1,1,68,0,0.654651," ","integrate(x^4*arccosh(a*x),x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} \operatorname{arcosh}\left(a x\right) - \frac{1}{75} \, {\left(\frac{3 \, \sqrt{a^{2} x^{2} - 1} x^{4}}{a^{2}} + \frac{4 \, \sqrt{a^{2} x^{2} - 1} x^{2}}{a^{4}} + \frac{8 \, \sqrt{a^{2} x^{2} - 1}}{a^{6}}\right)} a"," ",0,"1/5*x^5*arccosh(a*x) - 1/75*(3*sqrt(a^2*x^2 - 1)*x^4/a^2 + 4*sqrt(a^2*x^2 - 1)*x^2/a^4 + 8*sqrt(a^2*x^2 - 1)/a^6)*a","A",0
2,1,77,0,0.691507," ","integrate(x^3*arccosh(a*x),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arcosh}\left(a x\right) - \frac{1}{32} \, {\left(\frac{2 \, \sqrt{a^{2} x^{2} - 1} x^{3}}{a^{2}} + \frac{3 \, \sqrt{a^{2} x^{2} - 1} x}{a^{4}} + \frac{3 \, \log\left(2 \, a^{2} x + 2 \, \sqrt{a^{2} x^{2} - 1} a\right)}{a^{5}}\right)} a"," ",0,"1/4*x^4*arccosh(a*x) - 1/32*(2*sqrt(a^2*x^2 - 1)*x^3/a^2 + 3*sqrt(a^2*x^2 - 1)*x/a^4 + 3*log(2*a^2*x + 2*sqrt(a^2*x^2 - 1)*a)/a^5)*a","A",0
3,1,48,0,0.316389," ","integrate(x^2*arccosh(a*x),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcosh}\left(a x\right) - \frac{1}{9} \, a {\left(\frac{\sqrt{a^{2} x^{2} - 1} x^{2}}{a^{2}} + \frac{2 \, \sqrt{a^{2} x^{2} - 1}}{a^{4}}\right)}"," ",0,"1/3*x^3*arccosh(a*x) - 1/9*a*(sqrt(a^2*x^2 - 1)*x^2/a^2 + 2*sqrt(a^2*x^2 - 1)/a^4)","A",0
4,1,56,0,0.675519," ","integrate(x*arccosh(a*x),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arcosh}\left(a x\right) - \frac{1}{4} \, a {\left(\frac{\sqrt{a^{2} x^{2} - 1} x}{a^{2}} + \frac{\log\left(2 \, a^{2} x + 2 \, \sqrt{a^{2} x^{2} - 1} a\right)}{a^{3}}\right)}"," ",0,"1/2*x^2*arccosh(a*x) - 1/4*a*(sqrt(a^2*x^2 - 1)*x/a^2 + log(2*a^2*x + 2*sqrt(a^2*x^2 - 1)*a)/a^3)","A",0
5,1,25,0,0.620941," ","integrate(arccosh(a*x),x, algorithm=""maxima"")","\frac{a x \operatorname{arcosh}\left(a x\right) - \sqrt{a^{2} x^{2} - 1}}{a}"," ",0,"(a*x*arccosh(a*x) - sqrt(a^2*x^2 - 1))/a","A",0
6,0,0,0,0.000000," ","integrate(arccosh(a*x)/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)}{x}\,{d x}"," ",0,"integrate(arccosh(a*x)/x, x)","F",0
7,1,22,0,0.866983," ","integrate(arccosh(a*x)/x^2,x, algorithm=""maxima"")","-a \arcsin\left(\frac{1}{a {\left| x \right|}}\right) - \frac{\operatorname{arcosh}\left(a x\right)}{x}"," ",0,"-a*arcsin(1/(a*abs(x))) - arccosh(a*x)/x","A",0
8,1,27,0,0.872825," ","integrate(arccosh(a*x)/x^3,x, algorithm=""maxima"")","\frac{\sqrt{a^{2} x^{2} - 1} a}{2 \, x} - \frac{\operatorname{arcosh}\left(a x\right)}{2 \, x^{2}}"," ",0,"1/2*sqrt(a^2*x^2 - 1)*a/x - 1/2*arccosh(a*x)/x^2","A",0
9,1,43,0,0.858671," ","integrate(arccosh(a*x)/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(a^{2} \arcsin\left(\frac{1}{a {\left| x \right|}}\right) - \frac{\sqrt{a^{2} x^{2} - 1}}{x^{2}}\right)} a - \frac{\operatorname{arcosh}\left(a x\right)}{3 \, x^{3}}"," ",0,"-1/6*(a^2*arcsin(1/(a*abs(x))) - sqrt(a^2*x^2 - 1)/x^2)*a - 1/3*arccosh(a*x)/x^3","A",0
10,1,48,0,0.524133," ","integrate(arccosh(a*x)/x^5,x, algorithm=""maxima"")","\frac{1}{12} \, {\left(\frac{2 \, \sqrt{a^{2} x^{2} - 1} a^{2}}{x} + \frac{\sqrt{a^{2} x^{2} - 1}}{x^{3}}\right)} a - \frac{\operatorname{arcosh}\left(a x\right)}{4 \, x^{4}}"," ",0,"1/12*(2*sqrt(a^2*x^2 - 1)*a^2/x + sqrt(a^2*x^2 - 1)/x^3)*a - 1/4*arccosh(a*x)/x^4","A",0
11,1,63,0,0.875476," ","integrate(arccosh(a*x)/x^6,x, algorithm=""maxima"")","-\frac{1}{40} \, {\left(3 \, a^{4} \arcsin\left(\frac{1}{a {\left| x \right|}}\right) - \frac{3 \, \sqrt{a^{2} x^{2} - 1} a^{2}}{x^{2}} - \frac{2 \, \sqrt{a^{2} x^{2} - 1}}{x^{4}}\right)} a - \frac{\operatorname{arcosh}\left(a x\right)}{5 \, x^{5}}"," ",0,"-1/40*(3*a^4*arcsin(1/(a*abs(x))) - 3*sqrt(a^2*x^2 - 1)*a^2/x^2 - 2*sqrt(a^2*x^2 - 1)/x^4)*a - 1/5*arccosh(a*x)/x^5","A",0
12,1,99,0,0.684762," ","integrate(x^4*arccosh(a*x)^2,x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} \operatorname{arcosh}\left(a x\right)^{2} - \frac{2}{75} \, {\left(\frac{3 \, \sqrt{a^{2} x^{2} - 1} x^{4}}{a^{2}} + \frac{4 \, \sqrt{a^{2} x^{2} - 1} x^{2}}{a^{4}} + \frac{8 \, \sqrt{a^{2} x^{2} - 1}}{a^{6}}\right)} a \operatorname{arcosh}\left(a x\right) + \frac{2 \, {\left(9 \, a^{4} x^{5} + 20 \, a^{2} x^{3} + 120 \, x\right)}}{1125 \, a^{4}}"," ",0,"1/5*x^5*arccosh(a*x)^2 - 2/75*(3*sqrt(a^2*x^2 - 1)*x^4/a^2 + 4*sqrt(a^2*x^2 - 1)*x^2/a^4 + 8*sqrt(a^2*x^2 - 1)/a^6)*a*arccosh(a*x) + 2/1125*(9*a^4*x^5 + 20*a^2*x^3 + 120*x)/a^4","A",0
13,0,0,0,0.000000," ","integrate(x^3*arccosh(a*x)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2} - \int \frac{{\left(a^{3} x^{6} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x^{5} - a x^{4}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{2 \, {\left(a^{3} x^{3} + {\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x\right)}}\,{d x}"," ",0,"1/4*x^4*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2 - integrate(1/2*(a^3*x^6 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x^5 - a*x^4)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))/(a^3*x^3 + (a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x), x)","F",0
14,1,70,0,0.689812," ","integrate(x^2*arccosh(a*x)^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcosh}\left(a x\right)^{2} - \frac{2}{9} \, a {\left(\frac{\sqrt{a^{2} x^{2} - 1} x^{2}}{a^{2}} + \frac{2 \, \sqrt{a^{2} x^{2} - 1}}{a^{4}}\right)} \operatorname{arcosh}\left(a x\right) + \frac{2 \, {\left(a^{2} x^{3} + 6 \, x\right)}}{27 \, a^{2}}"," ",0,"1/3*x^3*arccosh(a*x)^2 - 2/9*a*(sqrt(a^2*x^2 - 1)*x^2/a^2 + 2*sqrt(a^2*x^2 - 1)/a^4)*arccosh(a*x) + 2/27*(a^2*x^3 + 6*x)/a^2","A",0
15,0,0,0,0.000000," ","integrate(x*arccosh(a*x)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2} - \int \frac{{\left(a^{3} x^{4} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x^{3} - a x^{2}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{a^{3} x^{3} + {\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x}\,{d x}"," ",0,"1/2*x^2*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2 - integrate((a^3*x^4 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x^3 - a*x^2)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))/(a^3*x^3 + (a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x), x)","F",0
16,1,32,0,0.601783," ","integrate(arccosh(a*x)^2,x, algorithm=""maxima"")","x \operatorname{arcosh}\left(a x\right)^{2} + 2 \, x - \frac{2 \, \sqrt{a^{2} x^{2} - 1} \operatorname{arcosh}\left(a x\right)}{a}"," ",0,"x*arccosh(a*x)^2 + 2*x - 2*sqrt(a^2*x^2 - 1)*arccosh(a*x)/a","A",0
17,0,0,0,0.000000," ","integrate(arccosh(a*x)^2/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{2}}{x}\,{d x}"," ",0,"integrate(arccosh(a*x)^2/x, x)","F",0
18,0,0,0,0.000000," ","integrate(arccosh(a*x)^2/x^2,x, algorithm=""maxima"")","-\frac{\log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{x} + \int \frac{2 \, {\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{a^{3} x^{4} - a x^{2} + {\left(a^{2} x^{3} - x\right)} \sqrt{a x + 1} \sqrt{a x - 1}}\,{d x}"," ",0,"-log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/x + integrate(2*(a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))/(a^3*x^4 - a*x^2 + (a^2*x^3 - x)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
19,1,39,0,0.679765," ","integrate(arccosh(a*x)^2/x^3,x, algorithm=""maxima"")","-a^{2} \log\left(x\right) + \frac{\sqrt{a^{2} x^{2} - 1} a \operatorname{arcosh}\left(a x\right)}{x} - \frac{\operatorname{arcosh}\left(a x\right)^{2}}{2 \, x^{2}}"," ",0,"-a^2*log(x) + sqrt(a^2*x^2 - 1)*a*arccosh(a*x)/x - 1/2*arccosh(a*x)^2/x^2","A",0
20,0,0,0,0.000000," ","integrate(arccosh(a*x)^2/x^4,x, algorithm=""maxima"")","-\frac{\log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{3 \, x^{3}} + \int \frac{2 \, {\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{3 \, {\left(a^{3} x^{6} - a x^{4} + {\left(a^{2} x^{5} - x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)}}\,{d x}"," ",0,"-1/3*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/x^3 + integrate(2/3*(a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))/(a^3*x^6 - a*x^4 + (a^2*x^5 - x^3)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
21,1,72,0,0.617959," ","integrate(arccosh(a*x)^2/x^5,x, algorithm=""maxima"")","-\frac{1}{12} \, {\left(4 \, a^{2} \log\left(x\right) - \frac{1}{x^{2}}\right)} a^{2} + \frac{1}{6} \, {\left(\frac{2 \, \sqrt{a^{2} x^{2} - 1} a^{2}}{x} + \frac{\sqrt{a^{2} x^{2} - 1}}{x^{3}}\right)} a \operatorname{arcosh}\left(a x\right) - \frac{\operatorname{arcosh}\left(a x\right)^{2}}{4 \, x^{4}}"," ",0,"-1/12*(4*a^2*log(x) - 1/x^2)*a^2 + 1/6*(2*sqrt(a^2*x^2 - 1)*a^2/x + sqrt(a^2*x^2 - 1)/x^3)*a*arccosh(a*x) - 1/4*arccosh(a*x)^2/x^4","A",0
22,1,165,0,0.693973," ","integrate(x^4*arccosh(a*x)^3,x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} \operatorname{arcosh}\left(a x\right)^{3} - \frac{1}{25} \, {\left(\frac{3 \, \sqrt{a^{2} x^{2} - 1} x^{4}}{a^{2}} + \frac{4 \, \sqrt{a^{2} x^{2} - 1} x^{2}}{a^{4}} + \frac{8 \, \sqrt{a^{2} x^{2} - 1}}{a^{6}}\right)} a \operatorname{arcosh}\left(a x\right)^{2} - \frac{2}{5625} \, a {\left(\frac{27 \, \sqrt{a^{2} x^{2} - 1} a^{2} x^{4} + 136 \, \sqrt{a^{2} x^{2} - 1} x^{2} + \frac{2072 \, \sqrt{a^{2} x^{2} - 1}}{a^{2}}}{a^{4}} - \frac{15 \, {\left(9 \, a^{4} x^{5} + 20 \, a^{2} x^{3} + 120 \, x\right)} \operatorname{arcosh}\left(a x\right)}{a^{5}}\right)}"," ",0,"1/5*x^5*arccosh(a*x)^3 - 1/25*(3*sqrt(a^2*x^2 - 1)*x^4/a^2 + 4*sqrt(a^2*x^2 - 1)*x^2/a^4 + 8*sqrt(a^2*x^2 - 1)/a^6)*a*arccosh(a*x)^2 - 2/5625*a*((27*sqrt(a^2*x^2 - 1)*a^2*x^4 + 136*sqrt(a^2*x^2 - 1)*x^2 + 2072*sqrt(a^2*x^2 - 1)/a^2)/a^4 - 15*(9*a^4*x^5 + 20*a^2*x^3 + 120*x)*arccosh(a*x)/a^5)","A",0
23,0,0,0,0.000000," ","integrate(x^3*arccosh(a*x)^3,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3} - \int \frac{3 \, {\left(a^{3} x^{6} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x^{5} - a x^{4}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{4 \, {\left(a^{3} x^{3} + {\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x\right)}}\,{d x}"," ",0,"1/4*x^4*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3 - integrate(3/4*(a^3*x^6 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x^5 - a*x^4)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(a^3*x^3 + (a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x), x)","F",0
24,1,116,0,0.673712," ","integrate(x^2*arccosh(a*x)^3,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcosh}\left(a x\right)^{3} - \frac{1}{3} \, a {\left(\frac{\sqrt{a^{2} x^{2} - 1} x^{2}}{a^{2}} + \frac{2 \, \sqrt{a^{2} x^{2} - 1}}{a^{4}}\right)} \operatorname{arcosh}\left(a x\right)^{2} - \frac{2}{27} \, a {\left(\frac{\sqrt{a^{2} x^{2} - 1} x^{2} + \frac{20 \, \sqrt{a^{2} x^{2} - 1}}{a^{2}}}{a^{2}} - \frac{3 \, {\left(a^{2} x^{3} + 6 \, x\right)} \operatorname{arcosh}\left(a x\right)}{a^{3}}\right)}"," ",0,"1/3*x^3*arccosh(a*x)^3 - 1/3*a*(sqrt(a^2*x^2 - 1)*x^2/a^2 + 2*sqrt(a^2*x^2 - 1)/a^4)*arccosh(a*x)^2 - 2/27*a*((sqrt(a^2*x^2 - 1)*x^2 + 20*sqrt(a^2*x^2 - 1)/a^2)/a^2 - 3*(a^2*x^3 + 6*x)*arccosh(a*x)/a^3)","A",0
25,0,0,0,0.000000," ","integrate(x*arccosh(a*x)^3,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3} - \int \frac{3 \, {\left(a^{3} x^{4} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x^{3} - a x^{2}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{2 \, {\left(a^{3} x^{3} + {\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x\right)}}\,{d x}"," ",0,"1/2*x^2*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3 - integrate(3/2*(a^3*x^4 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x^3 - a*x^2)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(a^3*x^3 + (a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x), x)","F",0
26,1,57,0,0.313202," ","integrate(arccosh(a*x)^3,x, algorithm=""maxima"")","x \operatorname{arcosh}\left(a x\right)^{3} - \frac{3 \, \sqrt{a^{2} x^{2} - 1} \operatorname{arcosh}\left(a x\right)^{2}}{a} + \frac{6 \, {\left(a x \operatorname{arcosh}\left(a x\right) - \sqrt{a^{2} x^{2} - 1}\right)}}{a}"," ",0,"x*arccosh(a*x)^3 - 3*sqrt(a^2*x^2 - 1)*arccosh(a*x)^2/a + 6*(a*x*arccosh(a*x) - sqrt(a^2*x^2 - 1))/a","A",0
27,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{3}}{x}\,{d x}"," ",0,"integrate(arccosh(a*x)^3/x, x)","F",0
28,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/x^2,x, algorithm=""maxima"")","-\frac{\log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{x} + \int \frac{3 \, {\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{a^{3} x^{4} - a x^{2} + {\left(a^{2} x^{3} - x\right)} \sqrt{a x + 1} \sqrt{a x - 1}}\,{d x}"," ",0,"-log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/x + integrate(3*(a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(a^3*x^4 - a*x^2 + (a^2*x^3 - x)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
29,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/x^3,x, algorithm=""maxima"")","-\frac{\log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{2 \, x^{2}} + \int \frac{3 \, {\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{2 \, {\left(a^{3} x^{5} - a x^{3} + {\left(a^{2} x^{4} - x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)}}\,{d x}"," ",0,"-1/2*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/x^2 + integrate(3/2*(a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(a^3*x^5 - a*x^3 + (a^2*x^4 - x^2)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
30,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/x^4,x, algorithm=""maxima"")","-\frac{\log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{3 \, x^{3}} + \int \frac{{\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{a^{3} x^{6} - a x^{4} + {\left(a^{2} x^{5} - x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}\,{d x}"," ",0,"-1/3*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/x^3 + integrate((a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(a^3*x^6 - a*x^4 + (a^2*x^5 - x^3)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
31,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/x^5,x, algorithm=""maxima"")","-\frac{\log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{4 \, x^{4}} + \int \frac{3 \, {\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{4 \, {\left(a^{3} x^{7} - a x^{5} + {\left(a^{2} x^{6} - x^{4}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)}}\,{d x}"," ",0,"-1/4*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/x^4 + integrate(3/4*(a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(a^3*x^7 - a*x^5 + (a^2*x^6 - x^4)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
32,0,0,0,0.000000," ","integrate(x^5*arccosh(a*x)^4,x, algorithm=""maxima"")","\frac{1}{6} \, x^{6} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{4} - \int \frac{2 \, {\left(a^{3} x^{8} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x^{7} - a x^{6}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{3 \, {\left(a^{3} x^{3} + {\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x\right)}}\,{d x}"," ",0,"1/6*x^6*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^4 - integrate(2/3*(a^3*x^8 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x^7 - a*x^6)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/(a^3*x^3 + (a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x), x)","F",0
33,1,201,0,0.701298," ","integrate(x^4*arccosh(a*x)^4,x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} \operatorname{arcosh}\left(a x\right)^{4} - \frac{4}{75} \, {\left(\frac{3 \, \sqrt{a^{2} x^{2} - 1} x^{4}}{a^{2}} + \frac{4 \, \sqrt{a^{2} x^{2} - 1} x^{2}}{a^{4}} + \frac{8 \, \sqrt{a^{2} x^{2} - 1}}{a^{6}}\right)} a \operatorname{arcosh}\left(a x\right)^{3} - \frac{4}{84375} \, {\left(2 \, a {\left(\frac{15 \, {\left(27 \, \sqrt{a^{2} x^{2} - 1} a^{2} x^{4} + 136 \, \sqrt{a^{2} x^{2} - 1} x^{2} + \frac{2072 \, \sqrt{a^{2} x^{2} - 1}}{a^{2}}\right)} \operatorname{arcosh}\left(a x\right)}{a^{5}} - \frac{81 \, a^{4} x^{5} + 680 \, a^{2} x^{3} + 31080 \, x}{a^{6}}\right)} - \frac{225 \, {\left(9 \, a^{4} x^{5} + 20 \, a^{2} x^{3} + 120 \, x\right)} \operatorname{arcosh}\left(a x\right)^{2}}{a^{5}}\right)} a"," ",0,"1/5*x^5*arccosh(a*x)^4 - 4/75*(3*sqrt(a^2*x^2 - 1)*x^4/a^2 + 4*sqrt(a^2*x^2 - 1)*x^2/a^4 + 8*sqrt(a^2*x^2 - 1)/a^6)*a*arccosh(a*x)^3 - 4/84375*(2*a*(15*(27*sqrt(a^2*x^2 - 1)*a^2*x^4 + 136*sqrt(a^2*x^2 - 1)*x^2 + 2072*sqrt(a^2*x^2 - 1)/a^2)*arccosh(a*x)/a^5 - (81*a^4*x^5 + 680*a^2*x^3 + 31080*x)/a^6) - 225*(9*a^4*x^5 + 20*a^2*x^3 + 120*x)*arccosh(a*x)^2/a^5)*a","A",0
34,0,0,0,0.000000," ","integrate(x^3*arccosh(a*x)^4,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{4} - \int \frac{{\left(a^{3} x^{6} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x^{5} - a x^{4}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{a^{3} x^{3} + {\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x}\,{d x}"," ",0,"1/4*x^4*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^4 - integrate((a^3*x^6 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x^5 - a*x^4)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/(a^3*x^3 + (a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x), x)","F",0
