1,-1,0,0,0.000000," ","integrate(x^4*arcsech(a*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2,0,0,0,0.000000," ","integrate(x^3*arcsech(a*x)^2,x, algorithm=""maxima"")","\int x^{3} \operatorname{arsech}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(x^3*arcsech(a*x)^2, x)","F",0
3,0,0,0,0.000000," ","integrate(x^2*arcsech(a*x)^2,x, algorithm=""maxima"")","\int x^{2} \operatorname{arsech}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(x^2*arcsech(a*x)^2, x)","F",0
4,1,40,0,0.329459," ","integrate(x*arcsech(a*x)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arsech}\left(a x\right)^{2} - \frac{x \sqrt{\frac{1}{a^{2} x^{2}} - 1} \operatorname{arsech}\left(a x\right)}{a} - \frac{\log\left(x\right)}{a^{2}}"," ",0,"1/2*x^2*arcsech(a*x)^2 - x*sqrt(1/(a^2*x^2) - 1)*arcsech(a*x)/a - log(x)/a^2","A",0
5,0,0,0,0.000000," ","integrate(arcsech(a*x)^2,x, algorithm=""maxima"")","x \log\left(\sqrt{a x + 1} \sqrt{-a x + 1} + 1\right)^{2} - \int -\frac{a^{2} x^{2} \log\left(a\right)^{2} + {\left(a^{2} x^{2} - 1\right)} \log\left(x\right)^{2} + {\left(a^{2} x^{2} \log\left(a\right)^{2} + {\left(a^{2} x^{2} - 1\right)} \log\left(x\right)^{2} - \log\left(a\right)^{2} + 2 \, {\left(a^{2} x^{2} \log\left(a\right) - \log\left(a\right)\right)} \log\left(x\right)\right)} \sqrt{a x + 1} \sqrt{-a x + 1} - 2 \, {\left(a^{2} x^{2} \log\left(a\right) + {\left(a^{2} x^{2} {\left(\log\left(a\right) + 1\right)} + {\left(a^{2} x^{2} - 1\right)} \log\left(x\right) - \log\left(a\right)\right)} \sqrt{a x + 1} \sqrt{-a x + 1} + {\left(a^{2} x^{2} - 1\right)} \log\left(x\right) - \log\left(a\right)\right)} \log\left(\sqrt{a x + 1} \sqrt{-a x + 1} + 1\right) - \log\left(a\right)^{2} + 2 \, {\left(a^{2} x^{2} \log\left(a\right) - \log\left(a\right)\right)} \log\left(x\right)}{a^{2} x^{2} + {\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{-a x + 1} - 1}\,{d x}"," ",0,"x*log(sqrt(a*x + 1)*sqrt(-a*x + 1) + 1)^2 - integrate(-(a^2*x^2*log(a)^2 + (a^2*x^2 - 1)*log(x)^2 + (a^2*x^2*log(a)^2 + (a^2*x^2 - 1)*log(x)^2 - log(a)^2 + 2*(a^2*x^2*log(a) - log(a))*log(x))*sqrt(a*x + 1)*sqrt(-a*x + 1) - 2*(a^2*x^2*log(a) + (a^2*x^2*(log(a) + 1) + (a^2*x^2 - 1)*log(x) - log(a))*sqrt(a*x + 1)*sqrt(-a*x + 1) + (a^2*x^2 - 1)*log(x) - log(a))*log(sqrt(a*x + 1)*sqrt(-a*x + 1) + 1) - log(a)^2 + 2*(a^2*x^2*log(a) - log(a))*log(x))/(a^2*x^2 + (a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(-a*x + 1) - 1), x)","F",0
6,0,0,0,0.000000," ","integrate(arcsech(a*x)^2/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arsech}\left(a x\right)^{2}}{x}\,{d x}"," ",0,"integrate(arcsech(a*x)^2/x, x)","F",0
7,1,35,0,0.328058," ","integrate(arcsech(a*x)^2/x^2,x, algorithm=""maxima"")","2 \, a \sqrt{\frac{1}{a^{2} x^{2}} - 1} \operatorname{arsech}\left(a x\right) - \frac{\operatorname{arsech}\left(a x\right)^{2}}{x} - \frac{2}{x}"," ",0,"2*a*sqrt(1/(a^2*x^2) - 1)*arcsech(a*x) - arcsech(a*x)^2/x - 2/x","A",0
8,0,0,0,0.000000," ","integrate(arcsech(a*x)^2/x^3,x, algorithm=""maxima"")","\int \frac{\operatorname{arsech}\left(a x\right)^{2}}{x^{3}}\,{d x}"," ",0,"integrate(arcsech(a*x)^2/x^3, x)","F",0
9,0,0,0,0.000000," ","integrate(arcsech(a*x)^2/x^4,x, algorithm=""maxima"")","\int \frac{\operatorname{arsech}\left(a x\right)^{2}}{x^{4}}\,{d x}"," ",0,"integrate(arcsech(a*x)^2/x^4, x)","F",0
10,0,0,0,0.000000," ","integrate(x^4*arcsech(a*x)^3,x, algorithm=""maxima"")","\int x^{4} \operatorname{arsech}\left(a x\right)^{3}\,{d x}"," ",0,"integrate(x^4*arcsech(a*x)^3, x)","F",0
11,0,0,0,0.000000," ","integrate(x^3*arcsech(a*x)^3,x, algorithm=""maxima"")","\int x^{3} \operatorname{arsech}\left(a x\right)^{3}\,{d x}"," ",0,"integrate(x^3*arcsech(a*x)^3, x)","F",0
12,0,0,0,0.000000," ","integrate(x^2*arcsech(a*x)^3,x, algorithm=""maxima"")","\int x^{2} \operatorname{arsech}\left(a x\right)^{3}\,{d x}"," ",0,"integrate(x^2*arcsech(a*x)^3, x)","F",0
13,0,0,0,0.000000," ","integrate(x*arcsech(a*x)^3,x, algorithm=""maxima"")","\int x \operatorname{arsech}\left(a x\right)^{3}\,{d x}"," ",0,"integrate(x*arcsech(a*x)^3, x)","F",0
14,0,0,0,0.000000," ","integrate(arcsech(a*x)^3,x, algorithm=""maxima"")","x \log\left(\sqrt{a x + 1} \sqrt{-a x + 1} + 1\right)^{3} - \int \frac{a^{2} x^{2} \log\left(a\right)^{3} + {\left(a^{2} x^{2} - 1\right)} \log\left(x\right)^{3} + 3 \, {\left(a^{2} x^{2} \log\left(a\right) + {\left(a^{2} x^{2} {\left(\log\left(a\right) + 1\right)} + {\left(a^{2} x^{2} - 1\right)} \log\left(x\right) - \log\left(a\right)\right)} \sqrt{a x + 1} \sqrt{-a x + 1} + {\left(a^{2} x^{2} - 1\right)} \log\left(x\right) - \log\left(a\right)\right)} \log\left(\sqrt{a x + 1} \sqrt{-a x + 1} + 1\right)^{2} - \log\left(a\right)^{3} + 3 \, {\left(a^{2} x^{2} \log\left(a\right) - \log\left(a\right)\right)} \log\left(x\right)^{2} + {\left(a^{2} x^{2} \log\left(a\right)^{3} + {\left(a^{2} x^{2} - 1\right)} \log\left(x\right)^{3} - \log\left(a\right)^{3} + 3 \, {\left(a^{2} x^{2} \log\left(a\right) - \log\left(a\right)\right)} \log\left(x\right)^{2} + 3 \, {\left(a^{2} x^{2} \log\left(a\right)^{2} - \log\left(a\right)^{2}\right)} \log\left(x\right)\right)} \sqrt{a x + 1} \sqrt{-a x + 1} - 3 \, {\left(a^{2} x^{2} \log\left(a\right)^{2} + {\left(a^{2} x^{2} - 1\right)} \log\left(x\right)^{2} + {\left(a^{2} x^{2} \log\left(a\right)^{2} + {\left(a^{2} x^{2} - 1\right)} \log\left(x\right)^{2} - \log\left(a\right)^{2} + 2 \, {\left(a^{2} x^{2} \log\left(a\right) - \log\left(a\right)\right)} \log\left(x\right)\right)} \sqrt{a x + 1} \sqrt{-a x + 1} - \log\left(a\right)^{2} + 2 \, {\left(a^{2} x^{2} \log\left(a\right) - \log\left(a\right)\right)} \log\left(x\right)\right)} \log\left(\sqrt{a x + 1} \sqrt{-a x + 1} + 1\right) + 3 \, {\left(a^{2} x^{2} \log\left(a\right)^{2} - \log\left(a\right)^{2}\right)} \log\left(x\right)}{a^{2} x^{2} + {\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{-a x + 1} - 1}\,{d x}"," ",0,"x*log(sqrt(a*x + 1)*sqrt(-a*x + 1) + 1)^3 - integrate((a^2*x^2*log(a)^3 + (a^2*x^2 - 1)*log(x)^3 + 3*(a^2*x^2*log(a) + (a^2*x^2*(log(a) + 1) + (a^2*x^2 - 1)*log(x) - log(a))*sqrt(a*x + 1)*sqrt(-a*x + 1) + (a^2*x^2 - 1)*log(x) - log(a))*log(sqrt(a*x + 1)*sqrt(-a*x + 1) + 1)^2 - log(a)^3 + 3*(a^2*x^2*log(a) - log(a))*log(x)^2 + (a^2*x^2*log(a)^3 + (a^2*x^2 - 1)*log(x)^3 - log(a)^3 + 3*(a^2*x^2*log(a) - log(a))*log(x)^2 + 3*(a^2*x^2*log(a)^2 - log(a)^2)*log(x))*sqrt(a*x + 1)*sqrt(-a*x + 1) - 3*(a^2*x^2*log(a)^2 + (a^2*x^2 - 1)*log(x)^2 + (a^2*x^2*log(a)^2 + (a^2*x^2 - 1)*log(x)^2 - log(a)^2 + 2*(a^2*x^2*log(a) - log(a))*log(x))*sqrt(a*x + 1)*sqrt(-a*x + 1) - log(a)^2 + 2*(a^2*x^2*log(a) - log(a))*log(x))*log(sqrt(a*x + 1)*sqrt(-a*x + 1) + 1) + 3*(a^2*x^2*log(a)^2 - log(a)^2)*log(x))/(a^2*x^2 + (a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(-a*x + 1) - 1), x)","F",0
15,0,0,0,0.000000," ","integrate(arcsech(a*x)^3/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arsech}\left(a x\right)^{3}}{x}\,{d x}"," ",0,"integrate(arcsech(a*x)^3/x, x)","F",0
16,1,55,0,0.321521," ","integrate(arcsech(a*x)^3/x^2,x, algorithm=""maxima"")","3 \, a \sqrt{\frac{1}{a^{2} x^{2}} - 1} \operatorname{arsech}\left(a x\right)^{2} - \frac{\operatorname{arsech}\left(a x\right)^{3}}{x} + 6 \, a \sqrt{\frac{1}{a^{2} x^{2}} - 1} - \frac{6 \, \operatorname{arsech}\left(a x\right)}{x}"," ",0,"3*a*sqrt(1/(a^2*x^2) - 1)*arcsech(a*x)^2 - arcsech(a*x)^3/x + 6*a*sqrt(1/(a^2*x^2) - 1) - 6*arcsech(a*x)/x","A",0
17,0,0,0,0.000000," ","integrate(arcsech(a*x)^3/x^3,x, algorithm=""maxima"")","\int \frac{\operatorname{arsech}\left(a x\right)^{3}}{x^{3}}\,{d x}"," ",0,"integrate(arcsech(a*x)^3/x^3, x)","F",0
18,0,0,0,0.000000," ","integrate(arcsech(a*x)^3/x^4,x, algorithm=""maxima"")","\int \frac{\operatorname{arsech}\left(a x\right)^{3}}{x^{4}}\,{d x}"," ",0,"integrate(arcsech(a*x)^3/x^4, x)","F",0
19,1,135,0,0.411639," ","integrate(x^6*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a x^{7} + \frac{1}{336} \, {\left(48 \, x^{7} \operatorname{arsech}\left(c x\right) - \frac{\frac{15 \, {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} + 40 \, {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 33 \, \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} + 3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{6}} + \frac{15 \, \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{6}}}{c}\right)} b"," ",0,"1/7*a*x^7 + 1/336*(48*x^7*arcsech(c*x) - ((15*(1/(c^2*x^2) - 1)^(5/2) + 40*(1/(c^2*x^2) - 1)^(3/2) + 33*sqrt(1/(c^2*x^2) - 1))/(c^6*(1/(c^2*x^2) - 1)^3 + 3*c^6*(1/(c^2*x^2) - 1)^2 + 3*c^6*(1/(c^2*x^2) - 1) + c^6) + 15*arctan(sqrt(1/(c^2*x^2) - 1))/c^6)/c)*b","A",0
20,1,78,0,0.311095," ","integrate(x^5*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} + \frac{1}{90} \, {\left(15 \, x^{6} \operatorname{arsech}\left(c x\right) - \frac{3 \, c^{4} x^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} - 10 \, c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 15 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{5}}\right)} b"," ",0,"1/6*a*x^6 + 1/90*(15*x^6*arcsech(c*x) - (3*c^4*x^5*(1/(c^2*x^2) - 1)^(5/2) - 10*c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) + 15*x*sqrt(1/(c^2*x^2) - 1))/c^5)*b","A",0
21,1,106,0,0.409816," ","integrate(x^4*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} + \frac{1}{40} \, {\left(8 \, x^{5} \operatorname{arsech}\left(c x\right) - \frac{\frac{3 \, {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 5 \, \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{4}} + \frac{3 \, \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{4}}}{c}\right)} b"," ",0,"1/5*a*x^5 + 1/40*(8*x^5*arcsech(c*x) - ((3*(1/(c^2*x^2) - 1)^(3/2) + 5*sqrt(1/(c^2*x^2) - 1))/(c^4*(1/(c^2*x^2) - 1)^2 + 2*c^4*(1/(c^2*x^2) - 1) + c^4) + 3*arctan(sqrt(1/(c^2*x^2) - 1))/c^4)/c)*b","A",0
22,1,57,0,0.305495," ","integrate(x^3*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{12} \, {\left(3 \, x^{4} \operatorname{arsech}\left(c x\right) + \frac{c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} - 3 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{3}}\right)} b"," ",0,"1/4*a*x^4 + 1/12*(3*x^4*arcsech(c*x) + (c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) - 3*x*sqrt(1/(c^2*x^2) - 1))/c^3)*b","A",0
23,1,73,0,0.403800," ","integrate(x^2*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{arsech}\left(c x\right) - \frac{\frac{\sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{2}}}{c}\right)} b"," ",0,"1/3*a*x^3 + 1/6*(2*x^3*arcsech(c*x) - (sqrt(1/(c^2*x^2) - 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + arctan(sqrt(1/(c^2*x^2) - 1))/c^2)/c)*b","A",0
24,1,36,0,0.301869," ","integrate(x*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{2} \, {\left(x^{2} \operatorname{arsech}\left(c x\right) - \frac{x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c}\right)} b"," ",0,"1/2*a*x^2 + 1/2*(x^2*arcsech(c*x) - x*sqrt(1/(c^2*x^2) - 1)/c)*b","A",0
25,1,31,0,0.300946," ","integrate(a+b*arcsech(c*x),x, algorithm=""maxima"")","a x + \frac{{\left(c x \operatorname{arsech}\left(c x\right) - \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)\right)} b}{c}"," ",0,"a*x + (c*x*arcsech(c*x) - arctan(sqrt(1/(c^2*x^2) - 1)))*b/c","A",0
26,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x,x, algorithm=""maxima"")","b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{x}\,{d x} + a \log\left(x\right)"," ",0,"b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/x, x) + a*log(x)","F",0
27,1,32,0,0.306832," ","integrate((a+b*arcsech(c*x))/x^2,x, algorithm=""maxima"")","{\left(c \sqrt{\frac{1}{c^{2} x^{2}} - 1} - \frac{\operatorname{arsech}\left(c x\right)}{x}\right)} b - \frac{a}{x}"," ",0,"(c*sqrt(1/(c^2*x^2) - 1) - arcsech(c*x)/x)*b - a/x","A",0
28,1,105,0,0.307260," ","integrate((a+b*arcsech(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{8} \, b {\left(\frac{\frac{2 \, c^{4} x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} - 1} - c^{3} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} + 1\right) + c^{3} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} - 1\right)}{c} + \frac{4 \, \operatorname{arsech}\left(c x\right)}{x^{2}}\right)} - \frac{a}{2 \, x^{2}}"," ",0,"-1/8*b*((2*c^4*x*sqrt(1/(c^2*x^2) - 1)/(c^2*x^2*(1/(c^2*x^2) - 1) - 1) - c^3*log(c*x*sqrt(1/(c^2*x^2) - 1) + 1) + c^3*log(c*x*sqrt(1/(c^2*x^2) - 1) - 1))/c + 4*arcsech(c*x)/x^2) - 1/2*a/x^2","A",0
29,1,56,0,0.303175," ","integrate((a+b*arcsech(c*x))/x^4,x, algorithm=""maxima"")","\frac{1}{9} \, b {\left(\frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 3 \, c^{4} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{3 \, \operatorname{arsech}\left(c x\right)}{x^{3}}\right)} - \frac{a}{3 \, x^{3}}"," ",0,"1/9*b*((c^4*(1/(c^2*x^2) - 1)^(3/2) + 3*c^4*sqrt(1/(c^2*x^2) - 1))/c - 3*arcsech(c*x)/x^3) - 1/3*a/x^3","A",0
30,1,147,0,0.305938," ","integrate((a+b*arcsech(c*x))/x^5,x, algorithm=""maxima"")","\frac{1}{64} \, b {\left(\frac{3 \, c^{5} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} + 1\right) - 3 \, c^{5} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} - 1\right) - \frac{2 \, {\left(3 \, c^{8} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} - 5 \, c^{6} x \sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}}{c^{4} x^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} - 2 \, c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + 1}}{c} - \frac{16 \, \operatorname{arsech}\left(c x\right)}{x^{4}}\right)} - \frac{a}{4 \, x^{4}}"," ",0,"1/64*b*((3*c^5*log(c*x*sqrt(1/(c^2*x^2) - 1) + 1) - 3*c^5*log(c*x*sqrt(1/(c^2*x^2) - 1) - 1) - 2*(3*c^8*x^3*(1/(c^2*x^2) - 1)^(3/2) - 5*c^6*x*sqrt(1/(c^2*x^2) - 1))/(c^4*x^4*(1/(c^2*x^2) - 1)^2 - 2*c^2*x^2*(1/(c^2*x^2) - 1) + 1))/c - 16*arcsech(c*x)/x^4) - 1/4*a/x^4","A",0
31,1,73,0,0.304645," ","integrate((a+b*arcsech(c*x))/x^6,x, algorithm=""maxima"")","\frac{1}{75} \, b {\left(\frac{3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} + 10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 15 \, c^{6} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{15 \, \operatorname{arsech}\left(c x\right)}{x^{5}}\right)} - \frac{a}{5 \, x^{5}}"," ",0,"1/75*b*((3*c^6*(1/(c^2*x^2) - 1)^(5/2) + 10*c^6*(1/(c^2*x^2) - 1)^(3/2) + 15*c^6*sqrt(1/(c^2*x^2) - 1))/c - 15*arcsech(c*x)/x^5) - 1/5*a/x^5","A",0
32,1,185,0,0.318241," ","integrate((a+b*arcsech(c*x))/x^7,x, algorithm=""maxima"")","\frac{1}{576} \, b {\left(\frac{15 \, c^{7} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} + 1\right) - 15 \, c^{7} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} - 1\right) - \frac{2 \, {\left(15 \, c^{12} x^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} - 40 \, c^{10} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 33 \, c^{8} x \sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}}{c^{6} x^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} - 3 \, c^{4} x^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 3 \, c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} - 1}}{c} - \frac{96 \, \operatorname{arsech}\left(c x\right)}{x^{6}}\right)} - \frac{a}{6 \, x^{6}}"," ",0,"1/576*b*((15*c^7*log(c*x*sqrt(1/(c^2*x^2) - 1) + 1) - 15*c^7*log(c*x*sqrt(1/(c^2*x^2) - 1) - 1) - 2*(15*c^12*x^5*(1/(c^2*x^2) - 1)^(5/2) - 40*c^10*x^3*(1/(c^2*x^2) - 1)^(3/2) + 33*c^8*x*sqrt(1/(c^2*x^2) - 1))/(c^6*x^6*(1/(c^2*x^2) - 1)^3 - 3*c^4*x^4*(1/(c^2*x^2) - 1)^2 + 3*c^2*x^2*(1/(c^2*x^2) - 1) - 1))/c - 96*arcsech(c*x)/x^6) - 1/6*a/x^6","A",0
33,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsech(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} x^{4} + \frac{1}{6} \, {\left(3 \, x^{4} \operatorname{arsech}\left(c x\right) + \frac{c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} - 3 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{3}}\right)} a b + b^{2} \int x^{3} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{2}\,{d x}"," ",0,"1/4*a^2*x^4 + 1/6*(3*x^4*arcsech(c*x) + (c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) - 3*x*sqrt(1/(c^2*x^2) - 1))/c^3)*a*b + b^2*integrate(x^3*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^2, x)","F",0
34,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsech(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{arsech}\left(c x\right) - \frac{\frac{\sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{2}}}{c}\right)} a b + b^{2} \int x^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{2}\,{d x}"," ",0,"1/3*a^2*x^3 + 1/3*(2*x^3*arcsech(c*x) - (sqrt(1/(c^2*x^2) - 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + arctan(sqrt(1/(c^2*x^2) - 1))/c^2)/c)*a*b + b^2*integrate(x^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^2, x)","F",0
35,1,84,0,0.320230," ","integrate(x*(a+b*arcsech(c*x))^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} x^{2} \operatorname{arsech}\left(c x\right)^{2} + \frac{1}{2} \, a^{2} x^{2} + {\left(x^{2} \operatorname{arsech}\left(c x\right) - \frac{x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c}\right)} a b - {\left(\frac{x \sqrt{\frac{1}{c^{2} x^{2}} - 1} \operatorname{arsech}\left(c x\right)}{c} + \frac{\log\left(x\right)}{c^{2}}\right)} b^{2}"," ",0,"1/2*b^2*x^2*arcsech(c*x)^2 + 1/2*a^2*x^2 + (x^2*arcsech(c*x) - x*sqrt(1/(c^2*x^2) - 1)/c)*a*b - (x*sqrt(1/(c^2*x^2) - 1)*arcsech(c*x)/c + log(x)/c^2)*b^2","A",0
36,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))^2,x, algorithm=""maxima"")","{\left(x \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)^{2} - \int -\frac{c^{2} x^{2} \log\left(c\right)^{2} + {\left(c^{2} x^{2} - 1\right)} \log\left(x\right)^{2} + {\left(c^{2} x^{2} \log\left(c\right)^{2} + {\left(c^{2} x^{2} - 1\right)} \log\left(x\right)^{2} - \log\left(c\right)^{2} + 2 \, {\left(c^{2} x^{2} \log\left(c\right) - \log\left(c\right)\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - 2 \, {\left(c^{2} x^{2} \log\left(c\right) + {\left(c^{2} x^{2} {\left(\log\left(c\right) + 1\right)} + {\left(c^{2} x^{2} - 1\right)} \log\left(x\right) - \log\left(c\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + {\left(c^{2} x^{2} - 1\right)} \log\left(x\right) - \log\left(c\right)\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) - \log\left(c\right)^{2} + 2 \, {\left(c^{2} x^{2} \log\left(c\right) - \log\left(c\right)\right)} \log\left(x\right)}{c^{2} x^{2} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - 1}\,{d x}\right)} b^{2} + a^{2} x + \frac{2 \, {\left(c x \operatorname{arsech}\left(c x\right) - \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)\right)} a b}{c}"," ",0,"(x*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)^2 - integrate(-(c^2*x^2*log(c)^2 + (c^2*x^2 - 1)*log(x)^2 + (c^2*x^2*log(c)^2 + (c^2*x^2 - 1)*log(x)^2 - log(c)^2 + 2*(c^2*x^2*log(c) - log(c))*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - 2*(c^2*x^2*log(c) + (c^2*x^2*(log(c) + 1) + (c^2*x^2 - 1)*log(x) - log(c))*sqrt(c*x + 1)*sqrt(-c*x + 1) + (c^2*x^2 - 1)*log(x) - log(c))*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) - log(c)^2 + 2*(c^2*x^2*log(c) - log(c))*log(x))/(c^2*x^2 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(-c*x + 1) - 1), x))*b^2 + a^2*x + 2*(c*x*arcsech(c*x) - arctan(sqrt(1/(c^2*x^2) - 1)))*a*b/c","F",0
37,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))^2/x,x, algorithm=""maxima"")","a^{2} \log\left(x\right) + \int \frac{b^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{2}}{x} + \frac{2 \, a b \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{x}\,{d x}"," ",0,"a^2*log(x) + integrate(b^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^2/x + 2*a*b*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/x, x)","F",0
38,1,78,0,0.317582," ","integrate((a+b*arcsech(c*x))^2/x^2,x, algorithm=""maxima"")","2 \, {\left(c \sqrt{\frac{1}{c^{2} x^{2}} - 1} - \frac{\operatorname{arsech}\left(c x\right)}{x}\right)} a b + 2 \, {\left(c \sqrt{\frac{1}{c^{2} x^{2}} - 1} \operatorname{arsech}\left(c x\right) - \frac{1}{x}\right)} b^{2} - \frac{b^{2} \operatorname{arsech}\left(c x\right)^{2}}{x} - \frac{a^{2}}{x}"," ",0,"2*(c*sqrt(1/(c^2*x^2) - 1) - arcsech(c*x)/x)*a*b + 2*(c*sqrt(1/(c^2*x^2) - 1)*arcsech(c*x) - 1/x)*b^2 - b^2*arcsech(c*x)^2/x - a^2/x","A",0
39,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))^2/x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a b {\left(\frac{\frac{2 \, c^{4} x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} - 1} - c^{3} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} + 1\right) + c^{3} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} - 1\right)}{c} + \frac{4 \, \operatorname{arsech}\left(c x\right)}{x^{2}}\right)} + b^{2} \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{2}}{x^{3}}\,{d x} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"-1/4*a*b*((2*c^4*x*sqrt(1/(c^2*x^2) - 1)/(c^2*x^2*(1/(c^2*x^2) - 1) - 1) - c^3*log(c*x*sqrt(1/(c^2*x^2) - 1) + 1) + c^3*log(c*x*sqrt(1/(c^2*x^2) - 1) - 1))/c + 4*arcsech(c*x)/x^2) + b^2*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^2/x^3, x) - 1/2*a^2/x^2","F",0
40,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))^2/x^4,x, algorithm=""maxima"")","\frac{2}{9} \, a b {\left(\frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 3 \, c^{4} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{3 \, \operatorname{arsech}\left(c x\right)}{x^{3}}\right)} + b^{2} \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{2}}{x^{4}}\,{d x} - \frac{a^{2}}{3 \, x^{3}}"," ",0,"2/9*a*b*((c^4*(1/(c^2*x^2) - 1)^(3/2) + 3*c^4*sqrt(1/(c^2*x^2) - 1))/c - 3*arcsech(c*x)/x^3) + b^2*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^2/x^4, x) - 1/3*a^2/x^3","F",0
41,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))^2/x^5,x, algorithm=""maxima"")","\frac{1}{32} \, a b {\left(\frac{3 \, c^{5} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} + 1\right) - 3 \, c^{5} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} - 1\right) - \frac{2 \, {\left(3 \, c^{8} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} - 5 \, c^{6} x \sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}}{c^{4} x^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} - 2 \, c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + 1}}{c} - \frac{16 \, \operatorname{arsech}\left(c x\right)}{x^{4}}\right)} + b^{2} \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{2}}{x^{5}}\,{d x} - \frac{a^{2}}{4 \, x^{4}}"," ",0,"1/32*a*b*((3*c^5*log(c*x*sqrt(1/(c^2*x^2) - 1) + 1) - 3*c^5*log(c*x*sqrt(1/(c^2*x^2) - 1) - 1) - 2*(3*c^8*x^3*(1/(c^2*x^2) - 1)^(3/2) - 5*c^6*x*sqrt(1/(c^2*x^2) - 1))/(c^4*x^4*(1/(c^2*x^2) - 1)^2 - 2*c^2*x^2*(1/(c^2*x^2) - 1) + 1))/c - 16*arcsech(c*x)/x^4) + b^2*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^2/x^5, x) - 1/4*a^2/x^4","F",0
42,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsech(c*x))^3,x, algorithm=""maxima"")","\frac{1}{4} \, a^{3} x^{4} + \frac{1}{4} \, {\left(3 \, x^{4} \operatorname{arsech}\left(c x\right) + \frac{c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} - 3 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{3}}\right)} a^{2} b + \int b^{3} x^{3} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{3} + 3 \, a b^{2} x^{3} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{2}\,{d x}"," ",0,"1/4*a^3*x^4 + 1/4*(3*x^4*arcsech(c*x) + (c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) - 3*x*sqrt(1/(c^2*x^2) - 1))/c^3)*a^2*b + integrate(b^3*x^3*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^3 + 3*a*b^2*x^3*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^2, x)","F",0
43,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsech(c*x))^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} x^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{arsech}\left(c x\right) - \frac{\frac{\sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{2}}}{c}\right)} a^{2} b + \int b^{3} x^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{3} + 3 \, a b^{2} x^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{2}\,{d x}"," ",0,"1/3*a^3*x^3 + 1/2*(2*x^3*arcsech(c*x) - (sqrt(1/(c^2*x^2) - 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + arctan(sqrt(1/(c^2*x^2) - 1))/c^2)/c)*a^2*b + integrate(b^3*x^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^3 + 3*a*b^2*x^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^2, x)","F",0
44,0,0,0,0.000000," ","integrate(x*(a+b*arcsech(c*x))^3,x, algorithm=""maxima"")","\frac{3}{2} \, a b^{2} x^{2} \operatorname{arsech}\left(c x\right)^{2} + \frac{1}{2} \, a^{3} x^{2} + \frac{3}{2} \, {\left(x^{2} \operatorname{arsech}\left(c x\right) - \frac{x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c}\right)} a^{2} b - 3 \, {\left(\frac{x \sqrt{\frac{1}{c^{2} x^{2}} - 1} \operatorname{arsech}\left(c x\right)}{c} + \frac{\log\left(x\right)}{c^{2}}\right)} a b^{2} + b^{3} \int x \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{3}\,{d x}"," ",0,"3/2*a*b^2*x^2*arcsech(c*x)^2 + 1/2*a^3*x^2 + 3/2*(x^2*arcsech(c*x) - x*sqrt(1/(c^2*x^2) - 1)/c)*a^2*b - 3*(x*sqrt(1/(c^2*x^2) - 1)*arcsech(c*x)/c + log(x)/c^2)*a*b^2 + b^3*integrate(x*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^3, x)","F",0
45,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))^3,x, algorithm=""maxima"")","b^{3} x \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)^{3} + a^{3} x + \frac{3 \, {\left(c x \operatorname{arsech}\left(c x\right) - \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)\right)} a^{2} b}{c} - \int -\frac{b^{3} \log\left(c\right)^{3} - 3 \, a b^{2} \log\left(c\right)^{2} - {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)^{3} - {\left(b^{3} c^{2} \log\left(c\right)^{3} - 3 \, a b^{2} c^{2} \log\left(c\right)^{2}\right)} x^{2} + 3 \, {\left(b^{3} \log\left(c\right) - a b^{2} - {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2} + {\left(b^{3} \log\left(c\right) - a b^{2} - {\left(b^{3} c^{2} {\left(\log\left(c\right) + 1\right)} - a b^{2} c^{2}\right)} x^{2} - {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)^{2} + 3 \, {\left(b^{3} \log\left(c\right) - a b^{2} - {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} \log\left(x\right)^{2} + {\left(b^{3} \log\left(c\right)^{3} - 3 \, a b^{2} \log\left(c\right)^{2} - {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)^{3} - {\left(b^{3} c^{2} \log\left(c\right)^{3} - 3 \, a b^{2} c^{2} \log\left(c\right)^{2}\right)} x^{2} + 3 \, {\left(b^{3} \log\left(c\right) - a b^{2} - {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} \log\left(x\right)^{2} + 3 \, {\left(b^{3} \log\left(c\right)^{2} - 2 \, a b^{2} \log\left(c\right) - {\left(b^{3} c^{2} \log\left(c\right)^{2} - 2 \, a b^{2} c^{2} \log\left(c\right)\right)} x^{2}\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - 3 \, {\left(b^{3} \log\left(c\right)^{2} - 2 \, a b^{2} \log\left(c\right) - {\left(b^{3} c^{2} \log\left(c\right)^{2} - 2 \, a b^{2} c^{2} \log\left(c\right)\right)} x^{2} - {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)^{2} + {\left(b^{3} \log\left(c\right)^{2} - 2 \, a b^{2} \log\left(c\right) - {\left(b^{3} c^{2} \log\left(c\right)^{2} - 2 \, a b^{2} c^{2} \log\left(c\right)\right)} x^{2} - {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)^{2} + 2 \, {\left(b^{3} \log\left(c\right) - a b^{2} - {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + 2 \, {\left(b^{3} \log\left(c\right) - a b^{2} - {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} \log\left(x\right)\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + 3 \, {\left(b^{3} \log\left(c\right)^{2} - 2 \, a b^{2} \log\left(c\right) - {\left(b^{3} c^{2} \log\left(c\right)^{2} - 2 \, a b^{2} c^{2} \log\left(c\right)\right)} x^{2}\right)} \log\left(x\right)}{c^{2} x^{2} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - 1}\,{d x}"," ",0,"b^3*x*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)^3 + a^3*x + 3*(c*x*arcsech(c*x) - arctan(sqrt(1/(c^2*x^2) - 1)))*a^2*b/c - integrate(-(b^3*log(c)^3 - 3*a*b^2*log(c)^2 - (b^3*c^2*x^2 - b^3)*log(x)^3 - (b^3*c^2*log(c)^3 - 3*a*b^2*c^2*log(c)^2)*x^2 + 3*(b^3*log(c) - a*b^2 - (b^3*c^2*log(c) - a*b^2*c^2)*x^2 + (b^3*log(c) - a*b^2 - (b^3*c^2*(log(c) + 1) - a*b^2*c^2)*x^2 - (b^3*c^2*x^2 - b^3)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - (b^3*c^2*x^2 - b^3)*log(x))*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)^2 + 3*(b^3*log(c) - a*b^2 - (b^3*c^2*log(c) - a*b^2*c^2)*x^2)*log(x)^2 + (b^3*log(c)^3 - 3*a*b^2*log(c)^2 - (b^3*c^2*x^2 - b^3)*log(x)^3 - (b^3*c^2*log(c)^3 - 3*a*b^2*c^2*log(c)^2)*x^2 + 3*(b^3*log(c) - a*b^2 - (b^3*c^2*log(c) - a*b^2*c^2)*x^2)*log(x)^2 + 3*(b^3*log(c)^2 - 2*a*b^2*log(c) - (b^3*c^2*log(c)^2 - 2*a*b^2*c^2*log(c))*x^2)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - 3*(b^3*log(c)^2 - 2*a*b^2*log(c) - (b^3*c^2*log(c)^2 - 2*a*b^2*c^2*log(c))*x^2 - (b^3*c^2*x^2 - b^3)*log(x)^2 + (b^3*log(c)^2 - 2*a*b^2*log(c) - (b^3*c^2*log(c)^2 - 2*a*b^2*c^2*log(c))*x^2 - (b^3*c^2*x^2 - b^3)*log(x)^2 + 2*(b^3*log(c) - a*b^2 - (b^3*c^2*log(c) - a*b^2*c^2)*x^2)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) + 2*(b^3*log(c) - a*b^2 - (b^3*c^2*log(c) - a*b^2*c^2)*x^2)*log(x))*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + 3*(b^3*log(c)^2 - 2*a*b^2*log(c) - (b^3*c^2*log(c)^2 - 2*a*b^2*c^2*log(c))*x^2)*log(x))/(c^2*x^2 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(-c*x + 1) - 1), x)","F",0
46,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))^3/x,x, algorithm=""maxima"")","a^{3} \log\left(x\right) + \int \frac{b^{3} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{3}}{x} + \frac{3 \, a b^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{2}}{x} + \frac{3 \, a^{2} b \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{x}\,{d x}"," ",0,"a^3*log(x) + integrate(b^3*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^3/x + 3*a*b^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^2/x + 3*a^2*b*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/x, x)","F",0
