{2 d \left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 e^3}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \text{sech}^{-1}(c x)\right)}{7 e^3}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(23 c^4 d^2+12 c^2 d e-75 e^2\right) \sqrt{d+e x^2}}{1680 c^6 e^2}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(-35 c^4 d^2 e+105 c^6 d^3+63 c^2 d e^2+75 e^3\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{1680 c^7 e^{5/2}}-\frac{8 b d^{7/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{105 e^3}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{5/2}}{42 c^2 e^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(29 c^2 d-25 e\right) \left(d+e x^2\right)^{3/2}}{840 c^4 e^2}","\frac{d^2 \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 e^3}-\frac{2 d \left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 e^3}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \text{sech}^{-1}(c x)\right)}{7 e^3}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(23 c^4 d^2+12 c^2 d e-75 e^2\right) \sqrt{d+e x^2}}{1680 c^6 e^2}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(-35 c^4 d^2 e+105 c^6 d^3+63 c^2 d e^2+75 e^3\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{1680 c^7 e^{5/2}}-\frac{8 b d^{7/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{105 e^3}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{5/2}}{42 c^2 e^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(29 c^2 d-25 e\right) \left(d+e x^2\right)^{3/2}}{840 c^4 e^2}",1,"(b*(23*c^4*d^2 + 12*c^2*d*e - 75*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(1680*c^6*e^2) + (b*(29*c^2*d - 25*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*(d + e*x^2)^(3/2))/(840*c^4*e^2) - (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*(d + e*x^2)^(5/2))/(42*c^2*e^2) + (d^2*(d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/(3*e^3) - (2*d*(d + e*x^2)^(5/2)*(a + b*ArcSech[c*x]))/(5*e^3) + ((d + e*x^2)^(7/2)*(a + b*ArcSech[c*x]))/(7*e^3) - (b*(105*c^6*d^3 - 35*c^4*d^2*e + 63*c^2*d*e^2 + 75*e^3)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTan[(Sqrt[e]*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(1680*c^7*e^(5/2)) - (8*b*d^(7/2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(105*e^3)","A",12,12,23,0.5217,1,"{266, 43, 6301, 12, 1615, 154, 157, 63, 217, 203, 93, 207}"
131,1,329,0,0.4271683,"\int x^3 \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^3*Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]),x]","-\frac{d \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 e^2}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 e^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(15 c^4 d^2-10 c^2 d e-9 e^2\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{120 c^5 e^{3/2}}+\frac{2 b d^{5/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{15 e^2}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{3/2}}{20 c^2 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(c^2 d+9 e\right) \sqrt{d+e x^2}}{120 c^4 e}","-\frac{d \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 e^2}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 e^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(15 c^4 d^2-10 c^2 d e-9 e^2\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{120 c^5 e^{3/2}}+\frac{2 b d^{5/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{15 e^2}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{3/2}}{20 c^2 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(c^2 d+9 e\right) \sqrt{d+e x^2}}{120 c^4 e}",1,"-(b*(c^2*d + 9*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(120*c^4*e) - (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*(d + e*x^2)^(3/2))/(20*c^2*e) - (d*(d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/(3*e^2) + ((d + e*x^2)^(5/2)*(a + b*ArcSech[c*x]))/(5*e^2) + (b*(15*c^4*d^2 - 10*c^2*d*e - 9*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTan[(Sqrt[e]*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(120*c^5*e^(3/2)) + (2*b*d^(5/2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(15*e^2)","A",11,12,23,0.5217,1,"{266, 43, 6301, 12, 573, 154, 157, 63, 217, 203, 93, 207}"
132,1,221,0,0.3574284,"\int x \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x*Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]),x]","\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 e}-\frac{b d^{3/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{3 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x^2}}{6 c^2}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(3 c^2 d+e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{6 c^3 \sqrt{e}}","\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 e}-\frac{b d^{3/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{3 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x^2}}{6 c^2}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(3 c^2 d+e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{6 c^3 \sqrt{e}}",1,"-(b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(6*c^2) + ((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/(3*e) - (b*(3*c^2*d + e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTan[(Sqrt[e]*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(6*c^3*Sqrt[e]) - (b*d^(3/2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(3*e)","A",10,10,21,0.4762,1,"{6299, 517, 446, 102, 157, 63, 217, 203, 93, 207}"
133,0,0,0,0.098762,"\int \frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{x} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/x,x]","\int \frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{x} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{x},x\right)",0,"Defer[Int][(Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/x, x]","A",0,0,0,0,-1,"{}"
134,0,0,0,0.1043843,"\int \frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^3} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/x^3,x]","\int \frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^3} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^3},x\right)",0,"Defer[Int][(Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/x^3, x]","A",0,0,0,0,-1,"{}"
135,0,0,0,0.0982496,"\int x^2 \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^2*Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]),x]","\int x^2 \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","\text{Int}\left(x^2 \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right),x\right)",0,"Defer[Int][x^2*Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]), x]","A",0,0,0,0,-1,"{}"
136,0,0,0,0.0363176,"\int \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]),x]","\int \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","\text{Int}\left(\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right),x\right)",0,"Defer[Int][Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]), x]","A",0,0,0,0,-1,"{}"
137,0,0,0,0.0874494,"\int \frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^2} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/x^2,x]","\int \frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^2} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^2},x\right)",0,"Defer[Int][(Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/x^2, x]","A",0,0,0,0,-1,"{}"