35,1,143,0,0.546319," ","integrate(x^2*arccosh(a*x)^4,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcosh}\left(a x\right)^{4} - \frac{4}{9} \, a {\left(\frac{\sqrt{a^{2} x^{2} - 1} x^{2}}{a^{2}} + \frac{2 \, \sqrt{a^{2} x^{2} - 1}}{a^{4}}\right)} \operatorname{arcosh}\left(a x\right)^{3} - \frac{4}{81} \, {\left(2 \, a {\left(\frac{3 \, {\left(\sqrt{a^{2} x^{2} - 1} x^{2} + \frac{20 \, \sqrt{a^{2} x^{2} - 1}}{a^{2}}\right)} \operatorname{arcosh}\left(a x\right)}{a^{3}} - \frac{a^{2} x^{3} + 60 \, x}{a^{4}}\right)} - \frac{9 \, {\left(a^{2} x^{3} + 6 \, x\right)} \operatorname{arcosh}\left(a x\right)^{2}}{a^{3}}\right)} a"," ",0,"1/3*x^3*arccosh(a*x)^4 - 4/9*a*(sqrt(a^2*x^2 - 1)*x^2/a^2 + 2*sqrt(a^2*x^2 - 1)/a^4)*arccosh(a*x)^3 - 4/81*(2*a*(3*(sqrt(a^2*x^2 - 1)*x^2 + 20*sqrt(a^2*x^2 - 1)/a^2)*arccosh(a*x)/a^3 - (a^2*x^3 + 60*x)/a^4) - 9*(a^2*x^3 + 6*x)*arccosh(a*x)^2/a^3)*a","A",0
36,0,0,0,0.000000," ","integrate(x*arccosh(a*x)^4,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{4} - \int \frac{2 \, {\left(a^{3} x^{4} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x^{3} - a x^{2}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{a^{3} x^{3} + {\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x}\,{d x}"," ",0,"1/2*x^2*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^4 - integrate(2*(a^3*x^4 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x^3 - a*x^2)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/(a^3*x^3 + (a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x), x)","F",0
37,1,73,0,0.316126," ","integrate(arccosh(a*x)^4,x, algorithm=""maxima"")","x \operatorname{arcosh}\left(a x\right)^{4} - \frac{4 \, \sqrt{a^{2} x^{2} - 1} \operatorname{arcosh}\left(a x\right)^{3}}{a} + 12 \, {\left(\frac{x \operatorname{arcosh}\left(a x\right)^{2}}{a} + \frac{2 \, {\left(x - \frac{\sqrt{a^{2} x^{2} - 1} \operatorname{arcosh}\left(a x\right)}{a}\right)}}{a}\right)} a"," ",0,"x*arccosh(a*x)^4 - 4*sqrt(a^2*x^2 - 1)*arccosh(a*x)^3/a + 12*(x*arccosh(a*x)^2/a + 2*(x - sqrt(a^2*x^2 - 1)*arccosh(a*x)/a)/a)*a","A",0
38,0,0,0,0.000000," ","integrate(arccosh(a*x)^4/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{4}}{x}\,{d x}"," ",0,"integrate(arccosh(a*x)^4/x, x)","F",0
39,0,0,0,0.000000," ","integrate(arccosh(a*x)^4/x^2,x, algorithm=""maxima"")","-\frac{\log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{4}}{x} + \int \frac{4 \, {\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{a^{3} x^{4} - a x^{2} + {\left(a^{2} x^{3} - x\right)} \sqrt{a x + 1} \sqrt{a x - 1}}\,{d x}"," ",0,"-log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^4/x + integrate(4*(a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/(a^3*x^4 - a*x^2 + (a^2*x^3 - x)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
40,0,0,0,0.000000," ","integrate(arccosh(a*x)^4/x^3,x, algorithm=""maxima"")","-\frac{\log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{4}}{2 \, x^{2}} + \int \frac{2 \, {\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{a^{3} x^{5} - a x^{3} + {\left(a^{2} x^{4} - x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}\,{d x}"," ",0,"-1/2*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^4/x^2 + integrate(2*(a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/(a^3*x^5 - a*x^3 + (a^2*x^4 - x^2)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
41,0,0,0,0.000000," ","integrate(arccosh(a*x)^4/x^4,x, algorithm=""maxima"")","-\frac{\log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{4}}{3 \, x^{3}} + \int \frac{4 \, {\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{3 \, {\left(a^{3} x^{6} - a x^{4} + {\left(a^{2} x^{5} - x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)}}\,{d x}"," ",0,"-1/3*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^4/x^3 + integrate(4/3*(a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/(a^3*x^6 - a*x^4 + (a^2*x^5 - x^3)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
42,0,0,0,0.000000," ","integrate(x^6/arccosh(a*x),x, algorithm=""maxima"")","\int \frac{x^{6}}{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^6/arccosh(a*x), x)","F",0
43,0,0,0,0.000000," ","integrate(x^5/arccosh(a*x),x, algorithm=""maxima"")","\int \frac{x^{5}}{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^5/arccosh(a*x), x)","F",0
44,0,0,0,0.000000," ","integrate(x^4/arccosh(a*x),x, algorithm=""maxima"")","\int \frac{x^{4}}{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^4/arccosh(a*x), x)","F",0
45,0,0,0,0.000000," ","integrate(x^3/arccosh(a*x),x, algorithm=""maxima"")","\int \frac{x^{3}}{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^3/arccosh(a*x), x)","F",0
46,0,0,0,0.000000," ","integrate(x^2/arccosh(a*x),x, algorithm=""maxima"")","\int \frac{x^{2}}{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^2/arccosh(a*x), x)","F",0
47,0,0,0,0.000000," ","integrate(x/arccosh(a*x),x, algorithm=""maxima"")","\int \frac{x}{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x/arccosh(a*x), x)","F",0
48,0,0,0,0.000000," ","integrate(1/arccosh(a*x),x, algorithm=""maxima"")","\int \frac{1}{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/arccosh(a*x), x)","F",0
49,0,0,0,0.000000," ","integrate(1/x/arccosh(a*x),x, algorithm=""maxima"")","\int \frac{1}{x \operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/(x*arccosh(a*x)), x)","F",0
50,0,0,0,0.000000," ","integrate(1/x^2/arccosh(a*x),x, algorithm=""maxima"")","\int \frac{1}{x^{2} \operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/(x^2*arccosh(a*x)), x)","F",0
51,0,0,0,0.000000," ","integrate(x^4/arccosh(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{3} x^{7} - a x^{5} + {\left(a^{2} x^{6} - x^{4}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{{\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)} + \int \frac{5 \, a^{5} x^{8} - 10 \, a^{3} x^{6} + 5 \, a x^{4} + {\left(5 \, a^{3} x^{6} - 3 \, a x^{4}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(10 \, a^{4} x^{7} - 13 \, a^{2} x^{5} + 4 \, x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{{\left(a^{5} x^{4} + {\left(a x + 1\right)} {\left(a x - 1\right)} a^{3} x^{2} - 2 \, a^{3} x^{2} + 2 \, {\left(a^{4} x^{3} - a^{2} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-(a^3*x^7 - a*x^5 + (a^2*x^6 - x^4)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))) + integrate((5*a^5*x^8 - 10*a^3*x^6 + 5*a*x^4 + (5*a^3*x^6 - 3*a*x^4)*(a*x + 1)*(a*x - 1) + (10*a^4*x^7 - 13*a^2*x^5 + 4*x^3)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^5*x^4 + (a*x + 1)*(a*x - 1)*a^3*x^2 - 2*a^3*x^2 + 2*(a^4*x^3 - a^2*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
52,0,0,0,0.000000," ","integrate(x^3/arccosh(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{3} x^{6} - a x^{4} + {\left(a^{2} x^{5} - x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{{\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)} + \int \frac{4 \, a^{5} x^{7} - 8 \, a^{3} x^{5} + 4 \, a x^{3} + 2 \, {\left(2 \, a^{3} x^{5} - a x^{3}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(8 \, a^{4} x^{6} - 10 \, a^{2} x^{4} + 3 \, x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{{\left(a^{5} x^{4} + {\left(a x + 1\right)} {\left(a x - 1\right)} a^{3} x^{2} - 2 \, a^{3} x^{2} + 2 \, {\left(a^{4} x^{3} - a^{2} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-(a^3*x^6 - a*x^4 + (a^2*x^5 - x^3)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))) + integrate((4*a^5*x^7 - 8*a^3*x^5 + 4*a*x^3 + 2*(2*a^3*x^5 - a*x^3)*(a*x + 1)*(a*x - 1) + (8*a^4*x^6 - 10*a^2*x^4 + 3*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^5*x^4 + (a*x + 1)*(a*x - 1)*a^3*x^2 - 2*a^3*x^2 + 2*(a^4*x^3 - a^2*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
53,0,0,0,0.000000," ","integrate(x^2/arccosh(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{3} x^{5} - a x^{3} + {\left(a^{2} x^{4} - x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{{\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)} + \int \frac{3 \, a^{5} x^{6} - 6 \, a^{3} x^{4} + {\left(3 \, a^{3} x^{4} - a x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 3 \, a x^{2} + {\left(6 \, a^{4} x^{5} - 7 \, a^{2} x^{3} + 2 \, x\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{{\left(a^{5} x^{4} + {\left(a x + 1\right)} {\left(a x - 1\right)} a^{3} x^{2} - 2 \, a^{3} x^{2} + 2 \, {\left(a^{4} x^{3} - a^{2} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-(a^3*x^5 - a*x^3 + (a^2*x^4 - x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))) + integrate((3*a^5*x^6 - 6*a^3*x^4 + (3*a^3*x^4 - a*x^2)*(a*x + 1)*(a*x - 1) + 3*a*x^2 + (6*a^4*x^5 - 7*a^2*x^3 + 2*x)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^5*x^4 + (a*x + 1)*(a*x - 1)*a^3*x^2 - 2*a^3*x^2 + 2*(a^4*x^3 - a^2*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
54,0,0,0,0.000000," ","integrate(x/arccosh(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{3} x^{4} - a x^{2} + {\left(a^{2} x^{3} - x\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{{\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)} + \int \frac{2 \, a^{5} x^{5} + 2 \, {\left(a x + 1\right)} {\left(a x - 1\right)} a^{3} x^{3} - 4 \, a^{3} x^{3} + {\left(4 \, a^{4} x^{4} - 4 \, a^{2} x^{2} + 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 2 \, a x}{{\left(a^{5} x^{4} + {\left(a x + 1\right)} {\left(a x - 1\right)} a^{3} x^{2} - 2 \, a^{3} x^{2} + 2 \, {\left(a^{4} x^{3} - a^{2} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-(a^3*x^4 - a*x^2 + (a^2*x^3 - x)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))) + integrate((2*a^5*x^5 + 2*(a*x + 1)*(a*x - 1)*a^3*x^3 - 4*a^3*x^3 + (4*a^4*x^4 - 4*a^2*x^2 + 1)*sqrt(a*x + 1)*sqrt(a*x - 1) + 2*a*x)/((a^5*x^4 + (a*x + 1)*(a*x - 1)*a^3*x^2 - 2*a^3*x^2 + 2*(a^4*x^3 - a^2*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
55,0,0,0,0.000000," ","integrate(1/arccosh(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{3} x^{3} + {\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x}{{\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)} + \int \frac{a^{4} x^{4} - 2 \, a^{2} x^{2} + {\left(a^{2} x^{2} + 1\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(2 \, a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 1}{{\left(a^{4} x^{4} + {\left(a x + 1\right)} {\left(a x - 1\right)} a^{2} x^{2} - 2 \, a^{2} x^{2} + 2 \, {\left(a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 1\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-(a^3*x^3 + (a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x)/((a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))) + integrate((a^4*x^4 - 2*a^2*x^2 + (a^2*x^2 + 1)*(a*x + 1)*(a*x - 1) + (2*a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + 1)/((a^4*x^4 + (a*x + 1)*(a*x - 1)*a^2*x^2 - 2*a^2*x^2 + 2*(a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + 1)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
56,0,0,0,0.000000," ","integrate(1/x/arccosh(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{3} x^{3} + {\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x}{{\left(a^{3} x^{3} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x^{2} - a x\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)} + \int \frac{2 \, {\left(a x + 1\right)} {\left(a x - 1\right)} a x + {\left(2 \, a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{{\left(a^{5} x^{6} + {\left(a x + 1\right)} {\left(a x - 1\right)} a^{3} x^{4} - 2 \, a^{3} x^{4} + a x^{2} + 2 \, {\left(a^{4} x^{5} - a^{2} x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-(a^3*x^3 + (a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x)/((a^3*x^3 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x^2 - a*x)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))) + integrate((2*(a*x + 1)*(a*x - 1)*a*x + (2*a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^5*x^6 + (a*x + 1)*(a*x - 1)*a^3*x^4 - 2*a^3*x^4 + a*x^2 + 2*(a^4*x^5 - a^2*x^3)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
57,0,0,0,0.000000," ","integrate(1/x^2/arccosh(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{3} x^{3} + {\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x}{{\left(a^{3} x^{4} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x^{3} - a x^{2}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)} - \int \frac{a^{5} x^{5} - 2 \, a^{3} x^{3} + {\left(a^{3} x^{3} - 3 \, a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(2 \, a^{4} x^{4} - 5 \, a^{2} x^{2} + 2\right)} \sqrt{a x + 1} \sqrt{a x - 1} + a x}{{\left(a^{5} x^{7} + {\left(a x + 1\right)} {\left(a x - 1\right)} a^{3} x^{5} - 2 \, a^{3} x^{5} + a x^{3} + 2 \, {\left(a^{4} x^{6} - a^{2} x^{4}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-(a^3*x^3 + (a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x)/((a^3*x^4 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x^3 - a*x^2)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))) - integrate((a^5*x^5 - 2*a^3*x^3 + (a^3*x^3 - 3*a*x)*(a*x + 1)*(a*x - 1) + (2*a^4*x^4 - 5*a^2*x^2 + 2)*sqrt(a*x + 1)*sqrt(a*x - 1) + a*x)/((a^5*x^7 + (a*x + 1)*(a*x - 1)*a^3*x^5 - 2*a^3*x^5 + a*x^3 + 2*(a^4*x^6 - a^2*x^4)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
58,0,0,0,0.000000," ","integrate(x^4/arccosh(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{8} x^{11} - 3 \, a^{6} x^{9} + 3 \, a^{4} x^{7} - a^{2} x^{5} + {\left(a^{5} x^{8} - a^{3} x^{6}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + {\left(3 \, a^{6} x^{9} - 5 \, a^{4} x^{7} + 2 \, a^{2} x^{5}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(3 \, a^{7} x^{10} - 7 \, a^{5} x^{8} + 5 \, a^{3} x^{6} - a x^{4}\right)} \sqrt{a x + 1} \sqrt{a x - 1} + {\left(5 \, a^{8} x^{11} - 15 \, a^{6} x^{9} + 15 \, a^{4} x^{7} - 5 \, a^{2} x^{5} + {\left(5 \, a^{5} x^{8} - 8 \, a^{3} x^{6} + 3 \, a x^{4}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + {\left(15 \, a^{6} x^{9} - 31 \, a^{4} x^{7} + 20 \, a^{2} x^{5} - 4 \, x^{3}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(15 \, a^{7} x^{10} - 38 \, a^{5} x^{8} + 32 \, a^{3} x^{6} - 9 \, a x^{4}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{2 \, {\left(a^{8} x^{6} + {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} a^{5} x^{3} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} + 3 \, {\left(a^{6} x^{4} - a^{4} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 3 \, {\left(a^{7} x^{5} - 2 \, a^{5} x^{3} + a^{3} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a^{2}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}} + \int \frac{25 \, a^{10} x^{12} - 100 \, a^{8} x^{10} + 150 \, a^{6} x^{8} - 100 \, a^{4} x^{6} + 25 \, a^{2} x^{4} + {\left(25 \, a^{6} x^{8} - 24 \, a^{4} x^{6} + 3 \, a^{2} x^{4}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(100 \, a^{7} x^{9} - 172 \, a^{5} x^{7} + 87 \, a^{3} x^{5} - 12 \, a x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 3 \, {\left(50 \, a^{8} x^{10} - 124 \, a^{6} x^{8} + 105 \, a^{4} x^{6} - 35 \, a^{2} x^{4} + 4 \, x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(100 \, a^{9} x^{11} - 324 \, a^{7} x^{9} + 381 \, a^{5} x^{7} - 193 \, a^{3} x^{5} + 36 \, a x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{2 \, {\left(a^{10} x^{8} + {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} a^{6} x^{4} - 4 \, a^{8} x^{6} + 6 \, a^{6} x^{4} - 4 \, a^{4} x^{2} + 4 \, {\left(a^{7} x^{5} - a^{5} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 6 \, {\left(a^{8} x^{6} - 2 \, a^{6} x^{4} + a^{4} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 4 \, {\left(a^{9} x^{7} - 3 \, a^{7} x^{5} + 3 \, a^{5} x^{3} - a^{3} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + a^{2}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/2*(a^8*x^11 - 3*a^6*x^9 + 3*a^4*x^7 - a^2*x^5 + (a^5*x^8 - a^3*x^6)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (3*a^6*x^9 - 5*a^4*x^7 + 2*a^2*x^5)*(a*x + 1)*(a*x - 1) + (3*a^7*x^10 - 7*a^5*x^8 + 5*a^3*x^6 - a*x^4)*sqrt(a*x + 1)*sqrt(a*x - 1) + (5*a^8*x^11 - 15*a^6*x^9 + 15*a^4*x^7 - 5*a^2*x^5 + (5*a^5*x^8 - 8*a^3*x^6 + 3*a*x^4)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (15*a^6*x^9 - 31*a^4*x^7 + 20*a^2*x^5 - 4*x^3)*(a*x + 1)*(a*x - 1) + (15*a^7*x^10 - 38*a^5*x^8 + 32*a^3*x^6 - 9*a*x^4)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^8*x^6 + (a*x + 1)^(3/2)*(a*x - 1)^(3/2)*a^5*x^3 - 3*a^6*x^4 + 3*a^4*x^2 + 3*(a^6*x^4 - a^4*x^2)*(a*x + 1)*(a*x - 1) + 3*(a^7*x^5 - 2*a^5*x^3 + a^3*x)*sqrt(a*x + 1)*sqrt(a*x - 1) - a^2)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2) + integrate(1/2*(25*a^10*x^12 - 100*a^8*x^10 + 150*a^6*x^8 - 100*a^4*x^6 + 25*a^2*x^4 + (25*a^6*x^8 - 24*a^4*x^6 + 3*a^2*x^4)*(a*x + 1)^2*(a*x - 1)^2 + (100*a^7*x^9 - 172*a^5*x^7 + 87*a^3*x^5 - 12*a*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 3*(50*a^8*x^10 - 124*a^6*x^8 + 105*a^4*x^6 - 35*a^2*x^4 + 4*x^2)*(a*x + 1)*(a*x - 1) + (100*a^9*x^11 - 324*a^7*x^9 + 381*a^5*x^7 - 193*a^3*x^5 + 36*a*x^3)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^10*x^8 + (a*x + 1)^2*(a*x - 1)^2*a^6*x^4 - 4*a^8*x^6 + 6*a^6*x^4 - 4*a^4*x^2 + 4*(a^7*x^5 - a^5*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 6*(a^8*x^6 - 2*a^6*x^4 + a^4*x^2)*(a*x + 1)*(a*x - 1) + 4*(a^9*x^7 - 3*a^7*x^5 + 3*a^5*x^3 - a^3*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + a^2)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