47,1,144,0,0.329499," ","integrate((a+b*arcsech(c*x))^3/x^2,x, algorithm=""maxima"")","-\frac{b^{3} \operatorname{arsech}\left(c x\right)^{3}}{x} + 3 \, {\left(c \sqrt{\frac{1}{c^{2} x^{2}} - 1} - \frac{\operatorname{arsech}\left(c x\right)}{x}\right)} a^{2} b + 6 \, {\left(c \sqrt{\frac{1}{c^{2} x^{2}} - 1} \operatorname{arsech}\left(c x\right) - \frac{1}{x}\right)} a b^{2} + 3 \, {\left(c \sqrt{\frac{1}{c^{2} x^{2}} - 1} \operatorname{arsech}\left(c x\right)^{2} + 2 \, c \sqrt{\frac{1}{c^{2} x^{2}} - 1} - \frac{2 \, \operatorname{arsech}\left(c x\right)}{x}\right)} b^{3} - \frac{3 \, a b^{2} \operatorname{arsech}\left(c x\right)^{2}}{x} - \frac{a^{3}}{x}"," ",0,"-b^3*arcsech(c*x)^3/x + 3*(c*sqrt(1/(c^2*x^2) - 1) - arcsech(c*x)/x)*a^2*b + 6*(c*sqrt(1/(c^2*x^2) - 1)*arcsech(c*x) - 1/x)*a*b^2 + 3*(c*sqrt(1/(c^2*x^2) - 1)*arcsech(c*x)^2 + 2*c*sqrt(1/(c^2*x^2) - 1) - 2*arcsech(c*x)/x)*b^3 - 3*a*b^2*arcsech(c*x)^2/x - a^3/x","A",0
48,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))^3/x^3,x, algorithm=""maxima"")","-\frac{3}{8} \, a^{2} b {\left(\frac{\frac{2 \, c^{4} x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} - 1} - c^{3} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} + 1\right) + c^{3} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} - 1\right)}{c} + \frac{4 \, \operatorname{arsech}\left(c x\right)}{x^{2}}\right)} - \frac{a^{3}}{2 \, x^{2}} + \int \frac{b^{3} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{3}}{x^{3}} + \frac{3 \, a b^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{2}}{x^{3}}\,{d x}"," ",0,"-3/8*a^2*b*((2*c^4*x*sqrt(1/(c^2*x^2) - 1)/(c^2*x^2*(1/(c^2*x^2) - 1) - 1) - c^3*log(c*x*sqrt(1/(c^2*x^2) - 1) + 1) + c^3*log(c*x*sqrt(1/(c^2*x^2) - 1) - 1))/c + 4*arcsech(c*x)/x^2) - 1/2*a^3/x^2 + integrate(b^3*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^3/x^3 + 3*a*b^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^2/x^3, x)","F",0
49,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))^3/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} b {\left(\frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 3 \, c^{4} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{3 \, \operatorname{arsech}\left(c x\right)}{x^{3}}\right)} - \frac{a^{3}}{3 \, x^{3}} + \int \frac{b^{3} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{3}}{x^{4}} + \frac{3 \, a b^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{2}}{x^{4}}\,{d x}"," ",0,"1/3*a^2*b*((c^4*(1/(c^2*x^2) - 1)^(3/2) + 3*c^4*sqrt(1/(c^2*x^2) - 1))/c - 3*arcsech(c*x)/x^3) - 1/3*a^3/x^3 + integrate(b^3*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^3/x^4 + 3*a*b^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^2/x^4, x)","F",0
50,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))^3/x^5,x, algorithm=""maxima"")","\frac{3}{64} \, a^{2} b {\left(\frac{3 \, c^{5} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} + 1\right) - 3 \, c^{5} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} - 1\right) - \frac{2 \, {\left(3 \, c^{8} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} - 5 \, c^{6} x \sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}}{c^{4} x^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} - 2 \, c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + 1}}{c} - \frac{16 \, \operatorname{arsech}\left(c x\right)}{x^{4}}\right)} - \frac{a^{3}}{4 \, x^{4}} + \int \frac{b^{3} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{3}}{x^{5}} + \frac{3 \, a b^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)^{2}}{x^{5}}\,{d x}"," ",0,"3/64*a^2*b*((3*c^5*log(c*x*sqrt(1/(c^2*x^2) - 1) + 1) - 3*c^5*log(c*x*sqrt(1/(c^2*x^2) - 1) - 1) - 2*(3*c^8*x^3*(1/(c^2*x^2) - 1)^(3/2) - 5*c^6*x*sqrt(1/(c^2*x^2) - 1))/(c^4*x^4*(1/(c^2*x^2) - 1)^2 - 2*c^2*x^2*(1/(c^2*x^2) - 1) + 1))/c - 16*arcsech(c*x)/x^4) - 1/4*a^3/x^4 + integrate(b^3*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^3/x^5 + 3*a*b^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))^2/x^5, x)","F",0
51,0,0,0,0.000000," ","integrate(x/(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\int \frac{x}{b \operatorname{arsech}\left(c x\right) + a}\,{d x}"," ",0,"integrate(x/(b*arcsech(c*x) + a), x)","F",0
52,0,0,0,0.000000," ","integrate(1/(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\int \frac{1}{b \operatorname{arsech}\left(c x\right) + a}\,{d x}"," ",0,"integrate(1/(b*arcsech(c*x) + a), x)","F",0
53,0,0,0,0.000000," ","integrate(1/x/(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsech}\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*arcsech(c*x) + a)*x), x)","F",0
54,0,0,0,0.000000," ","integrate(1/x^2/(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsech}\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((b*arcsech(c*x) + a)*x^2), x)","F",0
55,0,0,0,0.000000," ","integrate(1/x^3/(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsech}\left(c x\right) + a\right)} x^{3}}\,{d x}"," ",0,"integrate(1/((b*arcsech(c*x) + a)*x^3), x)","F",0
56,0,0,0,0.000000," ","integrate(1/x^4/(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsech}\left(c x\right) + a\right)} x^{4}}\,{d x}"," ",0,"integrate(1/((b*arcsech(c*x) + a)*x^4), x)","F",0
57,0,0,0,0.000000," ","integrate(x/(a+b*arcsech(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} x^{3} - x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x + {\left(c^{2} x^{3} - x\right)} x}{{\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} - b^{2} \log\left(c\right) - {\left(b^{2} \log\left(c\right) + b^{2} \log\left(x\right) - a b\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + a b - {\left(b^{2} c^{2} x^{2} - \sqrt{c x + 1} \sqrt{-c x + 1} b^{2} - b^{2}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \log\left(x\right)} + \int \frac{2 \, {\left(2 \, c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x + {\left(3 \, c^{4} x^{4} - 8 \, c^{2} x^{2} + 4\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x + 2 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} x}{{\left(b^{2} c^{4} \log\left(c\right) - a b c^{4}\right)} x^{4} - {\left(b^{2} \log\left(c\right) + b^{2} \log\left(x\right) - a b\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - 2 \, {\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} + b^{2} \log\left(c\right) - 2 \, {\left({\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} - b^{2} \log\left(c\right) + a b + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - a b - {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} - {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} - 2 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + b^{2}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \log\left(x\right)}\,{d x}"," ",0,"-((c^2*x^3 - x)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x + (c^2*x^3 - x)*x)/((b^2*c^2*log(c) - a*b*c^2)*x^2 - b^2*log(c) - (b^2*log(c) + b^2*log(x) - a*b)*sqrt(c*x + 1)*sqrt(-c*x + 1) + a*b - (b^2*c^2*x^2 - sqrt(c*x + 1)*sqrt(-c*x + 1)*b^2 - b^2)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + (b^2*c^2*x^2 - b^2)*log(x)) + integrate((2*(2*c^2*x^2 - 1)*(c*x + 1)*(c*x - 1)*x + (3*c^4*x^4 - 8*c^2*x^2 + 4)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x + 2*(c^4*x^4 - 2*c^2*x^2 + 1)*x)/((b^2*c^4*log(c) - a*b*c^4)*x^4 - (b^2*log(c) + b^2*log(x) - a*b)*(c*x + 1)*(c*x - 1) - 2*(b^2*c^2*log(c) - a*b*c^2)*x^2 + b^2*log(c) - 2*((b^2*c^2*log(c) - a*b*c^2)*x^2 - b^2*log(c) + a*b + (b^2*c^2*x^2 - b^2)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - a*b - (b^2*c^4*x^4 - 2*b^2*c^2*x^2 - (c*x + 1)*(c*x - 1)*b^2 - 2*(b^2*c^2*x^2 - b^2)*sqrt(c*x + 1)*sqrt(-c*x + 1) + b^2)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*log(x)), x)","F",0
58,0,0,0,0.000000," ","integrate(1/(a+b*arcsech(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{2} x^{3} + {\left(c^{2} x^{3} - x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - x}{{\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} - b^{2} \log\left(c\right) - {\left(b^{2} \log\left(c\right) + b^{2} \log\left(x\right) - a b\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + a b - {\left(b^{2} c^{2} x^{2} - \sqrt{c x + 1} \sqrt{-c x + 1} b^{2} - b^{2}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \log\left(x\right)} + \int \frac{c^{4} x^{4} - 2 \, c^{2} x^{2} + {\left(3 \, c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(2 \, c^{4} x^{4} - 5 \, c^{2} x^{2} + 2\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + 1}{{\left(b^{2} c^{4} \log\left(c\right) - a b c^{4}\right)} x^{4} - {\left(b^{2} \log\left(c\right) + b^{2} \log\left(x\right) - a b\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - 2 \, {\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} + b^{2} \log\left(c\right) - 2 \, {\left({\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} - b^{2} \log\left(c\right) + a b + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - a b - {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} - {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} - 2 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + b^{2}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \log\left(x\right)}\,{d x}"," ",0,"-(c^2*x^3 + (c^2*x^3 - x)*sqrt(c*x + 1)*sqrt(-c*x + 1) - x)/((b^2*c^2*log(c) - a*b*c^2)*x^2 - b^2*log(c) - (b^2*log(c) + b^2*log(x) - a*b)*sqrt(c*x + 1)*sqrt(-c*x + 1) + a*b - (b^2*c^2*x^2 - sqrt(c*x + 1)*sqrt(-c*x + 1)*b^2 - b^2)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + (b^2*c^2*x^2 - b^2)*log(x)) + integrate((c^4*x^4 - 2*c^2*x^2 + (3*c^2*x^2 - 1)*(c*x + 1)*(c*x - 1) + (2*c^4*x^4 - 5*c^2*x^2 + 2)*sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/((b^2*c^4*log(c) - a*b*c^4)*x^4 - (b^2*log(c) + b^2*log(x) - a*b)*(c*x + 1)*(c*x - 1) - 2*(b^2*c^2*log(c) - a*b*c^2)*x^2 + b^2*log(c) - 2*((b^2*c^2*log(c) - a*b*c^2)*x^2 - b^2*log(c) + a*b + (b^2*c^2*x^2 - b^2)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - a*b - (b^2*c^4*x^4 - 2*b^2*c^2*x^2 - (c*x + 1)*(c*x - 1)*b^2 - 2*(b^2*c^2*x^2 - b^2)*sqrt(c*x + 1)*sqrt(-c*x + 1) + b^2)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*log(x)), x)","F",0
59,0,0,0,0.000000," ","integrate(1/x/(a+b*arcsech(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{2} x^{3} + {\left(c^{2} x^{3} - x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - x}{{\left(b^{2} c^{2} x^{2} - b^{2}\right)} x \log\left(x\right) - {\left(b^{2} x \log\left(x\right) + {\left(b^{2} \log\left(c\right) - a b\right)} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + {\left({\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} - b^{2} \log\left(c\right) + a b\right)} x + {\left(\sqrt{c x + 1} \sqrt{-c x + 1} b^{2} x - {\left(b^{2} c^{2} x^{2} - b^{2}\right)} x\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)} + \int -\frac{2 \, {\left(c x + 1\right)} {\left(c x - 1\right)} c^{2} x^{2} + {\left(c^{4} x^{4} - 2 \, c^{2} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{{\left(b^{2} x \log\left(x\right) + {\left(b^{2} \log\left(c\right) - a b\right)} x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} x \log\left(x\right) + 2 \, {\left({\left(b^{2} c^{2} x^{2} - b^{2}\right)} x \log\left(x\right) + {\left({\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} - b^{2} \log\left(c\right) + a b\right)} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left({\left(b^{2} c^{4} \log\left(c\right) - a b c^{4}\right)} x^{4} - 2 \, {\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} + b^{2} \log\left(c\right) - a b\right)} x - {\left({\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} x + 2 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x - {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} x\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}\,{d x}"," ",0,"-(c^2*x^3 + (c^2*x^3 - x)*sqrt(c*x + 1)*sqrt(-c*x + 1) - x)/((b^2*c^2*x^2 - b^2)*x*log(x) - (b^2*x*log(x) + (b^2*log(c) - a*b)*x)*sqrt(c*x + 1)*sqrt(-c*x + 1) + ((b^2*c^2*log(c) - a*b*c^2)*x^2 - b^2*log(c) + a*b)*x + (sqrt(c*x + 1)*sqrt(-c*x + 1)*b^2*x - (b^2*c^2*x^2 - b^2)*x)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)) + integrate(-(2*(c*x + 1)*(c*x - 1)*c^2*x^2 + (c^4*x^4 - 2*c^2*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1))/((b^2*x*log(x) + (b^2*log(c) - a*b)*x)*(c*x + 1)*(c*x - 1) - (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*x*log(x) + 2*((b^2*c^2*x^2 - b^2)*x*log(x) + ((b^2*c^2*log(c) - a*b*c^2)*x^2 - b^2*log(c) + a*b)*x)*sqrt(c*x + 1)*sqrt(-c*x + 1) - ((b^2*c^4*log(c) - a*b*c^4)*x^4 - 2*(b^2*c^2*log(c) - a*b*c^2)*x^2 + b^2*log(c) - a*b)*x - ((c*x + 1)*(c*x - 1)*b^2*x + 2*(b^2*c^2*x^2 - b^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x - (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*x)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)), x)","F",0
60,0,0,0,0.000000," ","integrate(1/x^2/(a+b*arcsech(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{2} x^{3} + {\left(c^{2} x^{3} - x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - x}{{\left(b^{2} c^{2} x^{2} - b^{2}\right)} x^{2} \log\left(x\right) + {\left({\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} - b^{2} \log\left(c\right) + a b\right)} x^{2} - {\left(b^{2} x^{2} \log\left(x\right) + {\left(b^{2} \log\left(c\right) - a b\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + {\left(\sqrt{c x + 1} \sqrt{-c x + 1} b^{2} x^{2} - {\left(b^{2} c^{2} x^{2} - b^{2}\right)} x^{2}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)} + \int -\frac{c^{4} x^{4} - 2 \, c^{2} x^{2} - {\left(c^{2} x^{2} + 1\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - {\left(c^{2} x^{2} - 2\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + 1}{{\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} x^{2} \log\left(x\right) - {\left(b^{2} x^{2} \log\left(x\right) + {\left(b^{2} \log\left(c\right) - a b\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left({\left(b^{2} c^{4} \log\left(c\right) - a b c^{4}\right)} x^{4} - 2 \, {\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} + b^{2} \log\left(c\right) - a b\right)} x^{2} - 2 \, {\left({\left(b^{2} c^{2} x^{2} - b^{2}\right)} x^{2} \log\left(x\right) + {\left({\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} - b^{2} \log\left(c\right) + a b\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + {\left({\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} x^{2} + 2 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{2} - {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} x^{2}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}\,{d x}"," ",0,"-(c^2*x^3 + (c^2*x^3 - x)*sqrt(c*x + 1)*sqrt(-c*x + 1) - x)/((b^2*c^2*x^2 - b^2)*x^2*log(x) + ((b^2*c^2*log(c) - a*b*c^2)*x^2 - b^2*log(c) + a*b)*x^2 - (b^2*x^2*log(x) + (b^2*log(c) - a*b)*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1) + (sqrt(c*x + 1)*sqrt(-c*x + 1)*b^2*x^2 - (b^2*c^2*x^2 - b^2)*x^2)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)) + integrate(-(c^4*x^4 - 2*c^2*x^2 - (c^2*x^2 + 1)*(c*x + 1)*(c*x - 1) - (c^2*x^2 - 2)*sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/((b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*x^2*log(x) - (b^2*x^2*log(x) + (b^2*log(c) - a*b)*x^2)*(c*x + 1)*(c*x - 1) + ((b^2*c^4*log(c) - a*b*c^4)*x^4 - 2*(b^2*c^2*log(c) - a*b*c^2)*x^2 + b^2*log(c) - a*b)*x^2 - 2*((b^2*c^2*x^2 - b^2)*x^2*log(x) + ((b^2*c^2*log(c) - a*b*c^2)*x^2 - b^2*log(c) + a*b)*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1) + ((c*x + 1)*(c*x - 1)*b^2*x^2 + 2*(b^2*c^2*x^2 - b^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^2 - (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*x^2)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)), x)","F",0
61,0,0,0,0.000000," ","integrate(1/x^3/(a+b*arcsech(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{2} x^{3} + {\left(c^{2} x^{3} - x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - x}{{\left(b^{2} c^{2} x^{2} - b^{2}\right)} x^{3} \log\left(x\right) + {\left({\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} - b^{2} \log\left(c\right) + a b\right)} x^{3} - {\left(b^{2} x^{3} \log\left(x\right) + {\left(b^{2} \log\left(c\right) - a b\right)} x^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + {\left(\sqrt{c x + 1} \sqrt{-c x + 1} b^{2} x^{3} - {\left(b^{2} c^{2} x^{2} - b^{2}\right)} x^{3}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)} + \int -\frac{2 \, c^{4} x^{4} - 4 \, c^{2} x^{2} - 2 \, {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(c^{4} x^{4} - 4 \, c^{2} x^{2} + 4\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + 2}{{\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} x^{3} \log\left(x\right) + {\left({\left(b^{2} c^{4} \log\left(c\right) - a b c^{4}\right)} x^{4} - 2 \, {\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} + b^{2} \log\left(c\right) - a b\right)} x^{3} - {\left(b^{2} x^{3} \log\left(x\right) + {\left(b^{2} \log\left(c\right) - a b\right)} x^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - 2 \, {\left({\left(b^{2} c^{2} x^{2} - b^{2}\right)} x^{3} \log\left(x\right) + {\left({\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} - b^{2} \log\left(c\right) + a b\right)} x^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + {\left({\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} x^{3} + 2 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{3} - {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} x^{3}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}\,{d x}"," ",0,"-(c^2*x^3 + (c^2*x^3 - x)*sqrt(c*x + 1)*sqrt(-c*x + 1) - x)/((b^2*c^2*x^2 - b^2)*x^3*log(x) + ((b^2*c^2*log(c) - a*b*c^2)*x^2 - b^2*log(c) + a*b)*x^3 - (b^2*x^3*log(x) + (b^2*log(c) - a*b)*x^3)*sqrt(c*x + 1)*sqrt(-c*x + 1) + (sqrt(c*x + 1)*sqrt(-c*x + 1)*b^2*x^3 - (b^2*c^2*x^2 - b^2)*x^3)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)) + integrate(-(2*c^4*x^4 - 4*c^2*x^2 - 2*(c*x + 1)*(c*x - 1) + (c^4*x^4 - 4*c^2*x^2 + 4)*sqrt(c*x + 1)*sqrt(-c*x + 1) + 2)/((b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*x^3*log(x) + ((b^2*c^4*log(c) - a*b*c^4)*x^4 - 2*(b^2*c^2*log(c) - a*b*c^2)*x^2 + b^2*log(c) - a*b)*x^3 - (b^2*x^3*log(x) + (b^2*log(c) - a*b)*x^3)*(c*x + 1)*(c*x - 1) - 2*((b^2*c^2*x^2 - b^2)*x^3*log(x) + ((b^2*c^2*log(c) - a*b*c^2)*x^2 - b^2*log(c) + a*b)*x^3)*sqrt(c*x + 1)*sqrt(-c*x + 1) + ((c*x + 1)*(c*x - 1)*b^2*x^3 + 2*(b^2*c^2*x^2 - b^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^3 - (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*x^3)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)), x)","F",0
62,0,0,0,0.000000," ","integrate(1/x^4/(a+b*arcsech(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{2} x^{3} + {\left(c^{2} x^{3} - x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - x}{{\left(b^{2} c^{2} x^{2} - b^{2}\right)} x^{4} \log\left(x\right) + {\left({\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} - b^{2} \log\left(c\right) + a b\right)} x^{4} - {\left(b^{2} x^{4} \log\left(x\right) + {\left(b^{2} \log\left(c\right) - a b\right)} x^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + {\left(\sqrt{c x + 1} \sqrt{-c x + 1} b^{2} x^{4} - {\left(b^{2} c^{2} x^{2} - b^{2}\right)} x^{4}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)} - \int \frac{3 \, c^{4} x^{4} - 6 \, c^{2} x^{2} + {\left(c^{2} x^{2} - 3\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(2 \, c^{4} x^{4} - 7 \, c^{2} x^{2} + 6\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + 3}{{\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} x^{4} \log\left(x\right) + {\left({\left(b^{2} c^{4} \log\left(c\right) - a b c^{4}\right)} x^{4} - 2 \, {\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} + b^{2} \log\left(c\right) - a b\right)} x^{4} - {\left(b^{2} x^{4} \log\left(x\right) + {\left(b^{2} \log\left(c\right) - a b\right)} x^{4}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - 2 \, {\left({\left(b^{2} c^{2} x^{2} - b^{2}\right)} x^{4} \log\left(x\right) + {\left({\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} - b^{2} \log\left(c\right) + a b\right)} x^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + {\left({\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} x^{4} + 2 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{4} - {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} x^{4}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}\,{d x}"," ",0,"-(c^2*x^3 + (c^2*x^3 - x)*sqrt(c*x + 1)*sqrt(-c*x + 1) - x)/((b^2*c^2*x^2 - b^2)*x^4*log(x) + ((b^2*c^2*log(c) - a*b*c^2)*x^2 - b^2*log(c) + a*b)*x^4 - (b^2*x^4*log(x) + (b^2*log(c) - a*b)*x^4)*sqrt(c*x + 1)*sqrt(-c*x + 1) + (sqrt(c*x + 1)*sqrt(-c*x + 1)*b^2*x^4 - (b^2*c^2*x^2 - b^2)*x^4)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)) - integrate((3*c^4*x^4 - 6*c^2*x^2 + (c^2*x^2 - 3)*(c*x + 1)*(c*x - 1) + (2*c^4*x^4 - 7*c^2*x^2 + 6)*sqrt(c*x + 1)*sqrt(-c*x + 1) + 3)/((b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*x^4*log(x) + ((b^2*c^4*log(c) - a*b*c^4)*x^4 - 2*(b^2*c^2*log(c) - a*b*c^2)*x^2 + b^2*log(c) - a*b)*x^4 - (b^2*x^4*log(x) + (b^2*log(c) - a*b)*x^4)*(c*x + 1)*(c*x - 1) - 2*((b^2*c^2*x^2 - b^2)*x^4*log(x) + ((b^2*c^2*log(c) - a*b*c^2)*x^2 - b^2*log(c) + a*b)*x^4)*sqrt(c*x + 1)*sqrt(-c*x + 1) + ((c*x + 1)*(c*x - 1)*b^2*x^4 + 2*(b^2*c^2*x^2 - b^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^4 - (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*x^4)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)), x)","F",0
63,0,0,0,0.000000," ","integrate(x/(a+b*arcsech(c*x))^3,x, algorithm=""maxima"")","-\frac{{\left(2 \, {\left(2 \, b c^{4} x^{5} - 3 \, b c^{2} x^{3} + b x\right)} x \log\left(x\right) + {\left(4 \, {\left(b c^{4} \log\left(c\right) - a c^{4}\right)} x^{5} - {\left(b c^{2} {\left(6 \, \log\left(c\right) + 1\right)} - 6 \, a c^{2}\right)} x^{3} + {\left(b {\left(2 \, \log\left(c\right) + 1\right)} - 2 \, a\right)} x\right)} x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + {\left(3 \, {\left(b c^{6} x^{7} - 5 \, b c^{4} x^{5} + 6 \, b c^{2} x^{3} - 2 \, b x\right)} x \log\left(x\right) + {\left(3 \, {\left(b c^{6} \log\left(c\right) - a c^{6}\right)} x^{7} - {\left(b c^{4} {\left(15 \, \log\left(c\right) + 2\right)} - 15 \, a c^{4}\right)} x^{5} + {\left(b c^{2} {\left(18 \, \log\left(c\right) + 5\right)} - 18 \, a c^{2}\right)} x^{3} - 3 \, {\left(b {\left(2 \, \log\left(c\right) + 1\right)} - 2 \, a\right)} x\right)} x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - 2 \, {\left(b c^{6} x^{7} - 3 \, b c^{4} x^{5} + 3 \, b c^{2} x^{3} - b x\right)} x \log\left(x\right) - {\left({\left(5 \, b c^{6} x^{7} - 17 \, b c^{4} x^{5} + 18 \, b c^{2} x^{3} - 6 \, b x\right)} x \log\left(x\right) + {\left({\left(b c^{6} {\left(5 \, \log\left(c\right) + 1\right)} - 5 \, a c^{6}\right)} x^{7} - {\left(b c^{4} {\left(17 \, \log\left(c\right) + 5\right)} - 17 \, a c^{4}\right)} x^{5} + {\left(b c^{2} {\left(18 \, \log\left(c\right) + 7\right)} - 18 \, a c^{2}\right)} x^{3} - 3 \, {\left(b {\left(2 \, \log\left(c\right) + 1\right)} - 2 \, a\right)} x\right)} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left({\left(b c^{6} {\left(2 \, \log\left(c\right) + 1\right)} - 2 \, a c^{6}\right)} x^{7} - 3 \, {\left(b c^{4} {\left(2 \, \log\left(c\right) + 1\right)} - 2 \, a c^{4}\right)} x^{5} + 3 \, {\left(b c^{2} {\left(2 \, \log\left(c\right) + 1\right)} - 2 \, a c^{2}\right)} x^{3} - {\left(b {\left(2 \, \log\left(c\right) + 1\right)} - 2 \, a\right)} x\right)} x - {\left(2 \, {\left(2 \, b c^{4} x^{5} - 3 \, b c^{2} x^{3} + b x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} x + 3 \, {\left(b c^{6} x^{7} - 5 \, b c^{4} x^{5} + 6 \, b c^{2} x^{3} - 2 \, b x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x - {\left(5 \, b c^{6} x^{7} - 17 \, b c^{4} x^{5} + 18 \, b c^{2} x^{3} - 6 \, b x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x - 2 \, {\left(b c^{6} x^{7} - 3 \, b c^{4} x^{5} + 3 \, b c^{2} x^{3} - b x\right)} x\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{2 \, {\left({\left(b^{4} c^{6} \log\left(c\right)^{2} - 2 \, a b^{3} c^{6} \log\left(c\right) + a^{2} b^{2} c^{6}\right)} x^{6} - b^{4} \log\left(c\right)^{2} - 3 \, {\left(b^{4} c^{4} \log\left(c\right)^{2} - 2 \, a b^{3} c^{4} \log\left(c\right) + a^{2} b^{2} c^{4}\right)} x^{4} + 2 \, a b^{3} \log\left(c\right) - {\left(b^{4} \log\left(c\right)^{2} + b^{4} \log\left(x\right)^{2} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2} + 2 \, {\left(b^{4} \log\left(c\right) - a b^{3}\right)} \log\left(x\right)\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - a^{2} b^{2} + 3 \, {\left(b^{4} \log\left(c\right)^{2} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2} - {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2} - {\left(b^{4} c^{2} x^{2} - b^{4}\right)} \log\left(x\right)^{2} + 2 \, {\left(b^{4} \log\left(c\right) - a b^{3} - {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} \log\left(x\right)\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 3 \, {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2} + {\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} b^{4} - b^{4} - 3 \, {\left(b^{4} c^{2} x^{2} - b^{4}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - 3 \, {\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)^{2} + {\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} \log\left(x\right)^{2} - 3 \, {\left(b^{4} \log\left(c\right)^{2} + {\left(b^{4} c^{4} \log\left(c\right)^{2} - 2 \, a b^{3} c^{4} \log\left(c\right) + a^{2} b^{2} c^{4}\right)} x^{4} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2} - 2 \, {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2} + {\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} \log\left(x\right)^{2} + 2 \, {\left({\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} + b^{4} \log\left(c\right) - a b^{3} - 2 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - 2 \, {\left({\left(b^{4} c^{6} \log\left(c\right) - a b^{3} c^{6}\right)} x^{6} - 3 \, {\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} - b^{4} \log\left(c\right) - {\left(b^{4} \log\left(c\right) + b^{4} \log\left(x\right) - a b^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + a b^{3} + 3 \, {\left(b^{4} \log\left(c\right) - a b^{3} - {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2} - {\left(b^{4} c^{2} x^{2} - b^{4}\right)} \log\left(x\right)\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 3 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2} - 3 \, {\left({\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} + b^{4} \log\left(c\right) - a b^{3} - 2 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2} + {\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + {\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} \log\left(x\right)\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + 2 \, {\left({\left(b^{4} c^{6} \log\left(c\right) - a b^{3} c^{6}\right)} x^{6} - 3 \, {\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} - b^{4} \log\left(c\right) + a b^{3} + 3 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} \log\left(x\right)\right)}} + \int -\frac{4 \, {\left(6 \, c^{4} x^{4} - 6 \, c^{2} x^{2} + 1\right)} {\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} x - {\left(33 \, c^{6} x^{6} - 108 \, c^{4} x^{4} + 88 \, c^{2} x^{2} - 16\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} x - 12 \, {\left(c^{8} x^{8} - 7 \, c^{6} x^{6} + 14 \, c^{4} x^{4} - 10 \, c^{2} x^{2} + 2\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x + {\left(15 \, c^{8} x^{8} - 67 \, c^{6} x^{6} + 108 \, c^{4} x^{4} - 72 \, c^{2} x^{2} + 16\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x + 4 \, {\left(c^{8} x^{8} - 4 \, c^{6} x^{6} + 6 \, c^{4} x^{4} - 4 \, c^{2} x^{2} + 1\right)} x}{2 \, {\left({\left(b^{3} c^{8} \log\left(c\right) - a b^{2} c^{8}\right)} x^{8} - 4 \, {\left(b^{3} c^{6} \log\left(c\right) - a b^{2} c^{6}\right)} x^{6} + {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right) - a b^{2}\right)} {\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} + 6 \, {\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} + 4 \, {\left(b^{3} \log\left(c\right) - a b^{2} - {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2} - {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + b^{3} \log\left(c\right) - 6 \, {\left({\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} + b^{3} \log\left(c\right) - a b^{2} - 2 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2} + {\left(b^{3} c^{4} x^{4} - 2 \, b^{3} c^{2} x^{2} + b^{3}\right)} \log\left(x\right)\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - a b^{2} - 4 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2} - 4 \, {\left({\left(b^{3} c^{6} \log\left(c\right) - a b^{2} c^{6}\right)} x^{6} - 3 \, {\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} - b^{3} \log\left(c\right) + a b^{2} + 3 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2} + {\left(b^{3} c^{6} x^{6} - 3 \, b^{3} c^{4} x^{4} + 3 \, b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left(b^{3} c^{8} x^{8} - 4 \, b^{3} c^{6} x^{6} + 6 \, b^{3} c^{4} x^{4} + {\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} b^{3} - 4 \, b^{3} c^{2} x^{2} - 4 \, {\left(b^{3} c^{2} x^{2} - b^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - 6 \, {\left(b^{3} c^{4} x^{4} - 2 \, b^{3} c^{2} x^{2} + b^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + b^{3} - 4 \, {\left(b^{3} c^{6} x^{6} - 3 \, b^{3} c^{4} x^{4} + 3 \, b^{3} c^{2} x^{2} - b^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + {\left(b^{3} c^{8} x^{8} - 4 \, b^{3} c^{6} x^{6} + 6 \, b^{3} c^{4} x^{4} - 4 \, b^{3} c^{2} x^{2} + b^{3}\right)} \log\left(x\right)\right)}}\,{d x}"," ",0,"-1/2*((2*(2*b*c^4*x^5 - 3*b*c^2*x^3 + b*x)*x*log(x) + (4*(b*c^4*log(c) - a*c^4)*x^5 - (b*c^2*(6*log(c) + 1) - 6*a*c^2)*x^3 + (b*(2*log(c) + 1) - 2*a)*x)*x)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + (3*(b*c^6*x^7 - 5*b*c^4*x^5 + 6*b*c^2*x^3 - 2*b*x)*x*log(x) + (3*(b*c^6*log(c) - a*c^6)*x^7 - (b*c^4*(15*log(c) + 2) - 15*a*c^4)*x^5 + (b*c^2*(18*log(c) + 5) - 18*a*c^2)*x^3 - 3*(b*(2*log(c) + 1) - 2*a)*x)*x)*(c*x + 1)*(c*x - 1) - 2*(b*c^6*x^7 - 3*b*c^4*x^5 + 3*b*c^2*x^3 - b*x)*x*log(x) - ((5*b*c^6*x^7 - 17*b*c^4*x^5 + 18*b*c^2*x^3 - 6*b*x)*x*log(x) + ((b*c^6*(5*log(c) + 1) - 5*a*c^6)*x^7 - (b*c^4*(17*log(c) + 5) - 17*a*c^4)*x^5 + (b*c^2*(18*log(c) + 7) - 18*a*c^2)*x^3 - 3*(b*(2*log(c) + 1) - 2*a)*x)*x)*sqrt(c*x + 1)*sqrt(-c*x + 1) - ((b*c^6*(2*log(c) + 1) - 2*a*c^6)*x^7 - 3*(b*c^4*(2*log(c) + 1) - 2*a*c^4)*x^5 + 3*(b*c^2*(2*log(c) + 1) - 2*a*c^2)*x^3 - (b*(2*log(c) + 1) - 2*a)*x)*x - (2*(2*b*c^4*x^5 - 3*b*c^2*x^3 + b*x)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2)*x + 3*(b*c^6*x^7 - 5*b*c^4*x^5 + 6*b*c^2*x^3 - 2*b*x)*(c*x + 1)*(c*x - 1)*x - (5*b*c^6*x^7 - 17*b*c^4*x^5 + 18*b*c^2*x^3 - 6*b*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x - 2*(b*c^6*x^7 - 3*b*c^4*x^5 + 3*b*c^2*x^3 - b*x)*x)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1))/((b^4*c^6*log(c)^2 - 2*a*b^3*c^6*log(c) + a^2*b^2*c^6)*x^6 - b^4*log(c)^2 - 3*(b^4*c^4*log(c)^2 - 2*a*b^3*c^4*log(c) + a^2*b^2*c^4)*x^4 + 2*a*b^3*log(c) - (b^4*log(c)^2 + b^4*log(x)^2 - 2*a*b^3*log(c) + a^2*b^2 + 2*(b^4*log(c) - a*b^3)*log(x))*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - a^2*b^2 + 3*(b^4*log(c)^2 - 2*a*b^3*log(c) + a^2*b^2 - (b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2 - (b^4*c^2*x^2 - b^4)*log(x)^2 + 2*(b^4*log(c) - a*b^3 - (b^4*c^2*log(c) - a*b^3*c^2)*x^2)*log(x))*(c*x + 1)*(c*x - 1) + 3*(b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2 + (b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - (c*x + 1)^(3/2)*(-c*x + 1)^(3/2)*b^4 - b^4 - 3*(b^4*c^2*x^2 - b^4)*(c*x + 1)*(c*x - 1) - 3*(b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*sqrt(c*x + 1)*sqrt(-c*x + 1))*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)^2 + (b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*log(x)^2 - 3*(b^4*log(c)^2 + (b^4*c^4*log(c)^2 - 2*a*b^3*c^4*log(c) + a^2*b^2*c^4)*x^4 - 2*a*b^3*log(c) + a^2*b^2 - 2*(b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2 + (b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*log(x)^2 + 2*((b^4*c^4*log(c) - a*b^3*c^4)*x^4 + b^4*log(c) - a*b^3 - 2*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - 2*((b^4*c^6*log(c) - a*b^3*c^6)*x^6 - 3*(b^4*c^4*log(c) - a*b^3*c^4)*x^4 - b^4*log(c) - (b^4*log(c) + b^4*log(x) - a*b^3)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + a*b^3 + 3*(b^4*log(c) - a*b^3 - (b^4*c^2*log(c) - a*b^3*c^2)*x^2 - (b^4*c^2*x^2 - b^4)*log(x))*(c*x + 1)*(c*x - 1) + 3*(b^4*c^2*log(c) - a*b^3*c^2)*x^2 - 3*((b^4*c^4*log(c) - a*b^3*c^4)*x^4 + b^4*log(c) - a*b^3 - 2*(b^4*c^2*log(c) - a*b^3*c^2)*x^2 + (b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) + (b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*log(x))*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + 2*((b^4*c^6*log(c) - a*b^3*c^6)*x^6 - 3*(b^4*c^4*log(c) - a*b^3*c^4)*x^4 - b^4*log(c) + a*b^3 + 3*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*log(x)) + integrate(-1/2*(4*(6*c^4*x^4 - 6*c^2*x^2 + 1)*(c*x + 1)^2*(c*x - 1)^2*x - (33*c^6*x^6 - 108*c^4*x^4 + 88*c^2*x^2 - 16)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2)*x - 12*(c^8*x^8 - 7*c^6*x^6 + 14*c^4*x^4 - 10*c^2*x^2 + 2)*(c*x + 1)*(c*x - 1)*x + (15*c^8*x^8 - 67*c^6*x^6 + 108*c^4*x^4 - 72*c^2*x^2 + 16)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x + 4*(c^8*x^8 - 4*c^6*x^6 + 6*c^4*x^4 - 4*c^2*x^2 + 1)*x)/((b^3*c^8*log(c) - a*b^2*c^8)*x^8 - 4*(b^3*c^6*log(c) - a*b^2*c^6)*x^6 + (b^3*log(c) + b^3*log(x) - a*b^2)*(c*x + 1)^2*(c*x - 1)^2 + 6*(b^3*c^4*log(c) - a*b^2*c^4)*x^4 + 4*(b^3*log(c) - a*b^2 - (b^3*c^2*log(c) - a*b^2*c^2)*x^2 - (b^3*c^2*x^2 - b^3)*log(x))*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + b^3*log(c) - 6*((b^3*c^4*log(c) - a*b^2*c^4)*x^4 + b^3*log(c) - a*b^2 - 2*(b^3*c^2*log(c) - a*b^2*c^2)*x^2 + (b^3*c^4*x^4 - 2*b^3*c^2*x^2 + b^3)*log(x))*(c*x + 1)*(c*x - 1) - a*b^2 - 4*(b^3*c^2*log(c) - a*b^2*c^2)*x^2 - 4*((b^3*c^6*log(c) - a*b^2*c^6)*x^6 - 3*(b^3*c^4*log(c) - a*b^2*c^4)*x^4 - b^3*log(c) + a*b^2 + 3*(b^3*c^2*log(c) - a*b^2*c^2)*x^2 + (b^3*c^6*x^6 - 3*b^3*c^4*x^4 + 3*b^3*c^2*x^2 - b^3)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - (b^3*c^8*x^8 - 4*b^3*c^6*x^6 + 6*b^3*c^4*x^4 + (c*x + 1)^2*(c*x - 1)^2*b^3 - 4*b^3*c^2*x^2 - 4*(b^3*c^2*x^2 - b^3)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - 6*(b^3*c^4*x^4 - 2*b^3*c^2*x^2 + b^3)*(c*x + 1)*(c*x - 1) + b^3 - 4*(b^3*c^6*x^6 - 3*b^3*c^4*x^4 + 3*b^3*c^2*x^2 - b^3)*sqrt(c*x + 1)*sqrt(-c*x + 1))*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + (b^3*c^8*x^8 - 4*b^3*c^6*x^6 + 6*b^3*c^4*x^4 - 4*b^3*c^2*x^2 + b^3)*log(x)), x)","F",0
64,0,0,0,0.000000," ","integrate(1/(a+b*arcsech(c*x))^3,x, algorithm=""maxima"")","\frac{{\left(b c^{6} {\left(\log\left(c\right) + 1\right)} - a c^{6}\right)} x^{7} - 3 \, {\left(b c^{4} {\left(\log\left(c\right) + 1\right)} - a c^{4}\right)} x^{5} - {\left(3 \, {\left(b c^{4} \log\left(c\right) - a c^{4}\right)} x^{5} - {\left(b c^{2} {\left(4 \, \log\left(c\right) + 1\right)} - 4 \, a c^{2}\right)} x^{3} + {\left(b {\left(\log\left(c\right) + 1\right)} - a\right)} x + {\left(3 \, b c^{4} x^{5} - 4 \, b c^{2} x^{3} + b x\right)} \log\left(x\right)\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b c^{2} {\left(\log\left(c\right) + 1\right)} - a c^{2}\right)} x^{3} - {\left(2 \, {\left(b c^{6} \log\left(c\right) - a c^{6}\right)} x^{7} - 2 \, {\left(b c^{4} {\left(5 \, \log\left(c\right) + 1\right)} - 5 \, a c^{4}\right)} x^{5} + {\left(b c^{2} {\left(11 \, \log\left(c\right) + 5\right)} - 11 \, a c^{2}\right)} x^{3} - 3 \, {\left(b {\left(\log\left(c\right) + 1\right)} - a\right)} x + {\left(2 \, b c^{6} x^{7} - 10 \, b c^{4} x^{5} + 11 \, b c^{2} x^{3} - 3 \, b x\right)} \log\left(x\right)\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left({\left(b c^{6} {\left(3 \, \log\left(c\right) + 1\right)} - 3 \, a c^{6}\right)} x^{7} - 5 \, {\left(b c^{4} {\left(2 \, \log\left(c\right) + 1\right)} - 2 \, a c^{4}\right)} x^{5} + {\left(b c^{2} {\left(10 \, \log\left(c\right) + 7\right)} - 10 \, a c^{2}\right)} x^{3} - 3 \, {\left(b {\left(\log\left(c\right) + 1\right)} - a\right)} x + {\left(3 \, b c^{6} x^{7} - 10 \, b c^{4} x^{5} + 10 \, b c^{2} x^{3} - 3 \, b x\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left(b {\left(\log\left(c\right) + 1\right)} - a\right)} x - {\left(b c^{6} x^{7} - 3 \, b c^{4} x^{5} + 3 \, b c^{2} x^{3} - {\left(3 \, b c^{4} x^{5} - 4 \, b c^{2} x^{3} + b x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - {\left(2 \, b c^{6} x^{7} - 10 \, b c^{4} x^{5} + 11 \, b c^{2} x^{3} - 3 \, b x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(3 \, b c^{6} x^{7} - 10 \, b c^{4} x^{5} + 10 \, b c^{2} x^{3} - 3 \, b x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - b x\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + {\left(b c^{6} x^{7} - 3 \, b c^{4} x^{5} + 3 \, b c^{2} x^{3} - b x\right)} \log\left(x\right)}{2 \, {\left({\left(b^{4} c^{6} \log\left(c\right)^{2} - 2 \, a b^{3} c^{6} \log\left(c\right) + a^{2} b^{2} c^{6}\right)} x^{6} - b^{4} \log\left(c\right)^{2} - 3 \, {\left(b^{4} c^{4} \log\left(c\right)^{2} - 2 \, a b^{3} c^{4} \log\left(c\right) + a^{2} b^{2} c^{4}\right)} x^{4} + 2 \, a b^{3} \log\left(c\right) - {\left(b^{4} \log\left(c\right)^{2} + b^{4} \log\left(x\right)^{2} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2} + 2 \, {\left(b^{4} \log\left(c\right) - a b^{3}\right)} \log\left(x\right)\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - a^{2} b^{2} + 3 \, {\left(b^{4} \log\left(c\right)^{2} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2} - {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2} - {\left(b^{4} c^{2} x^{2} - b^{4}\right)} \log\left(x\right)^{2} + 2 \, {\left(b^{4} \log\left(c\right) - a b^{3} - {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} \log\left(x\right)\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 3 \, {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2} + {\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} b^{4} - b^{4} - 3 \, {\left(b^{4} c^{2} x^{2} - b^{4}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - 3 \, {\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)^{2} + {\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} \log\left(x\right)^{2} - 3 \, {\left(b^{4} \log\left(c\right)^{2} + {\left(b^{4} c^{4} \log\left(c\right)^{2} - 2 \, a b^{3} c^{4} \log\left(c\right) + a^{2} b^{2} c^{4}\right)} x^{4} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2} - 2 \, {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2} + {\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} \log\left(x\right)^{2} + 2 \, {\left({\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} + b^{4} \log\left(c\right) - a b^{3} - 2 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - 2 \, {\left({\left(b^{4} c^{6} \log\left(c\right) - a b^{3} c^{6}\right)} x^{6} - 3 \, {\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} - b^{4} \log\left(c\right) - {\left(b^{4} \log\left(c\right) + b^{4} \log\left(x\right) - a b^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + a b^{3} + 3 \, {\left(b^{4} \log\left(c\right) - a b^{3} - {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2} - {\left(b^{4} c^{2} x^{2} - b^{4}\right)} \log\left(x\right)\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 3 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2} - 3 \, {\left({\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} + b^{4} \log\left(c\right) - a b^{3} - 2 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2} + {\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + {\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} \log\left(x\right)\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + 2 \, {\left({\left(b^{4} c^{6} \log\left(c\right) - a b^{3} c^{6}\right)} x^{6} - 3 \, {\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} - b^{4} \log\left(c\right) + a b^{3} + 3 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} \log\left(x\right)\right)}} + \int -\frac{c^{8} x^{8} - 4 \, c^{6} x^{6} + 6 \, c^{4} x^{4} + {\left(15 \, c^{4} x^{4} - 12 \, c^{2} x^{2} + 1\right)} {\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} - {\left(18 \, c^{6} x^{6} - 57 \, c^{4} x^{4} + 40 \, c^{2} x^{2} - 4\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - 4 \, c^{2} x^{2} - 3 \, {\left(2 \, c^{8} x^{8} - 13 \, c^{6} x^{6} + 25 \, c^{4} x^{4} - 16 \, c^{2} x^{2} + 2\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(6 \, c^{8} x^{8} - 25 \, c^{6} x^{6} + 39 \, c^{4} x^{4} - 24 \, c^{2} x^{2} + 4\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + 1}{2 \, {\left({\left(b^{3} c^{8} \log\left(c\right) - a b^{2} c^{8}\right)} x^{8} - 4 \, {\left(b^{3} c^{6} \log\left(c\right) - a b^{2} c^{6}\right)} x^{6} + {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right) - a b^{2}\right)} {\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} + 6 \, {\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} + 4 \, {\left(b^{3} \log\left(c\right) - a b^{2} - {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2} - {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + b^{3} \log\left(c\right) - 6 \, {\left({\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} + b^{3} \log\left(c\right) - a b^{2} - 2 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2} + {\left(b^{3} c^{4} x^{4} - 2 \, b^{3} c^{2} x^{2} + b^{3}\right)} \log\left(x\right)\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - a b^{2} - 4 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2} - 4 \, {\left({\left(b^{3} c^{6} \log\left(c\right) - a b^{2} c^{6}\right)} x^{6} - 3 \, {\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} - b^{3} \log\left(c\right) + a b^{2} + 3 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2} + {\left(b^{3} c^{6} x^{6} - 3 \, b^{3} c^{4} x^{4} + 3 \, b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left(b^{3} c^{8} x^{8} - 4 \, b^{3} c^{6} x^{6} + 6 \, b^{3} c^{4} x^{4} + {\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} b^{3} - 4 \, b^{3} c^{2} x^{2} - 4 \, {\left(b^{3} c^{2} x^{2} - b^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - 6 \, {\left(b^{3} c^{4} x^{4} - 2 \, b^{3} c^{2} x^{2} + b^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + b^{3} - 4 \, {\left(b^{3} c^{6} x^{6} - 3 \, b^{3} c^{4} x^{4} + 3 \, b^{3} c^{2} x^{2} - b^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + {\left(b^{3} c^{8} x^{8} - 4 \, b^{3} c^{6} x^{6} + 6 \, b^{3} c^{4} x^{4} - 4 \, b^{3} c^{2} x^{2} + b^{3}\right)} \log\left(x\right)\right)}}\,{d x}"," ",0,"1/2*((b*c^6*(log(c) + 1) - a*c^6)*x^7 - 3*(b*c^4*(log(c) + 1) - a*c^4)*x^5 - (3*(b*c^4*log(c) - a*c^4)*x^5 - (b*c^2*(4*log(c) + 1) - 4*a*c^2)*x^3 + (b*(log(c) + 1) - a)*x + (3*b*c^4*x^5 - 4*b*c^2*x^3 + b*x)*log(x))*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + 3*(b*c^2*(log(c) + 1) - a*c^2)*x^3 - (2*(b*c^6*log(c) - a*c^6)*x^7 - 2*(b*c^4*(5*log(c) + 1) - 5*a*c^4)*x^5 + (b*c^2*(11*log(c) + 5) - 11*a*c^2)*x^3 - 3*(b*(log(c) + 1) - a)*x + (2*b*c^6*x^7 - 10*b*c^4*x^5 + 11*b*c^2*x^3 - 3*b*x)*log(x))*(c*x + 1)*(c*x - 1) + ((b*c^6*(3*log(c) + 1) - 3*a*c^6)*x^7 - 5*(b*c^4*(2*log(c) + 1) - 2*a*c^4)*x^5 + (b*c^2*(10*log(c) + 7) - 10*a*c^2)*x^3 - 3*(b*(log(c) + 1) - a)*x + (3*b*c^6*x^7 - 10*b*c^4*x^5 + 10*b*c^2*x^3 - 3*b*x)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - (b*(log(c) + 1) - a)*x - (b*c^6*x^7 - 3*b*c^4*x^5 + 3*b*c^2*x^3 - (3*b*c^4*x^5 - 4*b*c^2*x^3 + b*x)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - (2*b*c^6*x^7 - 10*b*c^4*x^5 + 11*b*c^2*x^3 - 3*b*x)*(c*x + 1)*(c*x - 1) + (3*b*c^6*x^7 - 10*b*c^4*x^5 + 10*b*c^2*x^3 - 3*b*x)*sqrt(c*x + 1)*sqrt(-c*x + 1) - b*x)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + (b*c^6*x^7 - 3*b*c^4*x^5 + 3*b*c^2*x^3 - b*x)*log(x))/((b^4*c^6*log(c)^2 - 2*a*b^3*c^6*log(c) + a^2*b^2*c^6)*x^6 - b^4*log(c)^2 - 3*(b^4*c^4*log(c)^2 - 2*a*b^3*c^4*log(c) + a^2*b^2*c^4)*x^4 + 2*a*b^3*log(c) - (b^4*log(c)^2 + b^4*log(x)^2 - 2*a*b^3*log(c) + a^2*b^2 + 2*(b^4*log(c) - a*b^3)*log(x))*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - a^2*b^2 + 3*(b^4*log(c)^2 - 2*a*b^3*log(c) + a^2*b^2 - (b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2 - (b^4*c^2*x^2 - b^4)*log(x)^2 + 2*(b^4*log(c) - a*b^3 - (b^4*c^2*log(c) - a*b^3*c^2)*x^2)*log(x))*(c*x + 1)*(c*x - 1) + 3*(b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2 + (b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - (c*x + 1)^(3/2)*(-c*x + 1)^(3/2)*b^4 - b^4 - 3*(b^4*c^2*x^2 - b^4)*(c*x + 1)*(c*x - 1) - 3*(b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*sqrt(c*x + 1)*sqrt(-c*x + 1))*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)^2 + (b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*log(x)^2 - 3*(b^4*log(c)^2 + (b^4*c^4*log(c)^2 - 2*a*b^3*c^4*log(c) + a^2*b^2*c^4)*x^4 - 2*a*b^3*log(c) + a^2*b^2 - 2*(b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2 + (b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*log(x)^2 + 2*((b^4*c^4*log(c) - a*b^3*c^4)*x^4 + b^4*log(c) - a*b^3 - 2*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - 2*((b^4*c^6*log(c) - a*b^3*c^6)*x^6 - 3*(b^4*c^4*log(c) - a*b^3*c^4)*x^4 - b^4*log(c) - (b^4*log(c) + b^4*log(x) - a*b^3)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + a*b^3 + 3*(b^4*log(c) - a*b^3 - (b^4*c^2*log(c) - a*b^3*c^2)*x^2 - (b^4*c^2*x^2 - b^4)*log(x))*(c*x + 1)*(c*x - 1) + 3*(b^4*c^2*log(c) - a*b^3*c^2)*x^2 - 3*((b^4*c^4*log(c) - a*b^3*c^4)*x^4 + b^4*log(c) - a*b^3 - 2*(b^4*c^2*log(c) - a*b^3*c^2)*x^2 + (b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) + (b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*log(x))*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + 2*((b^4*c^6*log(c) - a*b^3*c^6)*x^6 - 3*(b^4*c^4*log(c) - a*b^3*c^4)*x^4 - b^4*log(c) + a*b^3 + 3*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*log(x)) + integrate(-1/2*(c^8*x^8 - 4*c^6*x^6 + 6*c^4*x^4 + (15*c^4*x^4 - 12*c^2*x^2 + 1)*(c*x + 1)^2*(c*x - 1)^2 - (18*c^6*x^6 - 57*c^4*x^4 + 40*c^2*x^2 - 4)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - 4*c^2*x^2 - 3*(2*c^8*x^8 - 13*c^6*x^6 + 25*c^4*x^4 - 16*c^2*x^2 + 2)*(c*x + 1)*(c*x - 1) + (6*c^8*x^8 - 25*c^6*x^6 + 39*c^4*x^4 - 24*c^2*x^2 + 4)*sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/((b^3*c^8*log(c) - a*b^2*c^8)*x^8 - 4*(b^3*c^6*log(c) - a*b^2*c^6)*x^6 + (b^3*log(c) + b^3*log(x) - a*b^2)*(c*x + 1)^2*(c*x - 1)^2 + 6*(b^3*c^4*log(c) - a*b^2*c^4)*x^4 + 4*(b^3*log(c) - a*b^2 - (b^3*c^2*log(c) - a*b^2*c^2)*x^2 - (b^3*c^2*x^2 - b^3)*log(x))*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + b^3*log(c) - 6*((b^3*c^4*log(c) - a*b^2*c^4)*x^4 + b^3*log(c) - a*b^2 - 2*(b^3*c^2*log(c) - a*b^2*c^2)*x^2 + (b^3*c^4*x^4 - 2*b^3*c^2*x^2 + b^3)*log(x))*(c*x + 1)*(c*x - 1) - a*b^2 - 4*(b^3*c^2*log(c) - a*b^2*c^2)*x^2 - 4*((b^3*c^6*log(c) - a*b^2*c^6)*x^6 - 3*(b^3*c^4*log(c) - a*b^2*c^4)*x^4 - b^3*log(c) + a*b^2 + 3*(b^3*c^2*log(c) - a*b^2*c^2)*x^2 + (b^3*c^6*x^6 - 3*b^3*c^4*x^4 + 3*b^3*c^2*x^2 - b^3)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - (b^3*c^8*x^8 - 4*b^3*c^6*x^6 + 6*b^3*c^4*x^4 + (c*x + 1)^2*(c*x - 1)^2*b^3 - 4*b^3*c^2*x^2 - 4*(b^3*c^2*x^2 - b^3)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - 6*(b^3*c^4*x^4 - 2*b^3*c^2*x^2 + b^3)*(c*x + 1)*(c*x - 1) + b^3 - 4*(b^3*c^6*x^6 - 3*b^3*c^4*x^4 + 3*b^3*c^2*x^2 - b^3)*sqrt(c*x + 1)*sqrt(-c*x + 1))*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + (b^3*c^8*x^8 - 4*b^3*c^6*x^6 + 6*b^3*c^4*x^4 - 4*b^3*c^2*x^2 + b^3)*log(x)), x)","F",0
65,0,0,0,0.000000," ","integrate(1/x/(a+b*arcsech(c*x))^3,x, algorithm=""maxima"")","-\frac{b c^{6} x^{7} - 3 \, b c^{4} x^{5} + 3 \, b c^{2} x^{3} - {\left(2 \, {\left(b c^{4} \log\left(c\right) - a c^{4}\right)} x^{5} - {\left(b c^{2} {\left(2 \, \log\left(c\right) + 1\right)} - 2 \, a c^{2}\right)} x^{3} + b x + 2 \, {\left(b c^{4} x^{5} - b c^{2} x^{3}\right)} \log\left(x\right)\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - {\left({\left(b c^{6} \log\left(c\right) - a c^{6}\right)} x^{7} - {\left(b c^{4} {\left(5 \, \log\left(c\right) + 2\right)} - 5 \, a c^{4}\right)} x^{5} + {\left(b c^{2} {\left(4 \, \log\left(c\right) + 5\right)} - 4 \, a c^{2}\right)} x^{3} - 3 \, b x + {\left(b c^{6} x^{7} - 5 \, b c^{4} x^{5} + 4 \, b c^{2} x^{3}\right)} \log\left(x\right)\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left({\left(b c^{6} {\left(\log\left(c\right) + 1\right)} - a c^{6}\right)} x^{7} - {\left(b c^{4} {\left(3 \, \log\left(c\right) + 5\right)} - 3 \, a c^{4}\right)} x^{5} + {\left(b c^{2} {\left(2 \, \log\left(c\right) + 7\right)} - 2 \, a c^{2}\right)} x^{3} - 3 \, b x + {\left(b c^{6} x^{7} - 3 \, b c^{4} x^{5} + 2 \, b c^{2} x^{3}\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - b x + {\left(2 \, {\left(b c^{4} x^{5} - b c^{2} x^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + {\left(b c^{6} x^{7} - 5 \, b c^{4} x^{5} + 4 \, b c^{2} x^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - {\left(b c^{6} x^{7} - 3 \, b c^{4} x^{5} + 2 \, b c^{2} x^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{2 \, {\left({\left(b^{4} x \log\left(x\right)^{2} + 2 \, {\left(b^{4} \log\left(c\right) - a b^{3}\right)} x \log\left(x\right) + {\left(b^{4} \log\left(c\right)^{2} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2}\right)} x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - {\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} x \log\left(x\right)^{2} + 3 \, {\left({\left(b^{4} c^{2} x^{2} - b^{4}\right)} x \log\left(x\right)^{2} - 2 \, {\left(b^{4} \log\left(c\right) - a b^{3} - {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x \log\left(x\right) - {\left(b^{4} \log\left(c\right)^{2} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2} - {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2}\right)} x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} b^{4} x + 3 \, {\left(b^{4} c^{2} x^{2} - b^{4}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x + 3 \, {\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x - {\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} x\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)^{2} - 2 \, {\left({\left(b^{4} c^{6} \log\left(c\right) - a b^{3} c^{6}\right)} x^{6} - 3 \, {\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} - b^{4} \log\left(c\right) + a b^{3} + 3 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x \log\left(x\right) + 3 \, {\left({\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} x \log\left(x\right)^{2} + 2 \, {\left({\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} + b^{4} \log\left(c\right) - a b^{3} - 2 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x \log\left(x\right) + {\left(b^{4} \log\left(c\right)^{2} + {\left(b^{4} c^{4} \log\left(c\right)^{2} - 2 \, a b^{3} c^{4} \log\left(c\right) + a^{2} b^{2} c^{4}\right)} x^{4} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2} - 2 \, {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2}\right)} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left({\left(b^{4} c^{6} \log\left(c\right)^{2} - 2 \, a b^{3} c^{6} \log\left(c\right) + a^{2} b^{2} c^{6}\right)} x^{6} - b^{4} \log\left(c\right)^{2} - 3 \, {\left(b^{4} c^{4} \log\left(c\right)^{2} - 2 \, a b^{3} c^{4} \log\left(c\right) + a^{2} b^{2} c^{4}\right)} x^{4} + 2 \, a b^{3} \log\left(c\right) - a^{2} b^{2} + 3 \, {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2}\right)} x - 2 \, {\left({\left(b^{4} x \log\left(x\right) + {\left(b^{4} \log\left(c\right) - a b^{3}\right)} x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + 3 \, {\left({\left(b^{4} c^{2} x^{2} - b^{4}\right)} x \log\left(x\right) - {\left(b^{4} \log\left(c\right) - a b^{3} - {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - {\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} x \log\left(x\right) + 3 \, {\left({\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} x \log\left(x\right) + {\left({\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} + b^{4} \log\left(c\right) - a b^{3} - 2 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left({\left(b^{4} c^{6} \log\left(c\right) - a b^{3} c^{6}\right)} x^{6} - 3 \, {\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} - b^{4} \log\left(c\right) + a b^{3} + 3 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)\right)}} + \int -\frac{4 \, {\left(2 \, c^{4} x^{4} - c^{2} x^{2}\right)} {\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} - {\left(7 \, c^{6} x^{6} - 22 \, c^{4} x^{4} + 12 \, c^{2} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - 2 \, {\left(c^{8} x^{8} - 5 \, c^{6} x^{6} + 10 \, c^{4} x^{4} - 6 \, c^{2} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(c^{8} x^{8} - 3 \, c^{6} x^{6} + 6 \, c^{4} x^{4} - 4 \, c^{2} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{2 \, {\left({\left(b^{3} x \log\left(x\right) + {\left(b^{3} \log\left(c\right) - a b^{2}\right)} x\right)} {\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} - 4 \, {\left({\left(b^{3} c^{2} x^{2} - b^{3}\right)} x \log\left(x\right) - {\left(b^{3} \log\left(c\right) - a b^{2} - {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - 6 \, {\left({\left(b^{3} c^{4} x^{4} - 2 \, b^{3} c^{2} x^{2} + b^{3}\right)} x \log\left(x\right) + {\left({\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} + b^{3} \log\left(c\right) - a b^{2} - 2 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(b^{3} c^{8} x^{8} - 4 \, b^{3} c^{6} x^{6} + 6 \, b^{3} c^{4} x^{4} - 4 \, b^{3} c^{2} x^{2} + b^{3}\right)} x \log\left(x\right) - 4 \, {\left({\left(b^{3} c^{6} x^{6} - 3 \, b^{3} c^{4} x^{4} + 3 \, b^{3} c^{2} x^{2} - b^{3}\right)} x \log\left(x\right) + {\left({\left(b^{3} c^{6} \log\left(c\right) - a b^{2} c^{6}\right)} x^{6} - 3 \, {\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} - b^{3} \log\left(c\right) + a b^{2} + 3 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + {\left({\left(b^{3} c^{8} \log\left(c\right) - a b^{2} c^{8}\right)} x^{8} - 4 \, {\left(b^{3} c^{6} \log\left(c\right) - a b^{2} c^{6}\right)} x^{6} + 6 \, {\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} + b^{3} \log\left(c\right) - a b^{2} - 4 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x - {\left({\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} b^{3} x - 4 \, {\left(b^{3} c^{2} x^{2} - b^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} x - 6 \, {\left(b^{3} c^{4} x^{4} - 2 \, b^{3} c^{2} x^{2} + b^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x - 4 \, {\left(b^{3} c^{6} x^{6} - 3 \, b^{3} c^{4} x^{4} + 3 \, b^{3} c^{2} x^{2} - b^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x + {\left(b^{3} c^{8} x^{8} - 4 \, b^{3} c^{6} x^{6} + 6 \, b^{3} c^{4} x^{4} - 4 \, b^{3} c^{2} x^{2} + b^{3}\right)} x\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)\right)}}\,{d x}"," ",0,"-1/2*(b*c^6*x^7 - 3*b*c^4*x^5 + 3*b*c^2*x^3 - (2*(b*c^4*log(c) - a*c^4)*x^5 - (b*c^2*(2*log(c) + 1) - 2*a*c^2)*x^3 + b*x + 2*(b*c^4*x^5 - b*c^2*x^3)*log(x))*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - ((b*c^6*log(c) - a*c^6)*x^7 - (b*c^4*(5*log(c) + 2) - 5*a*c^4)*x^5 + (b*c^2*(4*log(c) + 5) - 4*a*c^2)*x^3 - 3*b*x + (b*c^6*x^7 - 5*b*c^4*x^5 + 4*b*c^2*x^3)*log(x))*(c*x + 1)*(c*x - 1) + ((b*c^6*(log(c) + 1) - a*c^6)*x^7 - (b*c^4*(3*log(c) + 5) - 3*a*c^4)*x^5 + (b*c^2*(2*log(c) + 7) - 2*a*c^2)*x^3 - 3*b*x + (b*c^6*x^7 - 3*b*c^4*x^5 + 2*b*c^2*x^3)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - b*x + (2*(b*c^4*x^5 - b*c^2*x^3)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + (b*c^6*x^7 - 5*b*c^4*x^5 + 4*b*c^2*x^3)*(c*x + 1)*(c*x - 1) - (b*c^6*x^7 - 3*b*c^4*x^5 + 2*b*c^2*x^3)*sqrt(c*x + 1)*sqrt(-c*x + 1))*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1))/((b^4*x*log(x)^2 + 2*(b^4*log(c) - a*b^3)*x*log(x) + (b^4*log(c)^2 - 2*a*b^3*log(c) + a^2*b^2)*x)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - (b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*x*log(x)^2 + 3*((b^4*c^2*x^2 - b^4)*x*log(x)^2 - 2*(b^4*log(c) - a*b^3 - (b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x*log(x) - (b^4*log(c)^2 - 2*a*b^3*log(c) + a^2*b^2 - (b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2)*x)*(c*x + 1)*(c*x - 1) + ((c*x + 1)^(3/2)*(-c*x + 1)^(3/2)*b^4*x + 3*(b^4*c^2*x^2 - b^4)*(c*x + 1)*(c*x - 1)*x + 3*(b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x - (b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*x)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)^2 - 2*((b^4*c^6*log(c) - a*b^3*c^6)*x^6 - 3*(b^4*c^4*log(c) - a*b^3*c^4)*x^4 - b^4*log(c) + a*b^3 + 3*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x*log(x) + 3*((b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*x*log(x)^2 + 2*((b^4*c^4*log(c) - a*b^3*c^4)*x^4 + b^4*log(c) - a*b^3 - 2*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x*log(x) + (b^4*log(c)^2 + (b^4*c^4*log(c)^2 - 2*a*b^3*c^4*log(c) + a^2*b^2*c^4)*x^4 - 2*a*b^3*log(c) + a^2*b^2 - 2*(b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2)*x)*sqrt(c*x + 1)*sqrt(-c*x + 1) - ((b^4*c^6*log(c)^2 - 2*a*b^3*c^6*log(c) + a^2*b^2*c^6)*x^6 - b^4*log(c)^2 - 3*(b^4*c^4*log(c)^2 - 2*a*b^3*c^4*log(c) + a^2*b^2*c^4)*x^4 + 2*a*b^3*log(c) - a^2*b^2 + 3*(b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2)*x - 2*((b^4*x*log(x) + (b^4*log(c) - a*b^3)*x)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + 3*((b^4*c^2*x^2 - b^4)*x*log(x) - (b^4*log(c) - a*b^3 - (b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x)*(c*x + 1)*(c*x - 1) - (b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*x*log(x) + 3*((b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*x*log(x) + ((b^4*c^4*log(c) - a*b^3*c^4)*x^4 + b^4*log(c) - a*b^3 - 2*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x)*sqrt(c*x + 1)*sqrt(-c*x + 1) - ((b^4*c^6*log(c) - a*b^3*c^6)*x^6 - 3*(b^4*c^4*log(c) - a*b^3*c^4)*x^4 - b^4*log(c) + a*b^3 + 3*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)) + integrate(-1/2*(4*(2*c^4*x^4 - c^2*x^2)*(c*x + 1)^2*(c*x - 1)^2 - (7*c^6*x^6 - 22*c^4*x^4 + 12*c^2*x^2)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - 2*(c^8*x^8 - 5*c^6*x^6 + 10*c^4*x^4 - 6*c^2*x^2)*(c*x + 1)*(c*x - 1) + (c^8*x^8 - 3*c^6*x^6 + 6*c^4*x^4 - 4*c^2*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1))/((b^3*x*log(x) + (b^3*log(c) - a*b^2)*x)*(c*x + 1)^2*(c*x - 1)^2 - 4*((b^3*c^2*x^2 - b^3)*x*log(x) - (b^3*log(c) - a*b^2 - (b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - 6*((b^3*c^4*x^4 - 2*b^3*c^2*x^2 + b^3)*x*log(x) + ((b^3*c^4*log(c) - a*b^2*c^4)*x^4 + b^3*log(c) - a*b^2 - 2*(b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x)*(c*x + 1)*(c*x - 1) + (b^3*c^8*x^8 - 4*b^3*c^6*x^6 + 6*b^3*c^4*x^4 - 4*b^3*c^2*x^2 + b^3)*x*log(x) - 4*((b^3*c^6*x^6 - 3*b^3*c^4*x^4 + 3*b^3*c^2*x^2 - b^3)*x*log(x) + ((b^3*c^6*log(c) - a*b^2*c^6)*x^6 - 3*(b^3*c^4*log(c) - a*b^2*c^4)*x^4 - b^3*log(c) + a*b^2 + 3*(b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x)*sqrt(c*x + 1)*sqrt(-c*x + 1) + ((b^3*c^8*log(c) - a*b^2*c^8)*x^8 - 4*(b^3*c^6*log(c) - a*b^2*c^6)*x^6 + 6*(b^3*c^4*log(c) - a*b^2*c^4)*x^4 + b^3*log(c) - a*b^2 - 4*(b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x - ((c*x + 1)^2*(c*x - 1)^2*b^3*x - 4*(b^3*c^2*x^2 - b^3)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2)*x - 6*(b^3*c^4*x^4 - 2*b^3*c^2*x^2 + b^3)*(c*x + 1)*(c*x - 1)*x - 4*(b^3*c^6*x^6 - 3*b^3*c^4*x^4 + 3*b^3*c^2*x^2 - b^3)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x + (b^3*c^8*x^8 - 4*b^3*c^6*x^6 + 6*b^3*c^4*x^4 - 4*b^3*c^2*x^2 + b^3)*x)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)), x)","F",0