138,1,312,0,0.3798977,"\int \frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^4} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/x^4,x]","-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 d x^3}+\frac{2 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(c^2 d+2 e\right) \sqrt{d+e x^2}}{9 d x}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x^2}}{9 x^3}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+e\right) \left(2 c^2 d+3 e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 c d \sqrt{d+e x^2}}+\frac{2 b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+2 e\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 d \sqrt{\frac{e x^2}{d}+1}}","-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 d x^3}+\frac{2 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(c^2 d+2 e\right) \sqrt{d+e x^2}}{9 d x}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x^2}}{9 x^3}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+e\right) \left(2 c^2 d+3 e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 c d \sqrt{d+e x^2}}+\frac{2 b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+2 e\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 d \sqrt{\frac{e x^2}{d}+1}}",1,"(b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(9*x^3) + (2*b*(c^2*d + 2*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(9*d*x) - ((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/(3*d*x^3) + (2*b*c*(c^2*d + 2*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(9*d*Sqrt[1 + (e*x^2)/d]) - (b*(c^2*d + e)*(2*c^2*d + 3*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(9*c*d*Sqrt[d + e*x^2])","A",9,10,23,0.4348,1,"{264, 6301, 12, 474, 583, 524, 426, 424, 421, 419}"
139,1,446,0,0.5605983,"\int \frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^6} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/x^6,x]","\frac{2 e \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{15 d^2 x^3}-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 d x^5}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(24 c^4 d^2+19 c^2 d e-31 e^2\right) \sqrt{d+e x^2}}{225 d^2 x}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+e\right) \left(24 c^4 d^2+7 c^2 d e-30 e^2\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{225 c d^2 \sqrt{d+e x^2}}+\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(24 c^4 d^2+19 c^2 d e-31 e^2\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{225 d^2 \sqrt{\frac{e x^2}{d}+1}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{3/2}}{25 d x^5}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(12 c^2 d-e\right) \sqrt{d+e x^2}}{225 d x^3}","\frac{2 e \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{15 d^2 x^3}-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 d x^5}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(24 c^4 d^2+19 c^2 d e-31 e^2\right) \sqrt{d+e x^2}}{225 d^2 x}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+e\right) \left(24 c^4 d^2+7 c^2 d e-30 e^2\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{225 c d^2 \sqrt{d+e x^2}}+\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(24 c^4 d^2+19 c^2 d e-31 e^2\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{225 d^2 \sqrt{\frac{e x^2}{d}+1}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{3/2}}{25 d x^5}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(12 c^2 d-e\right) \sqrt{d+e x^2}}{225 d x^3}",1,"(b*(12*c^2*d - e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(225*d*x^3) + (b*(24*c^4*d^2 + 19*c^2*d*e - 31*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(225*d^2*x) + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*(d + e*x^2)^(3/2))/(25*d*x^5) - ((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/(5*d*x^5) + (2*e*(d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/(15*d^2*x^3) + (b*c*(24*c^4*d^2 + 19*c^2*d*e - 31*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(225*d^2*Sqrt[1 + (e*x^2)/d]) - (b*(c^2*d + e)*(24*c^4*d^2 + 7*c^2*d*e - 30*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(225*c*d^2*Sqrt[d + e*x^2])","A",10,11,23,0.4783,1,"{271, 264, 6301, 12, 580, 583, 524, 426, 424, 421, 419}"
140,1,418,0,0.5295048,"\int x^3 \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]),x]","-\frac{d \left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 e^2}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \text{sech}^{-1}(c x)\right)}{7 e^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(3 c^4 d^2-38 c^2 d e-25 e^2\right) \sqrt{d+e x^2}}{560 c^6 e}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(-35 c^4 d^2 e+35 c^6 d^3-63 c^2 d e^2-25 e^3\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{560 c^7 e^{3/2}}+\frac{2 b d^{7/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{35 e^2}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{5/2}}{42 c^2 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(13 c^2 d+25 e\right) \left(d+e x^2\right)^{3/2}}{840 c^4 e}","-\frac{d \left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 e^2}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \text{sech}^{-1}(c x)\right)}{7 e^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(3 c^4 d^2-38 c^2 d e-25 e^2\right) \sqrt{d+e x^2}}{560 c^6 e}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(-35 c^4 d^2 e+35 c^6 d^3-63 c^2 d e^2-25 e^3\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{560 c^7 e^{3/2}}+\frac{2 b d^{7/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{35 e^2}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{5/2}}{42 c^2 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(13 c^2 d+25 e\right) \left(d+e x^2\right)^{3/2}}{840 c^4 e}",1,"(b*(3*c^4*d^2 - 38*c^2*d*e - 25*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(560*c^6*e) - (b*(13*c^2*d + 25*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*(d + e*x^2)^(3/2))/(840*c^4*e) - (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*(d + e*x^2)^(5/2))/(42*c^2*e) - (d*(d + e*x^2)^(5/2)*(a + b*ArcSech[c*x]))/(5*e^2) + ((d + e*x^2)^(7/2)*(a + b*ArcSech[c*x]))/(7*e^2) + (b*(35*c^6*d^3 - 35*c^4*d^2*e - 63*c^2*d*e^2 - 25*e^3)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTan[(Sqrt[e]*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(560*c^7*e^(3/2)) + (2*b*d^(7/2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(35*e^2)","A",12,12,23,0.5217,1,"{266, 43, 6301, 12, 573, 154, 157, 63, 217, 203, 93, 207}"
141,1,297,0,0.4323504,"\int x \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]),x]","\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(15 c^4 d^2+10 c^2 d e+3 e^2\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{40 c^5 \sqrt{e}}-\frac{b d^{5/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{5 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{3/2}}{20 c^2}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(7 c^2 d+3 e\right) \sqrt{d+e x^2}}{40 c^4}","\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(15 c^4 d^2+10 c^2 d e+3 e^2\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{40 c^5 \sqrt{e}}-\frac{b d^{5/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{5 e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{3/2}}{20 c^2}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(7 c^2 d+3 e\right) \sqrt{d+e x^2}}{40 c^4}",1,"-(b*(7*c^2*d + 3*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(40*c^4) - (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*(d + e*x^2)^(3/2))/(20*c^2) + ((d + e*x^2)^(5/2)*(a + b*ArcSech[c*x]))/(5*e) - (b*(15*c^4*d^2 + 10*c^2*d*e + 3*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTan[(Sqrt[e]*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(40*c^5*Sqrt[e]) - (b*d^(5/2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(5*e)","A",11,11,21,0.5238,1,"{6299, 517, 446, 102, 154, 157, 63, 217, 203, 93, 207}"
142,0,0,0,0.1198157,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/x,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{x} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{x},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/x, x]","A",0,0,0,0,-1,"{}"
143,0,0,0,0.1248391,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/x^3,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^3} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^3},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/x^3, x]","A",0,0,0,0,-1,"{}"