59,0,0,0,0.000000," ","integrate(x^3/arccosh(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{8} x^{10} - 3 \, a^{6} x^{8} + 3 \, a^{4} x^{6} - a^{2} x^{4} + {\left(a^{5} x^{7} - a^{3} x^{5}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + {\left(3 \, a^{6} x^{8} - 5 \, a^{4} x^{6} + 2 \, a^{2} x^{4}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(3 \, a^{7} x^{9} - 7 \, a^{5} x^{7} + 5 \, a^{3} x^{5} - a x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1} + {\left(4 \, a^{8} x^{10} - 12 \, a^{6} x^{8} + 12 \, a^{4} x^{6} - 4 \, a^{2} x^{4} + 2 \, {\left(2 \, a^{5} x^{7} - 3 \, a^{3} x^{5} + a x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 3 \, {\left(4 \, a^{6} x^{8} - 8 \, a^{4} x^{6} + 5 \, a^{2} x^{4} - x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(12 \, a^{7} x^{9} - 30 \, a^{5} x^{7} + 25 \, a^{3} x^{5} - 7 \, a x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{2 \, {\left(a^{8} x^{6} + {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} a^{5} x^{3} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} + 3 \, {\left(a^{6} x^{4} - a^{4} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 3 \, {\left(a^{7} x^{5} - 2 \, a^{5} x^{3} + a^{3} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a^{2}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}} + \int \frac{16 \, a^{10} x^{11} - 64 \, a^{8} x^{9} + 96 \, a^{6} x^{7} - 64 \, a^{4} x^{5} + 4 \, {\left(4 \, a^{6} x^{7} - 3 \, a^{4} x^{5}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 16 \, a^{2} x^{3} + {\left(64 \, a^{7} x^{8} - 100 \, a^{5} x^{6} + 42 \, a^{3} x^{4} - 3 \, a x^{2}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 6 \, {\left(16 \, a^{8} x^{9} - 38 \, a^{6} x^{7} + 30 \, a^{4} x^{5} - 9 \, a^{2} x^{3} + x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(64 \, a^{9} x^{10} - 204 \, a^{7} x^{8} + 234 \, a^{5} x^{6} - 115 \, a^{3} x^{4} + 21 \, a x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{2 \, {\left(a^{10} x^{8} + {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} a^{6} x^{4} - 4 \, a^{8} x^{6} + 6 \, a^{6} x^{4} - 4 \, a^{4} x^{2} + 4 \, {\left(a^{7} x^{5} - a^{5} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 6 \, {\left(a^{8} x^{6} - 2 \, a^{6} x^{4} + a^{4} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 4 \, {\left(a^{9} x^{7} - 3 \, a^{7} x^{5} + 3 \, a^{5} x^{3} - a^{3} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + a^{2}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/2*(a^8*x^10 - 3*a^6*x^8 + 3*a^4*x^6 - a^2*x^4 + (a^5*x^7 - a^3*x^5)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (3*a^6*x^8 - 5*a^4*x^6 + 2*a^2*x^4)*(a*x + 1)*(a*x - 1) + (3*a^7*x^9 - 7*a^5*x^7 + 5*a^3*x^5 - a*x^3)*sqrt(a*x + 1)*sqrt(a*x - 1) + (4*a^8*x^10 - 12*a^6*x^8 + 12*a^4*x^6 - 4*a^2*x^4 + 2*(2*a^5*x^7 - 3*a^3*x^5 + a*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 3*(4*a^6*x^8 - 8*a^4*x^6 + 5*a^2*x^4 - x^2)*(a*x + 1)*(a*x - 1) + (12*a^7*x^9 - 30*a^5*x^7 + 25*a^3*x^5 - 7*a*x^3)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^8*x^6 + (a*x + 1)^(3/2)*(a*x - 1)^(3/2)*a^5*x^3 - 3*a^6*x^4 + 3*a^4*x^2 + 3*(a^6*x^4 - a^4*x^2)*(a*x + 1)*(a*x - 1) + 3*(a^7*x^5 - 2*a^5*x^3 + a^3*x)*sqrt(a*x + 1)*sqrt(a*x - 1) - a^2)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2) + integrate(1/2*(16*a^10*x^11 - 64*a^8*x^9 + 96*a^6*x^7 - 64*a^4*x^5 + 4*(4*a^6*x^7 - 3*a^4*x^5)*(a*x + 1)^2*(a*x - 1)^2 + 16*a^2*x^3 + (64*a^7*x^8 - 100*a^5*x^6 + 42*a^3*x^4 - 3*a*x^2)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 6*(16*a^8*x^9 - 38*a^6*x^7 + 30*a^4*x^5 - 9*a^2*x^3 + x)*(a*x + 1)*(a*x - 1) + (64*a^9*x^10 - 204*a^7*x^8 + 234*a^5*x^6 - 115*a^3*x^4 + 21*a*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^10*x^8 + (a*x + 1)^2*(a*x - 1)^2*a^6*x^4 - 4*a^8*x^6 + 6*a^6*x^4 - 4*a^4*x^2 + 4*(a^7*x^5 - a^5*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 6*(a^8*x^6 - 2*a^6*x^4 + a^4*x^2)*(a*x + 1)*(a*x - 1) + 4*(a^9*x^7 - 3*a^7*x^5 + 3*a^5*x^3 - a^3*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + a^2)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
60,0,0,0,0.000000," ","integrate(x^2/arccosh(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{8} x^{9} - 3 \, a^{6} x^{7} + 3 \, a^{4} x^{5} - a^{2} x^{3} + {\left(a^{5} x^{6} - a^{3} x^{4}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + {\left(3 \, a^{6} x^{7} - 5 \, a^{4} x^{5} + 2 \, a^{2} x^{3}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(3 \, a^{7} x^{8} - 7 \, a^{5} x^{6} + 5 \, a^{3} x^{4} - a x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1} + {\left(3 \, a^{8} x^{9} - 9 \, a^{6} x^{7} + 9 \, a^{4} x^{5} - 3 \, a^{2} x^{3} + {\left(3 \, a^{5} x^{6} - 4 \, a^{3} x^{4} + a x^{2}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + {\left(9 \, a^{6} x^{7} - 17 \, a^{4} x^{5} + 10 \, a^{2} x^{3} - 2 \, x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(9 \, a^{7} x^{8} - 22 \, a^{5} x^{6} + 18 \, a^{3} x^{4} - 5 \, a x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{2 \, {\left(a^{8} x^{6} + {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} a^{5} x^{3} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} + 3 \, {\left(a^{6} x^{4} - a^{4} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 3 \, {\left(a^{7} x^{5} - 2 \, a^{5} x^{3} + a^{3} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a^{2}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}} + \int \frac{9 \, a^{10} x^{10} - 36 \, a^{8} x^{8} + 54 \, a^{6} x^{6} - 36 \, a^{4} x^{4} + {\left(9 \, a^{6} x^{6} - 4 \, a^{4} x^{4} - a^{2} x^{2}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(36 \, a^{7} x^{7} - 48 \, a^{5} x^{5} + 13 \, a^{3} x^{3} + 2 \, a x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 9 \, a^{2} x^{2} + {\left(54 \, a^{8} x^{8} - 120 \, a^{6} x^{6} + 83 \, a^{4} x^{4} - 19 \, a^{2} x^{2} + 2\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(36 \, a^{9} x^{9} - 112 \, a^{7} x^{7} + 123 \, a^{5} x^{5} - 57 \, a^{3} x^{3} + 10 \, a x\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{2 \, {\left(a^{10} x^{8} + {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} a^{6} x^{4} - 4 \, a^{8} x^{6} + 6 \, a^{6} x^{4} - 4 \, a^{4} x^{2} + 4 \, {\left(a^{7} x^{5} - a^{5} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 6 \, {\left(a^{8} x^{6} - 2 \, a^{6} x^{4} + a^{4} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 4 \, {\left(a^{9} x^{7} - 3 \, a^{7} x^{5} + 3 \, a^{5} x^{3} - a^{3} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + a^{2}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/2*(a^8*x^9 - 3*a^6*x^7 + 3*a^4*x^5 - a^2*x^3 + (a^5*x^6 - a^3*x^4)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (3*a^6*x^7 - 5*a^4*x^5 + 2*a^2*x^3)*(a*x + 1)*(a*x - 1) + (3*a^7*x^8 - 7*a^5*x^6 + 5*a^3*x^4 - a*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1) + (3*a^8*x^9 - 9*a^6*x^7 + 9*a^4*x^5 - 3*a^2*x^3 + (3*a^5*x^6 - 4*a^3*x^4 + a*x^2)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (9*a^6*x^7 - 17*a^4*x^5 + 10*a^2*x^3 - 2*x)*(a*x + 1)*(a*x - 1) + (9*a^7*x^8 - 22*a^5*x^6 + 18*a^3*x^4 - 5*a*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^8*x^6 + (a*x + 1)^(3/2)*(a*x - 1)^(3/2)*a^5*x^3 - 3*a^6*x^4 + 3*a^4*x^2 + 3*(a^6*x^4 - a^4*x^2)*(a*x + 1)*(a*x - 1) + 3*(a^7*x^5 - 2*a^5*x^3 + a^3*x)*sqrt(a*x + 1)*sqrt(a*x - 1) - a^2)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2) + integrate(1/2*(9*a^10*x^10 - 36*a^8*x^8 + 54*a^6*x^6 - 36*a^4*x^4 + (9*a^6*x^6 - 4*a^4*x^4 - a^2*x^2)*(a*x + 1)^2*(a*x - 1)^2 + (36*a^7*x^7 - 48*a^5*x^5 + 13*a^3*x^3 + 2*a*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 9*a^2*x^2 + (54*a^8*x^8 - 120*a^6*x^6 + 83*a^4*x^4 - 19*a^2*x^2 + 2)*(a*x + 1)*(a*x - 1) + (36*a^9*x^9 - 112*a^7*x^7 + 123*a^5*x^5 - 57*a^3*x^3 + 10*a*x)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^10*x^8 + (a*x + 1)^2*(a*x - 1)^2*a^6*x^4 - 4*a^8*x^6 + 6*a^6*x^4 - 4*a^4*x^2 + 4*(a^7*x^5 - a^5*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 6*(a^8*x^6 - 2*a^6*x^4 + a^4*x^2)*(a*x + 1)*(a*x - 1) + 4*(a^9*x^7 - 3*a^7*x^5 + 3*a^5*x^3 - a^3*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + a^2)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
61,0,0,0,0.000000," ","integrate(x/arccosh(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{8} x^{8} - 3 \, a^{6} x^{6} + 3 \, a^{4} x^{4} + {\left(a^{5} x^{5} - a^{3} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} - a^{2} x^{2} + {\left(3 \, a^{6} x^{6} - 5 \, a^{4} x^{4} + 2 \, a^{2} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(3 \, a^{7} x^{7} - 7 \, a^{5} x^{5} + 5 \, a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + {\left(2 \, a^{8} x^{8} - 6 \, a^{6} x^{6} + 6 \, a^{4} x^{4} + 2 \, {\left(a^{5} x^{5} - a^{3} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} - 2 \, a^{2} x^{2} + {\left(6 \, a^{6} x^{6} - 10 \, a^{4} x^{4} + 5 \, a^{2} x^{2} - 1\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(6 \, a^{7} x^{7} - 14 \, a^{5} x^{5} + 11 \, a^{3} x^{3} - 3 \, a x\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{2 \, {\left(a^{8} x^{6} + {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} a^{5} x^{3} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} + 3 \, {\left(a^{6} x^{4} - a^{4} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 3 \, {\left(a^{7} x^{5} - 2 \, a^{5} x^{3} + a^{3} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a^{2}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}} + \int \frac{4 \, a^{9} x^{9} + 4 \, {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} a^{5} x^{5} - 16 \, a^{7} x^{7} + 24 \, a^{5} x^{5} - 16 \, a^{3} x^{3} + {\left(16 \, a^{6} x^{6} - 16 \, a^{4} x^{4} + 3\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 24 \, {\left(a^{7} x^{7} - 2 \, a^{5} x^{5} + a^{3} x^{3}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(16 \, a^{8} x^{8} - 48 \, a^{6} x^{6} + 48 \, a^{4} x^{4} - 19 \, a^{2} x^{2} + 3\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 4 \, a x}{2 \, {\left(a^{9} x^{8} + {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} a^{5} x^{4} - 4 \, a^{7} x^{6} + 6 \, a^{5} x^{4} - 4 \, a^{3} x^{2} + 4 \, {\left(a^{6} x^{5} - a^{4} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 6 \, {\left(a^{7} x^{6} - 2 \, a^{5} x^{4} + a^{3} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 4 \, {\left(a^{8} x^{7} - 3 \, a^{6} x^{5} + 3 \, a^{4} x^{3} - a^{2} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/2*(a^8*x^8 - 3*a^6*x^6 + 3*a^4*x^4 + (a^5*x^5 - a^3*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) - a^2*x^2 + (3*a^6*x^6 - 5*a^4*x^4 + 2*a^2*x^2)*(a*x + 1)*(a*x - 1) + (3*a^7*x^7 - 7*a^5*x^5 + 5*a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + (2*a^8*x^8 - 6*a^6*x^6 + 6*a^4*x^4 + 2*(a^5*x^5 - a^3*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) - 2*a^2*x^2 + (6*a^6*x^6 - 10*a^4*x^4 + 5*a^2*x^2 - 1)*(a*x + 1)*(a*x - 1) + (6*a^7*x^7 - 14*a^5*x^5 + 11*a^3*x^3 - 3*a*x)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^8*x^6 + (a*x + 1)^(3/2)*(a*x - 1)^(3/2)*a^5*x^3 - 3*a^6*x^4 + 3*a^4*x^2 + 3*(a^6*x^4 - a^4*x^2)*(a*x + 1)*(a*x - 1) + 3*(a^7*x^5 - 2*a^5*x^3 + a^3*x)*sqrt(a*x + 1)*sqrt(a*x - 1) - a^2)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2) + integrate(1/2*(4*a^9*x^9 + 4*(a*x + 1)^2*(a*x - 1)^2*a^5*x^5 - 16*a^7*x^7 + 24*a^5*x^5 - 16*a^3*x^3 + (16*a^6*x^6 - 16*a^4*x^4 + 3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 24*(a^7*x^7 - 2*a^5*x^5 + a^3*x^3)*(a*x + 1)*(a*x - 1) + (16*a^8*x^8 - 48*a^6*x^6 + 48*a^4*x^4 - 19*a^2*x^2 + 3)*sqrt(a*x + 1)*sqrt(a*x - 1) + 4*a*x)/((a^9*x^8 + (a*x + 1)^2*(a*x - 1)^2*a^5*x^4 - 4*a^7*x^6 + 6*a^5*x^4 - 4*a^3*x^2 + 4*(a^6*x^5 - a^4*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 6*(a^7*x^6 - 2*a^5*x^4 + a^3*x^2)*(a*x + 1)*(a*x - 1) + 4*(a^8*x^7 - 3*a^6*x^5 + 3*a^4*x^3 - a^2*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
62,0,0,0,0.000000," ","integrate(1/arccosh(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{7} x^{7} - 3 \, a^{5} x^{5} + 3 \, a^{3} x^{3} + {\left(a^{4} x^{4} - a^{2} x^{2}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + {\left(3 \, a^{5} x^{5} - 5 \, a^{3} x^{3} + 2 \, a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(3 \, a^{6} x^{6} - 7 \, a^{4} x^{4} + 5 \, a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x + {\left(a^{7} x^{7} - 3 \, a^{5} x^{5} + 3 \, a^{3} x^{3} + {\left(a^{4} x^{4} - 1\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 3 \, {\left(a^{5} x^{5} - a^{3} x^{3}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(3 \, a^{6} x^{6} - 6 \, a^{4} x^{4} + 4 \, a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{2 \, {\left(a^{7} x^{6} + {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} a^{4} x^{3} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} + 3 \, {\left(a^{5} x^{4} - a^{3} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 3 \, {\left(a^{6} x^{5} - 2 \, a^{4} x^{3} + a^{2} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}} + \int \frac{a^{8} x^{8} - 4 \, a^{6} x^{6} + 6 \, a^{4} x^{4} + {\left(a^{4} x^{4} + 3\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(4 \, a^{5} x^{5} - 4 \, a^{3} x^{3} + 3 \, a x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} - 4 \, a^{2} x^{2} + 3 \, {\left(2 \, a^{6} x^{6} - 4 \, a^{4} x^{4} + a^{2} x^{2} + 1\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(4 \, a^{7} x^{7} - 12 \, a^{5} x^{5} + 9 \, a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 1}{2 \, {\left(a^{8} x^{8} + {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} a^{4} x^{4} - 4 \, a^{6} x^{6} + 6 \, a^{4} x^{4} + 4 \, {\left(a^{5} x^{5} - a^{3} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} - 4 \, a^{2} x^{2} + 6 \, {\left(a^{6} x^{6} - 2 \, a^{4} x^{4} + a^{2} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 4 \, {\left(a^{7} x^{7} - 3 \, a^{5} x^{5} + 3 \, a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 1\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/2*(a^7*x^7 - 3*a^5*x^5 + 3*a^3*x^3 + (a^4*x^4 - a^2*x^2)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (3*a^5*x^5 - 5*a^3*x^3 + 2*a*x)*(a*x + 1)*(a*x - 1) + (3*a^6*x^6 - 7*a^4*x^4 + 5*a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x + (a^7*x^7 - 3*a^5*x^5 + 3*a^3*x^3 + (a^4*x^4 - 1)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 3*(a^5*x^5 - a^3*x^3)*(a*x + 1)*(a*x - 1) + (3*a^6*x^6 - 6*a^4*x^4 + 4*a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^7*x^6 + (a*x + 1)^(3/2)*(a*x - 1)^(3/2)*a^4*x^3 - 3*a^5*x^4 + 3*a^3*x^2 + 3*(a^5*x^4 - a^3*x^2)*(a*x + 1)*(a*x - 1) + 3*(a^6*x^5 - 2*a^4*x^3 + a^2*x)*sqrt(a*x + 1)*sqrt(a*x - 1) - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2) + integrate(1/2*(a^8*x^8 - 4*a^6*x^6 + 6*a^4*x^4 + (a^4*x^4 + 3)*(a*x + 1)^2*(a*x - 1)^2 + (4*a^5*x^5 - 4*a^3*x^3 + 3*a*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) - 4*a^2*x^2 + 3*(2*a^6*x^6 - 4*a^4*x^4 + a^2*x^2 + 1)*(a*x + 1)*(a*x - 1) + (4*a^7*x^7 - 12*a^5*x^5 + 9*a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + 1)/((a^8*x^8 + (a*x + 1)^2*(a*x - 1)^2*a^4*x^4 - 4*a^6*x^6 + 6*a^4*x^4 + 4*(a^5*x^5 - a^3*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) - 4*a^2*x^2 + 6*(a^6*x^6 - 2*a^4*x^4 + a^2*x^2)*(a*x + 1)*(a*x - 1) + 4*(a^7*x^7 - 3*a^5*x^5 + 3*a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + 1)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