66,0,0,0,0.000000," ","integrate(1/x^2/(a+b*arcsech(c*x))^3,x, algorithm=""maxima"")","-\frac{{\left(b c^{6} {\left(\log\left(c\right) - 1\right)} - a c^{6}\right)} x^{7} - 3 \, {\left(b c^{4} {\left(\log\left(c\right) - 1\right)} - a c^{4}\right)} x^{5} - {\left(b c^{2} x^{3} - {\left(b c^{4} \log\left(c\right) - a c^{4}\right)} x^{5} + {\left(b {\left(\log\left(c\right) - 1\right)} - a\right)} x - {\left(b c^{4} x^{5} - b x\right)} \log\left(x\right)\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b c^{2} {\left(\log\left(c\right) - 1\right)} - a c^{2}\right)} x^{3} - {\left(2 \, b c^{4} x^{5} + {\left(b c^{2} {\left(3 \, \log\left(c\right) - 5\right)} - 3 \, a c^{2}\right)} x^{3} - 3 \, {\left(b {\left(\log\left(c\right) - 1\right)} - a\right)} x + 3 \, {\left(b c^{2} x^{3} - b x\right)} \log\left(x\right)\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left({\left(b c^{6} {\left(\log\left(c\right) - 1\right)} - a c^{6}\right)} x^{7} - {\left(b c^{4} {\left(4 \, \log\left(c\right) - 5\right)} - 4 \, a c^{4}\right)} x^{5} + {\left(b c^{2} {\left(6 \, \log\left(c\right) - 7\right)} - 6 \, a c^{2}\right)} x^{3} - 3 \, {\left(b {\left(\log\left(c\right) - 1\right)} - a\right)} x + {\left(b c^{6} x^{7} - 4 \, b c^{4} x^{5} + 6 \, b c^{2} x^{3} - 3 \, b x\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left(b {\left(\log\left(c\right) - 1\right)} - a\right)} x - {\left(b c^{6} x^{7} - 3 \, b c^{4} x^{5} + 3 \, b c^{2} x^{3} + {\left(b c^{4} x^{5} - b x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - 3 \, {\left(b c^{2} x^{3} - b x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(b c^{6} x^{7} - 4 \, b c^{4} x^{5} + 6 \, b c^{2} x^{3} - 3 \, b x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - b x\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + {\left(b c^{6} x^{7} - 3 \, b c^{4} x^{5} + 3 \, b c^{2} x^{3} - b x\right)} \log\left(x\right)}{2 \, {\left({\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} x^{2} \log\left(x\right)^{2} - {\left(b^{4} x^{2} \log\left(x\right)^{2} + 2 \, {\left(b^{4} \log\left(c\right) - a b^{3}\right)} x^{2} \log\left(x\right) + {\left(b^{4} \log\left(c\right)^{2} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2}\right)} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + 2 \, {\left({\left(b^{4} c^{6} \log\left(c\right) - a b^{3} c^{6}\right)} x^{6} - 3 \, {\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} - b^{4} \log\left(c\right) + a b^{3} + 3 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{2} \log\left(x\right) - 3 \, {\left({\left(b^{4} c^{2} x^{2} - b^{4}\right)} x^{2} \log\left(x\right)^{2} - 2 \, {\left(b^{4} \log\left(c\right) - a b^{3} - {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{2} \log\left(x\right) - {\left(b^{4} \log\left(c\right)^{2} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2} - {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2}\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left({\left(b^{4} c^{6} \log\left(c\right)^{2} - 2 \, a b^{3} c^{6} \log\left(c\right) + a^{2} b^{2} c^{6}\right)} x^{6} - b^{4} \log\left(c\right)^{2} - 3 \, {\left(b^{4} c^{4} \log\left(c\right)^{2} - 2 \, a b^{3} c^{4} \log\left(c\right) + a^{2} b^{2} c^{4}\right)} x^{4} + 2 \, a b^{3} \log\left(c\right) - a^{2} b^{2} + 3 \, {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2}\right)} x^{2} - {\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} b^{4} x^{2} + 3 \, {\left(b^{4} c^{2} x^{2} - b^{4}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x^{2} + 3 \, {\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{2} - {\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} x^{2}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)^{2} - 3 \, {\left({\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} x^{2} \log\left(x\right)^{2} + 2 \, {\left({\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} + b^{4} \log\left(c\right) - a b^{3} - 2 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{2} \log\left(x\right) + {\left(b^{4} \log\left(c\right)^{2} + {\left(b^{4} c^{4} \log\left(c\right)^{2} - 2 \, a b^{3} c^{4} \log\left(c\right) + a^{2} b^{2} c^{4}\right)} x^{4} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2} - 2 \, {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2}\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + 2 \, {\left({\left(b^{4} x^{2} \log\left(x\right) + {\left(b^{4} \log\left(c\right) - a b^{3}\right)} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - {\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} x^{2} \log\left(x\right) + 3 \, {\left({\left(b^{4} c^{2} x^{2} - b^{4}\right)} x^{2} \log\left(x\right) - {\left(b^{4} \log\left(c\right) - a b^{3} - {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - {\left({\left(b^{4} c^{6} \log\left(c\right) - a b^{3} c^{6}\right)} x^{6} - 3 \, {\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} - b^{4} \log\left(c\right) + a b^{3} + 3 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{2} + 3 \, {\left({\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} x^{2} \log\left(x\right) + {\left({\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} + b^{4} \log\left(c\right) - a b^{3} - 2 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)\right)}} + \int -\frac{c^{8} x^{8} - 4 \, c^{6} x^{6} + 6 \, c^{4} x^{4} + {\left(3 \, c^{4} x^{4} + 1\right)} {\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} + {\left(3 \, c^{4} x^{4} - 4 \, c^{2} x^{2} + 4\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - 4 \, c^{2} x^{2} - 3 \, {\left(c^{6} x^{6} + c^{4} x^{4} - 4 \, c^{2} x^{2} + 2\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - {\left(c^{6} x^{6} - 9 \, c^{4} x^{4} + 12 \, c^{2} x^{2} - 4\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + 1}{2 \, {\left({\left(b^{3} x^{2} \log\left(x\right) + {\left(b^{3} \log\left(c\right) - a b^{2}\right)} x^{2}\right)} {\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} - 4 \, {\left({\left(b^{3} c^{2} x^{2} - b^{3}\right)} x^{2} \log\left(x\right) - {\left(b^{3} \log\left(c\right) - a b^{2} - {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + {\left(b^{3} c^{8} x^{8} - 4 \, b^{3} c^{6} x^{6} + 6 \, b^{3} c^{4} x^{4} - 4 \, b^{3} c^{2} x^{2} + b^{3}\right)} x^{2} \log\left(x\right) - 6 \, {\left({\left(b^{3} c^{4} x^{4} - 2 \, b^{3} c^{2} x^{2} + b^{3}\right)} x^{2} \log\left(x\right) + {\left({\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} + b^{3} \log\left(c\right) - a b^{2} - 2 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left({\left(b^{3} c^{8} \log\left(c\right) - a b^{2} c^{8}\right)} x^{8} - 4 \, {\left(b^{3} c^{6} \log\left(c\right) - a b^{2} c^{6}\right)} x^{6} + 6 \, {\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} + b^{3} \log\left(c\right) - a b^{2} - 4 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x^{2} - 4 \, {\left({\left(b^{3} c^{6} x^{6} - 3 \, b^{3} c^{4} x^{4} + 3 \, b^{3} c^{2} x^{2} - b^{3}\right)} x^{2} \log\left(x\right) + {\left({\left(b^{3} c^{6} \log\left(c\right) - a b^{2} c^{6}\right)} x^{6} - 3 \, {\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} - b^{3} \log\left(c\right) + a b^{2} + 3 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left({\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} b^{3} x^{2} - 4 \, {\left(b^{3} c^{2} x^{2} - b^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} x^{2} - 6 \, {\left(b^{3} c^{4} x^{4} - 2 \, b^{3} c^{2} x^{2} + b^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x^{2} - 4 \, {\left(b^{3} c^{6} x^{6} - 3 \, b^{3} c^{4} x^{4} + 3 \, b^{3} c^{2} x^{2} - b^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{2} + {\left(b^{3} c^{8} x^{8} - 4 \, b^{3} c^{6} x^{6} + 6 \, b^{3} c^{4} x^{4} - 4 \, b^{3} c^{2} x^{2} + b^{3}\right)} x^{2}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)\right)}}\,{d x}"," ",0,"-1/2*((b*c^6*(log(c) - 1) - a*c^6)*x^7 - 3*(b*c^4*(log(c) - 1) - a*c^4)*x^5 - (b*c^2*x^3 - (b*c^4*log(c) - a*c^4)*x^5 + (b*(log(c) - 1) - a)*x - (b*c^4*x^5 - b*x)*log(x))*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + 3*(b*c^2*(log(c) - 1) - a*c^2)*x^3 - (2*b*c^4*x^5 + (b*c^2*(3*log(c) - 5) - 3*a*c^2)*x^3 - 3*(b*(log(c) - 1) - a)*x + 3*(b*c^2*x^3 - b*x)*log(x))*(c*x + 1)*(c*x - 1) + ((b*c^6*(log(c) - 1) - a*c^6)*x^7 - (b*c^4*(4*log(c) - 5) - 4*a*c^4)*x^5 + (b*c^2*(6*log(c) - 7) - 6*a*c^2)*x^3 - 3*(b*(log(c) - 1) - a)*x + (b*c^6*x^7 - 4*b*c^4*x^5 + 6*b*c^2*x^3 - 3*b*x)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - (b*(log(c) - 1) - a)*x - (b*c^6*x^7 - 3*b*c^4*x^5 + 3*b*c^2*x^3 + (b*c^4*x^5 - b*x)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - 3*(b*c^2*x^3 - b*x)*(c*x + 1)*(c*x - 1) + (b*c^6*x^7 - 4*b*c^4*x^5 + 6*b*c^2*x^3 - 3*b*x)*sqrt(c*x + 1)*sqrt(-c*x + 1) - b*x)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + (b*c^6*x^7 - 3*b*c^4*x^5 + 3*b*c^2*x^3 - b*x)*log(x))/((b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*x^2*log(x)^2 - (b^4*x^2*log(x)^2 + 2*(b^4*log(c) - a*b^3)*x^2*log(x) + (b^4*log(c)^2 - 2*a*b^3*log(c) + a^2*b^2)*x^2)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + 2*((b^4*c^6*log(c) - a*b^3*c^6)*x^6 - 3*(b^4*c^4*log(c) - a*b^3*c^4)*x^4 - b^4*log(c) + a*b^3 + 3*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^2*log(x) - 3*((b^4*c^2*x^2 - b^4)*x^2*log(x)^2 - 2*(b^4*log(c) - a*b^3 - (b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^2*log(x) - (b^4*log(c)^2 - 2*a*b^3*log(c) + a^2*b^2 - (b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2)*x^2)*(c*x + 1)*(c*x - 1) + ((b^4*c^6*log(c)^2 - 2*a*b^3*c^6*log(c) + a^2*b^2*c^6)*x^6 - b^4*log(c)^2 - 3*(b^4*c^4*log(c)^2 - 2*a*b^3*c^4*log(c) + a^2*b^2*c^4)*x^4 + 2*a*b^3*log(c) - a^2*b^2 + 3*(b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2)*x^2 - ((c*x + 1)^(3/2)*(-c*x + 1)^(3/2)*b^4*x^2 + 3*(b^4*c^2*x^2 - b^4)*(c*x + 1)*(c*x - 1)*x^2 + 3*(b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^2 - (b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*x^2)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)^2 - 3*((b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*x^2*log(x)^2 + 2*((b^4*c^4*log(c) - a*b^3*c^4)*x^4 + b^4*log(c) - a*b^3 - 2*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^2*log(x) + (b^4*log(c)^2 + (b^4*c^4*log(c)^2 - 2*a*b^3*c^4*log(c) + a^2*b^2*c^4)*x^4 - 2*a*b^3*log(c) + a^2*b^2 - 2*(b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2)*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1) + 2*((b^4*x^2*log(x) + (b^4*log(c) - a*b^3)*x^2)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - (b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*x^2*log(x) + 3*((b^4*c^2*x^2 - b^4)*x^2*log(x) - (b^4*log(c) - a*b^3 - (b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^2)*(c*x + 1)*(c*x - 1) - ((b^4*c^6*log(c) - a*b^3*c^6)*x^6 - 3*(b^4*c^4*log(c) - a*b^3*c^4)*x^4 - b^4*log(c) + a*b^3 + 3*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^2 + 3*((b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*x^2*log(x) + ((b^4*c^4*log(c) - a*b^3*c^4)*x^4 + b^4*log(c) - a*b^3 - 2*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1))*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)) + integrate(-1/2*(c^8*x^8 - 4*c^6*x^6 + 6*c^4*x^4 + (3*c^4*x^4 + 1)*(c*x + 1)^2*(c*x - 1)^2 + (3*c^4*x^4 - 4*c^2*x^2 + 4)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - 4*c^2*x^2 - 3*(c^6*x^6 + c^4*x^4 - 4*c^2*x^2 + 2)*(c*x + 1)*(c*x - 1) - (c^6*x^6 - 9*c^4*x^4 + 12*c^2*x^2 - 4)*sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/((b^3*x^2*log(x) + (b^3*log(c) - a*b^2)*x^2)*(c*x + 1)^2*(c*x - 1)^2 - 4*((b^3*c^2*x^2 - b^3)*x^2*log(x) - (b^3*log(c) - a*b^2 - (b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x^2)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + (b^3*c^8*x^8 - 4*b^3*c^6*x^6 + 6*b^3*c^4*x^4 - 4*b^3*c^2*x^2 + b^3)*x^2*log(x) - 6*((b^3*c^4*x^4 - 2*b^3*c^2*x^2 + b^3)*x^2*log(x) + ((b^3*c^4*log(c) - a*b^2*c^4)*x^4 + b^3*log(c) - a*b^2 - 2*(b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x^2)*(c*x + 1)*(c*x - 1) + ((b^3*c^8*log(c) - a*b^2*c^8)*x^8 - 4*(b^3*c^6*log(c) - a*b^2*c^6)*x^6 + 6*(b^3*c^4*log(c) - a*b^2*c^4)*x^4 + b^3*log(c) - a*b^2 - 4*(b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x^2 - 4*((b^3*c^6*x^6 - 3*b^3*c^4*x^4 + 3*b^3*c^2*x^2 - b^3)*x^2*log(x) + ((b^3*c^6*log(c) - a*b^2*c^6)*x^6 - 3*(b^3*c^4*log(c) - a*b^2*c^4)*x^4 - b^3*log(c) + a*b^2 + 3*(b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1) - ((c*x + 1)^2*(c*x - 1)^2*b^3*x^2 - 4*(b^3*c^2*x^2 - b^3)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2)*x^2 - 6*(b^3*c^4*x^4 - 2*b^3*c^2*x^2 + b^3)*(c*x + 1)*(c*x - 1)*x^2 - 4*(b^3*c^6*x^6 - 3*b^3*c^4*x^4 + 3*b^3*c^2*x^2 - b^3)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^2 + (b^3*c^8*x^8 - 4*b^3*c^6*x^6 + 6*b^3*c^4*x^4 - 4*b^3*c^2*x^2 + b^3)*x^2)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)), x)","F",0
67,0,0,0,0.000000," ","integrate(1/x^3/(a+b*arcsech(c*x))^3,x, algorithm=""maxima"")","-\frac{{\left(b c^{6} {\left(2 \, \log\left(c\right) - 1\right)} - 2 \, a c^{6}\right)} x^{7} - 3 \, {\left(b c^{4} {\left(2 \, \log\left(c\right) - 1\right)} - 2 \, a c^{4}\right)} x^{5} + {\left({\left(b c^{2} {\left(2 \, \log\left(c\right) - 1\right)} - 2 \, a c^{2}\right)} x^{3} - {\left(b {\left(2 \, \log\left(c\right) - 1\right)} - 2 \, a\right)} x + 2 \, {\left(b c^{2} x^{3} - b x\right)} \log\left(x\right)\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b c^{2} {\left(2 \, \log\left(c\right) - 1\right)} - 2 \, a c^{2}\right)} x^{3} - {\left({\left(b c^{6} \log\left(c\right) - a c^{6}\right)} x^{7} - {\left(b c^{4} {\left(5 \, \log\left(c\right) - 2\right)} - 5 \, a c^{4}\right)} x^{5} + 5 \, {\left(b c^{2} {\left(2 \, \log\left(c\right) - 1\right)} - 2 \, a c^{2}\right)} x^{3} - 3 \, {\left(b {\left(2 \, \log\left(c\right) - 1\right)} - 2 \, a\right)} x + {\left(b c^{6} x^{7} - 5 \, b c^{4} x^{5} + 10 \, b c^{2} x^{3} - 6 \, b x\right)} \log\left(x\right)\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left({\left(b c^{6} {\left(3 \, \log\left(c\right) - 1\right)} - 3 \, a c^{6}\right)} x^{7} - {\left(b c^{4} {\left(11 \, \log\left(c\right) - 5\right)} - 11 \, a c^{4}\right)} x^{5} + 7 \, {\left(b c^{2} {\left(2 \, \log\left(c\right) - 1\right)} - 2 \, a c^{2}\right)} x^{3} - 3 \, {\left(b {\left(2 \, \log\left(c\right) - 1\right)} - 2 \, a\right)} x + {\left(3 \, b c^{6} x^{7} - 11 \, b c^{4} x^{5} + 14 \, b c^{2} x^{3} - 6 \, b x\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left(b {\left(2 \, \log\left(c\right) - 1\right)} - 2 \, a\right)} x - {\left(2 \, b c^{6} x^{7} - 6 \, b c^{4} x^{5} + 6 \, b c^{2} x^{3} + 2 \, {\left(b c^{2} x^{3} - b x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - {\left(b c^{6} x^{7} - 5 \, b c^{4} x^{5} + 10 \, b c^{2} x^{3} - 6 \, b x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(3 \, b c^{6} x^{7} - 11 \, b c^{4} x^{5} + 14 \, b c^{2} x^{3} - 6 \, b x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - 2 \, b x\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + 2 \, {\left(b c^{6} x^{7} - 3 \, b c^{4} x^{5} + 3 \, b c^{2} x^{3} - b x\right)} \log\left(x\right)}{2 \, {\left({\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} x^{3} \log\left(x\right)^{2} + 2 \, {\left({\left(b^{4} c^{6} \log\left(c\right) - a b^{3} c^{6}\right)} x^{6} - 3 \, {\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} - b^{4} \log\left(c\right) + a b^{3} + 3 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{3} \log\left(x\right) - {\left(b^{4} x^{3} \log\left(x\right)^{2} + 2 \, {\left(b^{4} \log\left(c\right) - a b^{3}\right)} x^{3} \log\left(x\right) + {\left(b^{4} \log\left(c\right)^{2} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2}\right)} x^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + {\left({\left(b^{4} c^{6} \log\left(c\right)^{2} - 2 \, a b^{3} c^{6} \log\left(c\right) + a^{2} b^{2} c^{6}\right)} x^{6} - b^{4} \log\left(c\right)^{2} - 3 \, {\left(b^{4} c^{4} \log\left(c\right)^{2} - 2 \, a b^{3} c^{4} \log\left(c\right) + a^{2} b^{2} c^{4}\right)} x^{4} + 2 \, a b^{3} \log\left(c\right) - a^{2} b^{2} + 3 \, {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2}\right)} x^{3} - 3 \, {\left({\left(b^{4} c^{2} x^{2} - b^{4}\right)} x^{3} \log\left(x\right)^{2} - 2 \, {\left(b^{4} \log\left(c\right) - a b^{3} - {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{3} \log\left(x\right) - {\left(b^{4} \log\left(c\right)^{2} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2} - {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2}\right)} x^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - {\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} b^{4} x^{3} + 3 \, {\left(b^{4} c^{2} x^{2} - b^{4}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x^{3} + 3 \, {\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{3} - {\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} x^{3}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)^{2} - 3 \, {\left({\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} x^{3} \log\left(x\right)^{2} + 2 \, {\left({\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} + b^{4} \log\left(c\right) - a b^{3} - 2 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{3} \log\left(x\right) + {\left(b^{4} \log\left(c\right)^{2} + {\left(b^{4} c^{4} \log\left(c\right)^{2} - 2 \, a b^{3} c^{4} \log\left(c\right) + a^{2} b^{2} c^{4}\right)} x^{4} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2} - 2 \, {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2}\right)} x^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - 2 \, {\left({\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} x^{3} \log\left(x\right) - {\left(b^{4} x^{3} \log\left(x\right) + {\left(b^{4} \log\left(c\right) - a b^{3}\right)} x^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + {\left({\left(b^{4} c^{6} \log\left(c\right) - a b^{3} c^{6}\right)} x^{6} - 3 \, {\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} - b^{4} \log\left(c\right) + a b^{3} + 3 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{3} - 3 \, {\left({\left(b^{4} c^{2} x^{2} - b^{4}\right)} x^{3} \log\left(x\right) - {\left(b^{4} \log\left(c\right) - a b^{3} - {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - 3 \, {\left({\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} x^{3} \log\left(x\right) + {\left({\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} + b^{4} \log\left(c\right) - a b^{3} - 2 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)\right)}} + \int -\frac{4 \, c^{8} x^{8} - 16 \, c^{6} x^{6} + 24 \, c^{4} x^{4} + 4 \, {\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} + {\left(3 \, c^{6} x^{6} - 16 \, c^{2} x^{2} + 16\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - 16 \, c^{2} x^{2} - 24 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(3 \, c^{8} x^{8} - 19 \, c^{6} x^{6} + 48 \, c^{4} x^{4} - 48 \, c^{2} x^{2} + 16\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + 4}{2 \, {\left({\left(b^{3} x^{3} \log\left(x\right) + {\left(b^{3} \log\left(c\right) - a b^{2}\right)} x^{3}\right)} {\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} + {\left(b^{3} c^{8} x^{8} - 4 \, b^{3} c^{6} x^{6} + 6 \, b^{3} c^{4} x^{4} - 4 \, b^{3} c^{2} x^{2} + b^{3}\right)} x^{3} \log\left(x\right) - 4 \, {\left({\left(b^{3} c^{2} x^{2} - b^{3}\right)} x^{3} \log\left(x\right) - {\left(b^{3} \log\left(c\right) - a b^{2} - {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + {\left({\left(b^{3} c^{8} \log\left(c\right) - a b^{2} c^{8}\right)} x^{8} - 4 \, {\left(b^{3} c^{6} \log\left(c\right) - a b^{2} c^{6}\right)} x^{6} + 6 \, {\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} + b^{3} \log\left(c\right) - a b^{2} - 4 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x^{3} - 6 \, {\left({\left(b^{3} c^{4} x^{4} - 2 \, b^{3} c^{2} x^{2} + b^{3}\right)} x^{3} \log\left(x\right) + {\left({\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} + b^{3} \log\left(c\right) - a b^{2} - 2 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - 4 \, {\left({\left(b^{3} c^{6} x^{6} - 3 \, b^{3} c^{4} x^{4} + 3 \, b^{3} c^{2} x^{2} - b^{3}\right)} x^{3} \log\left(x\right) + {\left({\left(b^{3} c^{6} \log\left(c\right) - a b^{2} c^{6}\right)} x^{6} - 3 \, {\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} - b^{3} \log\left(c\right) + a b^{2} + 3 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left({\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} b^{3} x^{3} - 4 \, {\left(b^{3} c^{2} x^{2} - b^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} x^{3} - 6 \, {\left(b^{3} c^{4} x^{4} - 2 \, b^{3} c^{2} x^{2} + b^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x^{3} - 4 \, {\left(b^{3} c^{6} x^{6} - 3 \, b^{3} c^{4} x^{4} + 3 \, b^{3} c^{2} x^{2} - b^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{3} + {\left(b^{3} c^{8} x^{8} - 4 \, b^{3} c^{6} x^{6} + 6 \, b^{3} c^{4} x^{4} - 4 \, b^{3} c^{2} x^{2} + b^{3}\right)} x^{3}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)\right)}}\,{d x}"," ",0,"-1/2*((b*c^6*(2*log(c) - 1) - 2*a*c^6)*x^7 - 3*(b*c^4*(2*log(c) - 1) - 2*a*c^4)*x^5 + ((b*c^2*(2*log(c) - 1) - 2*a*c^2)*x^3 - (b*(2*log(c) - 1) - 2*a)*x + 2*(b*c^2*x^3 - b*x)*log(x))*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + 3*(b*c^2*(2*log(c) - 1) - 2*a*c^2)*x^3 - ((b*c^6*log(c) - a*c^6)*x^7 - (b*c^4*(5*log(c) - 2) - 5*a*c^4)*x^5 + 5*(b*c^2*(2*log(c) - 1) - 2*a*c^2)*x^3 - 3*(b*(2*log(c) - 1) - 2*a)*x + (b*c^6*x^7 - 5*b*c^4*x^5 + 10*b*c^2*x^3 - 6*b*x)*log(x))*(c*x + 1)*(c*x - 1) + ((b*c^6*(3*log(c) - 1) - 3*a*c^6)*x^7 - (b*c^4*(11*log(c) - 5) - 11*a*c^4)*x^5 + 7*(b*c^2*(2*log(c) - 1) - 2*a*c^2)*x^3 - 3*(b*(2*log(c) - 1) - 2*a)*x + (3*b*c^6*x^7 - 11*b*c^4*x^5 + 14*b*c^2*x^3 - 6*b*x)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - (b*(2*log(c) - 1) - 2*a)*x - (2*b*c^6*x^7 - 6*b*c^4*x^5 + 6*b*c^2*x^3 + 2*(b*c^2*x^3 - b*x)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - (b*c^6*x^7 - 5*b*c^4*x^5 + 10*b*c^2*x^3 - 6*b*x)*(c*x + 1)*(c*x - 1) + (3*b*c^6*x^7 - 11*b*c^4*x^5 + 14*b*c^2*x^3 - 6*b*x)*sqrt(c*x + 1)*sqrt(-c*x + 1) - 2*b*x)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + 2*(b*c^6*x^7 - 3*b*c^4*x^5 + 3*b*c^2*x^3 - b*x)*log(x))/((b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*x^3*log(x)^2 + 2*((b^4*c^6*log(c) - a*b^3*c^6)*x^6 - 3*(b^4*c^4*log(c) - a*b^3*c^4)*x^4 - b^4*log(c) + a*b^3 + 3*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^3*log(x) - (b^4*x^3*log(x)^2 + 2*(b^4*log(c) - a*b^3)*x^3*log(x) + (b^4*log(c)^2 - 2*a*b^3*log(c) + a^2*b^2)*x^3)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + ((b^4*c^6*log(c)^2 - 2*a*b^3*c^6*log(c) + a^2*b^2*c^6)*x^6 - b^4*log(c)^2 - 3*(b^4*c^4*log(c)^2 - 2*a*b^3*c^4*log(c) + a^2*b^2*c^4)*x^4 + 2*a*b^3*log(c) - a^2*b^2 + 3*(b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2)*x^3 - 3*((b^4*c^2*x^2 - b^4)*x^3*log(x)^2 - 2*(b^4*log(c) - a*b^3 - (b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^3*log(x) - (b^4*log(c)^2 - 2*a*b^3*log(c) + a^2*b^2 - (b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2)*x^3)*(c*x + 1)*(c*x - 1) - ((c*x + 1)^(3/2)*(-c*x + 1)^(3/2)*b^4*x^3 + 3*(b^4*c^2*x^2 - b^4)*(c*x + 1)*(c*x - 1)*x^3 + 3*(b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^3 - (b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*x^3)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)^2 - 3*((b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*x^3*log(x)^2 + 2*((b^4*c^4*log(c) - a*b^3*c^4)*x^4 + b^4*log(c) - a*b^3 - 2*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^3*log(x) + (b^4*log(c)^2 + (b^4*c^4*log(c)^2 - 2*a*b^3*c^4*log(c) + a^2*b^2*c^4)*x^4 - 2*a*b^3*log(c) + a^2*b^2 - 2*(b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2)*x^3)*sqrt(c*x + 1)*sqrt(-c*x + 1) - 2*((b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*x^3*log(x) - (b^4*x^3*log(x) + (b^4*log(c) - a*b^3)*x^3)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + ((b^4*c^6*log(c) - a*b^3*c^6)*x^6 - 3*(b^4*c^4*log(c) - a*b^3*c^4)*x^4 - b^4*log(c) + a*b^3 + 3*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^3 - 3*((b^4*c^2*x^2 - b^4)*x^3*log(x) - (b^4*log(c) - a*b^3 - (b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^3)*(c*x + 1)*(c*x - 1) - 3*((b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*x^3*log(x) + ((b^4*c^4*log(c) - a*b^3*c^4)*x^4 + b^4*log(c) - a*b^3 - 2*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^3)*sqrt(c*x + 1)*sqrt(-c*x + 1))*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)) + integrate(-1/2*(4*c^8*x^8 - 16*c^6*x^6 + 24*c^4*x^4 + 4*(c*x + 1)^2*(c*x - 1)^2 + (3*c^6*x^6 - 16*c^2*x^2 + 16)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - 16*c^2*x^2 - 24*(c^4*x^4 - 2*c^2*x^2 + 1)*(c*x + 1)*(c*x - 1) + (3*c^8*x^8 - 19*c^6*x^6 + 48*c^4*x^4 - 48*c^2*x^2 + 16)*sqrt(c*x + 1)*sqrt(-c*x + 1) + 4)/((b^3*x^3*log(x) + (b^3*log(c) - a*b^2)*x^3)*(c*x + 1)^2*(c*x - 1)^2 + (b^3*c^8*x^8 - 4*b^3*c^6*x^6 + 6*b^3*c^4*x^4 - 4*b^3*c^2*x^2 + b^3)*x^3*log(x) - 4*((b^3*c^2*x^2 - b^3)*x^3*log(x) - (b^3*log(c) - a*b^2 - (b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x^3)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + ((b^3*c^8*log(c) - a*b^2*c^8)*x^8 - 4*(b^3*c^6*log(c) - a*b^2*c^6)*x^6 + 6*(b^3*c^4*log(c) - a*b^2*c^4)*x^4 + b^3*log(c) - a*b^2 - 4*(b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x^3 - 6*((b^3*c^4*x^4 - 2*b^3*c^2*x^2 + b^3)*x^3*log(x) + ((b^3*c^4*log(c) - a*b^2*c^4)*x^4 + b^3*log(c) - a*b^2 - 2*(b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x^3)*(c*x + 1)*(c*x - 1) - 4*((b^3*c^6*x^6 - 3*b^3*c^4*x^4 + 3*b^3*c^2*x^2 - b^3)*x^3*log(x) + ((b^3*c^6*log(c) - a*b^2*c^6)*x^6 - 3*(b^3*c^4*log(c) - a*b^2*c^4)*x^4 - b^3*log(c) + a*b^2 + 3*(b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x^3)*sqrt(c*x + 1)*sqrt(-c*x + 1) - ((c*x + 1)^2*(c*x - 1)^2*b^3*x^3 - 4*(b^3*c^2*x^2 - b^3)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2)*x^3 - 6*(b^3*c^4*x^4 - 2*b^3*c^2*x^2 + b^3)*(c*x + 1)*(c*x - 1)*x^3 - 4*(b^3*c^6*x^6 - 3*b^3*c^4*x^4 + 3*b^3*c^2*x^2 - b^3)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^3 + (b^3*c^8*x^8 - 4*b^3*c^6*x^6 + 6*b^3*c^4*x^4 - 4*b^3*c^2*x^2 + b^3)*x^3)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)), x)","F",0