144,0,0,0,0.1216312,"\int x^2 \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]),x]","\int x^2 \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","\text{Int}\left(x^2 \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right),x\right)",0,"Defer[Int][x^2*(d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]), x]","A",0,0,0,0,-1,"{}"
145,0,0,0,0.0444486,"\int \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]),x]","\int \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","\text{Int}\left(\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right),x\right)",0,"Defer[Int][(d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]), x]","A",0,0,0,0,-1,"{}"
146,0,0,0,0.1043908,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/x^2,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^2} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^2},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/x^2, x]","A",0,0,0,0,-1,"{}"
147,0,0,0,0.1284402,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/x^4,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^4} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^4},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/x^4, x]","A",0,0,0,0,-1,"{}"
148,1,409,0,0.5329075,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^6} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/x^6,x]","-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 d x^5}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(8 c^4 d^2+23 c^2 d e+23 e^2\right) \sqrt{d+e x^2}}{75 d x}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+e\right) \left(8 c^4 d^2+19 c^2 d e+15 e^2\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{75 c d \sqrt{d+e x^2}}+\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(8 c^4 d^2+23 c^2 d e+23 e^2\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{75 d \sqrt{\frac{e x^2}{d}+1}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{3/2}}{25 x^5}+\frac{4 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(c^2 d+2 e\right) \sqrt{d+e x^2}}{75 x^3}","-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 d x^5}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(8 c^4 d^2+23 c^2 d e+23 e^2\right) \sqrt{d+e x^2}}{75 d x}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+e\right) \left(8 c^4 d^2+19 c^2 d e+15 e^2\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{75 c d \sqrt{d+e x^2}}+\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(8 c^4 d^2+23 c^2 d e+23 e^2\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{75 d \sqrt{\frac{e x^2}{d}+1}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{3/2}}{25 x^5}+\frac{4 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(c^2 d+2 e\right) \sqrt{d+e x^2}}{75 x^3}",1,"(4*b*(c^2*d + 2*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(75*x^3) + (b*(8*c^4*d^2 + 23*c^2*d*e + 23*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(75*d*x) + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*(d + e*x^2)^(3/2))/(25*x^5) - ((d + e*x^2)^(5/2)*(a + b*ArcSech[c*x]))/(5*d*x^5) + (b*c*(8*c^4*d^2 + 23*c^2*d*e + 23*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(75*d*Sqrt[1 + (e*x^2)/d]) - (b*(c^2*d + e)*(8*c^4*d^2 + 19*c^2*d*e + 15*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(75*c*d*Sqrt[d + e*x^2])","A",10,11,23,0.4783,1,"{264, 6301, 12, 474, 580, 583, 524, 426, 424, 421, 419}"
149,1,556,0,0.7576061,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{x^8} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/x^8,x]","\frac{2 e \left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{35 d^2 x^5}-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{7 d x^7}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(528 c^4 d^2 e+240 c^6 d^3+193 c^2 d e^2-247 e^3\right) \sqrt{d+e x^2}}{3675 d^2 x}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(120 c^4 d^2+159 c^2 d e-37 e^2\right) \sqrt{d+e x^2}}{3675 d x^3}-\frac{2 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+e\right) \left(204 c^4 d^2 e+120 c^6 d^3+17 c^2 d e^2-105 e^3\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3675 c d^2 \sqrt{d+e x^2}}+\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(528 c^4 d^2 e+240 c^6 d^3+193 c^2 d e^2-247 e^3\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3675 d^2 \sqrt{\frac{e x^2}{d}+1}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{5/2}}{49 d x^7}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(30 c^2 d+11 e\right) \left(d+e x^2\right)^{3/2}}{1225 d x^5}","\frac{2 e \left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{35 d^2 x^5}-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{7 d x^7}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(528 c^4 d^2 e+240 c^6 d^3+193 c^2 d e^2-247 e^3\right) \sqrt{d+e x^2}}{3675 d^2 x}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(120 c^4 d^2+159 c^2 d e-37 e^2\right) \sqrt{d+e x^2}}{3675 d x^3}-\frac{2 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+e\right) \left(204 c^4 d^2 e+120 c^6 d^3+17 c^2 d e^2-105 e^3\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3675 c d^2 \sqrt{d+e x^2}}+\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(528 c^4 d^2 e+240 c^6 d^3+193 c^2 d e^2-247 e^3\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3675 d^2 \sqrt{\frac{e x^2}{d}+1}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{5/2}}{49 d x^7}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(30 c^2 d+11 e\right) \left(d+e x^2\right)^{3/2}}{1225 d x^5}",1,"(b*(120*c^4*d^2 + 159*c^2*d*e - 37*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(3675*d*x^3) + (b*(240*c^6*d^3 + 528*c^4*d^2*e + 193*c^2*d*e^2 - 247*e^3)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(3675*d^2*x) + (b*(30*c^2*d + 11*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*(d + e*x^2)^(3/2))/(1225*d*x^5) + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*(d + e*x^2)^(5/2))/(49*d*x^7) - ((d + e*x^2)^(5/2)*(a + b*ArcSech[c*x]))/(7*d*x^7) + (2*e*(d + e*x^2)^(5/2)*(a + b*ArcSech[c*x]))/(35*d^2*x^5) + (b*c*(240*c^6*d^3 + 528*c^4*d^2*e + 193*c^2*d*e^2 - 247*e^3)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(3675*d^2*Sqrt[1 + (e*x^2)/d]) - (2*b*(c^2*d + e)*(120*c^6*d^3 + 204*c^4*d^2*e + 17*c^2*d*e^2 - 105*e^3)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(3675*c*d^2*Sqrt[d + e*x^2])","A",11,11,23,0.4783,1,"{271, 264, 6301, 12, 580, 583, 524, 426, 424, 421, 419}"
150,1,356,0,1.1602754,"\int \frac{x^5 \left(a+b \text{sech}^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^5*(a + b*ArcSech[c*x]))/Sqrt[d + e*x^2],x]","\frac{d^2 \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{e^3}-\frac{2 d \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 e^3}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 e^3}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(45 c^4 d^2-10 c^2 d e+9 e^2\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{120 c^5 e^{5/2}}-\frac{8 b d^{5/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{15 e^3}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{3/2}}{20 c^2 e^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(19 c^2 d-9 e\right) \sqrt{d+e x^2}}{120 c^4 e^2}","\frac{d^2 \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{e^3}-\frac{2 d \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 e^3}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{5 e^3}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(45 c^4 d^2-10 c^2 d e+9 e^2\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{120 c^5 e^{5/2}}-\frac{8 b d^{5/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{15 e^3}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(d+e x^2\right)^{3/2}}{20 c^2 e^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(19 c^2 d-9 e\right) \sqrt{d+e x^2}}{120 c^4 e^2}",1,"(b*(19*c^2*d - 9*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(120*c^4*e^2) - (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*(d + e*x^2)^(3/2))/(20*c^2*e^2) + (d^2*Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/e^3 - (2*d*(d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/(3*e^3) + ((d + e*x^2)^(5/2)*(a + b*ArcSech[c*x]))/(5*e^3) - (b*(45*c^4*d^2 - 10*c^2*d*e + 9*e^2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTan[(Sqrt[e]*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(120*c^5*e^(5/2)) - (8*b*d^(5/2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(15*e^3)","A",11,12,23,0.5217,1,"{266, 43, 6301, 12, 1615, 154, 157, 63, 217, 203, 93, 207}"