63,0,0,0,0.000000," ","integrate(1/x/arccosh(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{8} x^{8} - 3 \, a^{6} x^{6} + 3 \, a^{4} x^{4} + {\left(a^{5} x^{5} - a^{3} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} - a^{2} x^{2} + {\left(3 \, a^{6} x^{6} - 5 \, a^{4} x^{4} + 2 \, a^{2} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(3 \, a^{7} x^{7} - 7 \, a^{5} x^{5} + 5 \, a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + {\left(2 \, {\left(a^{3} x^{3} - a x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + {\left(4 \, a^{4} x^{4} - 5 \, a^{2} x^{2} + 1\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(2 \, a^{5} x^{5} - 3 \, a^{3} x^{3} + a x\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{2 \, {\left(a^{8} x^{8} + {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} a^{5} x^{5} - 3 \, a^{6} x^{6} + 3 \, a^{4} x^{4} - a^{2} x^{2} + 3 \, {\left(a^{6} x^{6} - a^{4} x^{4}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 3 \, {\left(a^{7} x^{7} - 2 \, a^{5} x^{5} + a^{3} x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}} - \int \frac{4 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(12 \, a^{5} x^{5} - 22 \, a^{3} x^{3} + 7 \, a x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 2 \, {\left(6 \, a^{6} x^{6} - 10 \, a^{4} x^{4} + 5 \, a^{2} x^{2} - 1\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(4 \, a^{7} x^{7} - 6 \, a^{5} x^{5} + 3 \, a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{2 \, {\left(a^{10} x^{11} + {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} a^{6} x^{7} - 4 \, a^{8} x^{9} + 6 \, a^{6} x^{7} - 4 \, a^{4} x^{5} + a^{2} x^{3} + 4 \, {\left(a^{7} x^{8} - a^{5} x^{6}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 6 \, {\left(a^{8} x^{9} - 2 \, a^{6} x^{7} + a^{4} x^{5}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 4 \, {\left(a^{9} x^{10} - 3 \, a^{7} x^{8} + 3 \, a^{5} x^{6} - a^{3} x^{4}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/2*(a^8*x^8 - 3*a^6*x^6 + 3*a^4*x^4 + (a^5*x^5 - a^3*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) - a^2*x^2 + (3*a^6*x^6 - 5*a^4*x^4 + 2*a^2*x^2)*(a*x + 1)*(a*x - 1) + (3*a^7*x^7 - 7*a^5*x^5 + 5*a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + (2*(a^3*x^3 - a*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (4*a^4*x^4 - 5*a^2*x^2 + 1)*(a*x + 1)*(a*x - 1) + (2*a^5*x^5 - 3*a^3*x^3 + a*x)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^8*x^8 + (a*x + 1)^(3/2)*(a*x - 1)^(3/2)*a^5*x^5 - 3*a^6*x^6 + 3*a^4*x^4 - a^2*x^2 + 3*(a^6*x^6 - a^4*x^4)*(a*x + 1)*(a*x - 1) + 3*(a^7*x^7 - 2*a^5*x^5 + a^3*x^3)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2) - integrate(1/2*(4*(a^4*x^4 - 2*a^2*x^2)*(a*x + 1)^2*(a*x - 1)^2 + (12*a^5*x^5 - 22*a^3*x^3 + 7*a*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 2*(6*a^6*x^6 - 10*a^4*x^4 + 5*a^2*x^2 - 1)*(a*x + 1)*(a*x - 1) + (4*a^7*x^7 - 6*a^5*x^5 + 3*a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^10*x^11 + (a*x + 1)^2*(a*x - 1)^2*a^6*x^7 - 4*a^8*x^9 + 6*a^6*x^7 - 4*a^4*x^5 + a^2*x^3 + 4*(a^7*x^8 - a^5*x^6)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 6*(a^8*x^9 - 2*a^6*x^7 + a^4*x^5)*(a*x + 1)*(a*x - 1) + 4*(a^9*x^10 - 3*a^7*x^8 + 3*a^5*x^6 - a^3*x^4)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
64,0,0,0,0.000000," ","integrate(1/x^2/arccosh(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{8} x^{8} - 3 \, a^{6} x^{6} + 3 \, a^{4} x^{4} + {\left(a^{5} x^{5} - a^{3} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} - a^{2} x^{2} + {\left(3 \, a^{6} x^{6} - 5 \, a^{4} x^{4} + 2 \, a^{2} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(3 \, a^{7} x^{7} - 7 \, a^{5} x^{5} + 5 \, a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} - {\left(a^{8} x^{8} - 3 \, a^{6} x^{6} + 3 \, a^{4} x^{4} + {\left(a^{5} x^{5} - 4 \, a^{3} x^{3} + 3 \, a x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} - a^{2} x^{2} + {\left(3 \, a^{6} x^{6} - 11 \, a^{4} x^{4} + 10 \, a^{2} x^{2} - 2\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(3 \, a^{7} x^{7} - 10 \, a^{5} x^{5} + 10 \, a^{3} x^{3} - 3 \, a x\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{2 \, {\left(a^{8} x^{9} + {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} a^{5} x^{6} - 3 \, a^{6} x^{7} + 3 \, a^{4} x^{5} - a^{2} x^{3} + 3 \, {\left(a^{6} x^{7} - a^{4} x^{5}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 3 \, {\left(a^{7} x^{8} - 2 \, a^{5} x^{6} + a^{3} x^{4}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}} + \int \frac{a^{10} x^{10} - 4 \, a^{8} x^{8} + 6 \, a^{6} x^{6} - 4 \, a^{4} x^{4} + {\left(a^{6} x^{6} - 12 \, a^{4} x^{4} + 15 \, a^{2} x^{2}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(4 \, a^{7} x^{7} - 40 \, a^{5} x^{5} + 57 \, a^{3} x^{3} - 18 \, a x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + a^{2} x^{2} + 3 \, {\left(2 \, a^{8} x^{8} - 16 \, a^{6} x^{6} + 25 \, a^{4} x^{4} - 13 \, a^{2} x^{2} + 2\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(4 \, a^{9} x^{9} - 24 \, a^{7} x^{7} + 39 \, a^{5} x^{5} - 25 \, a^{3} x^{3} + 6 \, a x\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{2 \, {\left(a^{10} x^{12} + {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} a^{6} x^{8} - 4 \, a^{8} x^{10} + 6 \, a^{6} x^{8} - 4 \, a^{4} x^{6} + a^{2} x^{4} + 4 \, {\left(a^{7} x^{9} - a^{5} x^{7}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 6 \, {\left(a^{8} x^{10} - 2 \, a^{6} x^{8} + a^{4} x^{6}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 4 \, {\left(a^{9} x^{11} - 3 \, a^{7} x^{9} + 3 \, a^{5} x^{7} - a^{3} x^{5}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/2*(a^8*x^8 - 3*a^6*x^6 + 3*a^4*x^4 + (a^5*x^5 - a^3*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) - a^2*x^2 + (3*a^6*x^6 - 5*a^4*x^4 + 2*a^2*x^2)*(a*x + 1)*(a*x - 1) + (3*a^7*x^7 - 7*a^5*x^5 + 5*a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) - (a^8*x^8 - 3*a^6*x^6 + 3*a^4*x^4 + (a^5*x^5 - 4*a^3*x^3 + 3*a*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) - a^2*x^2 + (3*a^6*x^6 - 11*a^4*x^4 + 10*a^2*x^2 - 2)*(a*x + 1)*(a*x - 1) + (3*a^7*x^7 - 10*a^5*x^5 + 10*a^3*x^3 - 3*a*x)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^8*x^9 + (a*x + 1)^(3/2)*(a*x - 1)^(3/2)*a^5*x^6 - 3*a^6*x^7 + 3*a^4*x^5 - a^2*x^3 + 3*(a^6*x^7 - a^4*x^5)*(a*x + 1)*(a*x - 1) + 3*(a^7*x^8 - 2*a^5*x^6 + a^3*x^4)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2) + integrate(1/2*(a^10*x^10 - 4*a^8*x^8 + 6*a^6*x^6 - 4*a^4*x^4 + (a^6*x^6 - 12*a^4*x^4 + 15*a^2*x^2)*(a*x + 1)^2*(a*x - 1)^2 + (4*a^7*x^7 - 40*a^5*x^5 + 57*a^3*x^3 - 18*a*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + a^2*x^2 + 3*(2*a^8*x^8 - 16*a^6*x^6 + 25*a^4*x^4 - 13*a^2*x^2 + 2)*(a*x + 1)*(a*x - 1) + (4*a^9*x^9 - 24*a^7*x^7 + 39*a^5*x^5 - 25*a^3*x^3 + 6*a*x)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^10*x^12 + (a*x + 1)^2*(a*x - 1)^2*a^6*x^8 - 4*a^8*x^10 + 6*a^6*x^8 - 4*a^4*x^6 + a^2*x^4 + 4*(a^7*x^9 - a^5*x^7)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 6*(a^8*x^10 - 2*a^6*x^8 + a^4*x^6)*(a*x + 1)*(a*x - 1) + 4*(a^9*x^11 - 3*a^7*x^9 + 3*a^5*x^7 - a^3*x^5)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
65,0,0,0,0.000000," ","integrate(x^4/arccosh(a*x)^4,x, algorithm=""maxima"")","-\frac{2 \, a^{13} x^{15} - 10 \, a^{11} x^{13} + 20 \, a^{9} x^{11} - 20 \, a^{7} x^{9} + 10 \, a^{5} x^{7} - 2 \, a^{3} x^{5} + 2 \, {\left(a^{8} x^{10} - a^{6} x^{8}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + 2 \, {\left(5 \, a^{9} x^{11} - 9 \, a^{7} x^{9} + 4 \, a^{5} x^{7}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 4 \, {\left(5 \, a^{10} x^{12} - 13 \, a^{8} x^{10} + 11 \, a^{6} x^{8} - 3 \, a^{4} x^{6}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 4 \, {\left(5 \, a^{11} x^{13} - 17 \, a^{9} x^{11} + 21 \, a^{7} x^{9} - 11 \, a^{5} x^{7} + 2 \, a^{3} x^{5}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(25 \, a^{13} x^{15} - 125 \, a^{11} x^{13} + 250 \, a^{9} x^{11} - 250 \, a^{7} x^{9} + 125 \, a^{5} x^{7} - 25 \, a^{3} x^{5} + {\left(25 \, a^{8} x^{10} - 49 \, a^{6} x^{8} + 27 \, a^{4} x^{6} - 3 \, a^{2} x^{4}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + {\left(125 \, a^{9} x^{11} - 321 \, a^{7} x^{9} + 286 \, a^{5} x^{7} - 102 \, a^{3} x^{5} + 12 \, a x^{3}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(250 \, a^{10} x^{12} - 794 \, a^{8} x^{10} + 946 \, a^{6} x^{8} - 519 \, a^{4} x^{6} + 129 \, a^{2} x^{4} - 12 \, x^{2}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 2 \, {\left(125 \, a^{11} x^{13} - 473 \, a^{9} x^{11} + 696 \, a^{7} x^{9} - 497 \, a^{5} x^{7} + 173 \, a^{3} x^{5} - 24 \, a x^{3}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(125 \, a^{12} x^{14} - 549 \, a^{10} x^{12} + 955 \, a^{8} x^{10} - 824 \, a^{6} x^{8} + 354 \, a^{4} x^{6} - 61 \, a^{2} x^{4}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2} + 2 \, {\left(5 \, a^{12} x^{14} - 21 \, a^{10} x^{12} + 34 \, a^{8} x^{10} - 26 \, a^{6} x^{8} + 9 \, a^{4} x^{6} - a^{2} x^{4}\right)} \sqrt{a x + 1} \sqrt{a x - 1} + {\left(5 \, a^{13} x^{15} - 25 \, a^{11} x^{13} + 50 \, a^{9} x^{11} - 50 \, a^{7} x^{9} + 25 \, a^{5} x^{7} - 5 \, a^{3} x^{5} + {\left(5 \, a^{8} x^{10} - 8 \, a^{6} x^{8} + 3 \, a^{4} x^{6}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + {\left(25 \, a^{9} x^{11} - 57 \, a^{7} x^{9} + 42 \, a^{5} x^{7} - 10 \, a^{3} x^{5}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(50 \, a^{10} x^{12} - 148 \, a^{8} x^{10} + 158 \, a^{6} x^{8} - 71 \, a^{4} x^{6} + 11 \, a^{2} x^{4}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 2 \, {\left(25 \, a^{11} x^{13} - 91 \, a^{9} x^{11} + 126 \, a^{7} x^{9} - 81 \, a^{5} x^{7} + 23 \, a^{3} x^{5} - 2 \, a x^{3}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(25 \, a^{12} x^{14} - 108 \, a^{10} x^{12} + 183 \, a^{8} x^{10} - 151 \, a^{6} x^{8} + 60 \, a^{4} x^{6} - 9 \, a^{2} x^{4}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{6 \, {\left(a^{13} x^{10} - 5 \, a^{11} x^{8} + {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} a^{8} x^{5} + 10 \, a^{9} x^{6} - 10 \, a^{7} x^{4} + 5 \, a^{5} x^{2} + 5 \, {\left(a^{9} x^{6} - a^{7} x^{4}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 10 \, {\left(a^{10} x^{7} - 2 \, a^{8} x^{5} + a^{6} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 10 \, {\left(a^{11} x^{8} - 3 \, a^{9} x^{6} + 3 \, a^{7} x^{4} - a^{5} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} - a^{3} + 5 \, {\left(a^{12} x^{9} - 4 \, a^{10} x^{7} + 6 \, a^{8} x^{5} - 4 \, a^{6} x^{3} + a^{4} x\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}} + \int \frac{125 \, a^{15} x^{16} - 750 \, a^{13} x^{14} + 1875 \, a^{11} x^{12} - 2500 \, a^{9} x^{10} + 1875 \, a^{7} x^{8} - 750 \, a^{5} x^{6} + {\left(125 \, a^{9} x^{10} - 147 \, a^{7} x^{8} + 27 \, a^{5} x^{6} + 3 \, a^{3} x^{4}\right)} {\left(a x + 1\right)}^{3} {\left(a x - 1\right)}^{3} + 125 \, a^{3} x^{4} + {\left(750 \, a^{10} x^{11} - 1485 \, a^{8} x^{9} + 901 \, a^{6} x^{7} - 147 \, a^{4} x^{5} - 12 \, a^{2} x^{3}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + {\left(1875 \, a^{11} x^{12} - 5220 \, a^{9} x^{10} + 5209 \, a^{7} x^{8} - 2185 \, a^{5} x^{6} + 321 \, a^{3} x^{4}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(2500 \, a^{12} x^{13} - 8970 \, a^{10} x^{11} + 12366 \, a^{8} x^{9} - 8143 \, a^{6} x^{7} + 2583 \, a^{4} x^{5} - 360 \, a^{2} x^{3} + 24 \, x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + {\left(1875 \, a^{13} x^{14} - 8235 \, a^{11} x^{12} + 14449 \, a^{9} x^{10} - 12834 \, a^{7} x^{8} + 6030 \, a^{5} x^{6} - 1429 \, a^{3} x^{4} + 144 \, a x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(750 \, a^{14} x^{15} - 3897 \, a^{12} x^{13} + 8293 \, a^{10} x^{11} - 9226 \, a^{8} x^{9} + 5655 \, a^{6} x^{7} - 1819 \, a^{4} x^{5} + 244 \, a^{2} x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{6 \, {\left(a^{15} x^{12} - 6 \, a^{13} x^{10} + {\left(a x + 1\right)}^{3} {\left(a x - 1\right)}^{3} a^{9} x^{6} + 15 \, a^{11} x^{8} - 20 \, a^{9} x^{6} + 15 \, a^{7} x^{4} - 6 \, a^{5} x^{2} + 6 \, {\left(a^{10} x^{7} - a^{8} x^{5}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + 15 \, {\left(a^{11} x^{8} - 2 \, a^{9} x^{6} + a^{7} x^{4}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 20 \, {\left(a^{12} x^{9} - 3 \, a^{10} x^{7} + 3 \, a^{8} x^{5} - a^{6} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 15 \, {\left(a^{13} x^{10} - 4 \, a^{11} x^{8} + 6 \, a^{9} x^{6} - 4 \, a^{7} x^{4} + a^{5} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + a^{3} + 6 \, {\left(a^{14} x^{11} - 5 \, a^{12} x^{9} + 10 \, a^{10} x^{7} - 10 \, a^{8} x^{5} + 5 \, a^{6} x^{3} - a^{4} x\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/6*(2*a^13*x^15 - 10*a^11*x^13 + 20*a^9*x^11 - 20*a^7*x^9 + 10*a^5*x^7 - 2*a^3*x^5 + 2*(a^8*x^10 - a^6*x^8)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 2*(5*a^9*x^11 - 9*a^7*x^9 + 4*a^5*x^7)*(a*x + 1)^2*(a*x - 1)^2 + 4*(5*a^10*x^12 - 13*a^8*x^10 + 11*a^6*x^8 - 3*a^4*x^6)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 4*(5*a^11*x^13 - 17*a^9*x^11 + 21*a^7*x^9 - 11*a^5*x^7 + 2*a^3*x^5)*(a*x + 1)*(a*x - 1) + (25*a^13*x^15 - 125*a^11*x^13 + 250*a^9*x^11 - 250*a^7*x^9 + 125*a^5*x^7 - 25*a^3*x^5 + (25*a^8*x^10 - 49*a^6*x^8 + 27*a^4*x^6 - 3*a^2*x^4)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + (125*a^9*x^11 - 321*a^7*x^9 + 286*a^5*x^7 - 102*a^3*x^5 + 12*a*x^3)*(a*x + 1)^2*(a*x - 1)^2 + (250*a^10*x^12 - 794*a^8*x^10 + 946*a^6*x^8 - 519*a^4*x^6 + 129*a^2*x^4 - 12*x^2)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 2*(125*a^11*x^13 - 473*a^9*x^11 + 696*a^7*x^9 - 497*a^5*x^7 + 173*a^3*x^5 - 24*a*x^3)*(a*x + 1)*(a*x - 1) + (125*a^12*x^14 - 549*a^10*x^12 + 955*a^8*x^10 - 824*a^6*x^8 + 354*a^4*x^6 - 61*a^2*x^4)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2 + 2*(5*a^12*x^14 - 21*a^10*x^12 + 34*a^8*x^10 - 26*a^6*x^8 + 9*a^4*x^6 - a^2*x^4)*sqrt(a*x + 1)*sqrt(a*x - 1) + (5*a^13*x^15 - 25*a^11*x^13 + 50*a^9*x^11 - 50*a^7*x^9 + 25*a^5*x^7 - 5*a^3*x^5 + (5*a^8*x^10 - 8*a^6*x^8 + 3*a^4*x^6)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + (25*a^9*x^11 - 57*a^7*x^9 + 42*a^5*x^7 - 10*a^3*x^5)*(a*x + 1)^2*(a*x - 1)^2 + (50*a^10*x^12 - 148*a^8*x^10 + 158*a^6*x^8 - 71*a^4*x^6 + 11*a^2*x^4)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 2*(25*a^11*x^13 - 91*a^9*x^11 + 126*a^7*x^9 - 81*a^5*x^7 + 23*a^3*x^5 - 2*a*x^3)*(a*x + 1)*(a*x - 1) + (25*a^12*x^14 - 108*a^10*x^12 + 183*a^8*x^10 - 151*a^6*x^8 + 60*a^4*x^6 - 9*a^2*x^4)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^13*x^10 - 5*a^11*x^8 + (a*x + 1)^(5/2)*(a*x - 1)^(5/2)*a^8*x^5 + 10*a^9*x^6 - 10*a^7*x^4 + 5*a^5*x^2 + 5*(a^9*x^6 - a^7*x^4)*(a*x + 1)^2*(a*x - 1)^2 + 10*(a^10*x^7 - 2*a^8*x^5 + a^6*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 10*(a^11*x^8 - 3*a^9*x^6 + 3*a^7*x^4 - a^5*x^2)*(a*x + 1)*(a*x - 1) - a^3 + 5*(a^12*x^9 - 4*a^10*x^7 + 6*a^8*x^5 - 4*a^6*x^3 + a^4*x)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3) + integrate(1/6*(125*a^15*x^16 - 750*a^13*x^14 + 1875*a^11*x^12 - 2500*a^9*x^10 + 1875*a^7*x^8 - 750*a^5*x^6 + (125*a^9*x^10 - 147*a^7*x^8 + 27*a^5*x^6 + 3*a^3*x^4)*(a*x + 1)^3*(a*x - 1)^3 + 125*a^3*x^4 + (750*a^10*x^11 - 1485*a^8*x^9 + 901*a^6*x^7 - 147*a^4*x^5 - 12*a^2*x^3)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + (1875*a^11*x^12 - 5220*a^9*x^10 + 5209*a^7*x^8 - 2185*a^5*x^6 + 321*a^3*x^4)*(a*x + 1)^2*(a*x - 1)^2 + (2500*a^12*x^13 - 8970*a^10*x^11 + 12366*a^8*x^9 - 8143*a^6*x^7 + 2583*a^4*x^5 - 360*a^2*x^3 + 24*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (1875*a^13*x^14 - 8235*a^11*x^12 + 14449*a^9*x^10 - 12834*a^7*x^8 + 6030*a^5*x^6 - 1429*a^3*x^4 + 144*a*x^2)*(a*x + 1)*(a*x - 1) + (750*a^14*x^15 - 3897*a^12*x^13 + 8293*a^10*x^11 - 9226*a^8*x^9 + 5655*a^6*x^7 - 1819*a^4*x^5 + 244*a^2*x^3)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^15*x^12 - 6*a^13*x^10 + (a*x + 1)^3*(a*x - 1)^3*a^9*x^6 + 15*a^11*x^8 - 20*a^9*x^6 + 15*a^7*x^4 - 6*a^5*x^2 + 6*(a^10*x^7 - a^8*x^5)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 15*(a^11*x^8 - 2*a^9*x^6 + a^7*x^4)*(a*x + 1)^2*(a*x - 1)^2 + 20*(a^12*x^9 - 3*a^10*x^7 + 3*a^8*x^5 - a^6*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 15*(a^13*x^10 - 4*a^11*x^8 + 6*a^9*x^6 - 4*a^7*x^4 + a^5*x^2)*(a*x + 1)*(a*x - 1) + a^3 + 6*(a^14*x^11 - 5*a^12*x^9 + 10*a^10*x^7 - 10*a^8*x^5 + 5*a^6*x^3 - a^4*x)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