68,0,0,0,0.000000," ","integrate(1/x^4/(a+b*arcsech(c*x))^3,x, algorithm=""maxima"")","-\frac{{\left(b c^{6} {\left(3 \, \log\left(c\right) - 1\right)} - 3 \, a c^{6}\right)} x^{7} - 3 \, {\left(b c^{4} {\left(3 \, \log\left(c\right) - 1\right)} - 3 \, a c^{4}\right)} x^{5} - {\left({\left(b c^{4} \log\left(c\right) - a c^{4}\right)} x^{5} - {\left(b c^{2} {\left(4 \, \log\left(c\right) - 1\right)} - 4 \, a c^{2}\right)} x^{3} + {\left(b {\left(3 \, \log\left(c\right) - 1\right)} - 3 \, a\right)} x + {\left(b c^{4} x^{5} - 4 \, b c^{2} x^{3} + 3 \, b x\right)} \log\left(x\right)\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b c^{2} {\left(3 \, \log\left(c\right) - 1\right)} - 3 \, a c^{2}\right)} x^{3} - {\left(2 \, {\left(b c^{6} \log\left(c\right) - a c^{6}\right)} x^{7} - 2 \, {\left(b c^{4} {\left(5 \, \log\left(c\right) - 1\right)} - 5 \, a c^{4}\right)} x^{5} + {\left(b c^{2} {\left(17 \, \log\left(c\right) - 5\right)} - 17 \, a c^{2}\right)} x^{3} - 3 \, {\left(b {\left(3 \, \log\left(c\right) - 1\right)} - 3 \, a\right)} x + {\left(2 \, b c^{6} x^{7} - 10 \, b c^{4} x^{5} + 17 \, b c^{2} x^{3} - 9 \, b x\right)} \log\left(x\right)\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left({\left(b c^{6} {\left(5 \, \log\left(c\right) - 1\right)} - 5 \, a c^{6}\right)} x^{7} - {\left(b c^{4} {\left(18 \, \log\left(c\right) - 5\right)} - 18 \, a c^{4}\right)} x^{5} + {\left(b c^{2} {\left(22 \, \log\left(c\right) - 7\right)} - 22 \, a c^{2}\right)} x^{3} - 3 \, {\left(b {\left(3 \, \log\left(c\right) - 1\right)} - 3 \, a\right)} x + {\left(5 \, b c^{6} x^{7} - 18 \, b c^{4} x^{5} + 22 \, b c^{2} x^{3} - 9 \, b x\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left(b {\left(3 \, \log\left(c\right) - 1\right)} - 3 \, a\right)} x - {\left(3 \, b c^{6} x^{7} - 9 \, b c^{4} x^{5} + 9 \, b c^{2} x^{3} - {\left(b c^{4} x^{5} - 4 \, b c^{2} x^{3} + 3 \, b x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - {\left(2 \, b c^{6} x^{7} - 10 \, b c^{4} x^{5} + 17 \, b c^{2} x^{3} - 9 \, b x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(5 \, b c^{6} x^{7} - 18 \, b c^{4} x^{5} + 22 \, b c^{2} x^{3} - 9 \, b x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - 3 \, b x\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + 3 \, {\left(b c^{6} x^{7} - 3 \, b c^{4} x^{5} + 3 \, b c^{2} x^{3} - b x\right)} \log\left(x\right)}{2 \, {\left({\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} x^{4} \log\left(x\right)^{2} + 2 \, {\left({\left(b^{4} c^{6} \log\left(c\right) - a b^{3} c^{6}\right)} x^{6} - 3 \, {\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} - b^{4} \log\left(c\right) + a b^{3} + 3 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{4} \log\left(x\right) + {\left({\left(b^{4} c^{6} \log\left(c\right)^{2} - 2 \, a b^{3} c^{6} \log\left(c\right) + a^{2} b^{2} c^{6}\right)} x^{6} - b^{4} \log\left(c\right)^{2} - 3 \, {\left(b^{4} c^{4} \log\left(c\right)^{2} - 2 \, a b^{3} c^{4} \log\left(c\right) + a^{2} b^{2} c^{4}\right)} x^{4} + 2 \, a b^{3} \log\left(c\right) - a^{2} b^{2} + 3 \, {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2}\right)} x^{4} - {\left(b^{4} x^{4} \log\left(x\right)^{2} + 2 \, {\left(b^{4} \log\left(c\right) - a b^{3}\right)} x^{4} \log\left(x\right) + {\left(b^{4} \log\left(c\right)^{2} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2}\right)} x^{4}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - 3 \, {\left({\left(b^{4} c^{2} x^{2} - b^{4}\right)} x^{4} \log\left(x\right)^{2} - 2 \, {\left(b^{4} \log\left(c\right) - a b^{3} - {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{4} \log\left(x\right) - {\left(b^{4} \log\left(c\right)^{2} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2} - {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2}\right)} x^{4}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - {\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} b^{4} x^{4} + 3 \, {\left(b^{4} c^{2} x^{2} - b^{4}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x^{4} + 3 \, {\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{4} - {\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} x^{4}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)^{2} - 3 \, {\left({\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} x^{4} \log\left(x\right)^{2} + 2 \, {\left({\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} + b^{4} \log\left(c\right) - a b^{3} - 2 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{4} \log\left(x\right) + {\left(b^{4} \log\left(c\right)^{2} + {\left(b^{4} c^{4} \log\left(c\right)^{2} - 2 \, a b^{3} c^{4} \log\left(c\right) + a^{2} b^{2} c^{4}\right)} x^{4} - 2 \, a b^{3} \log\left(c\right) + a^{2} b^{2} - 2 \, {\left(b^{4} c^{2} \log\left(c\right)^{2} - 2 \, a b^{3} c^{2} \log\left(c\right) + a^{2} b^{2} c^{2}\right)} x^{2}\right)} x^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - 2 \, {\left({\left(b^{4} c^{6} x^{6} - 3 \, b^{4} c^{4} x^{4} + 3 \, b^{4} c^{2} x^{2} - b^{4}\right)} x^{4} \log\left(x\right) + {\left({\left(b^{4} c^{6} \log\left(c\right) - a b^{3} c^{6}\right)} x^{6} - 3 \, {\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} - b^{4} \log\left(c\right) + a b^{3} + 3 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{4} - {\left(b^{4} x^{4} \log\left(x\right) + {\left(b^{4} \log\left(c\right) - a b^{3}\right)} x^{4}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - 3 \, {\left({\left(b^{4} c^{2} x^{2} - b^{4}\right)} x^{4} \log\left(x\right) - {\left(b^{4} \log\left(c\right) - a b^{3} - {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{4}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - 3 \, {\left({\left(b^{4} c^{4} x^{4} - 2 \, b^{4} c^{2} x^{2} + b^{4}\right)} x^{4} \log\left(x\right) + {\left({\left(b^{4} c^{4} \log\left(c\right) - a b^{3} c^{4}\right)} x^{4} + b^{4} \log\left(c\right) - a b^{3} - 2 \, {\left(b^{4} c^{2} \log\left(c\right) - a b^{3} c^{2}\right)} x^{2}\right)} x^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)\right)}} - \int \frac{9 \, c^{8} x^{8} - 36 \, c^{6} x^{6} + 54 \, c^{4} x^{4} - {\left(c^{4} x^{4} + 4 \, c^{2} x^{2} - 9\right)} {\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} + {\left(2 \, c^{6} x^{6} + 13 \, c^{4} x^{4} - 48 \, c^{2} x^{2} + 36\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - 36 \, c^{2} x^{2} - {\left(2 \, c^{8} x^{8} - 19 \, c^{6} x^{6} + 83 \, c^{4} x^{4} - 120 \, c^{2} x^{2} + 54\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(10 \, c^{8} x^{8} - 57 \, c^{6} x^{6} + 123 \, c^{4} x^{4} - 112 \, c^{2} x^{2} + 36\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + 9}{2 \, {\left({\left(b^{3} c^{8} x^{8} - 4 \, b^{3} c^{6} x^{6} + 6 \, b^{3} c^{4} x^{4} - 4 \, b^{3} c^{2} x^{2} + b^{3}\right)} x^{4} \log\left(x\right) + {\left(b^{3} x^{4} \log\left(x\right) + {\left(b^{3} \log\left(c\right) - a b^{2}\right)} x^{4}\right)} {\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} + {\left({\left(b^{3} c^{8} \log\left(c\right) - a b^{2} c^{8}\right)} x^{8} - 4 \, {\left(b^{3} c^{6} \log\left(c\right) - a b^{2} c^{6}\right)} x^{6} + 6 \, {\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} + b^{3} \log\left(c\right) - a b^{2} - 4 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x^{4} - 4 \, {\left({\left(b^{3} c^{2} x^{2} - b^{3}\right)} x^{4} \log\left(x\right) - {\left(b^{3} \log\left(c\right) - a b^{2} - {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x^{4}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} - 6 \, {\left({\left(b^{3} c^{4} x^{4} - 2 \, b^{3} c^{2} x^{2} + b^{3}\right)} x^{4} \log\left(x\right) + {\left({\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} + b^{3} \log\left(c\right) - a b^{2} - 2 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x^{4}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - 4 \, {\left({\left(b^{3} c^{6} x^{6} - 3 \, b^{3} c^{4} x^{4} + 3 \, b^{3} c^{2} x^{2} - b^{3}\right)} x^{4} \log\left(x\right) + {\left({\left(b^{3} c^{6} \log\left(c\right) - a b^{2} c^{6}\right)} x^{6} - 3 \, {\left(b^{3} c^{4} \log\left(c\right) - a b^{2} c^{4}\right)} x^{4} - b^{3} \log\left(c\right) + a b^{2} + 3 \, {\left(b^{3} c^{2} \log\left(c\right) - a b^{2} c^{2}\right)} x^{2}\right)} x^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left({\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} b^{3} x^{4} - 4 \, {\left(b^{3} c^{2} x^{2} - b^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(-c x + 1\right)}^{\frac{3}{2}} x^{4} - 6 \, {\left(b^{3} c^{4} x^{4} - 2 \, b^{3} c^{2} x^{2} + b^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x^{4} - 4 \, {\left(b^{3} c^{6} x^{6} - 3 \, b^{3} c^{4} x^{4} + 3 \, b^{3} c^{2} x^{2} - b^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{4} + {\left(b^{3} c^{8} x^{8} - 4 \, b^{3} c^{6} x^{6} + 6 \, b^{3} c^{4} x^{4} - 4 \, b^{3} c^{2} x^{2} + b^{3}\right)} x^{4}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)\right)}}\,{d x}"," ",0,"-1/2*((b*c^6*(3*log(c) - 1) - 3*a*c^6)*x^7 - 3*(b*c^4*(3*log(c) - 1) - 3*a*c^4)*x^5 - ((b*c^4*log(c) - a*c^4)*x^5 - (b*c^2*(4*log(c) - 1) - 4*a*c^2)*x^3 + (b*(3*log(c) - 1) - 3*a)*x + (b*c^4*x^5 - 4*b*c^2*x^3 + 3*b*x)*log(x))*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) + 3*(b*c^2*(3*log(c) - 1) - 3*a*c^2)*x^3 - (2*(b*c^6*log(c) - a*c^6)*x^7 - 2*(b*c^4*(5*log(c) - 1) - 5*a*c^4)*x^5 + (b*c^2*(17*log(c) - 5) - 17*a*c^2)*x^3 - 3*(b*(3*log(c) - 1) - 3*a)*x + (2*b*c^6*x^7 - 10*b*c^4*x^5 + 17*b*c^2*x^3 - 9*b*x)*log(x))*(c*x + 1)*(c*x - 1) + ((b*c^6*(5*log(c) - 1) - 5*a*c^6)*x^7 - (b*c^4*(18*log(c) - 5) - 18*a*c^4)*x^5 + (b*c^2*(22*log(c) - 7) - 22*a*c^2)*x^3 - 3*(b*(3*log(c) - 1) - 3*a)*x + (5*b*c^6*x^7 - 18*b*c^4*x^5 + 22*b*c^2*x^3 - 9*b*x)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - (b*(3*log(c) - 1) - 3*a)*x - (3*b*c^6*x^7 - 9*b*c^4*x^5 + 9*b*c^2*x^3 - (b*c^4*x^5 - 4*b*c^2*x^3 + 3*b*x)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - (2*b*c^6*x^7 - 10*b*c^4*x^5 + 17*b*c^2*x^3 - 9*b*x)*(c*x + 1)*(c*x - 1) + (5*b*c^6*x^7 - 18*b*c^4*x^5 + 22*b*c^2*x^3 - 9*b*x)*sqrt(c*x + 1)*sqrt(-c*x + 1) - 3*b*x)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + 3*(b*c^6*x^7 - 3*b*c^4*x^5 + 3*b*c^2*x^3 - b*x)*log(x))/((b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*x^4*log(x)^2 + 2*((b^4*c^6*log(c) - a*b^3*c^6)*x^6 - 3*(b^4*c^4*log(c) - a*b^3*c^4)*x^4 - b^4*log(c) + a*b^3 + 3*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^4*log(x) + ((b^4*c^6*log(c)^2 - 2*a*b^3*c^6*log(c) + a^2*b^2*c^6)*x^6 - b^4*log(c)^2 - 3*(b^4*c^4*log(c)^2 - 2*a*b^3*c^4*log(c) + a^2*b^2*c^4)*x^4 + 2*a*b^3*log(c) - a^2*b^2 + 3*(b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2)*x^4 - (b^4*x^4*log(x)^2 + 2*(b^4*log(c) - a*b^3)*x^4*log(x) + (b^4*log(c)^2 - 2*a*b^3*log(c) + a^2*b^2)*x^4)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - 3*((b^4*c^2*x^2 - b^4)*x^4*log(x)^2 - 2*(b^4*log(c) - a*b^3 - (b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^4*log(x) - (b^4*log(c)^2 - 2*a*b^3*log(c) + a^2*b^2 - (b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2)*x^4)*(c*x + 1)*(c*x - 1) - ((c*x + 1)^(3/2)*(-c*x + 1)^(3/2)*b^4*x^4 + 3*(b^4*c^2*x^2 - b^4)*(c*x + 1)*(c*x - 1)*x^4 + 3*(b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^4 - (b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*x^4)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)^2 - 3*((b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*x^4*log(x)^2 + 2*((b^4*c^4*log(c) - a*b^3*c^4)*x^4 + b^4*log(c) - a*b^3 - 2*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^4*log(x) + (b^4*log(c)^2 + (b^4*c^4*log(c)^2 - 2*a*b^3*c^4*log(c) + a^2*b^2*c^4)*x^4 - 2*a*b^3*log(c) + a^2*b^2 - 2*(b^4*c^2*log(c)^2 - 2*a*b^3*c^2*log(c) + a^2*b^2*c^2)*x^2)*x^4)*sqrt(c*x + 1)*sqrt(-c*x + 1) - 2*((b^4*c^6*x^6 - 3*b^4*c^4*x^4 + 3*b^4*c^2*x^2 - b^4)*x^4*log(x) + ((b^4*c^6*log(c) - a*b^3*c^6)*x^6 - 3*(b^4*c^4*log(c) - a*b^3*c^4)*x^4 - b^4*log(c) + a*b^3 + 3*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^4 - (b^4*x^4*log(x) + (b^4*log(c) - a*b^3)*x^4)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - 3*((b^4*c^2*x^2 - b^4)*x^4*log(x) - (b^4*log(c) - a*b^3 - (b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^4)*(c*x + 1)*(c*x - 1) - 3*((b^4*c^4*x^4 - 2*b^4*c^2*x^2 + b^4)*x^4*log(x) + ((b^4*c^4*log(c) - a*b^3*c^4)*x^4 + b^4*log(c) - a*b^3 - 2*(b^4*c^2*log(c) - a*b^3*c^2)*x^2)*x^4)*sqrt(c*x + 1)*sqrt(-c*x + 1))*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)) - integrate(1/2*(9*c^8*x^8 - 36*c^6*x^6 + 54*c^4*x^4 - (c^4*x^4 + 4*c^2*x^2 - 9)*(c*x + 1)^2*(c*x - 1)^2 + (2*c^6*x^6 + 13*c^4*x^4 - 48*c^2*x^2 + 36)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - 36*c^2*x^2 - (2*c^8*x^8 - 19*c^6*x^6 + 83*c^4*x^4 - 120*c^2*x^2 + 54)*(c*x + 1)*(c*x - 1) + (10*c^8*x^8 - 57*c^6*x^6 + 123*c^4*x^4 - 112*c^2*x^2 + 36)*sqrt(c*x + 1)*sqrt(-c*x + 1) + 9)/((b^3*c^8*x^8 - 4*b^3*c^6*x^6 + 6*b^3*c^4*x^4 - 4*b^3*c^2*x^2 + b^3)*x^4*log(x) + (b^3*x^4*log(x) + (b^3*log(c) - a*b^2)*x^4)*(c*x + 1)^2*(c*x - 1)^2 + ((b^3*c^8*log(c) - a*b^2*c^8)*x^8 - 4*(b^3*c^6*log(c) - a*b^2*c^6)*x^6 + 6*(b^3*c^4*log(c) - a*b^2*c^4)*x^4 + b^3*log(c) - a*b^2 - 4*(b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x^4 - 4*((b^3*c^2*x^2 - b^3)*x^4*log(x) - (b^3*log(c) - a*b^2 - (b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x^4)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2) - 6*((b^3*c^4*x^4 - 2*b^3*c^2*x^2 + b^3)*x^4*log(x) + ((b^3*c^4*log(c) - a*b^2*c^4)*x^4 + b^3*log(c) - a*b^2 - 2*(b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x^4)*(c*x + 1)*(c*x - 1) - 4*((b^3*c^6*x^6 - 3*b^3*c^4*x^4 + 3*b^3*c^2*x^2 - b^3)*x^4*log(x) + ((b^3*c^6*log(c) - a*b^2*c^6)*x^6 - 3*(b^3*c^4*log(c) - a*b^2*c^4)*x^4 - b^3*log(c) + a*b^2 + 3*(b^3*c^2*log(c) - a*b^2*c^2)*x^2)*x^4)*sqrt(c*x + 1)*sqrt(-c*x + 1) - ((c*x + 1)^2*(c*x - 1)^2*b^3*x^4 - 4*(b^3*c^2*x^2 - b^3)*(c*x + 1)^(3/2)*(-c*x + 1)^(3/2)*x^4 - 6*(b^3*c^4*x^4 - 2*b^3*c^2*x^2 + b^3)*(c*x + 1)*(c*x - 1)*x^4 - 4*(b^3*c^6*x^6 - 3*b^3*c^4*x^4 + 3*b^3*c^2*x^2 - b^3)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^4 + (b^3*c^8*x^8 - 4*b^3*c^6*x^6 + 6*b^3*c^4*x^4 - 4*b^3*c^2*x^2 + b^3)*x^4)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)), x)","F",0
69,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arcsech(c*x))^3,x, algorithm=""maxima"")","\frac{b^{3} d^{m} x x^{m} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)^{3}}{m + 1} + \frac{\left(d x\right)^{m + 1} a^{3}}{d {\left(m + 1\right)}} - \int \frac{{\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} x^{2} - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x\right)^{3} - 3 \, {\left(b^{3} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b^{2} d^{m} {\left(m + 1\right)} - {\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b^{2} c^{2} d^{m} {\left(m + 1\right)}\right)} x^{2}\right)} x^{m} \log\left(x\right)^{2} + 3 \, {\left({\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} x^{2} - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x\right) + {\left({\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} x^{2} - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x\right) - {\left(b^{3} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b^{2} d^{m} {\left(m + 1\right)} + {\left(a b^{2} c^{2} d^{m} {\left(m + 1\right)} - {\left(d^{m} {\left(m + 1\right)} \log\left(c\right) + d^{m}\right)} b^{3} c^{2}\right)} x^{2}\right)} x^{m}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left(b^{3} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b^{2} d^{m} {\left(m + 1\right)} - {\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b^{2} c^{2} d^{m} {\left(m + 1\right)}\right)} x^{2}\right)} x^{m}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)^{2} - 3 \, {\left(b^{3} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} - 2 \, a b^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) + a^{2} b d^{m} {\left(m + 1\right)} - {\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} - 2 \, a b^{2} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) + a^{2} b c^{2} d^{m} {\left(m + 1\right)}\right)} x^{2}\right)} x^{m} \log\left(x\right) + {\left({\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} x^{2} - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x\right)^{3} - 3 \, {\left(b^{3} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b^{2} d^{m} {\left(m + 1\right)} - {\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b^{2} c^{2} d^{m} {\left(m + 1\right)}\right)} x^{2}\right)} x^{m} \log\left(x\right)^{2} - 3 \, {\left(b^{3} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} - 2 \, a b^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) + a^{2} b d^{m} {\left(m + 1\right)} - {\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} - 2 \, a b^{2} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) + a^{2} b c^{2} d^{m} {\left(m + 1\right)}\right)} x^{2}\right)} x^{m} \log\left(x\right) - {\left(b^{3} d^{m} {\left(m + 1\right)} \log\left(c\right)^{3} - 3 \, a b^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} + 3 \, a^{2} b d^{m} {\left(m + 1\right)} \log\left(c\right) - {\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)^{3} - 3 \, a b^{2} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} + 3 \, a^{2} b c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)\right)} x^{2}\right)} x^{m}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left(b^{3} d^{m} {\left(m + 1\right)} \log\left(c\right)^{3} - 3 \, a b^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} + 3 \, a^{2} b d^{m} {\left(m + 1\right)} \log\left(c\right) - {\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)^{3} - 3 \, a b^{2} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} + 3 \, a^{2} b c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)\right)} x^{2}\right)} x^{m} - 3 \, {\left({\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} x^{2} - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x\right)^{2} - 2 \, {\left(b^{3} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b^{2} d^{m} {\left(m + 1\right)} - {\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b^{2} c^{2} d^{m} {\left(m + 1\right)}\right)} x^{2}\right)} x^{m} \log\left(x\right) + {\left({\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} x^{2} - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x\right)^{2} - 2 \, {\left(b^{3} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b^{2} d^{m} {\left(m + 1\right)} - {\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b^{2} c^{2} d^{m} {\left(m + 1\right)}\right)} x^{2}\right)} x^{m} \log\left(x\right) - {\left(b^{3} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} - 2 \, a b^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) + a^{2} b d^{m} {\left(m + 1\right)} - {\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} - 2 \, a b^{2} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) + a^{2} b c^{2} d^{m} {\left(m + 1\right)}\right)} x^{2}\right)} x^{m}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left(b^{3} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} - 2 \, a b^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) + a^{2} b d^{m} {\left(m + 1\right)} - {\left(b^{3} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} - 2 \, a b^{2} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) + a^{2} b c^{2} d^{m} {\left(m + 1\right)}\right)} x^{2}\right)} x^{m}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{c^{2} {\left(m + 1\right)} x^{2} + {\left(c^{2} {\left(m + 1\right)} x^{2} - m - 1\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - m - 1}\,{d x}"," ",0,"b^3*d^m*x*x^m*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)^3/(m + 1) + (d*x)^(m + 1)*a^3/(d*(m + 1)) - integrate(((b^3*c^2*d^m*(m + 1)*x^2 - b^3*d^m*(m + 1))*x^m*log(x)^3 - 3*(b^3*d^m*(m + 1)*log(c) - a*b^2*d^m*(m + 1) - (b^3*c^2*d^m*(m + 1)*log(c) - a*b^2*c^2*d^m*(m + 1))*x^2)*x^m*log(x)^2 + 3*((b^3*c^2*d^m*(m + 1)*x^2 - b^3*d^m*(m + 1))*x^m*log(x) + ((b^3*c^2*d^m*(m + 1)*x^2 - b^3*d^m*(m + 1))*x^m*log(x) - (b^3*d^m*(m + 1)*log(c) - a*b^2*d^m*(m + 1) + (a*b^2*c^2*d^m*(m + 1) - (d^m*(m + 1)*log(c) + d^m)*b^3*c^2)*x^2)*x^m)*sqrt(c*x + 1)*sqrt(-c*x + 1) - (b^3*d^m*(m + 1)*log(c) - a*b^2*d^m*(m + 1) - (b^3*c^2*d^m*(m + 1)*log(c) - a*b^2*c^2*d^m*(m + 1))*x^2)*x^m)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)^2 - 3*(b^3*d^m*(m + 1)*log(c)^2 - 2*a*b^2*d^m*(m + 1)*log(c) + a^2*b*d^m*(m + 1) - (b^3*c^2*d^m*(m + 1)*log(c)^2 - 2*a*b^2*c^2*d^m*(m + 1)*log(c) + a^2*b*c^2*d^m*(m + 1))*x^2)*x^m*log(x) + ((b^3*c^2*d^m*(m + 1)*x^2 - b^3*d^m*(m + 1))*x^m*log(x)^3 - 3*(b^3*d^m*(m + 1)*log(c) - a*b^2*d^m*(m + 1) - (b^3*c^2*d^m*(m + 1)*log(c) - a*b^2*c^2*d^m*(m + 1))*x^2)*x^m*log(x)^2 - 3*(b^3*d^m*(m + 1)*log(c)^2 - 2*a*b^2*d^m*(m + 1)*log(c) + a^2*b*d^m*(m + 1) - (b^3*c^2*d^m*(m + 1)*log(c)^2 - 2*a*b^2*c^2*d^m*(m + 1)*log(c) + a^2*b*c^2*d^m*(m + 1))*x^2)*x^m*log(x) - (b^3*d^m*(m + 1)*log(c)^3 - 3*a*b^2*d^m*(m + 1)*log(c)^2 + 3*a^2*b*d^m*(m + 1)*log(c) - (b^3*c^2*d^m*(m + 1)*log(c)^3 - 3*a*b^2*c^2*d^m*(m + 1)*log(c)^2 + 3*a^2*b*c^2*d^m*(m + 1)*log(c))*x^2)*x^m)*sqrt(c*x + 1)*sqrt(-c*x + 1) - (b^3*d^m*(m + 1)*log(c)^3 - 3*a*b^2*d^m*(m + 1)*log(c)^2 + 3*a^2*b*d^m*(m + 1)*log(c) - (b^3*c^2*d^m*(m + 1)*log(c)^3 - 3*a*b^2*c^2*d^m*(m + 1)*log(c)^2 + 3*a^2*b*c^2*d^m*(m + 1)*log(c))*x^2)*x^m - 3*((b^3*c^2*d^m*(m + 1)*x^2 - b^3*d^m*(m + 1))*x^m*log(x)^2 - 2*(b^3*d^m*(m + 1)*log(c) - a*b^2*d^m*(m + 1) - (b^3*c^2*d^m*(m + 1)*log(c) - a*b^2*c^2*d^m*(m + 1))*x^2)*x^m*log(x) + ((b^3*c^2*d^m*(m + 1)*x^2 - b^3*d^m*(m + 1))*x^m*log(x)^2 - 2*(b^3*d^m*(m + 1)*log(c) - a*b^2*d^m*(m + 1) - (b^3*c^2*d^m*(m + 1)*log(c) - a*b^2*c^2*d^m*(m + 1))*x^2)*x^m*log(x) - (b^3*d^m*(m + 1)*log(c)^2 - 2*a*b^2*d^m*(m + 1)*log(c) + a^2*b*d^m*(m + 1) - (b^3*c^2*d^m*(m + 1)*log(c)^2 - 2*a*b^2*c^2*d^m*(m + 1)*log(c) + a^2*b*c^2*d^m*(m + 1))*x^2)*x^m)*sqrt(c*x + 1)*sqrt(-c*x + 1) - (b^3*d^m*(m + 1)*log(c)^2 - 2*a*b^2*d^m*(m + 1)*log(c) + a^2*b*d^m*(m + 1) - (b^3*c^2*d^m*(m + 1)*log(c)^2 - 2*a*b^2*c^2*d^m*(m + 1)*log(c) + a^2*b*c^2*d^m*(m + 1))*x^2)*x^m)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1))/(c^2*(m + 1)*x^2 + (c^2*(m + 1)*x^2 - m - 1)*sqrt(c*x + 1)*sqrt(-c*x + 1) - m - 1), x)","F",0
70,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arcsech(c*x))^2,x, algorithm=""maxima"")","\frac{b^{2} d^{m} x x^{m} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)^{2}}{m + 1} + \frac{\left(d x\right)^{m + 1} a^{2}}{d {\left(m + 1\right)}} - \int -\frac{{\left(b^{2} c^{2} d^{m} {\left(m + 1\right)} x^{2} - b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x\right)^{2} - 2 \, {\left(b^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b d^{m} {\left(m + 1\right)} - {\left(b^{2} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b c^{2} d^{m} {\left(m + 1\right)}\right)} x^{2}\right)} x^{m} \log\left(x\right) + {\left({\left(b^{2} c^{2} d^{m} {\left(m + 1\right)} x^{2} - b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x\right)^{2} - 2 \, {\left(b^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b d^{m} {\left(m + 1\right)} - {\left(b^{2} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b c^{2} d^{m} {\left(m + 1\right)}\right)} x^{2}\right)} x^{m} \log\left(x\right) - {\left(b^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} - 2 \, a b d^{m} {\left(m + 1\right)} \log\left(c\right) - {\left(b^{2} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} - 2 \, a b c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)\right)} x^{2}\right)} x^{m}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left(b^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} - 2 \, a b d^{m} {\left(m + 1\right)} \log\left(c\right) - {\left(b^{2} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)^{2} - 2 \, a b c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right)\right)} x^{2}\right)} x^{m} - 2 \, {\left({\left(b^{2} c^{2} d^{m} {\left(m + 1\right)} x^{2} - b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x\right) + {\left({\left(b^{2} c^{2} d^{m} {\left(m + 1\right)} x^{2} - b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x\right) - {\left(b^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b d^{m} {\left(m + 1\right)} + {\left(a b c^{2} d^{m} {\left(m + 1\right)} - {\left(d^{m} {\left(m + 1\right)} \log\left(c\right) + d^{m}\right)} b^{2} c^{2}\right)} x^{2}\right)} x^{m}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - {\left(b^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b d^{m} {\left(m + 1\right)} - {\left(b^{2} c^{2} d^{m} {\left(m + 1\right)} \log\left(c\right) - a b c^{2} d^{m} {\left(m + 1\right)}\right)} x^{2}\right)} x^{m}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{c^{2} {\left(m + 1\right)} x^{2} + {\left(c^{2} {\left(m + 1\right)} x^{2} - m - 1\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - m - 1}\,{d x}"," ",0,"b^2*d^m*x*x^m*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)^2/(m + 1) + (d*x)^(m + 1)*a^2/(d*(m + 1)) - integrate(-((b^2*c^2*d^m*(m + 1)*x^2 - b^2*d^m*(m + 1))*x^m*log(x)^2 - 2*(b^2*d^m*(m + 1)*log(c) - a*b*d^m*(m + 1) - (b^2*c^2*d^m*(m + 1)*log(c) - a*b*c^2*d^m*(m + 1))*x^2)*x^m*log(x) + ((b^2*c^2*d^m*(m + 1)*x^2 - b^2*d^m*(m + 1))*x^m*log(x)^2 - 2*(b^2*d^m*(m + 1)*log(c) - a*b*d^m*(m + 1) - (b^2*c^2*d^m*(m + 1)*log(c) - a*b*c^2*d^m*(m + 1))*x^2)*x^m*log(x) - (b^2*d^m*(m + 1)*log(c)^2 - 2*a*b*d^m*(m + 1)*log(c) - (b^2*c^2*d^m*(m + 1)*log(c)^2 - 2*a*b*c^2*d^m*(m + 1)*log(c))*x^2)*x^m)*sqrt(c*x + 1)*sqrt(-c*x + 1) - (b^2*d^m*(m + 1)*log(c)^2 - 2*a*b*d^m*(m + 1)*log(c) - (b^2*c^2*d^m*(m + 1)*log(c)^2 - 2*a*b*c^2*d^m*(m + 1)*log(c))*x^2)*x^m - 2*((b^2*c^2*d^m*(m + 1)*x^2 - b^2*d^m*(m + 1))*x^m*log(x) + ((b^2*c^2*d^m*(m + 1)*x^2 - b^2*d^m*(m + 1))*x^m*log(x) - (b^2*d^m*(m + 1)*log(c) - a*b*d^m*(m + 1) + (a*b*c^2*d^m*(m + 1) - (d^m*(m + 1)*log(c) + d^m)*b^2*c^2)*x^2)*x^m)*sqrt(c*x + 1)*sqrt(-c*x + 1) - (b^2*d^m*(m + 1)*log(c) - a*b*d^m*(m + 1) - (b^2*c^2*d^m*(m + 1)*log(c) - a*b*c^2*d^m*(m + 1))*x^2)*x^m)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1))/(c^2*(m + 1)*x^2 + (c^2*(m + 1)*x^2 - m - 1)*sqrt(c*x + 1)*sqrt(-c*x + 1) - m - 1), x)","F",0
71,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","{\left(c^{2} d^{m} \int \frac{x^{2} x^{m}}{c^{2} {\left(m + 1\right)} x^{2} + {\left(c^{2} {\left(m + 1\right)} x^{2} - m - 1\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - m - 1}\,{d x} + \frac{d^{m} x x^{m} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) - d^{m} x x^{m} \log\left(x\right)}{m + 1} - \int \frac{{\left(c^{2} d^{m} {\left(m + 1\right)} x^{2} \log\left(c\right) - d^{m} {\left(m + 1\right)} \log\left(c\right) + d^{m}\right)} x^{m}}{c^{2} {\left(m + 1\right)} x^{2} - m - 1}\,{d x}\right)} b + \frac{\left(d x\right)^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"(c^2*d^m*integrate(x^2*x^m/(c^2*(m + 1)*x^2 + (c^2*(m + 1)*x^2 - m - 1)*sqrt(c*x + 1)*sqrt(-c*x + 1) - m - 1), x) + (d^m*x*x^m*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) - d^m*x*x^m*log(x))/(m + 1) - integrate((c^2*d^m*(m + 1)*x^2*log(c) - d^m*(m + 1)*log(c) + d^m)*x^m/(c^2*(m + 1)*x^2 - m - 1), x))*b + (d*x)^(m + 1)*a/(d*(m + 1))","F",0
72,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\int \frac{\left(d x\right)^{m}}{b \operatorname{arsech}\left(c x\right) + a}\,{d x}"," ",0,"integrate((d*x)^m/(b*arcsech(c*x) + a), x)","F",0
73,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arcsech(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} d^{m} x^{3} - d^{m} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{m} + {\left(c^{2} d^{m} x^{3} - d^{m} x\right)} x^{m}}{{\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} - b^{2} \log\left(c\right) - {\left(b^{2} \log\left(c\right) + b^{2} \log\left(x\right) - a b\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + a b - {\left(b^{2} c^{2} x^{2} - \sqrt{c x + 1} \sqrt{-c x + 1} b^{2} - b^{2}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \log\left(x\right)} + \int \frac{{\left(c^{2} d^{m} {\left(m + 3\right)} x^{2} - d^{m} {\left(m + 1\right)}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x^{m} + {\left(c^{4} d^{m} {\left(m + 2\right)} x^{4} - c^{2} d^{m} {\left(3 \, m + 5\right)} x^{2} + 2 \, d^{m} {\left(m + 1\right)}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{m} + {\left(c^{4} d^{m} {\left(m + 1\right)} x^{4} - 2 \, c^{2} d^{m} {\left(m + 1\right)} x^{2} + d^{m} {\left(m + 1\right)}\right)} x^{m}}{{\left(b^{2} c^{4} \log\left(c\right) - a b c^{4}\right)} x^{4} - {\left(b^{2} \log\left(c\right) + b^{2} \log\left(x\right) - a b\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - 2 \, {\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} + b^{2} \log\left(c\right) - 2 \, {\left({\left(b^{2} c^{2} \log\left(c\right) - a b c^{2}\right)} x^{2} - b^{2} \log\left(c\right) + a b + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \log\left(x\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - a b - {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} - {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} - 2 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + b^{2}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) + {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \log\left(x\right)}\,{d x}"," ",0,"-((c^2*d^m*x^3 - d^m*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^m + (c^2*d^m*x^3 - d^m*x)*x^m)/((b^2*c^2*log(c) - a*b*c^2)*x^2 - b^2*log(c) - (b^2*log(c) + b^2*log(x) - a*b)*sqrt(c*x + 1)*sqrt(-c*x + 1) + a*b - (b^2*c^2*x^2 - sqrt(c*x + 1)*sqrt(-c*x + 1)*b^2 - b^2)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + (b^2*c^2*x^2 - b^2)*log(x)) + integrate(((c^2*d^m*(m + 3)*x^2 - d^m*(m + 1))*(c*x + 1)*(c*x - 1)*x^m + (c^4*d^m*(m + 2)*x^4 - c^2*d^m*(3*m + 5)*x^2 + 2*d^m*(m + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^m + (c^4*d^m*(m + 1)*x^4 - 2*c^2*d^m*(m + 1)*x^2 + d^m*(m + 1))*x^m)/((b^2*c^4*log(c) - a*b*c^4)*x^4 - (b^2*log(c) + b^2*log(x) - a*b)*(c*x + 1)*(c*x - 1) - 2*(b^2*c^2*log(c) - a*b*c^2)*x^2 + b^2*log(c) - 2*((b^2*c^2*log(c) - a*b*c^2)*x^2 - b^2*log(c) + a*b + (b^2*c^2*x^2 - b^2)*log(x))*sqrt(c*x + 1)*sqrt(-c*x + 1) - a*b - (b^2*c^4*x^4 - 2*b^2*c^2*x^2 - (c*x + 1)*(c*x - 1)*b^2 - 2*(b^2*c^2*x^2 - b^2)*sqrt(c*x + 1)*sqrt(-c*x + 1) + b^2)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) + (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*log(x)), x)","F",0
74,1,221,0,0.423584," ","integrate((e*x+d)^3*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a e^{3} x^{4} + a d e^{2} x^{3} + \frac{3}{2} \, a d^{2} e x^{2} + \frac{3}{2} \, {\left(x^{2} \operatorname{arsech}\left(c x\right) - \frac{x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c}\right)} b d^{2} e + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{arsech}\left(c x\right) - \frac{\frac{\sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{2}}}{c}\right)} b d e^{2} + \frac{1}{12} \, {\left(3 \, x^{4} \operatorname{arsech}\left(c x\right) + \frac{c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} - 3 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{3}}\right)} b e^{3} + a d^{3} x + \frac{{\left(c x \operatorname{arsech}\left(c x\right) - \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)\right)} b d^{3}}{c}"," ",0,"1/4*a*e^3*x^4 + a*d*e^2*x^3 + 3/2*a*d^2*e*x^2 + 3/2*(x^2*arcsech(c*x) - x*sqrt(1/(c^2*x^2) - 1)/c)*b*d^2*e + 1/2*(2*x^3*arcsech(c*x) - (sqrt(1/(c^2*x^2) - 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + arctan(sqrt(1/(c^2*x^2) - 1))/c^2)/c)*b*d*e^2 + 1/12*(3*x^4*arcsech(c*x) + (c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) - 3*x*sqrt(1/(c^2*x^2) - 1))/c^3)*b*e^3 + a*d^3*x + (c*x*arcsech(c*x) - arctan(sqrt(1/(c^2*x^2) - 1)))*b*d^3/c","A",0
75,1,152,0,0.421171," ","integrate((e*x+d)^2*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a e^{2} x^{3} + a d e x^{2} + {\left(x^{2} \operatorname{arsech}\left(c x\right) - \frac{x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c}\right)} b d e + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{arsech}\left(c x\right) - \frac{\frac{\sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{2}}}{c}\right)} b e^{2} + a d^{2} x + \frac{{\left(c x \operatorname{arsech}\left(c x\right) - \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)\right)} b d^{2}}{c}"," ",0,"1/3*a*e^2*x^3 + a*d*e*x^2 + (x^2*arcsech(c*x) - x*sqrt(1/(c^2*x^2) - 1)/c)*b*d*e + 1/6*(2*x^3*arcsech(c*x) - (sqrt(1/(c^2*x^2) - 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + arctan(sqrt(1/(c^2*x^2) - 1))/c^2)/c)*b*e^2 + a*d^2*x + (c*x*arcsech(c*x) - arctan(sqrt(1/(c^2*x^2) - 1)))*b*d^2/c","A",0