151,1,251,0,0.3300972,"\int \frac{x^3 \left(a+b \text{sech}^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^3*(a + b*ArcSech[c*x]))/Sqrt[d + e*x^2],x]","-\frac{d \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{e^2}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 e^2}+\frac{2 b d^{3/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{3 e^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(3 c^2 d-e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{6 c^3 e^{3/2}}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x^2}}{6 c^2 e}","-\frac{d \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{e^2}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 e^2}+\frac{2 b d^{3/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{3 e^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(3 c^2 d-e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{6 c^3 e^{3/2}}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x^2}}{6 c^2 e}",1,"-(b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(6*c^2*e) - (d*Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/e^2 + ((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/(3*e^2) + (b*(3*c^2*d - e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTan[(Sqrt[e]*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(6*c^3*e^(3/2)) + (2*b*d^(3/2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(3*e^2)","A",10,12,23,0.5217,1,"{266, 43, 6301, 12, 573, 154, 157, 63, 217, 203, 93, 207}"
152,1,153,0,0.2951146,"\int \frac{x \left(a+b \text{sech}^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x*(a + b*ArcSech[c*x]))/Sqrt[d + e*x^2],x]","\frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{c \sqrt{e}}-\frac{b \sqrt{d} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{e}","\frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{c \sqrt{e}}-\frac{b \sqrt{d} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{e}",1,"(Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/e - (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTan[(Sqrt[e]*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(c*Sqrt[e]) - (b*Sqrt[d]*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/e","A",9,9,21,0.4286,1,"{6299, 517, 446, 105, 63, 217, 203, 93, 207}"
153,0,0,0,0.0951646,"\int \frac{a+b \text{sech}^{-1}(c x)}{x \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSech[c*x])/(x*Sqrt[d + e*x^2]),x]","\int \frac{a+b \text{sech}^{-1}(c x)}{x \sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \text{sech}^{-1}(c x)}{x \sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcSech[c*x])/(x*Sqrt[d + e*x^2]), x]","A",0,0,0,0,-1,"{}"
154,0,0,0,0.1105681,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^3 \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSech[c*x])/(x^3*Sqrt[d + e*x^2]),x]","\int \frac{a+b \text{sech}^{-1}(c x)}{x^3 \sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \text{sech}^{-1}(c x)}{x^3 \sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcSech[c*x])/(x^3*Sqrt[d + e*x^2]), x]","A",0,0,0,0,-1,"{}"
155,0,0,0,0.0979238,"\int \frac{x^2 \left(a+b \text{sech}^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^2*(a + b*ArcSech[c*x]))/Sqrt[d + e*x^2],x]","\int \frac{x^2 \left(a+b \text{sech}^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{x^2 \left(a+b \text{sech}^{-1}(c x)\right)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][(x^2*(a + b*ArcSech[c*x]))/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
156,0,0,0,0.0354502,"\int \frac{a+b \text{sech}^{-1}(c x)}{\sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSech[c*x])/Sqrt[d + e*x^2],x]","\int \frac{a+b \text{sech}^{-1}(c x)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \text{sech}^{-1}(c x)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcSech[c*x])/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
157,1,221,0,0.2575379,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^2 \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSech[c*x])/(x^2*Sqrt[d + e*x^2]),x]","-\frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{d x}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x^2}}{d x}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{c d \sqrt{d+e x^2}}+\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d \sqrt{\frac{e x^2}{d}+1}}","-\frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{d x}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x^2}}{d x}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{c d \sqrt{d+e x^2}}+\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d \sqrt{\frac{e x^2}{d}+1}}",1,"(b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(d*x) - (Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/(d*x) + (b*c*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(d*Sqrt[1 + (e*x^2)/d]) - (b*(c^2*d + e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(c*d*Sqrt[d + e*x^2])","A",9,10,23,0.4348,1,"{264, 6301, 12, 475, 21, 423, 426, 424, 421, 419}"
158,1,346,0,0.4846862,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^4 \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSech[c*x])/(x^4*Sqrt[d + e*x^2]),x]","\frac{2 e \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 d^2 x}-\frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 d x^3}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(2 c^2 d-5 e\right) \sqrt{d+e x^2}}{9 d^2 x}-\frac{2 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d-3 e\right) \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 c d^2 \sqrt{d+e x^2}}+\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(2 c^2 d-5 e\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 d^2 \sqrt{\frac{e x^2}{d}+1}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x^2}}{9 d x^3}","\frac{2 e \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 d^2 x}-\frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 d x^3}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \left(2 c^2 d-5 e\right) \sqrt{d+e x^2}}{9 d^2 x}-\frac{2 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d-3 e\right) \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 c d^2 \sqrt{d+e x^2}}+\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(2 c^2 d-5 e\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 d^2 \sqrt{\frac{e x^2}{d}+1}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x^2}}{9 d x^3}",1,"(b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(9*d*x^3) + (b*(2*c^2*d - 5*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(9*d^2*x) - (Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/(3*d*x^3) + (2*e*Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/(3*d^2*x) + (b*c*(2*c^2*d - 5*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(9*d^2*Sqrt[1 + (e*x^2)/d]) - (2*b*(c^2*d - 3*e)*(c^2*d + e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(9*c*d^2*Sqrt[d + e*x^2])","A",9,11,23,0.4783,1,"{271, 264, 6301, 12, 580, 583, 524, 426, 424, 421, 419}"