66,0,0,0,0.000000," ","integrate(x^3/arccosh(a*x)^4,x, algorithm=""maxima"")","-\frac{2 \, a^{13} x^{14} - 10 \, a^{11} x^{12} + 20 \, a^{9} x^{10} - 20 \, a^{7} x^{8} + 10 \, a^{5} x^{6} - 2 \, a^{3} x^{4} + 2 \, {\left(a^{8} x^{9} - a^{6} x^{7}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + 2 \, {\left(5 \, a^{9} x^{10} - 9 \, a^{7} x^{8} + 4 \, a^{5} x^{6}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 4 \, {\left(5 \, a^{10} x^{11} - 13 \, a^{8} x^{9} + 11 \, a^{6} x^{7} - 3 \, a^{4} x^{5}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 4 \, {\left(5 \, a^{11} x^{12} - 17 \, a^{9} x^{10} + 21 \, a^{7} x^{8} - 11 \, a^{5} x^{6} + 2 \, a^{3} x^{4}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(16 \, a^{13} x^{14} - 80 \, a^{11} x^{12} + 160 \, a^{9} x^{10} - 160 \, a^{7} x^{8} + 80 \, a^{5} x^{6} - 16 \, a^{3} x^{4} + 4 \, {\left(4 \, a^{8} x^{9} - 7 \, a^{6} x^{7} + 3 \, a^{4} x^{5}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + {\left(80 \, a^{9} x^{10} - 192 \, a^{7} x^{8} + 154 \, a^{5} x^{6} - 45 \, a^{3} x^{4} + 3 \, a x^{2}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(160 \, a^{10} x^{11} - 488 \, a^{8} x^{9} + 550 \, a^{6} x^{7} - 279 \, a^{4} x^{5} + 63 \, a^{2} x^{3} - 6 \, x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + {\left(160 \, a^{11} x^{12} - 592 \, a^{9} x^{10} + 846 \, a^{7} x^{8} - 583 \, a^{5} x^{6} + 196 \, a^{3} x^{4} - 27 \, a x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(80 \, a^{12} x^{13} - 348 \, a^{10} x^{11} + 598 \, a^{8} x^{9} - 509 \, a^{6} x^{7} + 216 \, a^{4} x^{5} - 37 \, a^{2} x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2} + 2 \, {\left(5 \, a^{12} x^{13} - 21 \, a^{10} x^{11} + 34 \, a^{8} x^{9} - 26 \, a^{6} x^{7} + 9 \, a^{4} x^{5} - a^{2} x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1} + {\left(4 \, a^{13} x^{14} - 20 \, a^{11} x^{12} + 40 \, a^{9} x^{10} - 40 \, a^{7} x^{8} + 20 \, a^{5} x^{6} - 4 \, a^{3} x^{4} + 2 \, {\left(2 \, a^{8} x^{9} - 3 \, a^{6} x^{7} + a^{4} x^{5}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + {\left(20 \, a^{9} x^{10} - 44 \, a^{7} x^{8} + 31 \, a^{5} x^{6} - 7 \, a^{3} x^{4}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(40 \, a^{10} x^{11} - 116 \, a^{8} x^{9} + 121 \, a^{6} x^{7} - 53 \, a^{4} x^{5} + 8 \, a^{2} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + {\left(40 \, a^{11} x^{12} - 144 \, a^{9} x^{10} + 197 \, a^{7} x^{8} - 125 \, a^{5} x^{6} + 35 \, a^{3} x^{4} - 3 \, a x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(20 \, a^{12} x^{13} - 86 \, a^{10} x^{11} + 145 \, a^{8} x^{9} - 119 \, a^{6} x^{7} + 47 \, a^{4} x^{5} - 7 \, a^{2} x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{6 \, {\left(a^{13} x^{10} - 5 \, a^{11} x^{8} + {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} a^{8} x^{5} + 10 \, a^{9} x^{6} - 10 \, a^{7} x^{4} + 5 \, a^{5} x^{2} + 5 \, {\left(a^{9} x^{6} - a^{7} x^{4}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 10 \, {\left(a^{10} x^{7} - 2 \, a^{8} x^{5} + a^{6} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 10 \, {\left(a^{11} x^{8} - 3 \, a^{9} x^{6} + 3 \, a^{7} x^{4} - a^{5} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} - a^{3} + 5 \, {\left(a^{12} x^{9} - 4 \, a^{10} x^{7} + 6 \, a^{8} x^{5} - 4 \, a^{6} x^{3} + a^{4} x\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}} + \int \frac{64 \, a^{15} x^{15} - 384 \, a^{13} x^{13} + 960 \, a^{11} x^{11} - 1280 \, a^{9} x^{9} + 960 \, a^{7} x^{7} - 384 \, a^{5} x^{5} + 8 \, {\left(8 \, a^{9} x^{9} - 7 \, a^{7} x^{7}\right)} {\left(a x + 1\right)}^{3} {\left(a x - 1\right)}^{3} + {\left(384 \, a^{10} x^{10} - 664 \, a^{8} x^{8} + 308 \, a^{6} x^{6} - 12 \, a^{4} x^{4} - 9 \, a^{2} x^{2}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + 64 \, a^{3} x^{3} + 2 \, {\left(480 \, a^{11} x^{11} - 1240 \, a^{9} x^{9} + 1096 \, a^{7} x^{7} - 360 \, a^{5} x^{5} + 15 \, a^{3} x^{3} + 9 \, a x\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 2 \, {\left(640 \, a^{12} x^{12} - 2200 \, a^{10} x^{10} + 2844 \, a^{8} x^{8} - 1684 \, a^{6} x^{6} + 433 \, a^{4} x^{4} - 36 \, a^{2} x^{2} + 3\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 2 \, {\left(480 \, a^{13} x^{13} - 2060 \, a^{11} x^{11} + 3496 \, a^{9} x^{9} - 2952 \, a^{7} x^{7} + 1283 \, a^{5} x^{5} - 274 \, a^{3} x^{3} + 27 \, a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(384 \, a^{14} x^{14} - 1976 \, a^{12} x^{12} + 4148 \, a^{10} x^{10} - 4524 \, a^{8} x^{8} + 2699 \, a^{6} x^{6} - 842 \, a^{4} x^{4} + 111 \, a^{2} x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{6 \, {\left(a^{15} x^{12} - 6 \, a^{13} x^{10} + {\left(a x + 1\right)}^{3} {\left(a x - 1\right)}^{3} a^{9} x^{6} + 15 \, a^{11} x^{8} - 20 \, a^{9} x^{6} + 15 \, a^{7} x^{4} - 6 \, a^{5} x^{2} + 6 \, {\left(a^{10} x^{7} - a^{8} x^{5}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + 15 \, {\left(a^{11} x^{8} - 2 \, a^{9} x^{6} + a^{7} x^{4}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 20 \, {\left(a^{12} x^{9} - 3 \, a^{10} x^{7} + 3 \, a^{8} x^{5} - a^{6} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 15 \, {\left(a^{13} x^{10} - 4 \, a^{11} x^{8} + 6 \, a^{9} x^{6} - 4 \, a^{7} x^{4} + a^{5} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + a^{3} + 6 \, {\left(a^{14} x^{11} - 5 \, a^{12} x^{9} + 10 \, a^{10} x^{7} - 10 \, a^{8} x^{5} + 5 \, a^{6} x^{3} - a^{4} x\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/6*(2*a^13*x^14 - 10*a^11*x^12 + 20*a^9*x^10 - 20*a^7*x^8 + 10*a^5*x^6 - 2*a^3*x^4 + 2*(a^8*x^9 - a^6*x^7)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 2*(5*a^9*x^10 - 9*a^7*x^8 + 4*a^5*x^6)*(a*x + 1)^2*(a*x - 1)^2 + 4*(5*a^10*x^11 - 13*a^8*x^9 + 11*a^6*x^7 - 3*a^4*x^5)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 4*(5*a^11*x^12 - 17*a^9*x^10 + 21*a^7*x^8 - 11*a^5*x^6 + 2*a^3*x^4)*(a*x + 1)*(a*x - 1) + (16*a^13*x^14 - 80*a^11*x^12 + 160*a^9*x^10 - 160*a^7*x^8 + 80*a^5*x^6 - 16*a^3*x^4 + 4*(4*a^8*x^9 - 7*a^6*x^7 + 3*a^4*x^5)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + (80*a^9*x^10 - 192*a^7*x^8 + 154*a^5*x^6 - 45*a^3*x^4 + 3*a*x^2)*(a*x + 1)^2*(a*x - 1)^2 + (160*a^10*x^11 - 488*a^8*x^9 + 550*a^6*x^7 - 279*a^4*x^5 + 63*a^2*x^3 - 6*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (160*a^11*x^12 - 592*a^9*x^10 + 846*a^7*x^8 - 583*a^5*x^6 + 196*a^3*x^4 - 27*a*x^2)*(a*x + 1)*(a*x - 1) + (80*a^12*x^13 - 348*a^10*x^11 + 598*a^8*x^9 - 509*a^6*x^7 + 216*a^4*x^5 - 37*a^2*x^3)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2 + 2*(5*a^12*x^13 - 21*a^10*x^11 + 34*a^8*x^9 - 26*a^6*x^7 + 9*a^4*x^5 - a^2*x^3)*sqrt(a*x + 1)*sqrt(a*x - 1) + (4*a^13*x^14 - 20*a^11*x^12 + 40*a^9*x^10 - 40*a^7*x^8 + 20*a^5*x^6 - 4*a^3*x^4 + 2*(2*a^8*x^9 - 3*a^6*x^7 + a^4*x^5)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + (20*a^9*x^10 - 44*a^7*x^8 + 31*a^5*x^6 - 7*a^3*x^4)*(a*x + 1)^2*(a*x - 1)^2 + (40*a^10*x^11 - 116*a^8*x^9 + 121*a^6*x^7 - 53*a^4*x^5 + 8*a^2*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (40*a^11*x^12 - 144*a^9*x^10 + 197*a^7*x^8 - 125*a^5*x^6 + 35*a^3*x^4 - 3*a*x^2)*(a*x + 1)*(a*x - 1) + (20*a^12*x^13 - 86*a^10*x^11 + 145*a^8*x^9 - 119*a^6*x^7 + 47*a^4*x^5 - 7*a^2*x^3)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^13*x^10 - 5*a^11*x^8 + (a*x + 1)^(5/2)*(a*x - 1)^(5/2)*a^8*x^5 + 10*a^9*x^6 - 10*a^7*x^4 + 5*a^5*x^2 + 5*(a^9*x^6 - a^7*x^4)*(a*x + 1)^2*(a*x - 1)^2 + 10*(a^10*x^7 - 2*a^8*x^5 + a^6*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 10*(a^11*x^8 - 3*a^9*x^6 + 3*a^7*x^4 - a^5*x^2)*(a*x + 1)*(a*x - 1) - a^3 + 5*(a^12*x^9 - 4*a^10*x^7 + 6*a^8*x^5 - 4*a^6*x^3 + a^4*x)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3) + integrate(1/6*(64*a^15*x^15 - 384*a^13*x^13 + 960*a^11*x^11 - 1280*a^9*x^9 + 960*a^7*x^7 - 384*a^5*x^5 + 8*(8*a^9*x^9 - 7*a^7*x^7)*(a*x + 1)^3*(a*x - 1)^3 + (384*a^10*x^10 - 664*a^8*x^8 + 308*a^6*x^6 - 12*a^4*x^4 - 9*a^2*x^2)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 64*a^3*x^3 + 2*(480*a^11*x^11 - 1240*a^9*x^9 + 1096*a^7*x^7 - 360*a^5*x^5 + 15*a^3*x^3 + 9*a*x)*(a*x + 1)^2*(a*x - 1)^2 + 2*(640*a^12*x^12 - 2200*a^10*x^10 + 2844*a^8*x^8 - 1684*a^6*x^6 + 433*a^4*x^4 - 36*a^2*x^2 + 3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 2*(480*a^13*x^13 - 2060*a^11*x^11 + 3496*a^9*x^9 - 2952*a^7*x^7 + 1283*a^5*x^5 - 274*a^3*x^3 + 27*a*x)*(a*x + 1)*(a*x - 1) + (384*a^14*x^14 - 1976*a^12*x^12 + 4148*a^10*x^10 - 4524*a^8*x^8 + 2699*a^6*x^6 - 842*a^4*x^4 + 111*a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^15*x^12 - 6*a^13*x^10 + (a*x + 1)^3*(a*x - 1)^3*a^9*x^6 + 15*a^11*x^8 - 20*a^9*x^6 + 15*a^7*x^4 - 6*a^5*x^2 + 6*(a^10*x^7 - a^8*x^5)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 15*(a^11*x^8 - 2*a^9*x^6 + a^7*x^4)*(a*x + 1)^2*(a*x - 1)^2 + 20*(a^12*x^9 - 3*a^10*x^7 + 3*a^8*x^5 - a^6*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 15*(a^13*x^10 - 4*a^11*x^8 + 6*a^9*x^6 - 4*a^7*x^4 + a^5*x^2)*(a*x + 1)*(a*x - 1) + a^3 + 6*(a^14*x^11 - 5*a^12*x^9 + 10*a^10*x^7 - 10*a^8*x^5 + 5*a^6*x^3 - a^4*x)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
67,0,0,0,0.000000," ","integrate(x^2/arccosh(a*x)^4,x, algorithm=""maxima"")","-\frac{2 \, a^{13} x^{13} - 10 \, a^{11} x^{11} + 20 \, a^{9} x^{9} - 20 \, a^{7} x^{7} + 10 \, a^{5} x^{5} + 2 \, {\left(a^{8} x^{8} - a^{6} x^{6}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} - 2 \, a^{3} x^{3} + 2 \, {\left(5 \, a^{9} x^{9} - 9 \, a^{7} x^{7} + 4 \, a^{5} x^{5}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 4 \, {\left(5 \, a^{10} x^{10} - 13 \, a^{8} x^{8} + 11 \, a^{6} x^{6} - 3 \, a^{4} x^{4}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 4 \, {\left(5 \, a^{11} x^{11} - 17 \, a^{9} x^{9} + 21 \, a^{7} x^{7} - 11 \, a^{5} x^{5} + 2 \, a^{3} x^{3}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(9 \, a^{13} x^{13} - 45 \, a^{11} x^{11} + 90 \, a^{9} x^{9} - 90 \, a^{7} x^{7} + 45 \, a^{5} x^{5} + {\left(9 \, a^{8} x^{8} - 13 \, a^{6} x^{6} + 3 \, a^{4} x^{4} + a^{2} x^{2}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} - 9 \, a^{3} x^{3} + {\left(45 \, a^{9} x^{9} - 97 \, a^{7} x^{7} + 64 \, a^{5} x^{5} - 10 \, a^{3} x^{3} - 2 \, a x\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(90 \, a^{10} x^{10} - 258 \, a^{8} x^{8} + 264 \, a^{6} x^{6} - 113 \, a^{4} x^{4} + 19 \, a^{2} x^{2} - 2\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 2 \, {\left(45 \, a^{11} x^{11} - 161 \, a^{9} x^{9} + 219 \, a^{7} x^{7} - 141 \, a^{5} x^{5} + 44 \, a^{3} x^{3} - 6 \, a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(45 \, a^{12} x^{12} - 193 \, a^{10} x^{10} + 325 \, a^{8} x^{8} - 270 \, a^{6} x^{6} + 112 \, a^{4} x^{4} - 19 \, a^{2} x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2} + 2 \, {\left(5 \, a^{12} x^{12} - 21 \, a^{10} x^{10} + 34 \, a^{8} x^{8} - 26 \, a^{6} x^{6} + 9 \, a^{4} x^{4} - a^{2} x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1} + {\left(3 \, a^{13} x^{13} - 15 \, a^{11} x^{11} + 30 \, a^{9} x^{9} - 30 \, a^{7} x^{7} + 15 \, a^{5} x^{5} + {\left(3 \, a^{8} x^{8} - 4 \, a^{6} x^{6} + a^{4} x^{4}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} - 3 \, a^{3} x^{3} + {\left(15 \, a^{9} x^{9} - 31 \, a^{7} x^{7} + 20 \, a^{5} x^{5} - 4 \, a^{3} x^{3}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(30 \, a^{10} x^{10} - 84 \, a^{8} x^{8} + 84 \, a^{6} x^{6} - 35 \, a^{4} x^{4} + 5 \, a^{2} x^{2}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 2 \, {\left(15 \, a^{11} x^{11} - 53 \, a^{9} x^{9} + 71 \, a^{7} x^{7} - 44 \, a^{5} x^{5} + 12 \, a^{3} x^{3} - a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(15 \, a^{12} x^{12} - 64 \, a^{10} x^{10} + 107 \, a^{8} x^{8} - 87 \, a^{6} x^{6} + 34 \, a^{4} x^{4} - 5 \, a^{2} x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{6 \, {\left(a^{13} x^{10} - 5 \, a^{11} x^{8} + {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} a^{8} x^{5} + 10 \, a^{9} x^{6} - 10 \, a^{7} x^{4} + 5 \, a^{5} x^{2} + 5 \, {\left(a^{9} x^{6} - a^{7} x^{4}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 10 \, {\left(a^{10} x^{7} - 2 \, a^{8} x^{5} + a^{6} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 10 \, {\left(a^{11} x^{8} - 3 \, a^{9} x^{6} + 3 \, a^{7} x^{4} - a^{5} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} - a^{3} + 5 \, {\left(a^{12} x^{9} - 4 \, a^{10} x^{7} + 6 \, a^{8} x^{5} - 4 \, a^{6} x^{3} + a^{4} x\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}} + \int \frac{27 \, a^{14} x^{14} - 162 \, a^{12} x^{12} + 405 \, a^{10} x^{10} - 540 \, a^{8} x^{8} + 405 \, a^{6} x^{6} - 162 \, a^{4} x^{4} + {\left(27 \, a^{8} x^{8} - 13 \, a^{6} x^{6} - 3 \, a^{4} x^{4} - 3 \, a^{2} x^{2}\right)} {\left(a x + 1\right)}^{3} {\left(a x - 1\right)}^{3} + {\left(162 \, a^{9} x^{9} - 227 \, a^{7} x^{7} + 63 \, a^{5} x^{5} + 3 \, a^{3} x^{3} + 6 \, a x\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + {\left(405 \, a^{10} x^{10} - 940 \, a^{8} x^{8} + 687 \, a^{6} x^{6} - 143 \, a^{4} x^{4} - 21 \, a^{2} x^{2} + 12\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(540 \, a^{11} x^{11} - 1750 \, a^{9} x^{9} + 2058 \, a^{7} x^{7} - 1017 \, a^{5} x^{5} + 145 \, a^{3} x^{3} + 24 \, a x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 27 \, a^{2} x^{2} + {\left(405 \, a^{12} x^{12} - 1685 \, a^{10} x^{10} + 2727 \, a^{8} x^{8} - 2118 \, a^{6} x^{6} + 782 \, a^{4} x^{4} - 123 \, a^{2} x^{2} + 12\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(162 \, a^{13} x^{13} - 823 \, a^{11} x^{11} + 1695 \, a^{9} x^{9} - 1790 \, a^{7} x^{7} + 1015 \, a^{5} x^{5} - 297 \, a^{3} x^{3} + 38 \, a x\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{6 \, {\left(a^{14} x^{12} - 6 \, a^{12} x^{10} + {\left(a x + 1\right)}^{3} {\left(a x - 1\right)}^{3} a^{8} x^{6} + 15 \, a^{10} x^{8} - 20 \, a^{8} x^{6} + 15 \, a^{6} x^{4} + 6 \, {\left(a^{9} x^{7} - a^{7} x^{5}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} - 6 \, a^{4} x^{2} + 15 \, {\left(a^{10} x^{8} - 2 \, a^{8} x^{6} + a^{6} x^{4}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 20 \, {\left(a^{11} x^{9} - 3 \, a^{9} x^{7} + 3 \, a^{7} x^{5} - a^{5} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 15 \, {\left(a^{12} x^{10} - 4 \, a^{10} x^{8} + 6 \, a^{8} x^{6} - 4 \, a^{6} x^{4} + a^{4} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 6 \, {\left(a^{13} x^{11} - 5 \, a^{11} x^{9} + 10 \, a^{9} x^{7} - 10 \, a^{7} x^{5} + 5 \, a^{5} x^{3} - a^{3} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + a^{2}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/6*(2*a^13*x^13 - 10*a^11*x^11 + 20*a^9*x^9 - 20*a^7*x^7 + 10*a^5*x^5 + 2*(a^8*x^8 - a^6*x^6)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) - 2*a^3*x^3 + 2*(5*a^9*x^9 - 9*a^7*x^7 + 4*a^5*x^5)*(a*x + 1)^2*(a*x - 1)^2 + 4*(5*a^10*x^10 - 13*a^8*x^8 + 11*a^6*x^6 - 3*a^4*x^4)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 4*(5*a^11*x^11 - 17*a^9*x^9 + 21*a^7*x^7 - 11*a^5*x^5 + 2*a^3*x^3)*(a*x + 1)*(a*x - 1) + (9*a^13*x^13 - 45*a^11*x^11 + 90*a^9*x^9 - 90*a^7*x^7 + 45*a^5*x^5 + (9*a^8*x^8 - 13*a^6*x^6 + 3*a^4*x^4 + a^2*x^2)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) - 9*a^3*x^3 + (45*a^9*x^9 - 97*a^7*x^7 + 64*a^5*x^5 - 10*a^3*x^3 - 2*a*x)*(a*x + 1)^2*(a*x - 1)^2 + (90*a^10*x^10 - 258*a^8*x^8 + 264*a^6*x^6 - 113*a^4*x^4 + 19*a^2*x^2 - 2)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 2*(45*a^11*x^11 - 161*a^9*x^9 + 219*a^7*x^7 - 141*a^5*x^5 + 44*a^3*x^3 - 6*a*x)*(a*x + 1)*(a*x - 1) + (45*a^12*x^12 - 193*a^10*x^10 + 325*a^8*x^8 - 270*a^6*x^6 + 112*a^4*x^4 - 19*a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2 + 2*(5*a^12*x^12 - 21*a^10*x^10 + 34*a^8*x^8 - 26*a^6*x^6 + 9*a^4*x^4 - a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1) + (3*a^13*x^13 - 15*a^11*x^11 + 30*a^9*x^9 - 30*a^7*x^7 + 15*a^5*x^5 + (3*a^8*x^8 - 4*a^6*x^6 + a^4*x^4)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) - 3*a^3*x^3 + (15*a^9*x^9 - 31*a^7*x^7 + 20*a^5*x^5 - 4*a^3*x^3)*(a*x + 1)^2*(a*x - 1)^2 + (30*a^10*x^10 - 84*a^8*x^8 + 84*a^6*x^6 - 35*a^4*x^4 + 5*a^2*x^2)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 2*(15*a^11*x^11 - 53*a^9*x^9 + 71*a^7*x^7 - 44*a^5*x^5 + 12*a^3*x^3 - a*x)*(a*x + 1)*(a*x - 1) + (15*a^12*x^12 - 64*a^10*x^10 + 107*a^8*x^8 - 87*a^6*x^6 + 34*a^4*x^4 - 5*a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^13*x^10 - 5*a^11*x^8 + (a*x + 1)^(5/2)*(a*x - 1)^(5/2)*a^8*x^5 + 10*a^9*x^6 - 10*a^7*x^4 + 5*a^5*x^2 + 5*(a^9*x^6 - a^7*x^4)*(a*x + 1)^2*(a*x - 1)^2 + 10*(a^10*x^7 - 2*a^8*x^5 + a^6*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 10*(a^11*x^8 - 3*a^9*x^6 + 3*a^7*x^4 - a^5*x^2)*(a*x + 1)*(a*x - 1) - a^3 + 5*(a^12*x^9 - 4*a^10*x^7 + 6*a^8*x^5 - 4*a^6*x^3 + a^4*x)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3) + integrate(1/6*(27*a^14*x^14 - 162*a^12*x^12 + 405*a^10*x^10 - 540*a^8*x^8 + 405*a^6*x^6 - 162*a^4*x^4 + (27*a^8*x^8 - 13*a^6*x^6 - 3*a^4*x^4 - 3*a^2*x^2)*(a*x + 1)^3*(a*x - 1)^3 + (162*a^9*x^9 - 227*a^7*x^7 + 63*a^5*x^5 + 3*a^3*x^3 + 6*a*x)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + (405*a^10*x^10 - 940*a^8*x^8 + 687*a^6*x^6 - 143*a^4*x^4 - 21*a^2*x^2 + 12)*(a*x + 1)^2*(a*x - 1)^2 + (540*a^11*x^11 - 1750*a^9*x^9 + 2058*a^7*x^7 - 1017*a^5*x^5 + 145*a^3*x^3 + 24*a*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 27*a^2*x^2 + (405*a^12*x^12 - 1685*a^10*x^10 + 2727*a^8*x^8 - 2118*a^6*x^6 + 782*a^4*x^4 - 123*a^2*x^2 + 12)*(a*x + 1)*(a*x - 1) + (162*a^13*x^13 - 823*a^11*x^11 + 1695*a^9*x^9 - 1790*a^7*x^7 + 1015*a^5*x^5 - 297*a^3*x^3 + 38*a*x)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^14*x^12 - 6*a^12*x^10 + (a*x + 1)^3*(a*x - 1)^3*a^8*x^6 + 15*a^10*x^8 - 20*a^8*x^6 + 15*a^6*x^4 + 6*(a^9*x^7 - a^7*x^5)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) - 6*a^4*x^2 + 15*(a^10*x^8 - 2*a^8*x^6 + a^6*x^4)*(a*x + 1)^2*(a*x - 1)^2 + 20*(a^11*x^9 - 3*a^9*x^7 + 3*a^7*x^5 - a^5*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 15*(a^12*x^10 - 4*a^10*x^8 + 6*a^8*x^6 - 4*a^6*x^4 + a^4*x^2)*(a*x + 1)*(a*x - 1) + 6*(a^13*x^11 - 5*a^11*x^9 + 10*a^9*x^7 - 10*a^7*x^5 + 5*a^5*x^3 - a^3*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + a^2)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