76,1,70,0,0.318577," ","integrate((e*x+d)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} + \frac{1}{2} \, {\left(x^{2} \operatorname{arsech}\left(c x\right) - \frac{x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c}\right)} b e + a d x + \frac{{\left(c x \operatorname{arsech}\left(c x\right) - \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)\right)} b d}{c}"," ",0,"1/2*a*e*x^2 + 1/2*(x^2*arcsech(c*x) - x*sqrt(1/(c^2*x^2) - 1)/c)*b*e + a*d*x + (c*x*arcsech(c*x) - arctan(sqrt(1/(c^2*x^2) - 1)))*b*d/c","A",0
77,1,31,0,0.312650," ","integrate(a+b*arcsech(c*x),x, algorithm=""maxima"")","a x + \frac{{\left(c x \operatorname{arsech}\left(c x\right) - \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)\right)} b}{c}"," ",0,"a*x + (c*x*arcsech(c*x) - arctan(sqrt(1/(c^2*x^2) - 1)))*b/c","A",0
78,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x+d),x, algorithm=""maxima"")","b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{e x + d}\,{d x} + \frac{a \log\left(e x + d\right)}{e}"," ",0,"b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x + d), x) + a*log(e*x + d)/e","F",0
79,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x+d)^2,x, algorithm=""maxima"")","{\left(c^{2} \int \frac{x^{2}}{c^{2} d^{2} x^{2} + {\left(c^{2} d^{2} x^{2} - d^{2} + {\left(c^{2} d e x^{2} - d e\right)} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - d^{2} + {\left(c^{2} d e x^{2} - d e\right)} x}\,{d x} + \frac{x \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) - x \log\left(c\right) - x \log\left(x\right)}{d e x + d^{2}} - \int \frac{1}{c^{2} d^{2} x^{2} - d^{2} + {\left(c^{2} d e x^{2} - d e\right)} x}\,{d x}\right)} b - \frac{a}{e^{2} x + d e}"," ",0,"(c^2*integrate(x^2/(c^2*d^2*x^2 + (c^2*d^2*x^2 - d^2 + (c^2*d*e*x^2 - d*e)*x)*sqrt(c*x + 1)*sqrt(-c*x + 1) - d^2 + (c^2*d*e*x^2 - d*e)*x), x) + (x*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) - x*log(c) - x*log(x))/(d*e*x + d^2) - integrate(1/(c^2*d^2*x^2 - d^2 + (c^2*d*e*x^2 - d*e)*x), x))*b - a/(e^2*x + d*e)","F",0
80,-2,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x+d)^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
81,-2,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c*d-e>0)', see `assume?` for more details)Is c*d-e positive or negative?","F(-2)",0
82,-2,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c*d-e>0)', see `assume?` for more details)Is c*d-e positive or negative?","F(-2)",0
83,-2,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c*d-e>0)', see `assume?` for more details)Is c*d-e positive or negative?","F(-2)",0
84,-2,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x+d)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c*d-e>0)', see `assume?` for more details)Is c*d-e positive or negative?","F(-2)",0
85,-2,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x+d)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c*d-e>0)', see `assume?` for more details)Is c*d-e positive or negative?","F(-2)",0
86,-2,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x+d)^(7/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c*d-e>0)', see `assume?` for more details)Is c*d-e positive or negative?","F(-2)",0
87,0,0,0,0.000000," ","integrate((e*x+d)^m*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","b {\left(\frac{{\left(e x + d\right)} {\left(e x + d\right)}^{m} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) - {\left(e x + d\right)} {\left(e x + d\right)}^{m} \log\left(x\right)}{e {\left(m + 1\right)}} - \int \frac{{\left(c^{2} e {\left(m + 1\right)} x^{3} \log\left(c\right) - {\left(e {\left(m + 1\right)} \log\left(c\right) - e\right)} x + d\right)} {\left(e x + d\right)}^{m}}{c^{2} e {\left(m + 1\right)} x^{3} - e {\left(m + 1\right)} x}\,{d x} + \int \frac{{\left(c^{2} e x^{2} + c^{2} d x\right)} {\left(e x + d\right)}^{m}}{c^{2} e {\left(m + 1\right)} x^{2} + {\left(c^{2} e {\left(m + 1\right)} x^{2} - e {\left(m + 1\right)}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - e {\left(m + 1\right)}}\,{d x}\right)} + \frac{{\left(e x + d\right)}^{m + 1} a}{e {\left(m + 1\right)}}"," ",0,"b*(((e*x + d)*(e*x + d)^m*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) - (e*x + d)*(e*x + d)^m*log(x))/(e*(m + 1)) - integrate((c^2*e*(m + 1)*x^3*log(c) - (e*(m + 1)*log(c) - e)*x + d)*(e*x + d)^m/(c^2*e*(m + 1)*x^3 - e*(m + 1)*x), x) + integrate((c^2*e*x^2 + c^2*d*x)*(e*x + d)^m/(c^2*e*(m + 1)*x^2 + (c^2*e*(m + 1)*x^2 - e*(m + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1) - e*(m + 1)), x)) + (e*x + d)^(m + 1)*a/(e*(m + 1))","F",0
88,1,244,0,0.419171," ","integrate(x^4*(e*x^2+d)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a e x^{7} + \frac{1}{5} \, a d x^{5} + \frac{1}{40} \, {\left(8 \, x^{5} \operatorname{arsech}\left(c x\right) - \frac{\frac{3 \, {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 5 \, \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{4}} + \frac{3 \, \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{4}}}{c}\right)} b d + \frac{1}{336} \, {\left(48 \, x^{7} \operatorname{arsech}\left(c x\right) - \frac{\frac{15 \, {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} + 40 \, {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 33 \, \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} + 3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{6}} + \frac{15 \, \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{6}}}{c}\right)} b e"," ",0,"1/7*a*e*x^7 + 1/5*a*d*x^5 + 1/40*(8*x^5*arcsech(c*x) - ((3*(1/(c^2*x^2) - 1)^(3/2) + 5*sqrt(1/(c^2*x^2) - 1))/(c^4*(1/(c^2*x^2) - 1)^2 + 2*c^4*(1/(c^2*x^2) - 1) + c^4) + 3*arctan(sqrt(1/(c^2*x^2) - 1))/c^4)/c)*b*d + 1/336*(48*x^7*arcsech(c*x) - ((15*(1/(c^2*x^2) - 1)^(5/2) + 40*(1/(c^2*x^2) - 1)^(3/2) + 33*sqrt(1/(c^2*x^2) - 1))/(c^6*(1/(c^2*x^2) - 1)^3 + 3*c^6*(1/(c^2*x^2) - 1)^2 + 3*c^6*(1/(c^2*x^2) - 1) + c^6) + 15*arctan(sqrt(1/(c^2*x^2) - 1))/c^6)/c)*b*e","A",0
89,1,182,0,0.420260," ","integrate(x^2*(e*x^2+d)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e x^{5} + \frac{1}{3} \, a d x^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{arsech}\left(c x\right) - \frac{\frac{\sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{2}}}{c}\right)} b d + \frac{1}{40} \, {\left(8 \, x^{5} \operatorname{arsech}\left(c x\right) - \frac{\frac{3 \, {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 5 \, \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{4}} + \frac{3 \, \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{4}}}{c}\right)} b e"," ",0,"1/5*a*e*x^5 + 1/3*a*d*x^3 + 1/6*(2*x^3*arcsech(c*x) - (sqrt(1/(c^2*x^2) - 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + arctan(sqrt(1/(c^2*x^2) - 1))/c^2)/c)*b*d + 1/40*(8*x^5*arcsech(c*x) - ((3*(1/(c^2*x^2) - 1)^(3/2) + 5*sqrt(1/(c^2*x^2) - 1))/(c^4*(1/(c^2*x^2) - 1)^2 + 2*c^4*(1/(c^2*x^2) - 1) + c^4) + 3*arctan(sqrt(1/(c^2*x^2) - 1))/c^4)/c)*b*e","A",0
90,1,107,0,0.414985," ","integrate((e*x^2+d)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a e x^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{arsech}\left(c x\right) - \frac{\frac{\sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{2}}}{c}\right)} b e + a d x + \frac{{\left(c x \operatorname{arsech}\left(c x\right) - \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)\right)} b d}{c}"," ",0,"1/3*a*e*x^3 + 1/6*(2*x^3*arcsech(c*x) - (sqrt(1/(c^2*x^2) - 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + arctan(sqrt(1/(c^2*x^2) - 1))/c^2)/c)*b*e + a*d*x + (c*x*arcsech(c*x) - arctan(sqrt(1/(c^2*x^2) - 1)))*b*d/c","A",0
91,1,66,0,0.315506," ","integrate((e*x^2+d)*(a+b*arcsech(c*x))/x^2,x, algorithm=""maxima"")","{\left(c \sqrt{\frac{1}{c^{2} x^{2}} - 1} - \frac{\operatorname{arsech}\left(c x\right)}{x}\right)} b d + a e x + \frac{{\left(c x \operatorname{arsech}\left(c x\right) - \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)\right)} b e}{c} - \frac{a d}{x}"," ",0,"(c*sqrt(1/(c^2*x^2) - 1) - arcsech(c*x)/x)*b*d + a*e*x + (c*x*arcsech(c*x) - arctan(sqrt(1/(c^2*x^2) - 1)))*b*e/c - a*d/x","A",0
92,1,91,0,0.314866," ","integrate((e*x^2+d)*(a+b*arcsech(c*x))/x^4,x, algorithm=""maxima"")","{\left(c \sqrt{\frac{1}{c^{2} x^{2}} - 1} - \frac{\operatorname{arsech}\left(c x\right)}{x}\right)} b e + \frac{1}{9} \, b d {\left(\frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 3 \, c^{4} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{3 \, \operatorname{arsech}\left(c x\right)}{x^{3}}\right)} - \frac{a e}{x} - \frac{a d}{3 \, x^{3}}"," ",0,"(c*sqrt(1/(c^2*x^2) - 1) - arcsech(c*x)/x)*b*e + 1/9*b*d*((c^4*(1/(c^2*x^2) - 1)^(3/2) + 3*c^4*sqrt(1/(c^2*x^2) - 1))/c - 3*arcsech(c*x)/x^3) - a*e/x - 1/3*a*d/x^3","A",0
93,1,132,0,0.316114," ","integrate((e*x^2+d)*(a+b*arcsech(c*x))/x^6,x, algorithm=""maxima"")","\frac{1}{75} \, b d {\left(\frac{3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} + 10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 15 \, c^{6} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{15 \, \operatorname{arsech}\left(c x\right)}{x^{5}}\right)} + \frac{1}{9} \, b e {\left(\frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 3 \, c^{4} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{3 \, \operatorname{arsech}\left(c x\right)}{x^{3}}\right)} - \frac{a e}{3 \, x^{3}} - \frac{a d}{5 \, x^{5}}"," ",0,"1/75*b*d*((3*c^6*(1/(c^2*x^2) - 1)^(5/2) + 10*c^6*(1/(c^2*x^2) - 1)^(3/2) + 15*c^6*sqrt(1/(c^2*x^2) - 1))/c - 15*arcsech(c*x)/x^5) + 1/9*b*e*((c^4*(1/(c^2*x^2) - 1)^(3/2) + 3*c^4*sqrt(1/(c^2*x^2) - 1))/c - 3*arcsech(c*x)/x^3) - 1/3*a*e/x^3 - 1/5*a*d/x^5","A",0
94,1,165,0,0.318258," ","integrate((e*x^2+d)*(a+b*arcsech(c*x))/x^8,x, algorithm=""maxima"")","\frac{1}{245} \, b d {\left(\frac{5 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{7}{2}} + 21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} + 35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 35 \, c^{8} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{35 \, \operatorname{arsech}\left(c x\right)}{x^{7}}\right)} + \frac{1}{75} \, b e {\left(\frac{3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} + 10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 15 \, c^{6} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{15 \, \operatorname{arsech}\left(c x\right)}{x^{5}}\right)} - \frac{a e}{5 \, x^{5}} - \frac{a d}{7 \, x^{7}}"," ",0,"1/245*b*d*((5*c^8*(1/(c^2*x^2) - 1)^(7/2) + 21*c^8*(1/(c^2*x^2) - 1)^(5/2) + 35*c^8*(1/(c^2*x^2) - 1)^(3/2) + 35*c^8*sqrt(1/(c^2*x^2) - 1))/c - 35*arcsech(c*x)/x^7) + 1/75*b*e*((3*c^6*(1/(c^2*x^2) - 1)^(5/2) + 10*c^6*(1/(c^2*x^2) - 1)^(3/2) + 15*c^6*sqrt(1/(c^2*x^2) - 1))/c - 15*arcsech(c*x)/x^5) - 1/5*a*e/x^5 - 1/7*a*d/x^7","A",0
95,1,177,0,0.322562," ","integrate(x^5*(e*x^2+d)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a e x^{8} + \frac{1}{6} \, a d x^{6} + \frac{1}{90} \, {\left(15 \, x^{6} \operatorname{arsech}\left(c x\right) - \frac{3 \, c^{4} x^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} - 10 \, c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 15 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{5}}\right)} b d + \frac{1}{280} \, {\left(35 \, x^{8} \operatorname{arsech}\left(c x\right) + \frac{5 \, c^{6} x^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{7}{2}} - 21 \, c^{4} x^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} + 35 \, c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} - 35 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{7}}\right)} b e"," ",0,"1/8*a*e*x^8 + 1/6*a*d*x^6 + 1/90*(15*x^6*arcsech(c*x) - (3*c^4*x^5*(1/(c^2*x^2) - 1)^(5/2) - 10*c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) + 15*x*sqrt(1/(c^2*x^2) - 1))/c^5)*b*d + 1/280*(35*x^8*arcsech(c*x) + (5*c^6*x^7*(1/(c^2*x^2) - 1)^(7/2) - 21*c^4*x^5*(1/(c^2*x^2) - 1)^(5/2) + 35*c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) - 35*x*sqrt(1/(c^2*x^2) - 1))/c^7)*b*e","A",0
96,1,138,0,0.315686," ","integrate(x^3*(e*x^2+d)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a e x^{6} + \frac{1}{4} \, a d x^{4} + \frac{1}{12} \, {\left(3 \, x^{4} \operatorname{arsech}\left(c x\right) + \frac{c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} - 3 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{3}}\right)} b d + \frac{1}{90} \, {\left(15 \, x^{6} \operatorname{arsech}\left(c x\right) - \frac{3 \, c^{4} x^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} - 10 \, c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 15 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{5}}\right)} b e"," ",0,"1/6*a*e*x^6 + 1/4*a*d*x^4 + 1/12*(3*x^4*arcsech(c*x) + (c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) - 3*x*sqrt(1/(c^2*x^2) - 1))/c^3)*b*d + 1/90*(15*x^6*arcsech(c*x) - (3*c^4*x^5*(1/(c^2*x^2) - 1)^(5/2) - 10*c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) + 15*x*sqrt(1/(c^2*x^2) - 1))/c^5)*b*e","A",0
97,1,96,0,0.318401," ","integrate(x*(e*x^2+d)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a e x^{4} + \frac{1}{2} \, a d x^{2} + \frac{1}{2} \, {\left(x^{2} \operatorname{arsech}\left(c x\right) - \frac{x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c}\right)} b d + \frac{1}{12} \, {\left(3 \, x^{4} \operatorname{arsech}\left(c x\right) + \frac{c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} - 3 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{3}}\right)} b e"," ",0,"1/4*a*e*x^4 + 1/2*a*d*x^2 + 1/2*(x^2*arcsech(c*x) - x*sqrt(1/(c^2*x^2) - 1)/c)*b*d + 1/12*(3*x^4*arcsech(c*x) + (c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) - 3*x*sqrt(1/(c^2*x^2) - 1))/c^3)*b*e","A",0
98,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arcsech(c*x))/x,x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} + a d \log\left(x\right) + \int b e x \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right) + \frac{b d \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{x}\,{d x}"," ",0,"1/2*a*e*x^2 + a*d*log(x) + integrate(b*e*x*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x)) + b*d*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/x, x)","F",0
99,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arcsech(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{8} \, b d {\left(\frac{\frac{2 \, c^{4} x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} - 1} - c^{3} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} + 1\right) + c^{3} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} - 1\right)}{c} + \frac{4 \, \operatorname{arsech}\left(c x\right)}{x^{2}}\right)} + b e \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{x}\,{d x} + a e \log\left(x\right) - \frac{a d}{2 \, x^{2}}"," ",0,"-1/8*b*d*((2*c^4*x*sqrt(1/(c^2*x^2) - 1)/(c^2*x^2*(1/(c^2*x^2) - 1) - 1) - c^3*log(c*x*sqrt(1/(c^2*x^2) - 1) + 1) + c^3*log(c*x*sqrt(1/(c^2*x^2) - 1) - 1))/c + 4*arcsech(c*x)/x^2) + b*e*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/x, x) + a*e*log(x) - 1/2*a*d/x^2","F",0
100,1,328,0,0.421698," ","integrate(x^2*(e*x^2+d)^2*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a e^{2} x^{7} + \frac{2}{5} \, a d e x^{5} + \frac{1}{3} \, a d^{2} x^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{arsech}\left(c x\right) - \frac{\frac{\sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{2}}}{c}\right)} b d^{2} + \frac{1}{20} \, {\left(8 \, x^{5} \operatorname{arsech}\left(c x\right) - \frac{\frac{3 \, {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 5 \, \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{4}} + \frac{3 \, \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{4}}}{c}\right)} b d e + \frac{1}{336} \, {\left(48 \, x^{7} \operatorname{arsech}\left(c x\right) - \frac{\frac{15 \, {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} + 40 \, {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 33 \, \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} + 3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{6}} + \frac{15 \, \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{6}}}{c}\right)} b e^{2}"," ",0,"1/7*a*e^2*x^7 + 2/5*a*d*e*x^5 + 1/3*a*d^2*x^3 + 1/6*(2*x^3*arcsech(c*x) - (sqrt(1/(c^2*x^2) - 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + arctan(sqrt(1/(c^2*x^2) - 1))/c^2)/c)*b*d^2 + 1/20*(8*x^5*arcsech(c*x) - ((3*(1/(c^2*x^2) - 1)^(3/2) + 5*sqrt(1/(c^2*x^2) - 1))/(c^4*(1/(c^2*x^2) - 1)^2 + 2*c^4*(1/(c^2*x^2) - 1) + c^4) + 3*arctan(sqrt(1/(c^2*x^2) - 1))/c^4)/c)*b*d*e + 1/336*(48*x^7*arcsech(c*x) - ((15*(1/(c^2*x^2) - 1)^(5/2) + 40*(1/(c^2*x^2) - 1)^(3/2) + 33*sqrt(1/(c^2*x^2) - 1))/(c^6*(1/(c^2*x^2) - 1)^3 + 3*c^6*(1/(c^2*x^2) - 1)^2 + 3*c^6*(1/(c^2*x^2) - 1) + c^6) + 15*arctan(sqrt(1/(c^2*x^2) - 1))/c^6)/c)*b*e^2","A",0
101,1,224,0,0.427158," ","integrate((e*x^2+d)^2*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e^{2} x^{5} + \frac{2}{3} \, a d e x^{3} + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{arsech}\left(c x\right) - \frac{\frac{\sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{2}}}{c}\right)} b d e + \frac{1}{40} \, {\left(8 \, x^{5} \operatorname{arsech}\left(c x\right) - \frac{\frac{3 \, {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 5 \, \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{4}} + \frac{3 \, \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{4}}}{c}\right)} b e^{2} + a d^{2} x + \frac{{\left(c x \operatorname{arsech}\left(c x\right) - \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)\right)} b d^{2}}{c}"," ",0,"1/5*a*e^2*x^5 + 2/3*a*d*e*x^3 + 1/3*(2*x^3*arcsech(c*x) - (sqrt(1/(c^2*x^2) - 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + arctan(sqrt(1/(c^2*x^2) - 1))/c^2)/c)*b*d*e + 1/40*(8*x^5*arcsech(c*x) - ((3*(1/(c^2*x^2) - 1)^(3/2) + 5*sqrt(1/(c^2*x^2) - 1))/(c^4*(1/(c^2*x^2) - 1)^2 + 2*c^4*(1/(c^2*x^2) - 1) + c^4) + 3*arctan(sqrt(1/(c^2*x^2) - 1))/c^4)/c)*b*e^2 + a*d^2*x + (c*x*arcsech(c*x) - arctan(sqrt(1/(c^2*x^2) - 1)))*b*d^2/c","A",0
102,1,152,0,0.414082," ","integrate((e*x^2+d)^2*(a+b*arcsech(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, a e^{2} x^{3} + {\left(c \sqrt{\frac{1}{c^{2} x^{2}} - 1} - \frac{\operatorname{arsech}\left(c x\right)}{x}\right)} b d^{2} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{arsech}\left(c x\right) - \frac{\frac{\sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)}{c^{2}}}{c}\right)} b e^{2} + 2 \, a d e x + \frac{2 \, {\left(c x \operatorname{arsech}\left(c x\right) - \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)\right)} b d e}{c} - \frac{a d^{2}}{x}"," ",0,"1/3*a*e^2*x^3 + (c*sqrt(1/(c^2*x^2) - 1) - arcsech(c*x)/x)*b*d^2 + 1/6*(2*x^3*arcsech(c*x) - (sqrt(1/(c^2*x^2) - 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + arctan(sqrt(1/(c^2*x^2) - 1))/c^2)/c)*b*e^2 + 2*a*d*e*x + 2*(c*x*arcsech(c*x) - arctan(sqrt(1/(c^2*x^2) - 1)))*b*d*e/c - a*d^2/x","A",0
103,1,134,0,0.311128," ","integrate((e*x^2+d)^2*(a+b*arcsech(c*x))/x^4,x, algorithm=""maxima"")","2 \, {\left(c \sqrt{\frac{1}{c^{2} x^{2}} - 1} - \frac{\operatorname{arsech}\left(c x\right)}{x}\right)} b d e + a e^{2} x + \frac{1}{9} \, b d^{2} {\left(\frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 3 \, c^{4} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{3 \, \operatorname{arsech}\left(c x\right)}{x^{3}}\right)} + \frac{{\left(c x \operatorname{arsech}\left(c x\right) - \arctan\left(\sqrt{\frac{1}{c^{2} x^{2}} - 1}\right)\right)} b e^{2}}{c} - \frac{2 \, a d e}{x} - \frac{a d^{2}}{3 \, x^{3}}"," ",0,"2*(c*sqrt(1/(c^2*x^2) - 1) - arcsech(c*x)/x)*b*d*e + a*e^2*x + 1/9*b*d^2*((c^4*(1/(c^2*x^2) - 1)^(3/2) + 3*c^4*sqrt(1/(c^2*x^2) - 1))/c - 3*arcsech(c*x)/x^3) + (c*x*arcsech(c*x) - arctan(sqrt(1/(c^2*x^2) - 1)))*b*e^2/c - 2*a*d*e/x - 1/3*a*d^2/x^3","A",0
104,1,175,0,0.326248," ","integrate((e*x^2+d)^2*(a+b*arcsech(c*x))/x^6,x, algorithm=""maxima"")","{\left(c \sqrt{\frac{1}{c^{2} x^{2}} - 1} - \frac{\operatorname{arsech}\left(c x\right)}{x}\right)} b e^{2} + \frac{1}{75} \, b d^{2} {\left(\frac{3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} + 10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 15 \, c^{6} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{15 \, \operatorname{arsech}\left(c x\right)}{x^{5}}\right)} + \frac{2}{9} \, b d e {\left(\frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 3 \, c^{4} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{3 \, \operatorname{arsech}\left(c x\right)}{x^{3}}\right)} - \frac{a e^{2}}{x} - \frac{2 \, a d e}{3 \, x^{3}} - \frac{a d^{2}}{5 \, x^{5}}"," ",0,"(c*sqrt(1/(c^2*x^2) - 1) - arcsech(c*x)/x)*b*e^2 + 1/75*b*d^2*((3*c^6*(1/(c^2*x^2) - 1)^(5/2) + 10*c^6*(1/(c^2*x^2) - 1)^(3/2) + 15*c^6*sqrt(1/(c^2*x^2) - 1))/c - 15*arcsech(c*x)/x^5) + 2/9*b*d*e*((c^4*(1/(c^2*x^2) - 1)^(3/2) + 3*c^4*sqrt(1/(c^2*x^2) - 1))/c - 3*arcsech(c*x)/x^3) - a*e^2/x - 2/3*a*d*e/x^3 - 1/5*a*d^2/x^5","A",0
105,1,232,0,0.324360," ","integrate((e*x^2+d)^2*(a+b*arcsech(c*x))/x^8,x, algorithm=""maxima"")","\frac{1}{245} \, b d^{2} {\left(\frac{5 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{7}{2}} + 21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} + 35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 35 \, c^{8} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{35 \, \operatorname{arsech}\left(c x\right)}{x^{7}}\right)} + \frac{2}{75} \, b d e {\left(\frac{3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} + 10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 15 \, c^{6} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{15 \, \operatorname{arsech}\left(c x\right)}{x^{5}}\right)} + \frac{1}{9} \, b e^{2} {\left(\frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 3 \, c^{4} \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c} - \frac{3 \, \operatorname{arsech}\left(c x\right)}{x^{3}}\right)} - \frac{a e^{2}}{3 \, x^{3}} - \frac{2 \, a d e}{5 \, x^{5}} - \frac{a d^{2}}{7 \, x^{7}}"," ",0,"1/245*b*d^2*((5*c^8*(1/(c^2*x^2) - 1)^(7/2) + 21*c^8*(1/(c^2*x^2) - 1)^(5/2) + 35*c^8*(1/(c^2*x^2) - 1)^(3/2) + 35*c^8*sqrt(1/(c^2*x^2) - 1))/c - 35*arcsech(c*x)/x^7) + 2/75*b*d*e*((3*c^6*(1/(c^2*x^2) - 1)^(5/2) + 10*c^6*(1/(c^2*x^2) - 1)^(3/2) + 15*c^6*sqrt(1/(c^2*x^2) - 1))/c - 15*arcsech(c*x)/x^5) + 1/9*b*e^2*((c^4*(1/(c^2*x^2) - 1)^(3/2) + 3*c^4*sqrt(1/(c^2*x^2) - 1))/c - 3*arcsech(c*x)/x^3) - 1/3*a*e^2/x^3 - 2/5*a*d*e/x^5 - 1/7*a*d^2/x^7","A",0
106,1,245,0,0.329481," ","integrate(x^3*(e*x^2+d)^2*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a e^{2} x^{8} + \frac{1}{3} \, a d e x^{6} + \frac{1}{4} \, a d^{2} x^{4} + \frac{1}{12} \, {\left(3 \, x^{4} \operatorname{arsech}\left(c x\right) + \frac{c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} - 3 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{3}}\right)} b d^{2} + \frac{1}{45} \, {\left(15 \, x^{6} \operatorname{arsech}\left(c x\right) - \frac{3 \, c^{4} x^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} - 10 \, c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 15 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{5}}\right)} b d e + \frac{1}{280} \, {\left(35 \, x^{8} \operatorname{arsech}\left(c x\right) + \frac{5 \, c^{6} x^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{7}{2}} - 21 \, c^{4} x^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} + 35 \, c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} - 35 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{7}}\right)} b e^{2}"," ",0,"1/8*a*e^2*x^8 + 1/3*a*d*e*x^6 + 1/4*a*d^2*x^4 + 1/12*(3*x^4*arcsech(c*x) + (c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) - 3*x*sqrt(1/(c^2*x^2) - 1))/c^3)*b*d^2 + 1/45*(15*x^6*arcsech(c*x) - (3*c^4*x^5*(1/(c^2*x^2) - 1)^(5/2) - 10*c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) + 15*x*sqrt(1/(c^2*x^2) - 1))/c^5)*b*d*e + 1/280*(35*x^8*arcsech(c*x) + (5*c^6*x^7*(1/(c^2*x^2) - 1)^(7/2) - 21*c^4*x^5*(1/(c^2*x^2) - 1)^(5/2) + 35*c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) - 35*x*sqrt(1/(c^2*x^2) - 1))/c^7)*b*e^2","A",0
107,1,185,0,0.327314," ","integrate(x*(e*x^2+d)^2*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a e^{2} x^{6} + \frac{1}{2} \, a d e x^{4} + \frac{1}{2} \, a d^{2} x^{2} + \frac{1}{2} \, {\left(x^{2} \operatorname{arsech}\left(c x\right) - \frac{x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c}\right)} b d^{2} + \frac{1}{6} \, {\left(3 \, x^{4} \operatorname{arsech}\left(c x\right) + \frac{c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} - 3 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{3}}\right)} b d e + \frac{1}{90} \, {\left(15 \, x^{6} \operatorname{arsech}\left(c x\right) - \frac{3 \, c^{4} x^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{5}{2}} - 10 \, c^{2} x^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{\frac{3}{2}} + 15 \, x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{5}}\right)} b e^{2}"," ",0,"1/6*a*e^2*x^6 + 1/2*a*d*e*x^4 + 1/2*a*d^2*x^2 + 1/2*(x^2*arcsech(c*x) - x*sqrt(1/(c^2*x^2) - 1)/c)*b*d^2 + 1/6*(3*x^4*arcsech(c*x) + (c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) - 3*x*sqrt(1/(c^2*x^2) - 1))/c^3)*b*d*e + 1/90*(15*x^6*arcsech(c*x) - (3*c^4*x^5*(1/(c^2*x^2) - 1)^(5/2) - 10*c^2*x^3*(1/(c^2*x^2) - 1)^(3/2) + 15*x*sqrt(1/(c^2*x^2) - 1))/c^5)*b*e^2","A",0
108,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arcsech(c*x))/x,x, algorithm=""maxima"")","\frac{1}{4} \, a e^{2} x^{4} + a d e x^{2} + a d^{2} \log\left(x\right) + \int b e^{2} x^{3} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right) + 2 \, b d e x \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right) + \frac{b d^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{x}\,{d x}"," ",0,"1/4*a*e^2*x^4 + a*d*e*x^2 + a*d^2*log(x) + integrate(b*e^2*x^3*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x)) + 2*b*d*e*x*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x)) + b*d^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/x, x)","F",0
109,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arcsech(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, a e^{2} x^{2} - \frac{1}{8} \, b d^{2} {\left(\frac{\frac{2 \, c^{4} x \sqrt{\frac{1}{c^{2} x^{2}} - 1}}{c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} - 1} - c^{3} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} + 1\right) + c^{3} \log\left(c x \sqrt{\frac{1}{c^{2} x^{2}} - 1} - 1\right)}{c} + \frac{4 \, \operatorname{arsech}\left(c x\right)}{x^{2}}\right)} + 2 \, a d e \log\left(x\right) - \frac{a d^{2}}{2 \, x^{2}} + \int b e^{2} x \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right) + \frac{2 \, b d e \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{x}\,{d x}"," ",0,"1/2*a*e^2*x^2 - 1/8*b*d^2*((2*c^4*x*sqrt(1/(c^2*x^2) - 1)/(c^2*x^2*(1/(c^2*x^2) - 1) - 1) - c^3*log(c*x*sqrt(1/(c^2*x^2) - 1) + 1) + c^3*log(c*x*sqrt(1/(c^2*x^2) - 1) - 1))/c + 4*arcsech(c*x)/x^2) + 2*a*d*e*log(x) - 1/2*a*d^2/x^2 + integrate(b*e^2*x*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x)) + 2*b*d*e*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/x, x)","F",0
110,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsech(c*x))/(e*x^2+d),x, algorithm=""maxima"")","-a {\left(\frac{d \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e} - \frac{x}{e}\right)} + b \int \frac{x^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{e x^{2} + d}\,{d x}"," ",0,"-a*(d*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e) - x/e) + b*integrate(x^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d), x)","F",0
111,0,0,0,0.000000," ","integrate(x*(a+b*arcsech(c*x))/(e*x^2+d),x, algorithm=""maxima"")","b \int \frac{x \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{e x^{2} + d}\,{d x} + \frac{a \log\left(e x^{2} + d\right)}{2 \, e}"," ",0,"b*integrate(x*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d), x) + 1/2*a*log(e*x^2 + d)/e","F",0
112,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x^2+d),x, algorithm=""maxima"")","b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{e x^{2} + d}\,{d x} + \frac{a \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}"," ",0,"b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d), x) + a*arctan(e*x/sqrt(d*e))/sqrt(d*e)","F",0
113,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x/(e*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\log\left(e x^{2} + d\right)}{d} - \frac{2 \, \log\left(x\right)}{d}\right)} + b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{e x^{3} + d x}\,{d x}"," ",0,"-1/2*a*(log(e*x^2 + d)/d - 2*log(x)/d) + b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^3 + d*x), x)","F",0
114,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x^2/(e*x^2+d),x, algorithm=""maxima"")","-a {\left(\frac{e \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d} + \frac{1}{d x}\right)} + b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{e x^{4} + d x^{2}}\,{d x}"," ",0,"-a*(e*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d) + 1/(d*x)) + b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^4 + d*x^2), x)","F",0
115,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{d^{2}}{e^{4} x^{2} + d e^{3}} - \frac{x^{2}}{e^{2}} + \frac{2 \, d \log\left(e x^{2} + d\right)}{e^{3}}\right)} + b \int \frac{x^{5} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"-1/2*a*(d^2/(e^4*x^2 + d*e^3) - x^2/e^2 + 2*d*log(e*x^2 + d)/e^3) + b*integrate(x^5*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
116,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{d}{e^{3} x^{2} + d e^{2}} + \frac{\log\left(e x^{2} + d\right)}{e^{2}}\right)} + b \int \frac{x^{3} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a*(d/(e^3*x^2 + d*e^2) + log(e*x^2 + d)/e^2) + b*integrate(x^3*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