159,1,278,0,1.1168055,"\int \frac{x^5 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^5*(a + b*ArcSech[c*x]))/(d + e*x^2)^(3/2),x]","-\frac{d^2 \left(a+b \text{sech}^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}-\frac{2 d \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{e^3}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 e^3}+\frac{8 b d^{3/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{3 e^3}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x^2}}{6 c^2 e^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(9 c^2 d-e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{6 c^3 e^{5/2}}","-\frac{d^2 \left(a+b \text{sech}^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}-\frac{2 d \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{e^3}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 e^3}+\frac{8 b d^{3/2} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{3 e^3}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x^2}}{6 c^2 e^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(9 c^2 d-e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{6 c^3 e^{5/2}}",1,"-(b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(6*c^2*e^2) - (d^2*(a + b*ArcSech[c*x]))/(e^3*Sqrt[d + e*x^2]) - (2*d*Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/e^3 + ((d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]))/(3*e^3) + (b*(9*c^2*d - e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTan[(Sqrt[e]*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(6*c^3*e^(5/2)) + (8*b*d^(3/2)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(3*e^3)","A",10,11,23,0.4783,1,"{266, 43, 6301, 12, 1615, 157, 63, 217, 203, 93, 207}"
160,1,177,0,0.2722048,"\int \frac{x^3 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*ArcSech[c*x]))/(d + e*x^2)^(3/2),x]","\frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{e^2}+\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{e^2 \sqrt{d+e x^2}}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{c e^{3/2}}-\frac{2 b \sqrt{d} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{e^2}","\frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{e^2}+\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{e^2 \sqrt{d+e x^2}}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{c e^{3/2}}-\frac{2 b \sqrt{d} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{e^2}",1,"(d*(a + b*ArcSech[c*x]))/(e^2*Sqrt[d + e*x^2]) + (Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/e^2 - (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTan[(Sqrt[e]*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(c*e^(3/2)) - (2*b*Sqrt[d]*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/e^2","A",9,11,23,0.4783,1,"{266, 43, 6301, 12, 573, 157, 63, 217, 203, 93, 207}"
161,1,87,0,0.2450753,"\int \frac{x \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x*(a + b*ArcSech[c*x]))/(d + e*x^2)^(3/2),x]","\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{\sqrt{d} e}-\frac{a+b \text{sech}^{-1}(c x)}{e \sqrt{d+e x^2}}","\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{\sqrt{d} e}-\frac{a+b \text{sech}^{-1}(c x)}{e \sqrt{d+e x^2}}",1,"-((a + b*ArcSech[c*x])/(e*Sqrt[d + e*x^2])) + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(Sqrt[d]*e)","A",5,5,21,0.2381,1,"{6299, 517, 446, 93, 207}"
162,0,0,0,0.1161891,"\int \frac{a+b \text{sech}^{-1}(c x)}{x \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSech[c*x])/(x*(d + e*x^2)^(3/2)),x]","\int \frac{a+b \text{sech}^{-1}(c x)}{x \left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{a+b \text{sech}^{-1}(c x)}{x \left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcSech[c*x])/(x*(d + e*x^2)^(3/2)), x]","A",0,0,0,0,-1,"{}"
163,0,0,0,0.1330814,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^3 \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSech[c*x])/(x^3*(d + e*x^2)^(3/2)),x]","\int \frac{a+b \text{sech}^{-1}(c x)}{x^3 \left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{a+b \text{sech}^{-1}(c x)}{x^3 \left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcSech[c*x])/(x^3*(d + e*x^2)^(3/2)), x]","A",0,0,0,0,-1,"{}"
164,0,0,0,0.1114303,"\int \frac{x^4 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^4*(a + b*ArcSech[c*x]))/(d + e*x^2)^(3/2),x]","\int \frac{x^4 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x^4 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(x^4*(a + b*ArcSech[c*x]))/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
165,0,0,0,0.1063153,"\int \frac{x^2 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*ArcSech[c*x]))/(d + e*x^2)^(3/2),x]","\int \frac{x^2 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x^2 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(x^2*(a + b*ArcSech[c*x]))/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
166,1,92,0,0.0786416,"\int \frac{a+b \text{sech}^{-1}(c x)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSech[c*x])/(d + e*x^2)^(3/2),x]","\frac{x \left(a+b \text{sech}^{-1}(c x)\right)}{d \sqrt{d+e x^2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{c d \sqrt{d+e x^2}}","\frac{x \left(a+b \text{sech}^{-1}(c x)\right)}{d \sqrt{d+e x^2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{c d \sqrt{d+e x^2}}",1,"(x*(a + b*ArcSech[c*x]))/(d*Sqrt[d + e*x^2]) + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(c*d*Sqrt[d + e*x^2])","A",4,5,20,0.2500,1,"{191, 6291, 12, 421, 419}"
167,1,249,0,0.2866563,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^2 \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSech[c*x])/(x^2*(d + e*x^2)^(3/2)),x]","-\frac{2 e x \left(a+b \text{sech}^{-1}(c x)\right)}{d^2 \sqrt{d+e x^2}}-\frac{a+b \text{sech}^{-1}(c x)}{d x \sqrt{d+e x^2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x^2}}{d^2 x}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+2 e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{c d^2 \sqrt{d+e x^2}}+\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d^2 \sqrt{\frac{e x^2}{d}+1}}","-\frac{2 e x \left(a+b \text{sech}^{-1}(c x)\right)}{d^2 \sqrt{d+e x^2}}-\frac{a+b \text{sech}^{-1}(c x)}{d x \sqrt{d+e x^2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} \sqrt{d+e x^2}}{d^2 x}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \left(c^2 d+2 e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{c d^2 \sqrt{d+e x^2}}+\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d^2 \sqrt{\frac{e x^2}{d}+1}}",1,"(b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2])/(d^2*x) - (a + b*ArcSech[c*x])/(d*x*Sqrt[d + e*x^2]) - (2*e*x*(a + b*ArcSech[c*x]))/(d^2*Sqrt[d + e*x^2]) + (b*c*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(d^2*Sqrt[1 + (e*x^2)/d]) - (b*(c^2*d + 2*e)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(c*d^2*Sqrt[d + e*x^2])","A",8,10,23,0.4348,1,"{271, 191, 6301, 12, 583, 524, 426, 424, 421, 419}"