68,0,0,0,0.000000," ","integrate(x/arccosh(a*x)^4,x, algorithm=""maxima"")","-\frac{2 \, a^{12} x^{12} - 10 \, a^{10} x^{10} + 20 \, a^{8} x^{8} - 20 \, a^{6} x^{6} + 10 \, a^{4} x^{4} + 2 \, {\left(a^{7} x^{7} - a^{5} x^{5}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + 2 \, {\left(5 \, a^{8} x^{8} - 9 \, a^{6} x^{6} + 4 \, a^{4} x^{4}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 4 \, {\left(5 \, a^{9} x^{9} - 13 \, a^{7} x^{7} + 11 \, a^{5} x^{5} - 3 \, a^{3} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} - 2 \, a^{2} x^{2} + 4 \, {\left(5 \, a^{10} x^{10} - 17 \, a^{8} x^{8} + 21 \, a^{6} x^{6} - 11 \, a^{4} x^{4} + 2 \, a^{2} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(4 \, a^{12} x^{12} - 20 \, a^{10} x^{10} + 40 \, a^{8} x^{8} - 40 \, a^{6} x^{6} + 20 \, a^{4} x^{4} + 4 \, {\left(a^{7} x^{7} - a^{5} x^{5}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + {\left(20 \, a^{8} x^{8} - 36 \, a^{6} x^{6} + 16 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 3\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(40 \, a^{9} x^{9} - 104 \, a^{7} x^{7} + 88 \, a^{5} x^{5} - 21 \, a^{3} x^{3} - 3 \, a x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} - 4 \, a^{2} x^{2} + {\left(40 \, a^{10} x^{10} - 136 \, a^{8} x^{8} + 168 \, a^{6} x^{6} - 91 \, a^{4} x^{4} + 22 \, a^{2} x^{2} - 3\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(20 \, a^{11} x^{11} - 84 \, a^{9} x^{9} + 136 \, a^{7} x^{7} - 107 \, a^{5} x^{5} + 42 \, a^{3} x^{3} - 7 \, a x\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2} + 2 \, {\left(5 \, a^{11} x^{11} - 21 \, a^{9} x^{9} + 34 \, a^{7} x^{7} - 26 \, a^{5} x^{5} + 9 \, a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + {\left(2 \, a^{12} x^{12} - 10 \, a^{10} x^{10} + 20 \, a^{8} x^{8} - 20 \, a^{6} x^{6} + 10 \, a^{4} x^{4} + 2 \, {\left(a^{7} x^{7} - a^{5} x^{5}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + {\left(10 \, a^{8} x^{8} - 18 \, a^{6} x^{6} + 9 \, a^{4} x^{4} - a^{2} x^{2}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(20 \, a^{9} x^{9} - 52 \, a^{7} x^{7} + 47 \, a^{5} x^{5} - 17 \, a^{3} x^{3} + 2 \, a x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} - 2 \, a^{2} x^{2} + {\left(20 \, a^{10} x^{10} - 68 \, a^{8} x^{8} + 87 \, a^{6} x^{6} - 51 \, a^{4} x^{4} + 13 \, a^{2} x^{2} - 1\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(10 \, a^{11} x^{11} - 42 \, a^{9} x^{9} + 69 \, a^{7} x^{7} - 55 \, a^{5} x^{5} + 21 \, a^{3} x^{3} - 3 \, a x\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{6 \, {\left(a^{12} x^{10} - 5 \, a^{10} x^{8} + {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} a^{7} x^{5} + 10 \, a^{8} x^{6} - 10 \, a^{6} x^{4} + 5 \, a^{4} x^{2} + 5 \, {\left(a^{8} x^{6} - a^{6} x^{4}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 10 \, {\left(a^{9} x^{7} - 2 \, a^{7} x^{5} + a^{5} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 10 \, {\left(a^{10} x^{8} - 3 \, a^{8} x^{6} + 3 \, a^{6} x^{4} - a^{4} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 5 \, {\left(a^{11} x^{9} - 4 \, a^{9} x^{7} + 6 \, a^{7} x^{5} - 4 \, a^{5} x^{3} + a^{3} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a^{2}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}} + \int \frac{8 \, a^{13} x^{13} - 48 \, a^{11} x^{11} + 8 \, {\left(a x + 1\right)}^{3} {\left(a x - 1\right)}^{3} a^{7} x^{7} + 120 \, a^{9} x^{9} - 160 \, a^{7} x^{7} + 120 \, a^{5} x^{5} + {\left(48 \, a^{8} x^{8} - 48 \, a^{6} x^{6} + 4 \, a^{4} x^{4} - 12 \, a^{2} x^{2} + 15\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} - 48 \, a^{3} x^{3} + 8 \, {\left(15 \, a^{9} x^{9} - 30 \, a^{7} x^{7} + 17 \, a^{5} x^{5} - 5 \, a^{3} x^{3} + 3 \, a x\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 2 \, {\left(80 \, a^{10} x^{10} - 240 \, a^{8} x^{8} + 252 \, a^{6} x^{6} - 104 \, a^{4} x^{4} + 3 \, a^{2} x^{2} + 9\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 8 \, {\left(15 \, a^{11} x^{11} - 60 \, a^{9} x^{9} + 92 \, a^{7} x^{7} - 63 \, a^{5} x^{5} + 15 \, a^{3} x^{3} + a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(48 \, a^{12} x^{12} - 240 \, a^{10} x^{10} + 484 \, a^{8} x^{8} - 484 \, a^{6} x^{6} + 243 \, a^{4} x^{4} - 58 \, a^{2} x^{2} + 7\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 8 \, a x}{6 \, {\left(a^{13} x^{12} - 6 \, a^{11} x^{10} + {\left(a x + 1\right)}^{3} {\left(a x - 1\right)}^{3} a^{7} x^{6} + 15 \, a^{9} x^{8} - 20 \, a^{7} x^{6} + 15 \, a^{5} x^{4} + 6 \, {\left(a^{8} x^{7} - a^{6} x^{5}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + 15 \, {\left(a^{9} x^{8} - 2 \, a^{7} x^{6} + a^{5} x^{4}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} - 6 \, a^{3} x^{2} + 20 \, {\left(a^{10} x^{9} - 3 \, a^{8} x^{7} + 3 \, a^{6} x^{5} - a^{4} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 15 \, {\left(a^{11} x^{10} - 4 \, a^{9} x^{8} + 6 \, a^{7} x^{6} - 4 \, a^{5} x^{4} + a^{3} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 6 \, {\left(a^{12} x^{11} - 5 \, a^{10} x^{9} + 10 \, a^{8} x^{7} - 10 \, a^{6} x^{5} + 5 \, a^{4} x^{3} - a^{2} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/6*(2*a^12*x^12 - 10*a^10*x^10 + 20*a^8*x^8 - 20*a^6*x^6 + 10*a^4*x^4 + 2*(a^7*x^7 - a^5*x^5)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 2*(5*a^8*x^8 - 9*a^6*x^6 + 4*a^4*x^4)*(a*x + 1)^2*(a*x - 1)^2 + 4*(5*a^9*x^9 - 13*a^7*x^7 + 11*a^5*x^5 - 3*a^3*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) - 2*a^2*x^2 + 4*(5*a^10*x^10 - 17*a^8*x^8 + 21*a^6*x^6 - 11*a^4*x^4 + 2*a^2*x^2)*(a*x + 1)*(a*x - 1) + (4*a^12*x^12 - 20*a^10*x^10 + 40*a^8*x^8 - 40*a^6*x^6 + 20*a^4*x^4 + 4*(a^7*x^7 - a^5*x^5)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + (20*a^8*x^8 - 36*a^6*x^6 + 16*a^4*x^4 + 3*a^2*x^2 - 3)*(a*x + 1)^2*(a*x - 1)^2 + (40*a^9*x^9 - 104*a^7*x^7 + 88*a^5*x^5 - 21*a^3*x^3 - 3*a*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) - 4*a^2*x^2 + (40*a^10*x^10 - 136*a^8*x^8 + 168*a^6*x^6 - 91*a^4*x^4 + 22*a^2*x^2 - 3)*(a*x + 1)*(a*x - 1) + (20*a^11*x^11 - 84*a^9*x^9 + 136*a^7*x^7 - 107*a^5*x^5 + 42*a^3*x^3 - 7*a*x)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2 + 2*(5*a^11*x^11 - 21*a^9*x^9 + 34*a^7*x^7 - 26*a^5*x^5 + 9*a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + (2*a^12*x^12 - 10*a^10*x^10 + 20*a^8*x^8 - 20*a^6*x^6 + 10*a^4*x^4 + 2*(a^7*x^7 - a^5*x^5)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + (10*a^8*x^8 - 18*a^6*x^6 + 9*a^4*x^4 - a^2*x^2)*(a*x + 1)^2*(a*x - 1)^2 + (20*a^9*x^9 - 52*a^7*x^7 + 47*a^5*x^5 - 17*a^3*x^3 + 2*a*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) - 2*a^2*x^2 + (20*a^10*x^10 - 68*a^8*x^8 + 87*a^6*x^6 - 51*a^4*x^4 + 13*a^2*x^2 - 1)*(a*x + 1)*(a*x - 1) + (10*a^11*x^11 - 42*a^9*x^9 + 69*a^7*x^7 - 55*a^5*x^5 + 21*a^3*x^3 - 3*a*x)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^12*x^10 - 5*a^10*x^8 + (a*x + 1)^(5/2)*(a*x - 1)^(5/2)*a^7*x^5 + 10*a^8*x^6 - 10*a^6*x^4 + 5*a^4*x^2 + 5*(a^8*x^6 - a^6*x^4)*(a*x + 1)^2*(a*x - 1)^2 + 10*(a^9*x^7 - 2*a^7*x^5 + a^5*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 10*(a^10*x^8 - 3*a^8*x^6 + 3*a^6*x^4 - a^4*x^2)*(a*x + 1)*(a*x - 1) + 5*(a^11*x^9 - 4*a^9*x^7 + 6*a^7*x^5 - 4*a^5*x^3 + a^3*x)*sqrt(a*x + 1)*sqrt(a*x - 1) - a^2)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3) + integrate(1/6*(8*a^13*x^13 - 48*a^11*x^11 + 8*(a*x + 1)^3*(a*x - 1)^3*a^7*x^7 + 120*a^9*x^9 - 160*a^7*x^7 + 120*a^5*x^5 + (48*a^8*x^8 - 48*a^6*x^6 + 4*a^4*x^4 - 12*a^2*x^2 + 15)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) - 48*a^3*x^3 + 8*(15*a^9*x^9 - 30*a^7*x^7 + 17*a^5*x^5 - 5*a^3*x^3 + 3*a*x)*(a*x + 1)^2*(a*x - 1)^2 + 2*(80*a^10*x^10 - 240*a^8*x^8 + 252*a^6*x^6 - 104*a^4*x^4 + 3*a^2*x^2 + 9)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 8*(15*a^11*x^11 - 60*a^9*x^9 + 92*a^7*x^7 - 63*a^5*x^5 + 15*a^3*x^3 + a*x)*(a*x + 1)*(a*x - 1) + (48*a^12*x^12 - 240*a^10*x^10 + 484*a^8*x^8 - 484*a^6*x^6 + 243*a^4*x^4 - 58*a^2*x^2 + 7)*sqrt(a*x + 1)*sqrt(a*x - 1) + 8*a*x)/((a^13*x^12 - 6*a^11*x^10 + (a*x + 1)^3*(a*x - 1)^3*a^7*x^6 + 15*a^9*x^8 - 20*a^7*x^6 + 15*a^5*x^4 + 6*(a^8*x^7 - a^6*x^5)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 15*(a^9*x^8 - 2*a^7*x^6 + a^5*x^4)*(a*x + 1)^2*(a*x - 1)^2 - 6*a^3*x^2 + 20*(a^10*x^9 - 3*a^8*x^7 + 3*a^6*x^5 - a^4*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 15*(a^11*x^10 - 4*a^9*x^8 + 6*a^7*x^6 - 4*a^5*x^4 + a^3*x^2)*(a*x + 1)*(a*x - 1) + 6*(a^12*x^11 - 5*a^10*x^9 + 10*a^8*x^7 - 10*a^6*x^5 + 5*a^4*x^3 - a^2*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
69,0,0,0,0.000000," ","integrate(1/arccosh(a*x)^4,x, algorithm=""maxima"")","-\frac{2 \, a^{11} x^{11} - 10 \, a^{9} x^{9} + 20 \, a^{7} x^{7} - 20 \, a^{5} x^{5} + 2 \, {\left(a^{6} x^{6} - a^{4} x^{4}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + 10 \, a^{3} x^{3} + 2 \, {\left(5 \, a^{7} x^{7} - 9 \, a^{5} x^{5} + 4 \, a^{3} x^{3}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 4 \, {\left(5 \, a^{8} x^{8} - 13 \, a^{6} x^{6} + 11 \, a^{4} x^{4} - 3 \, a^{2} x^{2}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 4 \, {\left(5 \, a^{9} x^{9} - 17 \, a^{7} x^{7} + 21 \, a^{5} x^{5} - 11 \, a^{3} x^{3} + 2 \, a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(a^{11} x^{11} - 5 \, a^{9} x^{9} + 10 \, a^{7} x^{7} - 10 \, a^{5} x^{5} + {\left(a^{6} x^{6} - a^{4} x^{4} + 3 \, a^{2} x^{2} - 3\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + 5 \, a^{3} x^{3} + {\left(5 \, a^{7} x^{7} - 9 \, a^{5} x^{5} + 10 \, a^{3} x^{3} - 6 \, a x\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(10 \, a^{8} x^{8} - 26 \, a^{6} x^{6} + 22 \, a^{4} x^{4} - 3 \, a^{2} x^{2} - 3\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 2 \, {\left(5 \, a^{9} x^{9} - 17 \, a^{7} x^{7} + 18 \, a^{5} x^{5} - 5 \, a^{3} x^{3} - a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(5 \, a^{10} x^{10} - 21 \, a^{8} x^{8} + 31 \, a^{6} x^{6} - 20 \, a^{4} x^{4} + 6 \, a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2} + 2 \, {\left(5 \, a^{10} x^{10} - 21 \, a^{8} x^{8} + 34 \, a^{6} x^{6} - 26 \, a^{4} x^{4} + 9 \, a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - 2 \, a x + {\left(a^{11} x^{11} - 5 \, a^{9} x^{9} + 10 \, a^{7} x^{7} - 10 \, a^{5} x^{5} + {\left(a^{6} x^{6} - a^{2} x^{2}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + 5 \, a^{3} x^{3} + {\left(5 \, a^{7} x^{7} - 5 \, a^{5} x^{5} - 2 \, a^{3} x^{3} + 2 \, a x\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(10 \, a^{8} x^{8} - 20 \, a^{6} x^{6} + 10 \, a^{4} x^{4} + a^{2} x^{2} - 1\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 2 \, {\left(5 \, a^{9} x^{9} - 15 \, a^{7} x^{7} + 16 \, a^{5} x^{5} - 7 \, a^{3} x^{3} + a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(5 \, a^{10} x^{10} - 20 \, a^{8} x^{8} + 31 \, a^{6} x^{6} - 23 \, a^{4} x^{4} + 8 \, a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{6 \, {\left(a^{11} x^{10} - 5 \, a^{9} x^{8} + {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} a^{6} x^{5} + 10 \, a^{7} x^{6} - 10 \, a^{5} x^{4} + 5 \, {\left(a^{7} x^{6} - a^{5} x^{4}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 5 \, a^{3} x^{2} + 10 \, {\left(a^{8} x^{7} - 2 \, a^{6} x^{5} + a^{4} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 10 \, {\left(a^{9} x^{8} - 3 \, a^{7} x^{6} + 3 \, a^{5} x^{4} - a^{3} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 5 \, {\left(a^{10} x^{9} - 4 \, a^{8} x^{7} + 6 \, a^{6} x^{5} - 4 \, a^{4} x^{3} + a^{2} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}} + \int \frac{a^{12} x^{12} - 6 \, a^{10} x^{10} + 15 \, a^{8} x^{8} - 20 \, a^{6} x^{6} + 15 \, a^{4} x^{4} + {\left(a^{6} x^{6} + a^{4} x^{4} - 9 \, a^{2} x^{2} + 15\right)} {\left(a x + 1\right)}^{3} {\left(a x - 1\right)}^{3} + {\left(6 \, a^{7} x^{7} - a^{5} x^{5} - 31 \, a^{3} x^{3} + 33 \, a x\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + {\left(15 \, a^{8} x^{8} - 20 \, a^{6} x^{6} - 19 \, a^{4} x^{4} + 3 \, a^{2} x^{2} + 21\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(20 \, a^{9} x^{9} - 50 \, a^{7} x^{7} + 54 \, a^{5} x^{5} - 59 \, a^{3} x^{3} + 35 \, a x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} - 6 \, a^{2} x^{2} + {\left(15 \, a^{10} x^{10} - 55 \, a^{8} x^{8} + 101 \, a^{6} x^{6} - 90 \, a^{4} x^{4} + 22 \, a^{2} x^{2} + 7\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(6 \, a^{11} x^{11} - 29 \, a^{9} x^{9} + 65 \, a^{7} x^{7} - 66 \, a^{5} x^{5} + 23 \, a^{3} x^{3} + a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 1}{6 \, {\left(a^{12} x^{12} - 6 \, a^{10} x^{10} + {\left(a x + 1\right)}^{3} {\left(a x - 1\right)}^{3} a^{6} x^{6} + 15 \, a^{8} x^{8} - 20 \, a^{6} x^{6} + 15 \, a^{4} x^{4} + 6 \, {\left(a^{7} x^{7} - a^{5} x^{5}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + 15 \, {\left(a^{8} x^{8} - 2 \, a^{6} x^{6} + a^{4} x^{4}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 20 \, {\left(a^{9} x^{9} - 3 \, a^{7} x^{7} + 3 \, a^{5} x^{5} - a^{3} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} - 6 \, a^{2} x^{2} + 15 \, {\left(a^{10} x^{10} - 4 \, a^{8} x^{8} + 6 \, a^{6} x^{6} - 4 \, a^{4} x^{4} + a^{2} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 6 \, {\left(a^{11} x^{11} - 5 \, a^{9} x^{9} + 10 \, a^{7} x^{7} - 10 \, a^{5} x^{5} + 5 \, a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 1\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/6*(2*a^11*x^11 - 10*a^9*x^9 + 20*a^7*x^7 - 20*a^5*x^5 + 2*(a^6*x^6 - a^4*x^4)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 10*a^3*x^3 + 2*(5*a^7*x^7 - 9*a^5*x^5 + 4*a^3*x^3)*(a*x + 1)^2*(a*x - 1)^2 + 4*(5*a^8*x^8 - 13*a^6*x^6 + 11*a^4*x^4 - 3*a^2*x^2)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 4*(5*a^9*x^9 - 17*a^7*x^7 + 21*a^5*x^5 - 11*a^3*x^3 + 2*a*x)*(a*x + 1)*(a*x - 1) + (a^11*x^11 - 5*a^9*x^9 + 10*a^7*x^7 - 10*a^5*x^5 + (a^6*x^6 - a^4*x^4 + 3*a^2*x^2 - 3)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 5*a^3*x^3 + (5*a^7*x^7 - 9*a^5*x^5 + 10*a^3*x^3 - 6*a*x)*(a*x + 1)^2*(a*x - 1)^2 + (10*a^8*x^8 - 26*a^6*x^6 + 22*a^4*x^4 - 3*a^2*x^2 - 3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 2*(5*a^9*x^9 - 17*a^7*x^7 + 18*a^5*x^5 - 5*a^3*x^3 - a*x)*(a*x + 1)*(a*x - 1) + (5*a^10*x^10 - 21*a^8*x^8 + 31*a^6*x^6 - 20*a^4*x^4 + 6*a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2 + 2*(5*a^10*x^10 - 21*a^8*x^8 + 34*a^6*x^6 - 26*a^4*x^4 + 9*a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - 2*a*x + (a^11*x^11 - 5*a^9*x^9 + 10*a^7*x^7 - 10*a^5*x^5 + (a^6*x^6 - a^2*x^2)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 5*a^3*x^3 + (5*a^7*x^7 - 5*a^5*x^5 - 2*a^3*x^3 + 2*a*x)*(a*x + 1)^2*(a*x - 1)^2 + (10*a^8*x^8 - 20*a^6*x^6 + 10*a^4*x^4 + a^2*x^2 - 1)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 2*(5*a^9*x^9 - 15*a^7*x^7 + 16*a^5*x^5 - 7*a^3*x^3 + a*x)*(a*x + 1)*(a*x - 1) + (5*a^10*x^10 - 20*a^8*x^8 + 31*a^6*x^6 - 23*a^4*x^4 + 8*a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^11*x^10 - 5*a^9*x^8 + (a*x + 1)^(5/2)*(a*x - 1)^(5/2)*a^6*x^5 + 10*a^7*x^6 - 10*a^5*x^4 + 5*(a^7*x^6 - a^5*x^4)*(a*x + 1)^2*(a*x - 1)^2 + 5*a^3*x^2 + 10*(a^8*x^7 - 2*a^6*x^5 + a^4*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 10*(a^9*x^8 - 3*a^7*x^6 + 3*a^5*x^4 - a^3*x^2)*(a*x + 1)*(a*x - 1) + 5*(a^10*x^9 - 4*a^8*x^7 + 6*a^6*x^5 - 4*a^4*x^3 + a^2*x)*sqrt(a*x + 1)*sqrt(a*x - 1) - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3) + integrate(1/6*(a^12*x^12 - 6*a^10*x^10 + 15*a^8*x^8 - 20*a^6*x^6 + 15*a^4*x^4 + (a^6*x^6 + a^4*x^4 - 9*a^2*x^2 + 15)*(a*x + 1)^3*(a*x - 1)^3 + (6*a^7*x^7 - a^5*x^5 - 31*a^3*x^3 + 33*a*x)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + (15*a^8*x^8 - 20*a^6*x^6 - 19*a^4*x^4 + 3*a^2*x^2 + 21)*(a*x + 1)^2*(a*x - 1)^2 + (20*a^9*x^9 - 50*a^7*x^7 + 54*a^5*x^5 - 59*a^3*x^3 + 35*a*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) - 6*a^2*x^2 + (15*a^10*x^10 - 55*a^8*x^8 + 101*a^6*x^6 - 90*a^4*x^4 + 22*a^2*x^2 + 7)*(a*x + 1)*(a*x - 1) + (6*a^11*x^11 - 29*a^9*x^9 + 65*a^7*x^7 - 66*a^5*x^5 + 23*a^3*x^3 + a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + 1)/((a^12*x^12 - 6*a^10*x^10 + (a*x + 1)^3*(a*x - 1)^3*a^6*x^6 + 15*a^8*x^8 - 20*a^6*x^6 + 15*a^4*x^4 + 6*(a^7*x^7 - a^5*x^5)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 15*(a^8*x^8 - 2*a^6*x^6 + a^4*x^4)*(a*x + 1)^2*(a*x - 1)^2 + 20*(a^9*x^9 - 3*a^7*x^7 + 3*a^5*x^5 - a^3*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) - 6*a^2*x^2 + 15*(a^10*x^10 - 4*a^8*x^8 + 6*a^6*x^6 - 4*a^4*x^4 + a^2*x^2)*(a*x + 1)*(a*x - 1) + 6*(a^11*x^11 - 5*a^9*x^9 + 10*a^7*x^7 - 10*a^5*x^5 + 5*a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + 1)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