117,0,0,0,0.000000," ","integrate(x*(a+b*arcsech(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(2 \, c^{2} \int \frac{x^{3}}{2 \, {\left(c^{2} d^{2} x^{2} + {\left(c^{2} d e x^{2} - d e\right)} x^{2} + {\left(c^{2} d^{2} x^{2} + {\left(c^{2} d e x^{2} - d e\right)} x^{2} - d^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - d^{2}\right)}}\,{d x} + \frac{x^{2} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) - x^{2} \log\left(c\right) - x^{2} \log\left(x\right)}{d e x^{2} + d^{2}} - 2 \, \int \frac{x}{2 \, {\left(c^{2} d^{2} x^{2} + {\left(c^{2} d e x^{2} - d e\right)} x^{2} - d^{2}\right)}}\,{d x}\right)} b - \frac{a}{2 \, {\left(e^{2} x^{2} + d e\right)}}"," ",0,"1/2*(2*c^2*integrate(1/2*x^3/(c^2*d^2*x^2 + (c^2*d*e*x^2 - d*e)*x^2 + (c^2*d^2*x^2 + (c^2*d*e*x^2 - d*e)*x^2 - d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1) - d^2), x) + (x^2*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) - x^2*log(c) - x^2*log(x))/(d*e*x^2 + d^2) - 2*integrate(1/2*x/(c^2*d^2*x^2 + (c^2*d*e*x^2 - d*e)*x^2 - d^2), x))*b - 1/2*a/(e^2*x^2 + d*e)","F",0
118,-2,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x/(e*x^2+d)^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
119,-1,0,0,0.000000," ","integrate(x^4*(a+b*arcsech(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x^2/(e*x^2+d)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\frac{4 \, d e x^{2} + 3 \, d^{2}}{e^{5} x^{4} + 2 \, d e^{4} x^{2} + d^{2} e^{3}} + \frac{2 \, \log\left(e x^{2} + d\right)}{e^{3}}\right)} + b \int \frac{x^{5} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}"," ",0,"1/4*a*((4*d*e*x^2 + 3*d^2)/(e^5*x^4 + 2*d*e^4*x^2 + d^2*e^3) + 2*log(e*x^2 + d)/e^3) + b*integrate(x^5*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
124,-2,0,0,0.000000," ","integrate(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
125,-2,0,0,0.000000," ","integrate(x*(a+b*arcsech(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
126,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\frac{2 \, e x^{2} + 3 \, d}{d^{2} e^{2} x^{4} + 2 \, d^{3} e x^{2} + d^{4}} - \frac{2 \, \log\left(e x^{2} + d\right)}{d^{3}} + \frac{4 \, \log\left(x\right)}{d^{3}}\right)} + b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{e^{3} x^{7} + 3 \, d e^{2} x^{5} + 3 \, d^{2} e x^{3} + d^{3} x}\,{d x}"," ",0,"1/4*a*((2*e*x^2 + 3*d)/(d^2*e^2*x^4 + 2*d^3*e*x^2 + d^4) - 2*log(e*x^2 + d)/d^3 + 4*log(x)/d^3) + b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e^3*x^7 + 3*d*e^2*x^5 + 3*d^2*e*x^3 + d^3*x), x)","F",0
127,-1,0,0,0.000000," ","integrate(x^4*(a+b*arcsech(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{105} \, {\left(\frac{15 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} x^{4}}{e} - \frac{12 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d x^{2}}{e^{2}} + \frac{8 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{2}}{e^{3}}\right)} a + \frac{1}{105} \, b {\left(\frac{{\left(15 \, e^{3} x^{6} + 3 \, d e^{2} x^{4} - 4 \, d^{2} e x^{2} + 8 \, d^{3}\right)} \sqrt{e x^{2} + d} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{e^{3}} - 105 \, \int \frac{{\left(210 \, {\left(c^{2} e^{3} x^{6} - e^{3} x^{4}\right)} x^{5} \log\left(\sqrt{x}\right) + 105 \, {\left(c^{2} e^{3} x^{6} \log\left(c\right) - e^{3} x^{4} \log\left(c\right)\right)} x^{5} + {\left(210 \, {\left(c^{2} e^{3} x^{6} - e^{3} x^{4}\right)} x^{5} \log\left(\sqrt{x}\right) + {\left(15 \, {\left(7 \, e^{3} \log\left(c\right) + e^{3}\right)} c^{2} x^{6} - 4 \, c^{2} d^{2} e x^{2} + 8 \, c^{2} d^{3} + 3 \, {\left(c^{2} d e^{2} - 35 \, e^{3} \log\left(c\right)\right)} x^{4}\right)} x^{5}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}\right)} \sqrt{e x^{2} + d}}{105 \, {\left(c^{2} e^{3} x^{6} - e^{3} x^{4} + {\left(c^{2} e^{3} x^{6} - e^{3} x^{4}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}\right)}}\,{d x}\right)}"," ",0,"1/105*(15*(e*x^2 + d)^(3/2)*x^4/e - 12*(e*x^2 + d)^(3/2)*d*x^2/e^2 + 8*(e*x^2 + d)^(3/2)*d^2/e^3)*a + 1/105*b*((15*e^3*x^6 + 3*d*e^2*x^4 - 4*d^2*e*x^2 + 8*d^3)*sqrt(e*x^2 + d)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/e^3 - 105*integrate(1/105*(210*(c^2*e^3*x^6 - e^3*x^4)*x^5*log(sqrt(x)) + 105*(c^2*e^3*x^6*log(c) - e^3*x^4*log(c))*x^5 + (210*(c^2*e^3*x^6 - e^3*x^4)*x^5*log(sqrt(x)) + (15*(7*e^3*log(c) + e^3)*c^2*x^6 - 4*c^2*d^2*e*x^2 + 8*c^2*d^3 + 3*(c^2*d*e^2 - 35*e^3*log(c))*x^4)*x^5)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))*sqrt(e*x^2 + d)/(c^2*e^3*x^6 - e^3*x^4 + (c^2*e^3*x^6 - e^3*x^4)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))), x))","F",0
131,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{15} \, {\left(\frac{3 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{e} - \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d}{e^{2}}\right)} a + \frac{1}{15} \, b {\left(\frac{{\left(3 \, e^{2} x^{4} + d e x^{2} - 2 \, d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{e^{2}} - 15 \, \int \frac{{\left(30 \, {\left(c^{2} e^{2} x^{4} - e^{2} x^{2}\right)} x^{3} \log\left(\sqrt{x}\right) + 15 \, {\left(c^{2} e^{2} x^{4} \log\left(c\right) - e^{2} x^{2} \log\left(c\right)\right)} x^{3} + {\left(30 \, {\left(c^{2} e^{2} x^{4} - e^{2} x^{2}\right)} x^{3} \log\left(\sqrt{x}\right) + {\left(3 \, {\left(5 \, e^{2} \log\left(c\right) + e^{2}\right)} c^{2} x^{4} - 2 \, c^{2} d^{2} + {\left(c^{2} d e - 15 \, e^{2} \log\left(c\right)\right)} x^{2}\right)} x^{3}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}\right)} \sqrt{e x^{2} + d}}{15 \, {\left(c^{2} e^{2} x^{4} - e^{2} x^{2} + {\left(c^{2} e^{2} x^{4} - e^{2} x^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}\right)}}\,{d x}\right)}"," ",0,"1/15*(3*(e*x^2 + d)^(3/2)*x^2/e - 2*(e*x^2 + d)^(3/2)*d/e^2)*a + 1/15*b*((3*e^2*x^4 + d*e*x^2 - 2*d^2)*sqrt(e*x^2 + d)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/e^2 - 15*integrate(1/15*(30*(c^2*e^2*x^4 - e^2*x^2)*x^3*log(sqrt(x)) + 15*(c^2*e^2*x^4*log(c) - e^2*x^2*log(c))*x^3 + (30*(c^2*e^2*x^4 - e^2*x^2)*x^3*log(sqrt(x)) + (3*(5*e^2*log(c) + e^2)*c^2*x^4 - 2*c^2*d^2 + (c^2*d*e - 15*e^2*log(c))*x^2)*x^3)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))*sqrt(e*x^2 + d)/(c^2*e^2*x^4 - e^2*x^2 + (c^2*e^2*x^4 - e^2*x^2)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))), x))","F",0
132,0,0,0,0.000000," ","integrate(x*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{e} - 3 \, \int \frac{\sqrt{e x^{2} + d} {\left(6 \, {\left(c^{2} e x^{2} - e\right)} x \log\left(\sqrt{x}\right) + 3 \, {\left(c^{2} e x^{2} \log\left(c\right) - e \log\left(c\right)\right)} x + {\left(6 \, {\left(c^{2} e x^{2} - e\right)} x \log\left(\sqrt{x}\right) + {\left({\left(3 \, e \log\left(c\right) + e\right)} c^{2} x^{2} + c^{2} d - 3 \, e \log\left(c\right)\right)} x\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}\right)}}{3 \, {\left(c^{2} e x^{2} + {\left(c^{2} e x^{2} - e\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} - e\right)}}\,{d x}\right)} b + \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} a}{3 \, e}"," ",0,"1/3*((e*x^2 + d)^(3/2)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/e - 3*integrate(1/3*sqrt(e*x^2 + d)*(6*(c^2*e*x^2 - e)*x*log(sqrt(x)) + 3*(c^2*e*x^2*log(c) - e*log(c))*x + (6*(c^2*e*x^2 - e)*x*log(sqrt(x)) + ((3*e*log(c) + e)*c^2*x^2 + c^2*d - 3*e*log(c))*x)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))/(c^2*e*x^2 + (c^2*e*x^2 - e)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)) - e), x))*b + 1/3*(e*x^2 + d)^(3/2)*a/e","F",0
133,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x,x, algorithm=""maxima"")","-{\left(\sqrt{d} \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right) - \sqrt{e x^{2} + d}\right)} a + b \int \frac{\sqrt{e x^{2} + d} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{x}\,{d x}"," ",0,"-(sqrt(d)*arcsinh(d/(sqrt(d*e)*abs(x))) - sqrt(e*x^2 + d))*a + b*integrate(sqrt(e*x^2 + d)*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/x, x)","F",0
134,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{\sqrt{d}} - \frac{\sqrt{e x^{2} + d} e}{d} + \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}{d x^{2}}\right)} a + b \int \frac{\sqrt{e x^{2} + d} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{x^{3}}\,{d x}"," ",0,"-1/2*(e*arcsinh(d/(sqrt(d*e)*abs(x)))/sqrt(d) - sqrt(e*x^2 + d)*e/d + (e*x^2 + d)^(3/2)/(d*x^2))*a + b*integrate(sqrt(e*x^2 + d)*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/x^3, x)","F",0
135,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} x}{e} - \frac{\sqrt{e x^{2} + d} d x}{e} - \frac{d^{2} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{e^{\frac{3}{2}}}\right)} a + b \int \sqrt{e x^{2} + d} x^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)\,{d x}"," ",0,"1/8*(2*(e*x^2 + d)^(3/2)*x/e - sqrt(e*x^2 + d)*d*x/e - d^2*arcsinh(e*x/sqrt(d*e))/e^(3/2))*a + b*integrate(sqrt(e*x^2 + d)*x^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x)), x)","F",0
136,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\sqrt{e x^{2} + d} x + \frac{d \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}}\right)} a + b \int \sqrt{e x^{2} + d} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)\,{d x}"," ",0,"1/2*(sqrt(e*x^2 + d)*x + d*arcsinh(e*x/sqrt(d*e))/sqrt(e))*a + b*integrate(sqrt(e*x^2 + d)*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x)), x)","F",0
137,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^2,x, algorithm=""maxima"")","{\left(\sqrt{e} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right) - \frac{\sqrt{e x^{2} + d}}{x}\right)} a + b \int \frac{\sqrt{e x^{2} + d} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{x^{2}}\,{d x}"," ",0,"(sqrt(e)*arcsinh(e*x/sqrt(d*e)) - sqrt(e*x^2 + d)/x)*a + b*integrate(sqrt(e*x^2 + d)*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/x^2, x)","F",0
138,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^4,x, algorithm=""maxima"")","-\frac{1}{3} \, b {\left(\frac{{\left(e x^{3} + d x\right)} \sqrt{e x^{2} + d} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{d x^{4}} + 3 \, \int \frac{{\left(3 \, c^{2} d x^{2} \log\left(c\right) - {\left(c^{2} e x^{4} - {\left(3 \, d \log\left(c\right) - d\right)} c^{2} x^{2} + 3 \, d \log\left(c\right) - 6 \, {\left(c^{2} d x^{2} - d\right)} \log\left(\sqrt{x}\right)\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} - 3 \, d \log\left(c\right) + 6 \, {\left(c^{2} d x^{2} - d\right)} \log\left(\sqrt{x}\right)\right)} \sqrt{e x^{2} + d}}{3 \, {\left({\left(c^{2} d x^{2} - d\right)} x^{4} + {\left(c^{2} d x^{2} - d\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right) + 4 \, \log\left(x\right)\right)}\right)}}\,{d x}\right)} - \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} a}{3 \, d x^{3}}"," ",0,"-1/3*b*((e*x^3 + d*x)*sqrt(e*x^2 + d)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/(d*x^4) + 3*integrate(1/3*(3*c^2*d*x^2*log(c) - (c^2*e*x^4 - (3*d*log(c) - d)*c^2*x^2 + 3*d*log(c) - 6*(c^2*d*x^2 - d)*log(sqrt(x)))*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)) - 3*d*log(c) + 6*(c^2*d*x^2 - d)*log(sqrt(x)))*sqrt(e*x^2 + d)/((c^2*d*x^2 - d)*x^4 + (c^2*d*x^2 - d)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1) + 4*log(x))), x)) - 1/3*(e*x^2 + d)^(3/2)*a/(d*x^3)","F",0
139,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^6,x, algorithm=""maxima"")","\frac{1}{15} \, a {\left(\frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} e}{d^{2} x^{3}} - \frac{3 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}}}{d x^{5}}\right)} + \frac{1}{15} \, b {\left(\frac{{\left(2 \, e^{2} x^{5} - d e x^{3} - 3 \, d^{2} x\right)} \sqrt{e x^{2} + d} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{d^{2} x^{6}} - 15 \, \int \frac{{\left(15 \, c^{2} d^{2} x^{2} \log\left(c\right) - 15 \, d^{2} \log\left(c\right) + {\left(2 \, c^{2} e^{2} x^{6} - c^{2} d e x^{4} + 3 \, {\left(5 \, d^{2} \log\left(c\right) - d^{2}\right)} c^{2} x^{2} - 15 \, d^{2} \log\left(c\right) + 30 \, {\left(c^{2} d^{2} x^{2} - d^{2}\right)} \log\left(\sqrt{x}\right)\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} + 30 \, {\left(c^{2} d^{2} x^{2} - d^{2}\right)} \log\left(\sqrt{x}\right)\right)} \sqrt{e x^{2} + d}}{15 \, {\left({\left(c^{2} d^{2} x^{2} - d^{2}\right)} x^{6} + {\left(c^{2} d^{2} x^{2} - d^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right) + 6 \, \log\left(x\right)\right)}\right)}}\,{d x}\right)}"," ",0,"1/15*a*(2*(e*x^2 + d)^(3/2)*e/(d^2*x^3) - 3*(e*x^2 + d)^(3/2)/(d*x^5)) + 1/15*b*((2*e^2*x^5 - d*e*x^3 - 3*d^2*x)*sqrt(e*x^2 + d)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/(d^2*x^6) - 15*integrate(1/15*(15*c^2*d^2*x^2*log(c) - 15*d^2*log(c) + (2*c^2*e^2*x^6 - c^2*d*e*x^4 + 3*(5*d^2*log(c) - d^2)*c^2*x^2 - 15*d^2*log(c) + 30*(c^2*d^2*x^2 - d^2)*log(sqrt(x)))*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)) + 30*(c^2*d^2*x^2 - d^2)*log(sqrt(x)))*sqrt(e*x^2 + d)/((c^2*d^2*x^2 - d^2)*x^6 + (c^2*d^2*x^2 - d^2)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1) + 6*log(x))), x))","F",0
140,0,0,0,0.000000," ","integrate(x^3*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{35} \, {\left(\frac{5 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{e} - \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} d}{e^{2}}\right)} a + \frac{1}{105} \, b {\left(\frac{{\left({\left(15 \, e^{3} x^{6} + 3 \, d e^{2} x^{4} - 4 \, d^{2} e x^{2} + 8 \, d^{3}\right)} x^{5} + 7 \, {\left(3 \, d e^{2} x^{6} + d^{2} e x^{4} - 2 \, d^{3} x^{2}\right)} x^{3}\right)} \sqrt{e x^{2} + d} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{e^{2} x^{5}} - 105 \, \int \frac{{\left(105 \, {\left(c^{2} e^{3} x^{6} \log\left(c\right) - e^{3} x^{4} \log\left(c\right)\right)} x^{5} + 105 \, {\left(c^{2} d e^{2} x^{6} \log\left(c\right) - d e^{2} x^{4} \log\left(c\right)\right)} x^{3} + {\left({\left(15 \, {\left(7 \, e^{3} \log\left(c\right) + e^{3}\right)} c^{2} x^{6} - 4 \, c^{2} d^{2} e x^{2} + 8 \, c^{2} d^{3} + 3 \, {\left(c^{2} d e^{2} - 35 \, e^{3} \log\left(c\right)\right)} x^{4}\right)} x^{5} + 7 \, {\left(3 \, {\left(5 \, d e^{2} \log\left(c\right) + d e^{2}\right)} c^{2} x^{6} - 2 \, c^{2} d^{3} x^{2} + {\left(c^{2} d^{2} e - 15 \, d e^{2} \log\left(c\right)\right)} x^{4}\right)} x^{3} + 210 \, {\left({\left(c^{2} e^{3} x^{6} - e^{3} x^{4}\right)} x^{5} + {\left(c^{2} d e^{2} x^{6} - d e^{2} x^{4}\right)} x^{3}\right)} \log\left(\sqrt{x}\right)\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} + 210 \, {\left({\left(c^{2} e^{3} x^{6} - e^{3} x^{4}\right)} x^{5} + {\left(c^{2} d e^{2} x^{6} - d e^{2} x^{4}\right)} x^{3}\right)} \log\left(\sqrt{x}\right)\right)} \sqrt{e x^{2} + d}}{105 \, {\left(c^{2} e^{2} x^{6} - e^{2} x^{4} + {\left(c^{2} e^{2} x^{6} - e^{2} x^{4}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}\right)}}\,{d x}\right)}"," ",0,"1/35*(5*(e*x^2 + d)^(5/2)*x^2/e - 2*(e*x^2 + d)^(5/2)*d/e^2)*a + 1/105*b*(((15*e^3*x^6 + 3*d*e^2*x^4 - 4*d^2*e*x^2 + 8*d^3)*x^5 + 7*(3*d*e^2*x^6 + d^2*e*x^4 - 2*d^3*x^2)*x^3)*sqrt(e*x^2 + d)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/(e^2*x^5) - 105*integrate(1/105*(105*(c^2*e^3*x^6*log(c) - e^3*x^4*log(c))*x^5 + 105*(c^2*d*e^2*x^6*log(c) - d*e^2*x^4*log(c))*x^3 + ((15*(7*e^3*log(c) + e^3)*c^2*x^6 - 4*c^2*d^2*e*x^2 + 8*c^2*d^3 + 3*(c^2*d*e^2 - 35*e^3*log(c))*x^4)*x^5 + 7*(3*(5*d*e^2*log(c) + d*e^2)*c^2*x^6 - 2*c^2*d^3*x^2 + (c^2*d^2*e - 15*d*e^2*log(c))*x^4)*x^3 + 210*((c^2*e^3*x^6 - e^3*x^4)*x^5 + (c^2*d*e^2*x^6 - d*e^2*x^4)*x^3)*log(sqrt(x)))*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)) + 210*((c^2*e^3*x^6 - e^3*x^4)*x^5 + (c^2*d*e^2*x^6 - d*e^2*x^4)*x^3)*log(sqrt(x)))*sqrt(e*x^2 + d)/(c^2*e^2*x^6 - e^2*x^4 + (c^2*e^2*x^6 - e^2*x^4)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))), x))","F",0
141,0,0,0,0.000000," ","integrate(x*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{{\left(e x^{2} + d\right)}^{\frac{5}{2}} a}{5 \, e} + \frac{1}{15} \, b {\left(\frac{{\left({\left(3 \, e^{2} x^{4} + d e x^{2} - 2 \, d^{2}\right)} x^{3} + 5 \, {\left(d e x^{4} + d^{2} x^{2}\right)} x\right)} \sqrt{e x^{2} + d} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{e x^{3}} - 15 \, \int \frac{{\left(15 \, {\left(c^{2} e^{2} x^{4} \log\left(c\right) - e^{2} x^{2} \log\left(c\right)\right)} x^{3} + 15 \, {\left(c^{2} d e x^{4} \log\left(c\right) - d e x^{2} \log\left(c\right)\right)} x + {\left({\left(3 \, {\left(5 \, e^{2} \log\left(c\right) + e^{2}\right)} c^{2} x^{4} - 2 \, c^{2} d^{2} + {\left(c^{2} d e - 15 \, e^{2} \log\left(c\right)\right)} x^{2}\right)} x^{3} + 5 \, {\left({\left(3 \, d e \log\left(c\right) + d e\right)} c^{2} x^{4} + {\left(c^{2} d^{2} - 3 \, d e \log\left(c\right)\right)} x^{2}\right)} x + 30 \, {\left({\left(c^{2} e^{2} x^{4} - e^{2} x^{2}\right)} x^{3} + {\left(c^{2} d e x^{4} - d e x^{2}\right)} x\right)} \log\left(\sqrt{x}\right)\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} + 30 \, {\left({\left(c^{2} e^{2} x^{4} - e^{2} x^{2}\right)} x^{3} + {\left(c^{2} d e x^{4} - d e x^{2}\right)} x\right)} \log\left(\sqrt{x}\right)\right)} \sqrt{e x^{2} + d}}{15 \, {\left(c^{2} e x^{4} - e x^{2} + {\left(c^{2} e x^{4} - e x^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}\right)}}\,{d x}\right)}"," ",0,"1/5*(e*x^2 + d)^(5/2)*a/e + 1/15*b*(((3*e^2*x^4 + d*e*x^2 - 2*d^2)*x^3 + 5*(d*e*x^4 + d^2*x^2)*x)*sqrt(e*x^2 + d)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/(e*x^3) - 15*integrate(1/15*(15*(c^2*e^2*x^4*log(c) - e^2*x^2*log(c))*x^3 + 15*(c^2*d*e*x^4*log(c) - d*e*x^2*log(c))*x + ((3*(5*e^2*log(c) + e^2)*c^2*x^4 - 2*c^2*d^2 + (c^2*d*e - 15*e^2*log(c))*x^2)*x^3 + 5*((3*d*e*log(c) + d*e)*c^2*x^4 + (c^2*d^2 - 3*d*e*log(c))*x^2)*x + 30*((c^2*e^2*x^4 - e^2*x^2)*x^3 + (c^2*d*e*x^4 - d*e*x^2)*x)*log(sqrt(x)))*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)) + 30*((c^2*e^2*x^4 - e^2*x^2)*x^3 + (c^2*d*e*x^4 - d*e*x^2)*x)*log(sqrt(x)))*sqrt(e*x^2 + d)/(c^2*e*x^4 - e*x^2 + (c^2*e*x^4 - e*x^2)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))), x))","F",0
142,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(3 \, d^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right) - {\left(e x^{2} + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{e x^{2} + d} d\right)} a + b \int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{x}\,{d x}"," ",0,"-1/3*(3*d^(3/2)*arcsinh(d/(sqrt(d*e)*abs(x))) - (e*x^2 + d)^(3/2) - 3*sqrt(e*x^2 + d)*d)*a + b*integrate((e*x^2 + d)^(3/2)*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/x, x)","F",0
143,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(3 \, \sqrt{d} e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right) - 3 \, \sqrt{e x^{2} + d} e - \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e}{d} + \frac{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}{d x^{2}}\right)} a + b \int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{x^{3}}\,{d x}"," ",0,"-1/2*(3*sqrt(d)*e*arcsinh(d/(sqrt(d*e)*abs(x))) - 3*sqrt(e*x^2 + d)*e - (e*x^2 + d)^(3/2)*e/d + (e*x^2 + d)^(5/2)/(d*x^2))*a + b*integrate((e*x^2 + d)^(3/2)*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/x^3, x)","F",0
144,0,0,0,0.000000," ","integrate(x^2*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{48} \, {\left(\frac{8 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} x}{e} - \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d x}{e} - \frac{3 \, \sqrt{e x^{2} + d} d^{2} x}{e} - \frac{3 \, d^{3} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{e^{\frac{3}{2}}}\right)} a + b \int {\left(e x^{2} + d\right)}^{\frac{3}{2}} x^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)\,{d x}"," ",0,"1/48*(8*(e*x^2 + d)^(5/2)*x/e - 2*(e*x^2 + d)^(3/2)*d*x/e - 3*sqrt(e*x^2 + d)*d^2*x/e - 3*d^3*arcsinh(e*x/sqrt(d*e))/e^(3/2))*a + b*integrate((e*x^2 + d)^(3/2)*x^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x)), x)","F",0
145,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} x + 3 \, \sqrt{e x^{2} + d} d x + \frac{3 \, d^{2} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}}\right)} a + b \int {\left(e x^{2} + d\right)}^{\frac{3}{2}} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)\,{d x}"," ",0,"1/8*(2*(e*x^2 + d)^(3/2)*x + 3*sqrt(e*x^2 + d)*d*x + 3*d^2*arcsinh(e*x/sqrt(d*e))/sqrt(e))*a + b*integrate((e*x^2 + d)^(3/2)*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x)), x)","F",0
146,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(3 \, \sqrt{e x^{2} + d} e x + 3 \, d \sqrt{e} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right) - \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}}}{x}\right)} a + b \int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{x^{2}}\,{d x}"," ",0,"1/2*(3*sqrt(e*x^2 + d)*e*x + 3*d*sqrt(e)*arcsinh(e*x/sqrt(d*e)) - 2*(e*x^2 + d)^(3/2)/x)*a + b*integrate((e*x^2 + d)^(3/2)*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/x^2, x)","F",0
147,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{3 \, \sqrt{e x^{2} + d} e^{2} x}{d} + 3 \, e^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right) - \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} e}{d x} - \frac{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}{d x^{3}}\right)} a + b \int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{x^{4}}\,{d x}"," ",0,"1/3*(3*sqrt(e*x^2 + d)*e^2*x/d + 3*e^(3/2)*arcsinh(e*x/sqrt(d*e)) - 2*(e*x^2 + d)^(3/2)*e/(d*x) - (e*x^2 + d)^(5/2)/(d*x^3))*a + b*integrate((e*x^2 + d)^(3/2)*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/x^4, x)","F",0
148,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^6,x, algorithm=""maxima"")","\frac{1}{15} \, b {\left(\frac{{\left(2 \, e^{2} x^{5} - d e x^{3} - 3 \, d^{2} x - 5 \, {\left(e^{2} x^{3} + d e x\right)} x^{2}\right)} \sqrt{e x^{2} + d} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{d x^{6}} - 15 \, \int \frac{{\left(15 \, c^{2} d^{2} x^{2} \log\left(c\right) + 15 \, {\left(c^{2} d e x^{2} \log\left(c\right) - d e \log\left(c\right)\right)} x^{2} - 15 \, d^{2} \log\left(c\right) + {\left(2 \, c^{2} e^{2} x^{6} - c^{2} d e x^{4} + 3 \, {\left(5 \, d^{2} \log\left(c\right) - d^{2}\right)} c^{2} x^{2} - 5 \, {\left(c^{2} e^{2} x^{4} - {\left(3 \, d e \log\left(c\right) - d e\right)} c^{2} x^{2} + 3 \, d e \log\left(c\right)\right)} x^{2} - 15 \, d^{2} \log\left(c\right) + 30 \, {\left(c^{2} d^{2} x^{2} + {\left(c^{2} d e x^{2} - d e\right)} x^{2} - d^{2}\right)} \log\left(\sqrt{x}\right)\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} + 30 \, {\left(c^{2} d^{2} x^{2} + {\left(c^{2} d e x^{2} - d e\right)} x^{2} - d^{2}\right)} \log\left(\sqrt{x}\right)\right)} \sqrt{e x^{2} + d}}{15 \, {\left({\left(c^{2} d x^{2} - d\right)} x^{6} + {\left(c^{2} d x^{2} - d\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right) + 6 \, \log\left(x\right)\right)}\right)}}\,{d x}\right)} - \frac{{\left(e x^{2} + d\right)}^{\frac{5}{2}} a}{5 \, d x^{5}}"," ",0,"1/15*b*((2*e^2*x^5 - d*e*x^3 - 3*d^2*x - 5*(e^2*x^3 + d*e*x)*x^2)*sqrt(e*x^2 + d)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/(d*x^6) - 15*integrate(1/15*(15*c^2*d^2*x^2*log(c) + 15*(c^2*d*e*x^2*log(c) - d*e*log(c))*x^2 - 15*d^2*log(c) + (2*c^2*e^2*x^6 - c^2*d*e*x^4 + 3*(5*d^2*log(c) - d^2)*c^2*x^2 - 5*(c^2*e^2*x^4 - (3*d*e*log(c) - d*e)*c^2*x^2 + 3*d*e*log(c))*x^2 - 15*d^2*log(c) + 30*(c^2*d^2*x^2 + (c^2*d*e*x^2 - d*e)*x^2 - d^2)*log(sqrt(x)))*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)) + 30*(c^2*d^2*x^2 + (c^2*d*e*x^2 - d*e)*x^2 - d^2)*log(sqrt(x)))*sqrt(e*x^2 + d)/((c^2*d*x^2 - d)*x^6 + (c^2*d*x^2 - d)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1) + 6*log(x))), x)) - 1/5*(e*x^2 + d)^(5/2)*a/(d*x^5)","F",0
149,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^8,x, algorithm=""maxima"")","\frac{1}{35} \, a {\left(\frac{2 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} e}{d^{2} x^{5}} - \frac{5 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}}}{d x^{7}}\right)} - \frac{1}{105} \, b {\left(\frac{{\left(8 \, e^{3} x^{7} - 4 \, d e^{2} x^{5} + 3 \, d^{2} e x^{3} + 15 \, d^{3} x - 7 \, {\left(2 \, e^{3} x^{5} - d e^{2} x^{3} - 3 \, d^{2} e x\right)} x^{2}\right)} \sqrt{e x^{2} + d} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{d^{2} x^{8}} + 105 \, \int \frac{{\left(105 \, c^{2} d^{3} x^{2} \log\left(c\right) - 105 \, d^{3} \log\left(c\right) + 105 \, {\left(c^{2} d^{2} e x^{2} \log\left(c\right) - d^{2} e \log\left(c\right)\right)} x^{2} - {\left(8 \, c^{2} e^{3} x^{8} - 4 \, c^{2} d e^{2} x^{6} + 3 \, c^{2} d^{2} e x^{4} - 15 \, {\left(7 \, d^{3} \log\left(c\right) - d^{3}\right)} c^{2} x^{2} + 105 \, d^{3} \log\left(c\right) - 7 \, {\left(2 \, c^{2} e^{3} x^{6} - c^{2} d e^{2} x^{4} + 3 \, {\left(5 \, d^{2} e \log\left(c\right) - d^{2} e\right)} c^{2} x^{2} - 15 \, d^{2} e \log\left(c\right)\right)} x^{2} - 210 \, {\left(c^{2} d^{3} x^{2} - d^{3} + {\left(c^{2} d^{2} e x^{2} - d^{2} e\right)} x^{2}\right)} \log\left(\sqrt{x}\right)\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} + 210 \, {\left(c^{2} d^{3} x^{2} - d^{3} + {\left(c^{2} d^{2} e x^{2} - d^{2} e\right)} x^{2}\right)} \log\left(\sqrt{x}\right)\right)} \sqrt{e x^{2} + d}}{105 \, {\left({\left(c^{2} d^{2} x^{2} - d^{2}\right)} x^{8} + {\left(c^{2} d^{2} x^{2} - d^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right) + 8 \, \log\left(x\right)\right)}\right)}}\,{d x}\right)}"," ",0,"1/35*a*(2*(e*x^2 + d)^(5/2)*e/(d^2*x^5) - 5*(e*x^2 + d)^(5/2)/(d*x^7)) - 1/105*b*((8*e^3*x^7 - 4*d*e^2*x^5 + 3*d^2*e*x^3 + 15*d^3*x - 7*(2*e^3*x^5 - d*e^2*x^3 - 3*d^2*e*x)*x^2)*sqrt(e*x^2 + d)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/(d^2*x^8) + 105*integrate(1/105*(105*c^2*d^3*x^2*log(c) - 105*d^3*log(c) + 105*(c^2*d^2*e*x^2*log(c) - d^2*e*log(c))*x^2 - (8*c^2*e^3*x^8 - 4*c^2*d*e^2*x^6 + 3*c^2*d^2*e*x^4 - 15*(7*d^3*log(c) - d^3)*c^2*x^2 + 105*d^3*log(c) - 7*(2*c^2*e^3*x^6 - c^2*d*e^2*x^4 + 3*(5*d^2*e*log(c) - d^2*e)*c^2*x^2 - 15*d^2*e*log(c))*x^2 - 210*(c^2*d^3*x^2 - d^3 + (c^2*d^2*e*x^2 - d^2*e)*x^2)*log(sqrt(x)))*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)) + 210*(c^2*d^3*x^2 - d^3 + (c^2*d^2*e*x^2 - d^2*e)*x^2)*log(sqrt(x)))*sqrt(e*x^2 + d)/((c^2*d^2*x^2 - d^2)*x^8 + (c^2*d^2*x^2 - d^2)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1) + 8*log(x))), x))","F",0
150,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{15} \, {\left(\frac{3 \, \sqrt{e x^{2} + d} x^{4}}{e} - \frac{4 \, \sqrt{e x^{2} + d} d x^{2}}{e^{2}} + \frac{8 \, \sqrt{e x^{2} + d} d^{2}}{e^{3}}\right)} a + \frac{1}{15} \, b {\left(\frac{{\left(3 \, e^{3} x^{6} - d e^{2} x^{4} + 4 \, d^{2} e x^{2} + 8 \, d^{3}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{\sqrt{e x^{2} + d} e^{3}} - 15 \, \int \frac{30 \, {\left(c^{2} e^{3} x^{6} - e^{3} x^{4}\right)} x^{5} \log\left(\sqrt{x}\right) + 15 \, {\left(c^{2} e^{3} x^{6} \log\left(c\right) - e^{3} x^{4} \log\left(c\right)\right)} x^{5} + {\left(30 \, {\left(c^{2} e^{3} x^{6} - e^{3} x^{4}\right)} x^{5} \log\left(\sqrt{x}\right) + {\left(3 \, {\left(5 \, e^{3} \log\left(c\right) + e^{3}\right)} c^{2} x^{6} + 4 \, c^{2} d^{2} e x^{2} + 8 \, c^{2} d^{3} - {\left(c^{2} d e^{2} + 15 \, e^{3} \log\left(c\right)\right)} x^{4}\right)} x^{5}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{15 \, {\left(c^{2} e^{3} x^{6} - e^{3} x^{4} + {\left(c^{2} e^{3} x^{6} - e^{3} x^{4}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}\right)} \sqrt{e x^{2} + d}}\,{d x}\right)}"," ",0,"1/15*(3*sqrt(e*x^2 + d)*x^4/e - 4*sqrt(e*x^2 + d)*d*x^2/e^2 + 8*sqrt(e*x^2 + d)*d^2/e^3)*a + 1/15*b*((3*e^3*x^6 - d*e^2*x^4 + 4*d^2*e*x^2 + 8*d^3)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/(sqrt(e*x^2 + d)*e^3) - 15*integrate(1/15*(30*(c^2*e^3*x^6 - e^3*x^4)*x^5*log(sqrt(x)) + 15*(c^2*e^3*x^6*log(c) - e^3*x^4*log(c))*x^5 + (30*(c^2*e^3*x^6 - e^3*x^4)*x^5*log(sqrt(x)) + (3*(5*e^3*log(c) + e^3)*c^2*x^6 + 4*c^2*d^2*e*x^2 + 8*c^2*d^3 - (c^2*d*e^2 + 15*e^3*log(c))*x^4)*x^5)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))/((c^2*e^3*x^6 - e^3*x^4 + (c^2*e^3*x^6 - e^3*x^4)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))*sqrt(e*x^2 + d)), x))","F",0
151,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{\sqrt{e x^{2} + d} x^{2}}{e} - \frac{2 \, \sqrt{e x^{2} + d} d}{e^{2}}\right)} a + \frac{1}{3} \, b {\left(\frac{{\left(e^{2} x^{4} - d e x^{2} - 2 \, d^{2}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{\sqrt{e x^{2} + d} e^{2}} - 3 \, \int \frac{6 \, {\left(c^{2} e^{2} x^{4} - e^{2} x^{2}\right)} x^{3} \log\left(\sqrt{x}\right) + 3 \, {\left(c^{2} e^{2} x^{4} \log\left(c\right) - e^{2} x^{2} \log\left(c\right)\right)} x^{3} + {\left(6 \, {\left(c^{2} e^{2} x^{4} - e^{2} x^{2}\right)} x^{3} \log\left(\sqrt{x}\right) + {\left({\left(3 \, e^{2} \log\left(c\right) + e^{2}\right)} c^{2} x^{4} - 2 \, c^{2} d^{2} - {\left(c^{2} d e + 3 \, e^{2} \log\left(c\right)\right)} x^{2}\right)} x^{3}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{3 \, {\left(c^{2} e^{2} x^{4} - e^{2} x^{2} + {\left(c^{2} e^{2} x^{4} - e^{2} x^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}\right)} \sqrt{e x^{2} + d}}\,{d x}\right)}"," ",0,"1/3*(sqrt(e*x^2 + d)*x^2/e - 2*sqrt(e*x^2 + d)*d/e^2)*a + 1/3*b*((e^2*x^4 - d*e*x^2 - 2*d^2)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/(sqrt(e*x^2 + d)*e^2) - 3*integrate(1/3*(6*(c^2*e^2*x^4 - e^2*x^2)*x^3*log(sqrt(x)) + 3*(c^2*e^2*x^4*log(c) - e^2*x^2*log(c))*x^3 + (6*(c^2*e^2*x^4 - e^2*x^2)*x^3*log(sqrt(x)) + ((3*e^2*log(c) + e^2)*c^2*x^4 - 2*c^2*d^2 - (c^2*d*e + 3*e^2*log(c))*x^2)*x^3)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))/((c^2*e^2*x^4 - e^2*x^2 + (c^2*e^2*x^4 - e^2*x^2)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))*sqrt(e*x^2 + d)), x))","F",0