168,1,272,0,1.2810431,"\int \frac{x^5 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^5*(a + b*ArcSech[c*x]))/(d + e*x^2)^(5/2),x]","-\frac{d^2 \left(a+b \text{sech}^{-1}(c x)\right)}{3 e^3 \left(d+e x^2\right)^{3/2}}+\frac{2 d \left(a+b \text{sech}^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}+\frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{e^3}-\frac{b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{3 e^2 \left(c^2 d+e\right) \sqrt{d+e x^2}}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{c e^{5/2}}-\frac{8 b \sqrt{d} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{3 e^3}","-\frac{d^2 \left(a+b \text{sech}^{-1}(c x)\right)}{3 e^3 \left(d+e x^2\right)^{3/2}}+\frac{2 d \left(a+b \text{sech}^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}+\frac{\sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right)}{e^3}-\frac{b d \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{3 e^2 \left(c^2 d+e\right) \sqrt{d+e x^2}}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{c e^{5/2}}-\frac{8 b \sqrt{d} \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{3 e^3}",1,"-(b*d*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(3*e^2*(c^2*d + e)*Sqrt[d + e*x^2]) - (d^2*(a + b*ArcSech[c*x]))/(3*e^3*(d + e*x^2)^(3/2)) + (2*d*(a + b*ArcSech[c*x]))/(e^3*Sqrt[d + e*x^2]) + (Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]))/e^3 - (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTan[(Sqrt[e]*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(c*e^(5/2)) - (8*b*Sqrt[d]*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(3*e^3)","A",10,11,23,0.4783,1,"{266, 43, 6301, 12, 1614, 157, 63, 217, 203, 93, 207}"
169,1,179,0,0.2637078,"\int \frac{x^3 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*ArcSech[c*x]))/(d + e*x^2)^(5/2),x]","-\frac{a+b \text{sech}^{-1}(c x)}{e^2 \sqrt{d+e x^2}}+\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{3 e^2 \left(d+e x^2\right)^{3/2}}+\frac{2 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{3 \sqrt{d} e^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{3 e \left(c^2 d+e\right) \sqrt{d+e x^2}}","-\frac{a+b \text{sech}^{-1}(c x)}{e^2 \sqrt{d+e x^2}}+\frac{d \left(a+b \text{sech}^{-1}(c x)\right)}{3 e^2 \left(d+e x^2\right)^{3/2}}+\frac{2 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{3 \sqrt{d} e^2}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{3 e \left(c^2 d+e\right) \sqrt{d+e x^2}}",1,"(b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(3*e*(c^2*d + e)*Sqrt[d + e*x^2]) + (d*(a + b*ArcSech[c*x]))/(3*e^2*(d + e*x^2)^(3/2)) - (a + b*ArcSech[c*x])/(e^2*Sqrt[d + e*x^2]) + (2*b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(3*Sqrt[d]*e^2)","A",7,8,23,0.3478,1,"{266, 43, 6301, 12, 573, 152, 93, 207}"
170,1,154,0,0.2908986,"\int \frac{x \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x*(a + b*ArcSech[c*x]))/(d + e*x^2)^(5/2),x]","-\frac{a+b \text{sech}^{-1}(c x)}{3 e \left(d+e x^2\right)^{3/2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{3 d^{3/2} e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{3 d \left(c^2 d+e\right) \sqrt{d+e x^2}}","-\frac{a+b \text{sech}^{-1}(c x)}{3 e \left(d+e x^2\right)^{3/2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{3 d^{3/2} e}-\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{3 d \left(c^2 d+e\right) \sqrt{d+e x^2}}",1,"-(b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(3*d*(c^2*d + e)*Sqrt[d + e*x^2]) - (a + b*ArcSech[c*x])/(3*e*(d + e*x^2)^(3/2)) + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*ArcTanh[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(3*d^(3/2)*e)","A",6,6,21,0.2857,1,"{6299, 517, 446, 96, 93, 207}"
171,0,0,0,0.122709,"\int \frac{a+b \text{sech}^{-1}(c x)}{x \left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSech[c*x])/(x*(d + e*x^2)^(5/2)),x]","\int \frac{a+b \text{sech}^{-1}(c x)}{x \left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{a+b \text{sech}^{-1}(c x)}{x \left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcSech[c*x])/(x*(d + e*x^2)^(5/2)), x]","A",0,0,0,0,-1,"{}"
172,0,0,0,0.1421356,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^3 \left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSech[c*x])/(x^3*(d + e*x^2)^(5/2)),x]","\int \frac{a+b \text{sech}^{-1}(c x)}{x^3 \left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{a+b \text{sech}^{-1}(c x)}{x^3 \left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcSech[c*x])/(x^3*(d + e*x^2)^(5/2)), x]","A",0,0,0,0,-1,"{}"
173,0,0,0,0.1215662,"\int \frac{x^6 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^6*(a + b*ArcSech[c*x]))/(d + e*x^2)^(5/2),x]","\int \frac{x^6 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{x^6 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(x^6*(a + b*ArcSech[c*x]))/(d + e*x^2)^(5/2), x]","A",0,0,0,0,-1,"{}"
174,0,0,0,0.1114146,"\int \frac{x^4 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^4*(a + b*ArcSech[c*x]))/(d + e*x^2)^(5/2),x]","\int \frac{x^4 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{x^4 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(x^4*(a + b*ArcSech[c*x]))/(d + e*x^2)^(5/2), x]","A",0,0,0,0,-1,"{}"
175,1,246,0,0.2462322,"\int \frac{x^2 \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*ArcSech[c*x]))/(d + e*x^2)^(5/2),x]","\frac{x^3 \left(a+b \text{sech}^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}-\frac{b x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{3 d \left(c^2 d+e\right) \sqrt{d+e x^2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 c d e \sqrt{d+e x^2}}-\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 d e \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1}}","\frac{x^3 \left(a+b \text{sech}^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}-\frac{b x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{3 d \left(c^2 d+e\right) \sqrt{d+e x^2}}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 c d e \sqrt{d+e x^2}}-\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 d e \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1}}",1,"-(b*x*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(3*d*(c^2*d + e)*Sqrt[d + e*x^2]) + (x^3*(a + b*ArcSech[c*x]))/(3*d*(d + e*x^2)^(3/2)) - (b*c*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(3*d*e*(c^2*d + e)*Sqrt[1 + (e*x^2)/d]) + (b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(3*c*d*e*Sqrt[d + e*x^2])","A",8,9,23,0.3913,1,"{264, 6301, 12, 471, 423, 426, 424, 421, 419}"
176,1,266,0,0.2060801,"\int \frac{a+b \text{sech}^{-1}(c x)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSech[c*x])/(d + e*x^2)^(5/2),x]","\frac{2 x \left(a+b \text{sech}^{-1}(c x)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \text{sech}^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}+\frac{b e x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{3 d^2 \left(c^2 d+e\right) \sqrt{d+e x^2}}+\frac{2 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 c d^2 \sqrt{d+e x^2}}+\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 d^2 \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1}}","\frac{2 x \left(a+b \text{sech}^{-1}(c x)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \text{sech}^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}+\frac{b e x \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{3 d^2 \left(c^2 d+e\right) \sqrt{d+e x^2}}+\frac{2 b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 c d^2 \sqrt{d+e x^2}}+\frac{b c \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 d^2 \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1}}",1,"(b*e*x*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(3*d^2*(c^2*d + e)*Sqrt[d + e*x^2]) + (x*(a + b*ArcSech[c*x]))/(3*d*(d + e*x^2)^(3/2)) + (2*x*(a + b*ArcSech[c*x]))/(3*d^2*Sqrt[d + e*x^2]) + (b*c*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(3*d^2*(c^2*d + e)*Sqrt[1 + (e*x^2)/d]) + (2*b*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(3*c*d^2*Sqrt[d + e*x^2])","A",8,10,20,0.5000,1,"{192, 191, 6291, 12, 527, 524, 426, 424, 421, 419}"