70,0,0,0,0.000000," ","integrate(1/x/arccosh(a*x)^4,x, algorithm=""maxima"")","-\frac{2 \, a^{13} x^{13} - 10 \, a^{11} x^{11} + 20 \, a^{9} x^{9} - 20 \, a^{7} x^{7} + 10 \, a^{5} x^{5} + 2 \, {\left(a^{8} x^{8} - a^{6} x^{6}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} - 2 \, a^{3} x^{3} + 2 \, {\left(5 \, a^{9} x^{9} - 9 \, a^{7} x^{7} + 4 \, a^{5} x^{5}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 4 \, {\left(5 \, a^{10} x^{10} - 13 \, a^{8} x^{8} + 11 \, a^{6} x^{6} - 3 \, a^{4} x^{4}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 4 \, {\left(5 \, a^{11} x^{11} - 17 \, a^{9} x^{9} + 21 \, a^{7} x^{7} - 11 \, a^{5} x^{5} + 2 \, a^{3} x^{3}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} - {\left(4 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 2 \, a^{2} x^{2}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + {\left(16 \, a^{7} x^{7} - 46 \, a^{5} x^{5} + 37 \, a^{3} x^{3} - 7 \, a x\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(24 \, a^{8} x^{8} - 66 \, a^{6} x^{6} + 59 \, a^{4} x^{4} - 19 \, a^{2} x^{2} + 2\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + {\left(16 \, a^{9} x^{9} - 42 \, a^{7} x^{7} + 39 \, a^{5} x^{5} - 16 \, a^{3} x^{3} + 3 \, a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(4 \, a^{10} x^{10} - 10 \, a^{8} x^{8} + 9 \, a^{6} x^{6} - 4 \, a^{4} x^{4} + a^{2} x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2} + 2 \, {\left(5 \, a^{12} x^{12} - 21 \, a^{10} x^{10} + 34 \, a^{8} x^{8} - 26 \, a^{6} x^{6} + 9 \, a^{4} x^{4} - a^{2} x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1} + {\left(2 \, {\left(a^{6} x^{6} - a^{4} x^{4}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + {\left(8 \, a^{7} x^{7} - 13 \, a^{5} x^{5} + 5 \, a^{3} x^{3}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(12 \, a^{8} x^{8} - 27 \, a^{6} x^{6} + 19 \, a^{4} x^{4} - 4 \, a^{2} x^{2}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + {\left(8 \, a^{9} x^{9} - 23 \, a^{7} x^{7} + 23 \, a^{5} x^{5} - 9 \, a^{3} x^{3} + a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(2 \, a^{10} x^{10} - 7 \, a^{8} x^{8} + 9 \, a^{6} x^{6} - 5 \, a^{4} x^{4} + a^{2} x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{6 \, {\left(a^{13} x^{13} - 5 \, a^{11} x^{11} + {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} a^{8} x^{8} + 10 \, a^{9} x^{9} - 10 \, a^{7} x^{7} + 5 \, a^{5} x^{5} - a^{3} x^{3} + 5 \, {\left(a^{9} x^{9} - a^{7} x^{7}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 10 \, {\left(a^{10} x^{10} - 2 \, a^{8} x^{8} + a^{6} x^{6}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 10 \, {\left(a^{11} x^{11} - 3 \, a^{9} x^{9} + 3 \, a^{7} x^{7} - a^{5} x^{5}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 5 \, {\left(a^{12} x^{12} - 4 \, a^{10} x^{10} + 6 \, a^{8} x^{8} - 4 \, a^{6} x^{6} + a^{4} x^{4}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}} + \int \frac{8 \, {\left(a^{7} x^{7} - 6 \, a^{5} x^{5} + 6 \, a^{3} x^{3}\right)} {\left(a x + 1\right)}^{3} {\left(a x - 1\right)}^{3} + {\left(40 \, a^{8} x^{8} - 204 \, a^{6} x^{6} + 228 \, a^{4} x^{4} - 57 \, a^{2} x^{2}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + 2 \, {\left(40 \, a^{9} x^{9} - 168 \, a^{7} x^{7} + 200 \, a^{5} x^{5} - 87 \, a^{3} x^{3} + 15 \, a x\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 2 \, {\left(40 \, a^{10} x^{10} - 132 \, a^{8} x^{8} + 156 \, a^{6} x^{6} - 91 \, a^{4} x^{4} + 30 \, a^{2} x^{2} - 3\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 2 \, {\left(20 \, a^{11} x^{11} - 48 \, a^{9} x^{9} + 48 \, a^{7} x^{7} - 35 \, a^{5} x^{5} + 18 \, a^{3} x^{3} - 3 \, a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(8 \, a^{12} x^{12} - 12 \, a^{10} x^{10} + 4 \, a^{8} x^{8} - 5 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - a^{2} x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{6 \, {\left(a^{15} x^{16} - 6 \, a^{13} x^{14} + {\left(a x + 1\right)}^{3} {\left(a x - 1\right)}^{3} a^{9} x^{10} + 15 \, a^{11} x^{12} - 20 \, a^{9} x^{10} + 15 \, a^{7} x^{8} - 6 \, a^{5} x^{6} + a^{3} x^{4} + 6 \, {\left(a^{10} x^{11} - a^{8} x^{9}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + 15 \, {\left(a^{11} x^{12} - 2 \, a^{9} x^{10} + a^{7} x^{8}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 20 \, {\left(a^{12} x^{13} - 3 \, a^{10} x^{11} + 3 \, a^{8} x^{9} - a^{6} x^{7}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 15 \, {\left(a^{13} x^{14} - 4 \, a^{11} x^{12} + 6 \, a^{9} x^{10} - 4 \, a^{7} x^{8} + a^{5} x^{6}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 6 \, {\left(a^{14} x^{15} - 5 \, a^{12} x^{13} + 10 \, a^{10} x^{11} - 10 \, a^{8} x^{9} + 5 \, a^{6} x^{7} - a^{4} x^{5}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/6*(2*a^13*x^13 - 10*a^11*x^11 + 20*a^9*x^9 - 20*a^7*x^7 + 10*a^5*x^5 + 2*(a^8*x^8 - a^6*x^6)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) - 2*a^3*x^3 + 2*(5*a^9*x^9 - 9*a^7*x^7 + 4*a^5*x^5)*(a*x + 1)^2*(a*x - 1)^2 + 4*(5*a^10*x^10 - 13*a^8*x^8 + 11*a^6*x^6 - 3*a^4*x^4)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 4*(5*a^11*x^11 - 17*a^9*x^9 + 21*a^7*x^7 - 11*a^5*x^5 + 2*a^3*x^3)*(a*x + 1)*(a*x - 1) - (4*(a^6*x^6 - 3*a^4*x^4 + 2*a^2*x^2)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + (16*a^7*x^7 - 46*a^5*x^5 + 37*a^3*x^3 - 7*a*x)*(a*x + 1)^2*(a*x - 1)^2 + (24*a^8*x^8 - 66*a^6*x^6 + 59*a^4*x^4 - 19*a^2*x^2 + 2)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (16*a^9*x^9 - 42*a^7*x^7 + 39*a^5*x^5 - 16*a^3*x^3 + 3*a*x)*(a*x + 1)*(a*x - 1) + (4*a^10*x^10 - 10*a^8*x^8 + 9*a^6*x^6 - 4*a^4*x^4 + a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2 + 2*(5*a^12*x^12 - 21*a^10*x^10 + 34*a^8*x^8 - 26*a^6*x^6 + 9*a^4*x^4 - a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1) + (2*(a^6*x^6 - a^4*x^4)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + (8*a^7*x^7 - 13*a^5*x^5 + 5*a^3*x^3)*(a*x + 1)^2*(a*x - 1)^2 + (12*a^8*x^8 - 27*a^6*x^6 + 19*a^4*x^4 - 4*a^2*x^2)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (8*a^9*x^9 - 23*a^7*x^7 + 23*a^5*x^5 - 9*a^3*x^3 + a*x)*(a*x + 1)*(a*x - 1) + (2*a^10*x^10 - 7*a^8*x^8 + 9*a^6*x^6 - 5*a^4*x^4 + a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^13*x^13 - 5*a^11*x^11 + (a*x + 1)^(5/2)*(a*x - 1)^(5/2)*a^8*x^8 + 10*a^9*x^9 - 10*a^7*x^7 + 5*a^5*x^5 - a^3*x^3 + 5*(a^9*x^9 - a^7*x^7)*(a*x + 1)^2*(a*x - 1)^2 + 10*(a^10*x^10 - 2*a^8*x^8 + a^6*x^6)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 10*(a^11*x^11 - 3*a^9*x^9 + 3*a^7*x^7 - a^5*x^5)*(a*x + 1)*(a*x - 1) + 5*(a^12*x^12 - 4*a^10*x^10 + 6*a^8*x^8 - 4*a^6*x^6 + a^4*x^4)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3) + integrate(1/6*(8*(a^7*x^7 - 6*a^5*x^5 + 6*a^3*x^3)*(a*x + 1)^3*(a*x - 1)^3 + (40*a^8*x^8 - 204*a^6*x^6 + 228*a^4*x^4 - 57*a^2*x^2)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 2*(40*a^9*x^9 - 168*a^7*x^7 + 200*a^5*x^5 - 87*a^3*x^3 + 15*a*x)*(a*x + 1)^2*(a*x - 1)^2 + 2*(40*a^10*x^10 - 132*a^8*x^8 + 156*a^6*x^6 - 91*a^4*x^4 + 30*a^2*x^2 - 3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 2*(20*a^11*x^11 - 48*a^9*x^9 + 48*a^7*x^7 - 35*a^5*x^5 + 18*a^3*x^3 - 3*a*x)*(a*x + 1)*(a*x - 1) + (8*a^12*x^12 - 12*a^10*x^10 + 4*a^8*x^8 - 5*a^6*x^6 + 6*a^4*x^4 - a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^15*x^16 - 6*a^13*x^14 + (a*x + 1)^3*(a*x - 1)^3*a^9*x^10 + 15*a^11*x^12 - 20*a^9*x^10 + 15*a^7*x^8 - 6*a^5*x^6 + a^3*x^4 + 6*(a^10*x^11 - a^8*x^9)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 15*(a^11*x^12 - 2*a^9*x^10 + a^7*x^8)*(a*x + 1)^2*(a*x - 1)^2 + 20*(a^12*x^13 - 3*a^10*x^11 + 3*a^8*x^9 - a^6*x^7)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 15*(a^13*x^14 - 4*a^11*x^12 + 6*a^9*x^10 - 4*a^7*x^8 + a^5*x^6)*(a*x + 1)*(a*x - 1) + 6*(a^14*x^15 - 5*a^12*x^13 + 10*a^10*x^11 - 10*a^8*x^9 + 5*a^6*x^7 - a^4*x^5)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
71,0,0,0,0.000000," ","integrate(1/x^2/arccosh(a*x)^4,x, algorithm=""maxima"")","-\frac{2 \, a^{13} x^{13} - 10 \, a^{11} x^{11} + 20 \, a^{9} x^{9} - 20 \, a^{7} x^{7} + 10 \, a^{5} x^{5} + 2 \, {\left(a^{8} x^{8} - a^{6} x^{6}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} - 2 \, a^{3} x^{3} + 2 \, {\left(5 \, a^{9} x^{9} - 9 \, a^{7} x^{7} + 4 \, a^{5} x^{5}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 4 \, {\left(5 \, a^{10} x^{10} - 13 \, a^{8} x^{8} + 11 \, a^{6} x^{6} - 3 \, a^{4} x^{4}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 4 \, {\left(5 \, a^{11} x^{11} - 17 \, a^{9} x^{9} + 21 \, a^{7} x^{7} - 11 \, a^{5} x^{5} + 2 \, a^{3} x^{3}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(a^{13} x^{13} - 5 \, a^{11} x^{11} + 10 \, a^{9} x^{9} - 10 \, a^{7} x^{7} + 5 \, a^{5} x^{5} + {\left(a^{8} x^{8} - 13 \, a^{6} x^{6} + 27 \, a^{4} x^{4} - 15 \, a^{2} x^{2}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} - a^{3} x^{3} + {\left(5 \, a^{9} x^{9} - 57 \, a^{7} x^{7} + 124 \, a^{5} x^{5} - 90 \, a^{3} x^{3} + 18 \, a x\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(10 \, a^{10} x^{10} - 98 \, a^{8} x^{8} + 220 \, a^{6} x^{6} - 189 \, a^{4} x^{4} + 63 \, a^{2} x^{2} - 6\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 2 \, {\left(5 \, a^{11} x^{11} - 41 \, a^{9} x^{9} + 93 \, a^{7} x^{7} - 89 \, a^{5} x^{5} + 38 \, a^{3} x^{3} - 6 \, a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(5 \, a^{12} x^{12} - 33 \, a^{10} x^{10} + 73 \, a^{8} x^{8} - 74 \, a^{6} x^{6} + 36 \, a^{4} x^{4} - 7 \, a^{2} x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2} + 2 \, {\left(5 \, a^{12} x^{12} - 21 \, a^{10} x^{10} + 34 \, a^{8} x^{8} - 26 \, a^{6} x^{6} + 9 \, a^{4} x^{4} - a^{2} x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1} - {\left(a^{13} x^{13} - 5 \, a^{11} x^{11} + 10 \, a^{9} x^{9} - 10 \, a^{7} x^{7} + 5 \, a^{5} x^{5} + {\left(a^{8} x^{8} - 4 \, a^{6} x^{6} + 3 \, a^{4} x^{4}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} - a^{3} x^{3} + {\left(5 \, a^{9} x^{9} - 21 \, a^{7} x^{7} + 24 \, a^{5} x^{5} - 8 \, a^{3} x^{3}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(10 \, a^{10} x^{10} - 44 \, a^{8} x^{8} + 64 \, a^{6} x^{6} - 37 \, a^{4} x^{4} + 7 \, a^{2} x^{2}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 2 \, {\left(5 \, a^{11} x^{11} - 23 \, a^{9} x^{9} + 39 \, a^{7} x^{7} - 30 \, a^{5} x^{5} + 10 \, a^{3} x^{3} - a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(5 \, a^{12} x^{12} - 24 \, a^{10} x^{10} + 45 \, a^{8} x^{8} - 41 \, a^{6} x^{6} + 18 \, a^{4} x^{4} - 3 \, a^{2} x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{6 \, {\left(a^{13} x^{14} - 5 \, a^{11} x^{12} + {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} a^{8} x^{9} + 10 \, a^{9} x^{10} - 10 \, a^{7} x^{8} + 5 \, a^{5} x^{6} - a^{3} x^{4} + 5 \, {\left(a^{9} x^{10} - a^{7} x^{8}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 10 \, {\left(a^{10} x^{11} - 2 \, a^{8} x^{9} + a^{6} x^{7}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 10 \, {\left(a^{11} x^{12} - 3 \, a^{9} x^{10} + 3 \, a^{7} x^{8} - a^{5} x^{6}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 5 \, {\left(a^{12} x^{13} - 4 \, a^{10} x^{11} + 6 \, a^{8} x^{9} - 4 \, a^{6} x^{7} + a^{4} x^{5}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}} - \int \frac{a^{15} x^{15} - 6 \, a^{13} x^{13} + 15 \, a^{11} x^{11} - 20 \, a^{9} x^{9} + 15 \, a^{7} x^{7} - 6 \, a^{5} x^{5} + {\left(a^{9} x^{9} - 39 \, a^{7} x^{7} + 135 \, a^{5} x^{5} - 105 \, a^{3} x^{3}\right)} {\left(a x + 1\right)}^{3} {\left(a x - 1\right)}^{3} + {\left(6 \, a^{10} x^{10} - 201 \, a^{8} x^{8} + 677 \, a^{6} x^{6} - 663 \, a^{4} x^{4} + 174 \, a^{2} x^{2}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + a^{3} x^{3} + {\left(15 \, a^{11} x^{11} - 420 \, a^{9} x^{9} + 1373 \, a^{7} x^{7} - 1565 \, a^{5} x^{5} + 705 \, a^{3} x^{3} - 108 \, a x\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + {\left(20 \, a^{12} x^{12} - 450 \, a^{10} x^{10} + 1422 \, a^{8} x^{8} - 1787 \, a^{6} x^{6} + 1059 \, a^{4} x^{4} - 288 \, a^{2} x^{2} + 24\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + {\left(15 \, a^{13} x^{13} - 255 \, a^{11} x^{11} + 773 \, a^{9} x^{9} - 1026 \, a^{7} x^{7} + 714 \, a^{5} x^{5} - 257 \, a^{3} x^{3} + 36 \, a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(6 \, a^{14} x^{14} - 69 \, a^{12} x^{12} + 197 \, a^{10} x^{10} - 266 \, a^{8} x^{8} + 201 \, a^{6} x^{6} - 83 \, a^{4} x^{4} + 14 \, a^{2} x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{6 \, {\left(a^{15} x^{17} - 6 \, a^{13} x^{15} + {\left(a x + 1\right)}^{3} {\left(a x - 1\right)}^{3} a^{9} x^{11} + 15 \, a^{11} x^{13} - 20 \, a^{9} x^{11} + 15 \, a^{7} x^{9} - 6 \, a^{5} x^{7} + a^{3} x^{5} + 6 \, {\left(a^{10} x^{12} - a^{8} x^{10}\right)} {\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{\frac{5}{2}} + 15 \, {\left(a^{11} x^{13} - 2 \, a^{9} x^{11} + a^{7} x^{9}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} + 20 \, {\left(a^{12} x^{14} - 3 \, a^{10} x^{12} + 3 \, a^{8} x^{10} - a^{6} x^{8}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + 15 \, {\left(a^{13} x^{15} - 4 \, a^{11} x^{13} + 6 \, a^{9} x^{11} - 4 \, a^{7} x^{9} + a^{5} x^{7}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 6 \, {\left(a^{14} x^{16} - 5 \, a^{12} x^{14} + 10 \, a^{10} x^{12} - 10 \, a^{8} x^{10} + 5 \, a^{6} x^{8} - a^{4} x^{6}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/6*(2*a^13*x^13 - 10*a^11*x^11 + 20*a^9*x^9 - 20*a^7*x^7 + 10*a^5*x^5 + 2*(a^8*x^8 - a^6*x^6)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) - 2*a^3*x^3 + 2*(5*a^9*x^9 - 9*a^7*x^7 + 4*a^5*x^5)*(a*x + 1)^2*(a*x - 1)^2 + 4*(5*a^10*x^10 - 13*a^8*x^8 + 11*a^6*x^6 - 3*a^4*x^4)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 4*(5*a^11*x^11 - 17*a^9*x^9 + 21*a^7*x^7 - 11*a^5*x^5 + 2*a^3*x^3)*(a*x + 1)*(a*x - 1) + (a^13*x^13 - 5*a^11*x^11 + 10*a^9*x^9 - 10*a^7*x^7 + 5*a^5*x^5 + (a^8*x^8 - 13*a^6*x^6 + 27*a^4*x^4 - 15*a^2*x^2)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) - a^3*x^3 + (5*a^9*x^9 - 57*a^7*x^7 + 124*a^5*x^5 - 90*a^3*x^3 + 18*a*x)*(a*x + 1)^2*(a*x - 1)^2 + (10*a^10*x^10 - 98*a^8*x^8 + 220*a^6*x^6 - 189*a^4*x^4 + 63*a^2*x^2 - 6)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 2*(5*a^11*x^11 - 41*a^9*x^9 + 93*a^7*x^7 - 89*a^5*x^5 + 38*a^3*x^3 - 6*a*x)*(a*x + 1)*(a*x - 1) + (5*a^12*x^12 - 33*a^10*x^10 + 73*a^8*x^8 - 74*a^6*x^6 + 36*a^4*x^4 - 7*a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2 + 2*(5*a^12*x^12 - 21*a^10*x^10 + 34*a^8*x^8 - 26*a^6*x^6 + 9*a^4*x^4 - a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1) - (a^13*x^13 - 5*a^11*x^11 + 10*a^9*x^9 - 10*a^7*x^7 + 5*a^5*x^5 + (a^8*x^8 - 4*a^6*x^6 + 3*a^4*x^4)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) - a^3*x^3 + (5*a^9*x^9 - 21*a^7*x^7 + 24*a^5*x^5 - 8*a^3*x^3)*(a*x + 1)^2*(a*x - 1)^2 + (10*a^10*x^10 - 44*a^8*x^8 + 64*a^6*x^6 - 37*a^4*x^4 + 7*a^2*x^2)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 2*(5*a^11*x^11 - 23*a^9*x^9 + 39*a^7*x^7 - 30*a^5*x^5 + 10*a^3*x^3 - a*x)*(a*x + 1)*(a*x - 1) + (5*a^12*x^12 - 24*a^10*x^10 + 45*a^8*x^8 - 41*a^6*x^6 + 18*a^4*x^4 - 3*a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^13*x^14 - 5*a^11*x^12 + (a*x + 1)^(5/2)*(a*x - 1)^(5/2)*a^8*x^9 + 10*a^9*x^10 - 10*a^7*x^8 + 5*a^5*x^6 - a^3*x^4 + 5*(a^9*x^10 - a^7*x^8)*(a*x + 1)^2*(a*x - 1)^2 + 10*(a^10*x^11 - 2*a^8*x^9 + a^6*x^7)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 10*(a^11*x^12 - 3*a^9*x^10 + 3*a^7*x^8 - a^5*x^6)*(a*x + 1)*(a*x - 1) + 5*(a^12*x^13 - 4*a^10*x^11 + 6*a^8*x^9 - 4*a^6*x^7 + a^4*x^5)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3) - integrate(1/6*(a^15*x^15 - 6*a^13*x^13 + 15*a^11*x^11 - 20*a^9*x^9 + 15*a^7*x^7 - 6*a^5*x^5 + (a^9*x^9 - 39*a^7*x^7 + 135*a^5*x^5 - 105*a^3*x^3)*(a*x + 1)^3*(a*x - 1)^3 + (6*a^10*x^10 - 201*a^8*x^8 + 677*a^6*x^6 - 663*a^4*x^4 + 174*a^2*x^2)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + a^3*x^3 + (15*a^11*x^11 - 420*a^9*x^9 + 1373*a^7*x^7 - 1565*a^5*x^5 + 705*a^3*x^3 - 108*a*x)*(a*x + 1)^2*(a*x - 1)^2 + (20*a^12*x^12 - 450*a^10*x^10 + 1422*a^8*x^8 - 1787*a^6*x^6 + 1059*a^4*x^4 - 288*a^2*x^2 + 24)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (15*a^13*x^13 - 255*a^11*x^11 + 773*a^9*x^9 - 1026*a^7*x^7 + 714*a^5*x^5 - 257*a^3*x^3 + 36*a*x)*(a*x + 1)*(a*x - 1) + (6*a^14*x^14 - 69*a^12*x^12 + 197*a^10*x^10 - 266*a^8*x^8 + 201*a^6*x^6 - 83*a^4*x^4 + 14*a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^15*x^17 - 6*a^13*x^15 + (a*x + 1)^3*(a*x - 1)^3*a^9*x^11 + 15*a^11*x^13 - 20*a^9*x^11 + 15*a^7*x^9 - 6*a^5*x^7 + a^3*x^5 + 6*(a^10*x^12 - a^8*x^10)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 15*(a^11*x^13 - 2*a^9*x^11 + a^7*x^9)*(a*x + 1)^2*(a*x - 1)^2 + 20*(a^12*x^14 - 3*a^10*x^12 + 3*a^8*x^10 - a^6*x^8)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 15*(a^13*x^15 - 4*a^11*x^13 + 6*a^9*x^11 - 4*a^7*x^9 + a^5*x^7)*(a*x + 1)*(a*x - 1) + 6*(a^14*x^16 - 5*a^12*x^14 + 10*a^10*x^12 - 10*a^8*x^10 + 5*a^6*x^8 - a^4*x^6)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
72,0,0,0,0.000000," ","integrate(x^4*arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int x^{4} \sqrt{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^4*sqrt(arccosh(a*x)), x)","F",0
73,0,0,0,0.000000," ","integrate(x^3*arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int x^{3} \sqrt{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^3*sqrt(arccosh(a*x)), x)","F",0
74,0,0,0,0.000000," ","integrate(x^2*arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int x^{2} \sqrt{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^2*sqrt(arccosh(a*x)), x)","F",0