152,0,0,0,0.000000," ","integrate(x*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","b {\left(\frac{\sqrt{e x^{2} + d} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{e} - \int \frac{2 \, {\left(c^{2} e x^{2} - e\right)} x \log\left(\sqrt{x}\right) + {\left(c^{2} e x^{2} \log\left(c\right) - e \log\left(c\right)\right)} x + {\left(2 \, {\left(c^{2} e x^{2} - e\right)} x \log\left(\sqrt{x}\right) + {\left({\left(e \log\left(c\right) + e\right)} c^{2} x^{2} + c^{2} d - e \log\left(c\right)\right)} x\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{{\left(c^{2} e x^{2} + {\left(c^{2} e x^{2} - e\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} - e\right)} \sqrt{e x^{2} + d}}\,{d x}\right)} + \frac{\sqrt{e x^{2} + d} a}{e}"," ",0,"b*(sqrt(e*x^2 + d)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/e - integrate((2*(c^2*e*x^2 - e)*x*log(sqrt(x)) + (c^2*e*x^2*log(c) - e*log(c))*x + (2*(c^2*e*x^2 - e)*x*log(sqrt(x)) + ((e*log(c) + e)*c^2*x^2 + c^2*d - e*log(c))*x)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))/((c^2*e*x^2 + (c^2*e*x^2 - e)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)) - e)*sqrt(e*x^2 + d)), x)) + sqrt(e*x^2 + d)*a/e","F",0
153,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{\sqrt{e x^{2} + d} x}\,{d x} - \frac{a \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{\sqrt{d}}"," ",0,"b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(sqrt(e*x^2 + d)*x), x) - a*arcsinh(d/(sqrt(d*e)*abs(x)))/sqrt(d)","F",0
154,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x^3/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{\sqrt{e x^{2} + d}}{d x^{2}}\right)} + b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{\sqrt{e x^{2} + d} x^{3}}\,{d x}"," ",0,"1/2*a*(e*arcsinh(d/(sqrt(d*e)*abs(x)))/d^(3/2) - sqrt(e*x^2 + d)/(d*x^2)) + b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(sqrt(e*x^2 + d)*x^3), x)","F",0
155,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{\sqrt{e x^{2} + d} x}{e} - \frac{d \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{e^{\frac{3}{2}}}\right)} + b \int \frac{x^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"1/2*a*(sqrt(e*x^2 + d)*x/e - d*arcsinh(e*x/sqrt(d*e))/e^(3/2)) + b*integrate(x^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/sqrt(e*x^2 + d), x)","F",0
156,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{\sqrt{e x^{2} + d}}\,{d x} + \frac{a \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}}"," ",0,"b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/sqrt(e*x^2 + d), x) + a*arcsinh(e*x/sqrt(d*e))/sqrt(e)","F",0
157,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x^2/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","-b {\left(\frac{{\left(e x^{3} + d x\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{\sqrt{e x^{2} + d} d x^{2}} + \int \frac{c^{2} d x^{2} \log\left(c\right) - {\left(c^{2} e x^{4} - {\left(d \log\left(c\right) - d\right)} c^{2} x^{2} + d \log\left(c\right) - 2 \, {\left(c^{2} d x^{2} - d\right)} \log\left(\sqrt{x}\right)\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} - d \log\left(c\right) + 2 \, {\left(c^{2} d x^{2} - d\right)} \log\left(\sqrt{x}\right)}{{\left({\left(c^{2} d x^{2} - d\right)} x^{2} + {\left(c^{2} d x^{2} - d\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right) + 2 \, \log\left(x\right)\right)}\right)} \sqrt{e x^{2} + d}}\,{d x}\right)} - \frac{\sqrt{e x^{2} + d} a}{d x}"," ",0,"-b*((e*x^3 + d*x)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/(sqrt(e*x^2 + d)*d*x^2) + integrate((c^2*d*x^2*log(c) - (c^2*e*x^4 - (d*log(c) - d)*c^2*x^2 + d*log(c) - 2*(c^2*d*x^2 - d)*log(sqrt(x)))*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)) - d*log(c) + 2*(c^2*d*x^2 - d)*log(sqrt(x)))/(((c^2*d*x^2 - d)*x^2 + (c^2*d*x^2 - d)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1) + 2*log(x)))*sqrt(e*x^2 + d)), x)) - sqrt(e*x^2 + d)*a/(d*x)","F",0
158,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x^4/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{2 \, \sqrt{e x^{2} + d} e}{d^{2} x} - \frac{\sqrt{e x^{2} + d}}{d x^{3}}\right)} + \frac{1}{3} \, b {\left(\frac{{\left(2 \, e^{2} x^{5} + d e x^{3} - d^{2} x\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{\sqrt{e x^{2} + d} d^{2} x^{4}} - 3 \, \int \frac{3 \, c^{2} d^{2} x^{2} \log\left(c\right) - 3 \, d^{2} \log\left(c\right) + {\left(2 \, c^{2} e^{2} x^{6} + c^{2} d e x^{4} + {\left(3 \, d^{2} \log\left(c\right) - d^{2}\right)} c^{2} x^{2} - 3 \, d^{2} \log\left(c\right) + 6 \, {\left(c^{2} d^{2} x^{2} - d^{2}\right)} \log\left(\sqrt{x}\right)\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} + 6 \, {\left(c^{2} d^{2} x^{2} - d^{2}\right)} \log\left(\sqrt{x}\right)}{3 \, {\left({\left(c^{2} d^{2} x^{2} - d^{2}\right)} x^{4} + {\left(c^{2} d^{2} x^{2} - d^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right) + 4 \, \log\left(x\right)\right)}\right)} \sqrt{e x^{2} + d}}\,{d x}\right)}"," ",0,"1/3*a*(2*sqrt(e*x^2 + d)*e/(d^2*x) - sqrt(e*x^2 + d)/(d*x^3)) + 1/3*b*((2*e^2*x^5 + d*e*x^3 - d^2*x)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/(sqrt(e*x^2 + d)*d^2*x^4) - 3*integrate(1/3*(3*c^2*d^2*x^2*log(c) - 3*d^2*log(c) + (2*c^2*e^2*x^6 + c^2*d*e*x^4 + (3*d^2*log(c) - d^2)*c^2*x^2 - 3*d^2*log(c) + 6*(c^2*d^2*x^2 - d^2)*log(sqrt(x)))*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)) + 6*(c^2*d^2*x^2 - d^2)*log(sqrt(x)))/(((c^2*d^2*x^2 - d^2)*x^4 + (c^2*d^2*x^2 - d^2)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1) + 4*log(x)))*sqrt(e*x^2 + d)), x))","F",0
159,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{x^{4}}{\sqrt{e x^{2} + d} e} - \frac{4 \, d x^{2}}{\sqrt{e x^{2} + d} e^{2}} - \frac{8 \, d^{2}}{\sqrt{e x^{2} + d} e^{3}}\right)} a + b \int \frac{x^{5} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"1/3*(x^4/(sqrt(e*x^2 + d)*e) - 4*d*x^2/(sqrt(e*x^2 + d)*e^2) - 8*d^2/(sqrt(e*x^2 + d)*e^3))*a + b*integrate(x^5*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d)^(3/2), x)","F",0
160,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","a {\left(\frac{x^{2}}{\sqrt{e x^{2} + d} e} + \frac{2 \, d}{\sqrt{e x^{2} + d} e^{2}}\right)} + b \int \frac{x^{3} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"a*(x^2/(sqrt(e*x^2 + d)*e) + 2*d/(sqrt(e*x^2 + d)*e^2)) + b*integrate(x^3*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d)^(3/2), x)","F",0
161,0,0,0,0.000000," ","integrate(x*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","b \int \frac{x \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x} - \frac{a}{\sqrt{e x^{2} + d} e}"," ",0,"b*integrate(x*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d)^(3/2), x) - a/(sqrt(e*x^2 + d)*e)","F",0
162,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{\operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{1}{\sqrt{e x^{2} + d} d}\right)} + b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"-a*(arcsinh(d/(sqrt(d*e)*abs(x)))/d^(3/2) - 1/(sqrt(e*x^2 + d)*d)) + b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/((e*x^2 + d)^(3/2)*x), x)","F",0
163,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x^3/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{3 \, e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{3 \, e}{\sqrt{e x^{2} + d} d^{2}} - \frac{1}{\sqrt{e x^{2} + d} d x^{2}}\right)} + b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"1/2*a*(3*e*arcsinh(d/(sqrt(d*e)*abs(x)))/d^(5/2) - 3*e/(sqrt(e*x^2 + d)*d^2) - 1/(sqrt(e*x^2 + d)*d*x^2)) + b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/((e*x^2 + d)^(3/2)*x^3), x)","F",0
164,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{x^{3}}{\sqrt{e x^{2} + d} e} + \frac{3 \, d x}{\sqrt{e x^{2} + d} e^{2}} - \frac{3 \, d \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{e^{\frac{5}{2}}}\right)} a + b \int \frac{x^{4} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"1/2*(x^3/(sqrt(e*x^2 + d)*e) + 3*d*x/(sqrt(e*x^2 + d)*e^2) - 3*d*arcsinh(e*x/sqrt(d*e))/e^(5/2))*a + b*integrate(x^4*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d)^(3/2), x)","F",0
165,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{x}{\sqrt{e x^{2} + d} e} - \frac{\operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{e^{\frac{3}{2}}}\right)} + b \int \frac{x^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-a*(x/(sqrt(e*x^2 + d)*e) - arcsinh(e*x/sqrt(d*e))/e^(3/2)) + b*integrate(x^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d)^(3/2), x)","F",0
166,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x} + \frac{a x}{\sqrt{e x^{2} + d} d}"," ",0,"b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d)^(3/2), x) + a*x/(sqrt(e*x^2 + d)*d)","F",0
167,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x^2/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{2 \, e x}{\sqrt{e x^{2} + d} d^{2}} + \frac{1}{\sqrt{e x^{2} + d} d x}\right)} + b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"-a*(2*e*x/(sqrt(e*x^2 + d)*d^2) + 1/(sqrt(e*x^2 + d)*d*x)) + b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/((e*x^2 + d)^(3/2)*x^2), x)","F",0
168,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{3 \, x^{4}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e} + \frac{12 \, d x^{2}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e^{2}} + \frac{8 \, d^{2}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e^{3}}\right)} a + b \int \frac{x^{5} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/3*(3*x^4/((e*x^2 + d)^(3/2)*e) + 12*d*x^2/((e*x^2 + d)^(3/2)*e^2) + 8*d^2/((e*x^2 + d)^(3/2)*e^3))*a + b*integrate(x^5*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d)^(5/2), x)","F",0
169,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{3 \, x^{2}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e} + \frac{2 \, d}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e^{2}}\right)} + b \int \frac{x^{3} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-1/3*a*(3*x^2/((e*x^2 + d)^(3/2)*e) + 2*d/((e*x^2 + d)^(3/2)*e^2)) + b*integrate(x^3*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d)^(5/2), x)","F",0
170,0,0,0,0.000000," ","integrate(x*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","b \int \frac{x \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x} - \frac{a}{3 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} e}"," ",0,"b*integrate(x*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d)^(5/2), x) - 1/3*a/((e*x^2 + d)^(3/2)*e)","F",0
171,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{3 \, \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{3}{\sqrt{e x^{2} + d} d^{2}} - \frac{1}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"-1/3*a*(3*arcsinh(d/(sqrt(d*e)*abs(x)))/d^(5/2) - 3/(sqrt(e*x^2 + d)*d^2) - 1/((e*x^2 + d)^(3/2)*d)) + b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/((e*x^2 + d)^(5/2)*x), x)","F",0
172,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x^3/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{15 \, e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{7}{2}}} - \frac{15 \, e}{\sqrt{e x^{2} + d} d^{3}} - \frac{5 \, e}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{2}} - \frac{3}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d x^{2}}\right)} + b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{5}{2}} x^{3}}\,{d x}"," ",0,"1/6*a*(15*e*arcsinh(d/(sqrt(d*e)*abs(x)))/d^(7/2) - 15*e/(sqrt(e*x^2 + d)*d^3) - 5*e/((e*x^2 + d)^(3/2)*d^2) - 3/((e*x^2 + d)^(3/2)*d*x^2)) + b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/((e*x^2 + d)^(5/2)*x^3), x)","F",0
173,0,0,0,0.000000," ","integrate(x^6*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{3 \, x^{5}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e} + \frac{5 \, d x {\left(\frac{3 \, x^{2}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e} + \frac{2 \, d}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e^{2}}\right)}}{e} + \frac{5 \, d x}{\sqrt{e x^{2} + d} e^{3}} - \frac{15 \, d \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{e^{\frac{7}{2}}}\right)} a + b \int \frac{x^{6} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/6*(3*x^5/((e*x^2 + d)^(3/2)*e) + 5*d*x*(3*x^2/((e*x^2 + d)^(3/2)*e) + 2*d/((e*x^2 + d)^(3/2)*e^2))/e + 5*d*x/(sqrt(e*x^2 + d)*e^3) - 15*d*arcsinh(e*x/sqrt(d*e))/e^(7/2))*a + b*integrate(x^6*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d)^(5/2), x)","F",0
174,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(x {\left(\frac{3 \, x^{2}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e} + \frac{2 \, d}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e^{2}}\right)} + \frac{x}{\sqrt{e x^{2} + d} e^{2}} - \frac{3 \, \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{e^{\frac{5}{2}}}\right)} a + b \int \frac{x^{4} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-1/3*(x*(3*x^2/((e*x^2 + d)^(3/2)*e) + 2*d/((e*x^2 + d)^(3/2)*e^2)) + x/(sqrt(e*x^2 + d)*e^2) - 3*arcsinh(e*x/sqrt(d*e))/e^(5/2))*a + b*integrate(x^4*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d)^(5/2), x)","F",0
175,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e} - \frac{x}{\sqrt{e x^{2} + d} d e}\right)} + b \int \frac{x^{2} \log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-1/3*a*(x/((e*x^2 + d)^(3/2)*e) - x/(sqrt(e*x^2 + d)*d*e)) + b*integrate(x^2*log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d)^(5/2), x)","F",0
176,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{2 \, x}{\sqrt{e x^{2} + d} d^{2}} + \frac{x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/3*a*(2*x/(sqrt(e*x^2 + d)*d^2) + x/((e*x^2 + d)^(3/2)*d)) + b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(e*x^2 + d)^(5/2), x)","F",0
177,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^3*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{a e^{3} f^{m} x^{7} x^{m}}{m + 7} + \frac{3 \, a d e^{2} f^{m} x^{5} x^{m}}{m + 5} + \frac{3 \, a d^{2} e f^{m} x^{3} x^{m}}{m + 3} + \frac{\left(f x\right)^{m + 1} a d^{3}}{f {\left(m + 1\right)}} + \frac{{\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} b e^{3} f^{m} x^{7} x^{m} + 3 \, {\left(m^{3} + 11 \, m^{2} + 31 \, m + 21\right)} b d e^{2} f^{m} x^{5} x^{m} + 3 \, {\left(m^{3} + 13 \, m^{2} + 47 \, m + 35\right)} b d^{2} e f^{m} x^{3} x^{m} + {\left(m^{3} + 15 \, m^{2} + 71 \, m + 105\right)} b d^{3} f^{m} x x^{m}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) - {\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} b e^{3} f^{m} x^{7} x^{m} + 3 \, {\left(m^{3} + 11 \, m^{2} + 31 \, m + 21\right)} b d e^{2} f^{m} x^{5} x^{m} + 3 \, {\left(m^{3} + 13 \, m^{2} + 47 \, m + 35\right)} b d^{2} e f^{m} x^{3} x^{m} + {\left(m^{3} + 15 \, m^{2} + 71 \, m + 105\right)} b d^{3} f^{m} x x^{m}\right)} \log\left(x\right)}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105} - \int \frac{{\left(b c^{2} e^{3} f^{m} {\left(m + 7\right)} x^{2} \log\left(c\right) - {\left(e^{3} f^{m} {\left(m + 7\right)} \log\left(c\right) - e^{3} f^{m}\right)} b\right)} x^{6} x^{m}}{c^{2} {\left(m + 7\right)} x^{2} - m - 7}\,{d x} - \int \frac{3 \, {\left(b c^{2} d e^{2} f^{m} {\left(m + 5\right)} x^{2} \log\left(c\right) - {\left(d e^{2} f^{m} {\left(m + 5\right)} \log\left(c\right) - d e^{2} f^{m}\right)} b\right)} x^{4} x^{m}}{c^{2} {\left(m + 5\right)} x^{2} - m - 5}\,{d x} - \int \frac{3 \, {\left(b c^{2} d^{2} e f^{m} {\left(m + 3\right)} x^{2} \log\left(c\right) - {\left(d^{2} e f^{m} {\left(m + 3\right)} \log\left(c\right) - d^{2} e f^{m}\right)} b\right)} x^{2} x^{m}}{c^{2} {\left(m + 3\right)} x^{2} - m - 3}\,{d x} - \int \frac{{\left(b c^{2} d^{3} f^{m} {\left(m + 1\right)} x^{2} \log\left(c\right) - {\left(d^{3} f^{m} {\left(m + 1\right)} \log\left(c\right) - d^{3} f^{m}\right)} b\right)} x^{m}}{c^{2} {\left(m + 1\right)} x^{2} - m - 1}\,{d x} + \int \frac{{\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} b c^{2} e^{3} f^{m} x^{8} x^{m} + 3 \, {\left(m^{3} + 11 \, m^{2} + 31 \, m + 21\right)} b c^{2} d e^{2} f^{m} x^{6} x^{m} + 3 \, {\left(m^{3} + 13 \, m^{2} + 47 \, m + 35\right)} b c^{2} d^{2} e f^{m} x^{4} x^{m} + {\left(m^{3} + 15 \, m^{2} + 71 \, m + 105\right)} b c^{2} d^{3} f^{m} x^{2} x^{m}}{{\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} c^{2} x^{2} - m^{4} - 16 \, m^{3} + {\left({\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} c^{2} x^{2} - m^{4} - 16 \, m^{3} - 86 \, m^{2} - 176 \, m - 105\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - 86 \, m^{2} - 176 \, m - 105}\,{d x}"," ",0,"a*e^3*f^m*x^7*x^m/(m + 7) + 3*a*d*e^2*f^m*x^5*x^m/(m + 5) + 3*a*d^2*e*f^m*x^3*x^m/(m + 3) + (f*x)^(m + 1)*a*d^3/(f*(m + 1)) + (((m^3 + 9*m^2 + 23*m + 15)*b*e^3*f^m*x^7*x^m + 3*(m^3 + 11*m^2 + 31*m + 21)*b*d*e^2*f^m*x^5*x^m + 3*(m^3 + 13*m^2 + 47*m + 35)*b*d^2*e*f^m*x^3*x^m + (m^3 + 15*m^2 + 71*m + 105)*b*d^3*f^m*x*x^m)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) - ((m^3 + 9*m^2 + 23*m + 15)*b*e^3*f^m*x^7*x^m + 3*(m^3 + 11*m^2 + 31*m + 21)*b*d*e^2*f^m*x^5*x^m + 3*(m^3 + 13*m^2 + 47*m + 35)*b*d^2*e*f^m*x^3*x^m + (m^3 + 15*m^2 + 71*m + 105)*b*d^3*f^m*x*x^m)*log(x))/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105) - integrate((b*c^2*e^3*f^m*(m + 7)*x^2*log(c) - (e^3*f^m*(m + 7)*log(c) - e^3*f^m)*b)*x^6*x^m/(c^2*(m + 7)*x^2 - m - 7), x) - integrate(3*(b*c^2*d*e^2*f^m*(m + 5)*x^2*log(c) - (d*e^2*f^m*(m + 5)*log(c) - d*e^2*f^m)*b)*x^4*x^m/(c^2*(m + 5)*x^2 - m - 5), x) - integrate(3*(b*c^2*d^2*e*f^m*(m + 3)*x^2*log(c) - (d^2*e*f^m*(m + 3)*log(c) - d^2*e*f^m)*b)*x^2*x^m/(c^2*(m + 3)*x^2 - m - 3), x) - integrate((b*c^2*d^3*f^m*(m + 1)*x^2*log(c) - (d^3*f^m*(m + 1)*log(c) - d^3*f^m)*b)*x^m/(c^2*(m + 1)*x^2 - m - 1), x) + integrate(((m^3 + 9*m^2 + 23*m + 15)*b*c^2*e^3*f^m*x^8*x^m + 3*(m^3 + 11*m^2 + 31*m + 21)*b*c^2*d*e^2*f^m*x^6*x^m + 3*(m^3 + 13*m^2 + 47*m + 35)*b*c^2*d^2*e*f^m*x^4*x^m + (m^3 + 15*m^2 + 71*m + 105)*b*c^2*d^3*f^m*x^2*x^m)/((m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*c^2*x^2 - m^4 - 16*m^3 + ((m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*c^2*x^2 - m^4 - 16*m^3 - 86*m^2 - 176*m - 105)*sqrt(c*x + 1)*sqrt(-c*x + 1) - 86*m^2 - 176*m - 105), x)","F",0
178,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^2*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{a e^{2} f^{m} x^{5} x^{m}}{m + 5} + \frac{2 \, a d e f^{m} x^{3} x^{m}}{m + 3} + \frac{\left(f x\right)^{m + 1} a d^{2}}{f {\left(m + 1\right)}} + \frac{{\left({\left(m^{2} + 4 \, m + 3\right)} b e^{2} f^{m} x^{5} x^{m} + 2 \, {\left(m^{2} + 6 \, m + 5\right)} b d e f^{m} x^{3} x^{m} + {\left(m^{2} + 8 \, m + 15\right)} b d^{2} f^{m} x x^{m}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) - {\left({\left(m^{2} + 4 \, m + 3\right)} b e^{2} f^{m} x^{5} x^{m} + 2 \, {\left(m^{2} + 6 \, m + 5\right)} b d e f^{m} x^{3} x^{m} + {\left(m^{2} + 8 \, m + 15\right)} b d^{2} f^{m} x x^{m}\right)} \log\left(x\right)}{m^{3} + 9 \, m^{2} + 23 \, m + 15} - \int \frac{{\left(b c^{2} e^{2} f^{m} {\left(m + 5\right)} x^{2} \log\left(c\right) - {\left(e^{2} f^{m} {\left(m + 5\right)} \log\left(c\right) - e^{2} f^{m}\right)} b\right)} x^{4} x^{m}}{c^{2} {\left(m + 5\right)} x^{2} - m - 5}\,{d x} - \int \frac{2 \, {\left(b c^{2} d e f^{m} {\left(m + 3\right)} x^{2} \log\left(c\right) - {\left(d e f^{m} {\left(m + 3\right)} \log\left(c\right) - d e f^{m}\right)} b\right)} x^{2} x^{m}}{c^{2} {\left(m + 3\right)} x^{2} - m - 3}\,{d x} - \int \frac{{\left(b c^{2} d^{2} f^{m} {\left(m + 1\right)} x^{2} \log\left(c\right) - {\left(d^{2} f^{m} {\left(m + 1\right)} \log\left(c\right) - d^{2} f^{m}\right)} b\right)} x^{m}}{c^{2} {\left(m + 1\right)} x^{2} - m - 1}\,{d x} + \int \frac{{\left(m^{2} + 4 \, m + 3\right)} b c^{2} e^{2} f^{m} x^{6} x^{m} + 2 \, {\left(m^{2} + 6 \, m + 5\right)} b c^{2} d e f^{m} x^{4} x^{m} + {\left(m^{2} + 8 \, m + 15\right)} b c^{2} d^{2} f^{m} x^{2} x^{m}}{{\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} c^{2} x^{2} - m^{3} + {\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} c^{2} x^{2} - m^{3} - 9 \, m^{2} - 23 \, m - 15\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - 9 \, m^{2} - 23 \, m - 15}\,{d x}"," ",0,"a*e^2*f^m*x^5*x^m/(m + 5) + 2*a*d*e*f^m*x^3*x^m/(m + 3) + (f*x)^(m + 1)*a*d^2/(f*(m + 1)) + (((m^2 + 4*m + 3)*b*e^2*f^m*x^5*x^m + 2*(m^2 + 6*m + 5)*b*d*e*f^m*x^3*x^m + (m^2 + 8*m + 15)*b*d^2*f^m*x*x^m)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) - ((m^2 + 4*m + 3)*b*e^2*f^m*x^5*x^m + 2*(m^2 + 6*m + 5)*b*d*e*f^m*x^3*x^m + (m^2 + 8*m + 15)*b*d^2*f^m*x*x^m)*log(x))/(m^3 + 9*m^2 + 23*m + 15) - integrate((b*c^2*e^2*f^m*(m + 5)*x^2*log(c) - (e^2*f^m*(m + 5)*log(c) - e^2*f^m)*b)*x^4*x^m/(c^2*(m + 5)*x^2 - m - 5), x) - integrate(2*(b*c^2*d*e*f^m*(m + 3)*x^2*log(c) - (d*e*f^m*(m + 3)*log(c) - d*e*f^m)*b)*x^2*x^m/(c^2*(m + 3)*x^2 - m - 3), x) - integrate((b*c^2*d^2*f^m*(m + 1)*x^2*log(c) - (d^2*f^m*(m + 1)*log(c) - d^2*f^m)*b)*x^m/(c^2*(m + 1)*x^2 - m - 1), x) + integrate(((m^2 + 4*m + 3)*b*c^2*e^2*f^m*x^6*x^m + 2*(m^2 + 6*m + 5)*b*c^2*d*e*f^m*x^4*x^m + (m^2 + 8*m + 15)*b*c^2*d^2*f^m*x^2*x^m)/((m^3 + 9*m^2 + 23*m + 15)*c^2*x^2 - m^3 + ((m^3 + 9*m^2 + 23*m + 15)*c^2*x^2 - m^3 - 9*m^2 - 23*m - 15)*sqrt(c*x + 1)*sqrt(-c*x + 1) - 9*m^2 - 23*m - 15), x)","F",0
179,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\frac{a e f^{m} x^{3} x^{m}}{m + 3} + \frac{\left(f x\right)^{m + 1} a d}{f {\left(m + 1\right)}} + \frac{{\left(b e f^{m} {\left(m + 1\right)} x^{3} x^{m} + b d f^{m} {\left(m + 3\right)} x x^{m}\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right) - {\left(b e f^{m} {\left(m + 1\right)} x^{3} x^{m} + b d f^{m} {\left(m + 3\right)} x x^{m}\right)} \log\left(x\right)}{m^{2} + 4 \, m + 3} - \int \frac{{\left(b c^{2} e f^{m} {\left(m + 3\right)} x^{2} \log\left(c\right) - {\left(e f^{m} {\left(m + 3\right)} \log\left(c\right) - e f^{m}\right)} b\right)} x^{2} x^{m}}{c^{2} {\left(m + 3\right)} x^{2} - m - 3}\,{d x} - \int \frac{{\left(b c^{2} d f^{m} {\left(m + 1\right)} x^{2} \log\left(c\right) - {\left(d f^{m} {\left(m + 1\right)} \log\left(c\right) - d f^{m}\right)} b\right)} x^{m}}{c^{2} {\left(m + 1\right)} x^{2} - m - 1}\,{d x} + \int \frac{b c^{2} e f^{m} {\left(m + 1\right)} x^{4} x^{m} + b c^{2} d f^{m} {\left(m + 3\right)} x^{2} x^{m}}{{\left(m^{2} + 4 \, m + 3\right)} c^{2} x^{2} + {\left({\left(m^{2} + 4 \, m + 3\right)} c^{2} x^{2} - m^{2} - 4 \, m - 3\right)} \sqrt{c x + 1} \sqrt{-c x + 1} - m^{2} - 4 \, m - 3}\,{d x}"," ",0,"a*e*f^m*x^3*x^m/(m + 3) + (f*x)^(m + 1)*a*d/(f*(m + 1)) + ((b*e*f^m*(m + 1)*x^3*x^m + b*d*f^m*(m + 3)*x*x^m)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1) - (b*e*f^m*(m + 1)*x^3*x^m + b*d*f^m*(m + 3)*x*x^m)*log(x))/(m^2 + 4*m + 3) - integrate((b*c^2*e*f^m*(m + 3)*x^2*log(c) - (e*f^m*(m + 3)*log(c) - e*f^m)*b)*x^2*x^m/(c^2*(m + 3)*x^2 - m - 3), x) - integrate((b*c^2*d*f^m*(m + 1)*x^2*log(c) - (d*f^m*(m + 1)*log(c) - d*f^m)*b)*x^m/(c^2*(m + 1)*x^2 - m - 1), x) + integrate((b*c^2*e*f^m*(m + 1)*x^4*x^m + b*c^2*d*f^m*(m + 3)*x^2*x^m)/((m^2 + 4*m + 3)*c^2*x^2 + ((m^2 + 4*m + 3)*c^2*x^2 - m^2 - 4*m - 3)*sqrt(c*x + 1)*sqrt(-c*x + 1) - m^2 - 4*m - 3), x)","F",0
180,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsech}\left(c x\right) + a\right)} \left(f x\right)^{m}}{e x^{2} + d}\,{d x}"," ",0,"integrate((b*arcsech(c*x) + a)*(f*x)^m/(e*x^2 + d), x)","F",0
181,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsech}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsech(c*x) + a)*(f*x)^m/(e*x^2 + d)^2, x)","F",0
182,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x, algorithm=""maxima"")","\int {\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arsech}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arcsech(c*x) + a)*(f*x)^m, x)","F",0
183,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)*(f*x)^m, x)","F",0
184,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsech}\left(c x\right) + a\right)} \left(f x\right)^{m}}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arcsech(c*x) + a)*(f*x)^m/sqrt(e*x^2 + d), x)","F",0
185,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsech}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsech(c*x) + a)*(f*x)^m/(e*x^2 + d)^(3/2), x)","F",0
186,0,0,0,0.000000," ","integrate(x^11*(a+b*arcsech(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{30} \, a {\left(\frac{3 \, {\left(-c^{4} x^{4} + 1\right)}^{\frac{5}{2}}}{c^{12}} - \frac{10 \, {\left(-c^{4} x^{4} + 1\right)}^{\frac{3}{2}}}{c^{12}} + \frac{15 \, \sqrt{-c^{4} x^{4} + 1}}{c^{12}}\right)} + \frac{1}{30} \, b {\left(\frac{{\left(3 \, c^{12} x^{12} + c^{8} x^{8} + 4 \, c^{4} x^{4} - 8\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{\sqrt{c^{2} x^{2} + 1} \sqrt{c x + 1} \sqrt{-c x + 1} c^{12}} - 30 \, \int \frac{30 \, c^{10} x^{21} \log\left(c\right) + 60 \, c^{10} x^{21} \log\left(\sqrt{x}\right) + {\left(60 \, c^{10} x^{21} \log\left(\sqrt{x}\right) + {\left(3 \, c^{10} x^{10} {\left(10 \, \log\left(c\right) + 1\right)} + 3 \, c^{8} x^{8} + 4 \, c^{6} x^{6} + 4 \, c^{4} x^{4} + 8 \, c^{2} x^{2} + 8\right)} x^{11}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{30 \, {\left(c^{10} x^{10} e^{\left(\log\left(c x + 1\right) + \log\left(-c x + 1\right)\right)} + c^{10} x^{10} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}\right)}"," ",0,"-1/30*a*(3*(-c^4*x^4 + 1)^(5/2)/c^12 - 10*(-c^4*x^4 + 1)^(3/2)/c^12 + 15*sqrt(-c^4*x^4 + 1)/c^12) + 1/30*b*((3*c^12*x^12 + c^8*x^8 + 4*c^4*x^4 - 8)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/(sqrt(c^2*x^2 + 1)*sqrt(c*x + 1)*sqrt(-c*x + 1)*c^12) - 30*integrate(1/30*(30*c^10*x^21*log(c) + 60*c^10*x^21*log(sqrt(x)) + (60*c^10*x^21*log(sqrt(x)) + (3*c^10*x^10*(10*log(c) + 1) + 3*c^8*x^8 + 4*c^6*x^6 + 4*c^4*x^4 + 8*c^2*x^2 + 8)*x^11)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))/((c^10*x^10*e^(log(c*x + 1) + log(-c*x + 1)) + c^10*x^10*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))*sqrt(c^2*x^2 + 1)), x))","F",0
187,0,0,0,0.000000," ","integrate(x^7*(a+b*arcsech(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{{\left(-c^{4} x^{4} + 1\right)}^{\frac{3}{2}}}{c^{8}} - \frac{3 \, \sqrt{-c^{4} x^{4} + 1}}{c^{8}}\right)} + \frac{1}{6} \, b {\left(\frac{{\left(c^{8} x^{8} + c^{4} x^{4} - 2\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{\sqrt{c^{2} x^{2} + 1} \sqrt{c x + 1} \sqrt{-c x + 1} c^{8}} - 6 \, \int \frac{6 \, c^{6} x^{13} \log\left(c\right) + 12 \, c^{6} x^{13} \log\left(\sqrt{x}\right) + {\left(12 \, c^{6} x^{13} \log\left(\sqrt{x}\right) + {\left(c^{6} x^{6} {\left(6 \, \log\left(c\right) + 1\right)} + c^{4} x^{4} + 2 \, c^{2} x^{2} + 2\right)} x^{7}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{6 \, {\left(c^{6} x^{6} e^{\left(\log\left(c x + 1\right) + \log\left(-c x + 1\right)\right)} + c^{6} x^{6} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}\right)}"," ",0,"1/6*a*((-c^4*x^4 + 1)^(3/2)/c^8 - 3*sqrt(-c^4*x^4 + 1)/c^8) + 1/6*b*((c^8*x^8 + c^4*x^4 - 2)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/(sqrt(c^2*x^2 + 1)*sqrt(c*x + 1)*sqrt(-c*x + 1)*c^8) - 6*integrate(1/6*(6*c^6*x^13*log(c) + 12*c^6*x^13*log(sqrt(x)) + (12*c^6*x^13*log(sqrt(x)) + (c^6*x^6*(6*log(c) + 1) + c^4*x^4 + 2*c^2*x^2 + 2)*x^7)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))/((c^6*x^6*e^(log(c*x + 1) + log(-c*x + 1)) + c^6*x^6*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))*sqrt(c^2*x^2 + 1)), x))","F",0
188,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsech(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, b {\left(\frac{{\left(c^{4} x^{4} - 1\right)} \log\left(\sqrt{c x + 1} \sqrt{-c x + 1} + 1\right)}{\sqrt{c^{2} x^{2} + 1} \sqrt{c x + 1} \sqrt{-c x + 1} c^{4}} - 2 \, \int \frac{2 \, c^{2} x^{5} \log\left(c\right) + 4 \, c^{2} x^{5} \log\left(\sqrt{x}\right) + {\left(4 \, c^{2} x^{5} \log\left(\sqrt{x}\right) + {\left(c^{2} x^{2} {\left(2 \, \log\left(c\right) + 1\right)} + 1\right)} x^{3}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{2 \, {\left(c^{2} x^{2} e^{\left(\log\left(c x + 1\right) + \log\left(-c x + 1\right)\right)} + c^{2} x^{2} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}\right)} - \frac{\sqrt{-c^{4} x^{4} + 1} a}{2 \, c^{4}}"," ",0,"1/2*b*((c^4*x^4 - 1)*log(sqrt(c*x + 1)*sqrt(-c*x + 1) + 1)/(sqrt(c^2*x^2 + 1)*sqrt(c*x + 1)*sqrt(-c*x + 1)*c^4) - 2*integrate(1/2*(2*c^2*x^5*log(c) + 4*c^2*x^5*log(sqrt(x)) + (4*c^2*x^5*log(sqrt(x)) + (c^2*x^2*(2*log(c) + 1) + 1)*x^3)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))/((c^2*x^2*e^(log(c*x + 1) + log(-c*x + 1)) + c^2*x^2*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))*sqrt(c^2*x^2 + 1)), x)) - 1/2*sqrt(-c^4*x^4 + 1)*a/c^4","F",0
189,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x/(-c^4*x^4+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\log\left(\sqrt{-c^{4} x^{4} + 1} + 1\right) - \log\left(\sqrt{-c^{4} x^{4} + 1} - 1\right)\right)} + b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{\sqrt{-{\left(c^{2} x^{2} + 1\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}} x}\,{d x}"," ",0,"-1/4*a*(log(sqrt(-c^4*x^4 + 1) + 1) - log(sqrt(-c^4*x^4 + 1) - 1)) + b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(sqrt(-(c^2*x^2 + 1)*(c*x + 1)*(c*x - 1))*x), x)","F",0
190,0,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/x^5/(-c^4*x^4+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(c^{4} \log\left(\sqrt{-c^{4} x^{4} + 1} + 1\right) - c^{4} \log\left(\sqrt{-c^{4} x^{4} + 1} - 1\right) + \frac{2 \, \sqrt{-c^{4} x^{4} + 1}}{x^{4}}\right)} a + b \int \frac{\log\left(\sqrt{\frac{1}{c x} + 1} \sqrt{\frac{1}{c x} - 1} + \frac{1}{c x}\right)}{\sqrt{-{\left(c^{2} x^{2} + 1\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}} x^{5}}\,{d x}"," ",0,"-1/8*(c^4*log(sqrt(-c^4*x^4 + 1) + 1) - c^4*log(sqrt(-c^4*x^4 + 1) - 1) + 2*sqrt(-c^4*x^4 + 1)/x^4)*a + b*integrate(log(sqrt(1/(c*x) + 1)*sqrt(1/(c*x) - 1) + 1/(c*x))/(sqrt(-(c^2*x^2 + 1)*(c*x + 1)*(c*x - 1))*x^5), x)","F",0