177,1,576,0,2.5453346,"\int (f x)^m \left(d+e x^2\right)^3 \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^3*(a + b*ArcSech[c*x]),x]","\frac{3 d^2 e (f x)^{m+3} \left(a+b \text{sech}^{-1}(c x)\right)}{f^3 (m+3)}+\frac{d^3 (f x)^{m+1} \left(a+b \text{sech}^{-1}(c x)\right)}{f (m+1)}+\frac{3 d e^2 (f x)^{m+5} \left(a+b \text{sech}^{-1}(c x)\right)}{f^5 (m+5)}+\frac{e^3 (f x)^{m+7} \left(a+b \text{sech}^{-1}(c x)\right)}{f^7 (m+7)}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} (f x)^{m+1} \left(\frac{e \left(3 c^4 d^2 \left(m^4+22 m^3+179 m^2+638 m+840\right)+3 c^2 d e (m+3)^2 \left(m^2+13 m+42\right)+e^2 \left(m^2+8 m+15\right)^2\right)}{c^6 (m+2) (m+3) (m+4) (m+5) (m+6) (m+7)}+\frac{d^3}{(m+1)^2}\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right)}{f}-\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} (f x)^{m+1} \left(3 c^4 d^2 \left(m^4+22 m^3+179 m^2+638 m+840\right)+3 c^2 d e (m+3)^2 \left(m^2+13 m+42\right)+e^2 \left(m^2+8 m+15\right)^2\right)}{c^6 f (m+2) (m+3) (m+4) (m+5) (m+6) (m+7)}-\frac{b e^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} (f x)^{m+3} \left(3 c^2 d \left(m^2+13 m+42\right)+e (m+5)^2\right)}{c^4 f^3 (m+4) (m+5) (m+6) (m+7)}-\frac{b e^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} (f x)^{m+5}}{c^2 f^5 (m+6) (m+7)}","\frac{3 d^2 e (f x)^{m+3} \left(a+b \text{sech}^{-1}(c x)\right)}{f^3 (m+3)}+\frac{d^3 (f x)^{m+1} \left(a+b \text{sech}^{-1}(c x)\right)}{f (m+1)}+\frac{3 d e^2 (f x)^{m+5} \left(a+b \text{sech}^{-1}(c x)\right)}{f^5 (m+5)}+\frac{e^3 (f x)^{m+7} \left(a+b \text{sech}^{-1}(c x)\right)}{f^7 (m+7)}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} (f x)^{m+1} \left(\frac{e (m+1) \left(3 c^4 d^2 \left(m^4+22 m^3+179 m^2+638 m+840\right)+3 c^2 d e (m+3)^2 \left(m^2+13 m+42\right)+e^2 \left(m^2+8 m+15\right)^2\right)}{(m+3) (m+5) (m+7)}+\frac{c^6 d^3 (m+2) (m+4) (m+6)}{m+1}\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right)}{c^6 f (m+1) (m+2) (m+4) (m+6)}-\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} (f x)^{m+1} \left(3 c^4 d^2 \left(m^4+22 m^3+179 m^2+638 m+840\right)+3 c^2 d e (m+3)^2 \left(m^2+13 m+42\right)+e^2 \left(m^2+8 m+15\right)^2\right)}{c^6 f (m+2) (m+3) (m+4) (m+5) (m+6) (m+7)}-\frac{b e^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} (f x)^{m+3} \left(3 c^2 d \left(m^2+13 m+42\right)+e (m+5)^2\right)}{c^4 f^3 (m+4) (m+5) (m+6) (m+7)}-\frac{b e^3 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} (f x)^{m+5}}{c^2 f^5 (m+6) (m+7)}",1,"-((b*e*(e^2*(15 + 8*m + m^2)^2 + 3*c^2*d*e*(3 + m)^2*(42 + 13*m + m^2) + 3*c^4*d^2*(840 + 638*m + 179*m^2 + 22*m^3 + m^4))*(f*x)^(1 + m)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(c^6*f*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7 + m))) - (b*e^2*(e*(5 + m)^2 + 3*c^2*d*(42 + 13*m + m^2))*(f*x)^(3 + m)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(c^4*f^3*(4 + m)*(5 + m)*(6 + m)*(7 + m)) - (b*e^3*(f*x)^(5 + m)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(c^2*f^5*(6 + m)*(7 + m)) + (d^3*(f*x)^(1 + m)*(a + b*ArcSech[c*x]))/(f*(1 + m)) + (3*d^2*e*(f*x)^(3 + m)*(a + b*ArcSech[c*x]))/(f^3*(3 + m)) + (3*d*e^2*(f*x)^(5 + m)*(a + b*ArcSech[c*x]))/(f^5*(5 + m)) + (e^3*(f*x)^(7 + m)*(a + b*ArcSech[c*x]))/(f^7*(7 + m)) + (b*(d^3/(1 + m)^2 + (e*(e^2*(15 + 8*m + m^2)^2 + 3*c^2*d*e*(3 + m)^2*(42 + 13*m + m^2) + 3*c^4*d^2*(840 + 638*m + 179*m^2 + 22*m^3 + m^4)))/(c^6*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7 + m)))*(f*x)^(1 + m)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/f","A",5,6,23,0.2609,1,"{270, 6301, 1809, 1267, 459, 364}"
178,1,352,0,0.4317089,"\int (f x)^m \left(d+e x^2\right)^2 \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^2*(a + b*ArcSech[c*x]),x]","\frac{d^2 (f x)^{m+1} \left(a+b \text{sech}^{-1}(c x)\right)}{f (m+1)}+\frac{2 d e (f x)^{m+3} \left(a+b \text{sech}^{-1}(c x)\right)}{f^3 (m+3)}+\frac{e^2 (f x)^{m+5} \left(a+b \text{sech}^{-1}(c x)\right)}{f^5 (m+5)}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} (f x)^{m+1} \left(\frac{e \left(2 c^2 d \left(m^2+9 m+20\right)+e (m+3)^2\right)}{c^4 (m+2) (m+3) (m+4) (m+5)}+\frac{d^2}{(m+1)^2}\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right)}{f}-\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} (f x)^{m+1} \left(2 c^2 d \left(m^2+9 m+20\right)+e (m+3)^2\right)}{c^4 f (m+2) (m+3) (m+4) (m+5)}-\frac{b e^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} (f x)^{m+3}}{c^2 f^3 (m+4) (m+5)}","\frac{d^2 (f x)^{m+1} \left(a+b \text{sech}^{-1}(c x)\right)}{f (m+1)}+\frac{2 d e (f x)^{m+3} \left(a+b \text{sech}^{-1}(c x)\right)}{f^3 (m+3)}+\frac{e^2 (f x)^{m+5} \left(a+b \text{sech}^{-1}(c x)\right)}{f^5 (m+5)}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} (f x)^{m+1} \left(c^4 d^2 (m+2) (m+3) (m+4) (m+5)+e (m+1)^2 \left(2 c^2 d \left(m^2+9 m+20\right)+e (m+3)^2\right)\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right)}{c^4 f (m+1)^2 (m+2) (m+3) (m+4) (m+5)}-\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} (f x)^{m+1} \left(2 c^2 d \left(m^2+9 m+20\right)+e (m+3)^2\right)}{c^4 f (m+2) (m+3) (m+4) (m+5)}-\frac{b e^2 \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} (f x)^{m+3}}{c^2 f^3 (m+4) (m+5)}",1,"-((b*e*(e*(3 + m)^2 + 2*c^2*d*(20 + 9*m + m^2))*(f*x)^(1 + m)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(c^4*f*(2 + m)*(3 + m)*(4 + m)*(5 + m))) - (b*e^2*(f*x)^(3 + m)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(c^2*f^3*(4 + m)*(5 + m)) + (d^2*(f*x)^(1 + m)*(a + b*ArcSech[c*x]))/(f*(1 + m)) + (2*d*e*(f*x)^(3 + m)*(a + b*ArcSech[c*x]))/(f^3*(3 + m)) + (e^2*(f*x)^(5 + m)*(a + b*ArcSech[c*x]))/(f^5*(5 + m)) + (b*(d^2/(1 + m)^2 + (e*(e*(3 + m)^2 + 2*c^2*d*(20 + 9*m + m^2)))/(c^4*(2 + m)*(3 + m)*(4 + m)*(5 + m)))*(f*x)^(1 + m)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/f","A",5,6,23,0.2609,1,"{270, 6301, 12, 1267, 459, 364}"
179,1,192,0,0.1791433,"\int (f x)^m \left(d+e x^2\right) \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)*(a + b*ArcSech[c*x]),x]","\frac{d (f x)^{m+1} \left(a+b \text{sech}^{-1}(c x)\right)}{f (m+1)}+\frac{e (f x)^{m+3} \left(a+b \text{sech}^{-1}(c x)\right)}{f^3 (m+3)}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} (f x)^{m+1} \left(\frac{e}{c^2 (m+2) (m+3)}+\frac{d}{(m+1)^2}\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right)}{f}-\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} (f x)^{m+1}}{c^2 f (m+2) (m+3)}","\frac{d (f x)^{m+1} \left(a+b \text{sech}^{-1}(c x)\right)}{f (m+1)}+\frac{e (f x)^{m+3} \left(a+b \text{sech}^{-1}(c x)\right)}{f^3 (m+3)}+\frac{b \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} (f x)^{m+1} \left(c^2 d (m+2) (m+3)+e (m+1)^2\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right)}{c^2 f (m+1)^2 (m+2) (m+3)}-\frac{b e \sqrt{\frac{1}{c x+1}} \sqrt{c x+1} \sqrt{1-c^2 x^2} (f x)^{m+1}}{c^2 f (m+2) (m+3)}",1,"-((b*e*(f*x)^(1 + m)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(c^2*f*(2 + m)*(3 + m))) + (d*(f*x)^(1 + m)*(a + b*ArcSech[c*x]))/(f*(1 + m)) + (e*(f*x)^(3 + m)*(a + b*ArcSech[c*x]))/(f^3*(3 + m)) + (b*(d/(1 + m)^2 + e/(c^2*(2 + m)*(3 + m)))*(f*x)^(1 + m)*Sqrt[(1 + c*x)^(-1)]*Sqrt[1 + c*x]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/f","A",4,5,21,0.2381,1,"{14, 6301, 12, 459, 364}"
180,0,0,0,0.0755577,"\int \frac{(f x)^m \left(a+b \text{sech}^{-1}(c x)\right)}{d+e x^2} \, dx","Int[((f*x)^m*(a + b*ArcSech[c*x]))/(d + e*x^2),x]","\int \frac{(f x)^m \left(a+b \text{sech}^{-1}(c x)\right)}{d+e x^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \text{sech}^{-1}(c x)\right)}{d+e x^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcSech[c*x]))/(d + e*x^2), x]","A",0,0,0,0,-1,"{}"
181,0,0,0,0.0749564,"\int \frac{(f x)^m \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[((f*x)^m*(a + b*ArcSech[c*x]))/(d + e*x^2)^2,x]","\int \frac{(f x)^m \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcSech[c*x]))/(d + e*x^2)^2, x]","A",0,0,0,0,-1,"{}"
182,0,0,0,0.109657,"\int (f x)^m \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]),x]","\int (f x)^m \left(d+e x^2\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","\text{Int}\left(\left(d+e x^2\right)^{3/2} (f x)^m \left(a+b \text{sech}^{-1}(c x)\right),x\right)",0,"Defer[Int][(f*x)^m*(d + e*x^2)^(3/2)*(a + b*ArcSech[c*x]), x]","A",0,0,0,0,-1,"{}"
183,0,0,0,0.0986537,"\int (f x)^m \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","Int[(f*x)^m*Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]),x]","\int (f x)^m \sqrt{d+e x^2} \left(a+b \text{sech}^{-1}(c x)\right) \, dx","\text{Int}\left(\sqrt{d+e x^2} (f x)^m \left(a+b \text{sech}^{-1}(c x)\right),x\right)",0,"Defer[Int][(f*x)^m*Sqrt[d + e*x^2]*(a + b*ArcSech[c*x]), x]","A",0,0,0,0,-1,"{}"
184,0,0,0,0.0999564,"\int \frac{(f x)^m \left(a+b \text{sech}^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[((f*x)^m*(a + b*ArcSech[c*x]))/Sqrt[d + e*x^2],x]","\int \frac{(f x)^m \left(a+b \text{sech}^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \text{sech}^{-1}(c x)\right)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcSech[c*x]))/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
185,0,0,0,0.1104235,"\int \frac{(f x)^m \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[((f*x)^m*(a + b*ArcSech[c*x]))/(d + e*x^2)^(3/2),x]","\int \frac{(f x)^m \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \text{sech}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcSech[c*x]))/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
186,1,473,0,1.5794861,"\int \frac{x^{11} \left(a+b \text{sech}^{-1}(c x)\right)}{\sqrt{1-c^4 x^4}} \, dx","Int[(x^11*(a + b*ArcSech[c*x]))/Sqrt[1 - c^4*x^4],x]","-\frac{\left(1-c^4 x^4\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{10 c^{12}}+\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 c^{12}}-\frac{\sqrt{1-c^4 x^4} \left(a+b \text{sech}^{-1}(c x)\right)}{2 c^{12}}-\frac{b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{9/2}}{90 c^{13} x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{3 b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{7/2}}{70 c^{13} x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{13 b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{5/2}}{150 c^{13} x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{7 b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{3/2}}{90 c^{13} x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{c^2 x^2+1}}{15 c^{13} x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{4 b \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{15 c^{13} x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}","-\frac{\left(1-c^4 x^4\right)^{5/2} \left(a+b \text{sech}^{-1}(c x)\right)}{10 c^{12}}+\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{3 c^{12}}-\frac{\sqrt{1-c^4 x^4} \left(a+b \text{sech}^{-1}(c x)\right)}{2 c^{12}}-\frac{b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{9/2}}{90 c^{13} x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{3 b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{7/2}}{70 c^{13} x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{13 b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{5/2}}{150 c^{13} x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{7 b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{3/2}}{90 c^{13} x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{c^2 x^2+1}}{15 c^{13} x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{4 b \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{15 c^{13} x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}",1,"(-4*b*Sqrt[1 - c^2*x^2]*Sqrt[1 + c^2*x^2])/(15*c^13*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x) + (7*b*Sqrt[1 - c^2*x^2]*(1 + c^2*x^2)^(3/2))/(90*c^13*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x) - (13*b*Sqrt[1 - c^2*x^2]*(1 + c^2*x^2)^(5/2))/(150*c^13*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x) + (3*b*Sqrt[1 - c^2*x^2]*(1 + c^2*x^2)^(7/2))/(70*c^13*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x) - (b*Sqrt[1 - c^2*x^2]*(1 + c^2*x^2)^(9/2))/(90*c^13*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x) - (Sqrt[1 - c^4*x^4]*(a + b*ArcSech[c*x]))/(2*c^12) + ((1 - c^4*x^4)^(3/2)*(a + b*ArcSech[c*x]))/(3*c^12) - ((1 - c^4*x^4)^(5/2)*(a + b*ArcSech[c*x]))/(10*c^12) + (4*b*Sqrt[1 - c^2*x^2]*ArcTanh[Sqrt[1 + c^2*x^2]])/(15*c^13*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x)","A",15,10,26,0.3846,1,"{266, 43, 6309, 12, 6742, 848, 50, 63, 208, 783}"
187,1,316,0,1.3829378,"\int \frac{x^7 \left(a+b \text{sech}^{-1}(c x)\right)}{\sqrt{1-c^4 x^4}} \, dx","Int[(x^7*(a + b*ArcSech[c*x]))/Sqrt[1 - c^4*x^4],x]","\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{6 c^8}-\frac{\sqrt{1-c^4 x^4} \left(a+b \text{sech}^{-1}(c x)\right)}{2 c^8}-\frac{b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{5/2}}{30 c^9 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{3/2}}{18 c^9 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{b \sqrt{1-c^2 x^2} \sqrt{c^2 x^2+1}}{3 c^9 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{3 c^9 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}","\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \text{sech}^{-1}(c x)\right)}{6 c^8}-\frac{\sqrt{1-c^4 x^4} \left(a+b \text{sech}^{-1}(c x)\right)}{2 c^8}-\frac{b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{5/2}}{30 c^9 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{3/2}}{18 c^9 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}-\frac{b \sqrt{1-c^2 x^2} \sqrt{c^2 x^2+1}}{3 c^9 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{3 c^9 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}",1,"-(b*Sqrt[1 - c^2*x^2]*Sqrt[1 + c^2*x^2])/(3*c^9*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x) + (b*Sqrt[1 - c^2*x^2]*(1 + c^2*x^2)^(3/2))/(18*c^9*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x) - (b*Sqrt[1 - c^2*x^2]*(1 + c^2*x^2)^(5/2))/(30*c^9*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x) - (Sqrt[1 - c^4*x^4]*(a + b*ArcSech[c*x]))/(2*c^8) + ((1 - c^4*x^4)^(3/2)*(a + b*ArcSech[c*x]))/(6*c^8) + (b*Sqrt[1 - c^2*x^2]*ArcTanh[Sqrt[1 + c^2*x^2]])/(3*c^9*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x)","A",12,10,26,0.3846,1,"{266, 43, 6309, 12, 6742, 848, 50, 63, 208, 783}"
188,1,159,0,0.1637261,"\int \frac{x^3 \left(a+b \text{sech}^{-1}(c x)\right)}{\sqrt{1-c^4 x^4}} \, dx","Int[(x^3*(a + b*ArcSech[c*x]))/Sqrt[1 - c^4*x^4],x]","-\frac{\sqrt{1-c^4 x^4} \left(a+b \text{sech}^{-1}(c x)\right)}{2 c^4}-\frac{b \sqrt{1-c^2 x^2} \sqrt{c^2 x^2+1}}{2 c^5 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{2 c^5 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}","-\frac{\sqrt{1-c^4 x^4} \left(a+b \text{sech}^{-1}(c x)\right)}{2 c^4}-\frac{b \sqrt{1-c^2 x^2} \sqrt{c^2 x^2+1}}{2 c^5 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}+\frac{b \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{2 c^5 x \sqrt{\frac{1}{c x}-1} \sqrt{\frac{1}{c x}+1}}",1,"-(b*Sqrt[1 - c^2*x^2]*Sqrt[1 + c^2*x^2])/(2*c^5*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x) - (Sqrt[1 - c^4*x^4]*(a + b*ArcSech[c*x]))/(2*c^4) + (b*Sqrt[1 - c^2*x^2]*ArcTanh[Sqrt[1 + c^2*x^2]])/(2*c^5*Sqrt[-1 + 1/(c*x)]*Sqrt[1 + 1/(c*x)]*x)","A",7,8,26,0.3077,1,"{261, 6309, 12, 1252, 848, 50, 63, 208}"
189,0,0,0,0.0910904,"\int \frac{a+b \text{sech}^{-1}(c x)}{x \sqrt{1-c^4 x^4}} \, dx","Int[(a + b*ArcSech[c*x])/(x*Sqrt[1 - c^4*x^4]),x]","\int \frac{a+b \text{sech}^{-1}(c x)}{x \sqrt{1-c^4 x^4}} \, dx","\text{Int}\left(\frac{a+b \text{sech}^{-1}(c x)}{x \sqrt{1-c^4 x^4}},x\right)",0,"Defer[Int][(a + b*ArcSech[c*x])/(x*Sqrt[1 - c^4*x^4]), x]","A",0,0,0,0,-1,"{}"
190,0,0,0,0.1017061,"\int \frac{a+b \text{sech}^{-1}(c x)}{x^5 \sqrt{1-c^4 x^4}} \, dx","Int[(a + b*ArcSech[c*x])/(x^5*Sqrt[1 - c^4*x^4]),x]","\int \frac{a+b \text{sech}^{-1}(c x)}{x^5 \sqrt{1-c^4 x^4}} \, dx","\text{Int}\left(\frac{a+b \text{sech}^{-1}(c x)}{x^5 \sqrt{1-c^4 x^4}},x\right)",0,"Defer[Int][(a + b*ArcSech[c*x])/(x^5*Sqrt[1 - c^4*x^4]), x]","A",0,0,0,0,-1,"{}"