75,0,0,0,0.000000," ","integrate(x*arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int x \sqrt{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x*sqrt(arccosh(a*x)), x)","F",0
76,0,0,0,0.000000," ","integrate(arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \sqrt{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(sqrt(arccosh(a*x)), x)","F",0
77,0,0,0,0.000000," ","integrate(arccosh(a*x)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{arcosh}\left(a x\right)}}{x}\,{d x}"," ",0,"integrate(sqrt(arccosh(a*x))/x, x)","F",0
78,0,0,0,0.000000," ","integrate(x^4*arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int x^{4} \operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x^4*arccosh(a*x)^(3/2), x)","F",0
79,0,0,0,0.000000," ","integrate(x^3*arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int x^{3} \operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x^3*arccosh(a*x)^(3/2), x)","F",0
80,0,0,0,0.000000," ","integrate(x^2*arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int x^{2} \operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x^2*arccosh(a*x)^(3/2), x)","F",0
81,0,0,0,0.000000," ","integrate(x*arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int x \operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x*arccosh(a*x)^(3/2), x)","F",0
82,0,0,0,0.000000," ","integrate(arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(arccosh(a*x)^(3/2), x)","F",0
83,0,0,0,0.000000," ","integrate(arccosh(a*x)^(3/2)/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(arccosh(a*x)^(3/2)/x, x)","F",0
84,0,0,0,0.000000," ","integrate(x^4*arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int x^{4} \operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(x^4*arccosh(a*x)^(5/2), x)","F",0
85,0,0,0,0.000000," ","integrate(x^3*arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int x^{3} \operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(x^3*arccosh(a*x)^(5/2), x)","F",0
86,0,0,0,0.000000," ","integrate(x^2*arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int x^{2} \operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(x^2*arccosh(a*x)^(5/2), x)","F",0
87,0,0,0,0.000000," ","integrate(x*arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int x \operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(x*arccosh(a*x)^(5/2), x)","F",0
88,0,0,0,0.000000," ","integrate(arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int \operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(arccosh(a*x)^(5/2), x)","F",0
89,0,0,0,0.000000," ","integrate(arccosh(a*x)^(5/2)/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}}{x}\,{d x}"," ",0,"integrate(arccosh(a*x)^(5/2)/x, x)","F",0
90,0,0,0,0.000000," ","integrate(x^4/arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{\sqrt{\operatorname{arcosh}\left(a x\right)}}\,{d x}"," ",0,"integrate(x^4/sqrt(arccosh(a*x)), x)","F",0
91,0,0,0,0.000000," ","integrate(x^3/arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\sqrt{\operatorname{arcosh}\left(a x\right)}}\,{d x}"," ",0,"integrate(x^3/sqrt(arccosh(a*x)), x)","F",0
92,0,0,0,0.000000," ","integrate(x^2/arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{\operatorname{arcosh}\left(a x\right)}}\,{d x}"," ",0,"integrate(x^2/sqrt(arccosh(a*x)), x)","F",0
93,0,0,0,0.000000," ","integrate(x/arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{\operatorname{arcosh}\left(a x\right)}}\,{d x}"," ",0,"integrate(x/sqrt(arccosh(a*x)), x)","F",0
94,0,0,0,0.000000," ","integrate(1/arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\operatorname{arcosh}\left(a x\right)}}\,{d x}"," ",0,"integrate(1/sqrt(arccosh(a*x)), x)","F",0
95,0,0,0,0.000000," ","integrate(1/x/arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{x \sqrt{\operatorname{arcosh}\left(a x\right)}}\,{d x}"," ",0,"integrate(1/(x*sqrt(arccosh(a*x))), x)","F",0
96,0,0,0,0.000000," ","integrate(1/x^2/arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{x^{2} \sqrt{\operatorname{arcosh}\left(a x\right)}}\,{d x}"," ",0,"integrate(1/(x^2*sqrt(arccosh(a*x))), x)","F",0
97,0,0,0,0.000000," ","integrate(x^4/arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{\operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^4/arccosh(a*x)^(3/2), x)","F",0
98,0,0,0,0.000000," ","integrate(x^3/arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3/arccosh(a*x)^(3/2), x)","F",0
99,0,0,0,0.000000," ","integrate(x^2/arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/arccosh(a*x)^(3/2), x)","F",0
100,0,0,0,0.000000," ","integrate(x/arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{x}{\operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/arccosh(a*x)^(3/2), x)","F",0
101,0,0,0,0.000000," ","integrate(1/arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arccosh(a*x)^(-3/2), x)","F",0
102,0,0,0,0.000000," ","integrate(1/x/arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{x \operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x*arccosh(a*x)^(3/2)), x)","F",0
103,0,0,0,0.000000," ","integrate(x^4/arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{\operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^4/arccosh(a*x)^(5/2), x)","F",0
104,0,0,0,0.000000," ","integrate(x^3/arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^3/arccosh(a*x)^(5/2), x)","F",0
105,0,0,0,0.000000," ","integrate(x^2/arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^2/arccosh(a*x)^(5/2), x)","F",0
106,0,0,0,0.000000," ","integrate(x/arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{x}{\operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x/arccosh(a*x)^(5/2), x)","F",0
107,0,0,0,0.000000," ","integrate(1/arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(arccosh(a*x)^(-5/2), x)","F",0
108,0,0,0,0.000000," ","integrate(1/x/arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{x \operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(x*arccosh(a*x)^(5/2)), x)","F",0
109,0,0,0,0.000000," ","integrate(x^4/arccosh(a*x)^(7/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{\operatorname{arcosh}\left(a x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(x^4/arccosh(a*x)^(7/2), x)","F",0
110,0,0,0,0.000000," ","integrate(x^3/arccosh(a*x)^(7/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\operatorname{arcosh}\left(a x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(x^3/arccosh(a*x)^(7/2), x)","F",0
111,0,0,0,0.000000," ","integrate(x^2/arccosh(a*x)^(7/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\operatorname{arcosh}\left(a x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(x^2/arccosh(a*x)^(7/2), x)","F",0
112,0,0,0,0.000000," ","integrate(x/arccosh(a*x)^(7/2),x, algorithm=""maxima"")","\int \frac{x}{\operatorname{arcosh}\left(a x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(x/arccosh(a*x)^(7/2), x)","F",0
113,0,0,0,0.000000," ","integrate(1/arccosh(a*x)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{\operatorname{arcosh}\left(a x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(arccosh(a*x)^(-7/2), x)","F",0
114,0,0,0,0.000000," ","integrate(1/x/arccosh(a*x)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{x \operatorname{arcosh}\left(a x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/(x*arccosh(a*x)^(7/2)), x)","F",0
115,0,0,0,0.000000," ","integrate(x^m*arccosh(a*x)^4,x, algorithm=""maxima"")","\frac{x x^{m} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{4}}{m + 1} - \int \frac{4 \, {\left(\sqrt{a x + 1} \sqrt{a x - 1} a^{2} x^{2} x^{m} + {\left(a^{3} x^{3} - a x\right)} x^{m}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{a^{3} {\left(m + 1\right)} x^{3} - a {\left(m + 1\right)} x + {\left(a^{2} {\left(m + 1\right)} x^{2} - m - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1}}\,{d x}"," ",0,"x*x^m*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^4/(m + 1) - integrate(4*(sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x^2*x^m + (a^3*x^3 - a*x)*x^m)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/(a^3*(m + 1)*x^3 - a*(m + 1)*x + (a^2*(m + 1)*x^2 - m - 1)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
116,0,0,0,0.000000," ","integrate(x^m*arccosh(a*x)^3,x, algorithm=""maxima"")","\frac{x x^{m} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{m + 1} - \int \frac{3 \, {\left(\sqrt{a x + 1} \sqrt{a x - 1} a^{2} x^{2} x^{m} + {\left(a^{3} x^{3} - a x\right)} x^{m}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{a^{3} {\left(m + 1\right)} x^{3} - a {\left(m + 1\right)} x + {\left(a^{2} {\left(m + 1\right)} x^{2} - m - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1}}\,{d x}"," ",0,"x*x^m*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/(m + 1) - integrate(3*(sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x^2*x^m + (a^3*x^3 - a*x)*x^m)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(a^3*(m + 1)*x^3 - a*(m + 1)*x + (a^2*(m + 1)*x^2 - m - 1)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
117,0,0,0,0.000000," ","integrate(x^m*arccosh(a*x)^2,x, algorithm=""maxima"")","\frac{x x^{m} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{m + 1} - \int \frac{2 \, {\left(\sqrt{a x + 1} \sqrt{a x - 1} a^{2} x^{2} x^{m} + {\left(a^{3} x^{3} - a x\right)} x^{m}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{a^{3} {\left(m + 1\right)} x^{3} - a {\left(m + 1\right)} x + {\left(a^{2} {\left(m + 1\right)} x^{2} - m - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1}}\,{d x}"," ",0,"x*x^m*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(m + 1) - integrate(2*(sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x^2*x^m + (a^3*x^3 - a*x)*x^m)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))/(a^3*(m + 1)*x^3 - a*(m + 1)*x + (a^2*(m + 1)*x^2 - m - 1)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
118,0,0,0,0.000000," ","integrate(x^m*arccosh(a*x),x, algorithm=""maxima"")","-a^{2} \int \frac{x^{2} x^{m}}{a^{2} {\left(m + 1\right)} x^{2} - m - 1}\,{d x} + a \int \frac{x x^{m}}{a^{3} {\left(m + 1\right)} x^{3} - a {\left(m + 1\right)} x + {\left(a^{2} {\left(m + 1\right)} x^{2} - m - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1}}\,{d x} + \frac{x x^{m} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{m + 1}"," ",0,"-a^2*integrate(x^2*x^m/(a^2*(m + 1)*x^2 - m - 1), x) + a*integrate(x*x^m/(a^3*(m + 1)*x^3 - a*(m + 1)*x + (a^2*(m + 1)*x^2 - m - 1)*sqrt(a*x + 1)*sqrt(a*x - 1)), x) + x*x^m*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))/(m + 1)","F",0
119,0,0,0,0.000000," ","integrate(x^m/arccosh(a*x),x, algorithm=""maxima"")","\int \frac{x^{m}}{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^m/arccosh(a*x), x)","F",0
120,0,0,0,0.000000," ","integrate(x^m/arccosh(a*x)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} x^{m} + {\left(a^{3} x^{3} - a x\right)} x^{m}}{{\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)} + \int \frac{{\left(a^{3} {\left(m + 1\right)} x^{3} - a {\left(m - 1\right)} x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} x^{m} + {\left(2 \, a^{4} {\left(m + 1\right)} x^{4} - a^{2} {\left(3 \, m + 1\right)} x^{2} + m\right)} \sqrt{a x + 1} \sqrt{a x - 1} x^{m} + {\left(a^{5} {\left(m + 1\right)} x^{5} - 2 \, a^{3} {\left(m + 1\right)} x^{3} + a {\left(m + 1\right)} x\right)} x^{m}}{{\left(a^{5} x^{5} + {\left(a x + 1\right)} {\left(a x - 1\right)} a^{3} x^{3} - 2 \, a^{3} x^{3} + 2 \, {\left(a^{4} x^{4} - a^{2} x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1} + a x\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-((a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1)*x^m + (a^3*x^3 - a*x)*x^m)/((a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))) + integrate(((a^3*(m + 1)*x^3 - a*(m - 1)*x)*(a*x + 1)*(a*x - 1)*x^m + (2*a^4*(m + 1)*x^4 - a^2*(3*m + 1)*x^2 + m)*sqrt(a*x + 1)*sqrt(a*x - 1)*x^m + (a^5*(m + 1)*x^5 - 2*a^3*(m + 1)*x^3 + a*(m + 1)*x)*x^m)/((a^5*x^5 + (a*x + 1)*(a*x - 1)*a^3*x^3 - 2*a^3*x^3 + 2*(a^4*x^4 - a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1) + a*x)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
121,0,0,0,0.000000," ","integrate(x^m/arccosh(a*x)^3,x, algorithm=""maxima"")","-\frac{{\left(a^{5} x^{5} - a^{3} x^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} x^{m} + {\left(3 \, a^{6} x^{6} - 5 \, a^{4} x^{4} + 2 \, a^{2} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} x^{m} + {\left(3 \, a^{7} x^{7} - 7 \, a^{5} x^{5} + 5 \, a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} x^{m} + {\left(a^{8} x^{8} - 3 \, a^{6} x^{6} + 3 \, a^{4} x^{4} - a^{2} x^{2}\right)} x^{m} + {\left({\left(a^{5} {\left(m + 1\right)} x^{5} - 2 \, a^{3} m x^{3} + a {\left(m - 1\right)} x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} x^{m} + {\left(3 \, a^{6} {\left(m + 1\right)} x^{6} - a^{4} {\left(7 \, m + 3\right)} x^{4} + 5 \, a^{2} m x^{2} - m\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} x^{m} + {\left(3 \, a^{7} {\left(m + 1\right)} x^{7} - 2 \, a^{5} {\left(4 \, m + 3\right)} x^{5} + a^{3} {\left(7 \, m + 4\right)} x^{3} - a {\left(2 \, m + 1\right)} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} x^{m} + {\left(a^{8} {\left(m + 1\right)} x^{8} - 3 \, a^{6} {\left(m + 1\right)} x^{6} + 3 \, a^{4} {\left(m + 1\right)} x^{4} - a^{2} {\left(m + 1\right)} x^{2}\right)} x^{m}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{2 \, {\left(a^{8} x^{7} + {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} a^{5} x^{4} - 3 \, a^{6} x^{5} + 3 \, a^{4} x^{3} + 3 \, {\left(a^{6} x^{5} - a^{4} x^{3}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} - a^{2} x + 3 \, {\left(a^{7} x^{6} - 2 \, a^{5} x^{4} + a^{3} x^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}} + \int \frac{{\left({\left(m^{2} + 2 \, m + 1\right)} a^{6} x^{6} - 2 \, {\left(m^{2} - m\right)} a^{4} x^{4} + {\left(m^{2} - 4 \, m + 3\right)} a^{2} x^{2}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} x^{m} + {\left(4 \, {\left(m^{2} + 2 \, m + 1\right)} a^{7} x^{7} - 2 \, {\left(5 \, m^{2} + m + 2\right)} a^{5} x^{5} + {\left(8 \, m^{2} - 11 \, m + 3\right)} a^{3} x^{3} - {\left(2 \, m^{2} - 5 \, m\right)} a x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} x^{m} + {\left(6 \, {\left(m^{2} + 2 \, m + 1\right)} a^{8} x^{8} - 6 \, {\left(3 \, m^{2} + 3 \, m + 2\right)} a^{6} x^{6} + {\left(19 \, m^{2} + 2 \, m + 3\right)} a^{4} x^{4} - {\left(8 \, m^{2} - 5 \, m - 3\right)} a^{2} x^{2} + m^{2} - m\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} x^{m} + {\left(4 \, {\left(m^{2} + 2 \, m + 1\right)} a^{9} x^{9} - 2 \, {\left(7 \, m^{2} + 11 \, m + 6\right)} a^{7} x^{7} + 3 \, {\left(6 \, m^{2} + 7 \, m + 3\right)} a^{5} x^{5} - {\left(10 \, m^{2} + 8 \, m + 1\right)} a^{3} x^{3} + {\left(2 \, m^{2} + m\right)} a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} x^{m} + {\left({\left(m^{2} + 2 \, m + 1\right)} a^{10} x^{10} - 4 \, {\left(m^{2} + 2 \, m + 1\right)} a^{8} x^{8} + 6 \, {\left(m^{2} + 2 \, m + 1\right)} a^{6} x^{6} - 4 \, {\left(m^{2} + 2 \, m + 1\right)} a^{4} x^{4} + {\left(m^{2} + 2 \, m + 1\right)} a^{2} x^{2}\right)} x^{m}}{2 \, {\left(a^{10} x^{10} + {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} a^{6} x^{6} - 4 \, a^{8} x^{8} + 6 \, a^{6} x^{6} - 4 \, a^{4} x^{4} + 4 \, {\left(a^{7} x^{7} - a^{5} x^{5}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + a^{2} x^{2} + 6 \, {\left(a^{8} x^{8} - 2 \, a^{6} x^{6} + a^{4} x^{4}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 4 \, {\left(a^{9} x^{9} - 3 \, a^{7} x^{7} + 3 \, a^{5} x^{5} - a^{3} x^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/2*((a^5*x^5 - a^3*x^3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2)*x^m + (3*a^6*x^6 - 5*a^4*x^4 + 2*a^2*x^2)*(a*x + 1)*(a*x - 1)*x^m + (3*a^7*x^7 - 7*a^5*x^5 + 5*a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1)*x^m + (a^8*x^8 - 3*a^6*x^6 + 3*a^4*x^4 - a^2*x^2)*x^m + ((a^5*(m + 1)*x^5 - 2*a^3*m*x^3 + a*(m - 1)*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2)*x^m + (3*a^6*(m + 1)*x^6 - a^4*(7*m + 3)*x^4 + 5*a^2*m*x^2 - m)*(a*x + 1)*(a*x - 1)*x^m + (3*a^7*(m + 1)*x^7 - 2*a^5*(4*m + 3)*x^5 + a^3*(7*m + 4)*x^3 - a*(2*m + 1)*x)*sqrt(a*x + 1)*sqrt(a*x - 1)*x^m + (a^8*(m + 1)*x^8 - 3*a^6*(m + 1)*x^6 + 3*a^4*(m + 1)*x^4 - a^2*(m + 1)*x^2)*x^m)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^8*x^7 + (a*x + 1)^(3/2)*(a*x - 1)^(3/2)*a^5*x^4 - 3*a^6*x^5 + 3*a^4*x^3 + 3*(a^6*x^5 - a^4*x^3)*(a*x + 1)*(a*x - 1) - a^2*x + 3*(a^7*x^6 - 2*a^5*x^4 + a^3*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2) + integrate(1/2*(((m^2 + 2*m + 1)*a^6*x^6 - 2*(m^2 - m)*a^4*x^4 + (m^2 - 4*m + 3)*a^2*x^2)*(a*x + 1)^2*(a*x - 1)^2*x^m + (4*(m^2 + 2*m + 1)*a^7*x^7 - 2*(5*m^2 + m + 2)*a^5*x^5 + (8*m^2 - 11*m + 3)*a^3*x^3 - (2*m^2 - 5*m)*a*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2)*x^m + (6*(m^2 + 2*m + 1)*a^8*x^8 - 6*(3*m^2 + 3*m + 2)*a^6*x^6 + (19*m^2 + 2*m + 3)*a^4*x^4 - (8*m^2 - 5*m - 3)*a^2*x^2 + m^2 - m)*(a*x + 1)*(a*x - 1)*x^m + (4*(m^2 + 2*m + 1)*a^9*x^9 - 2*(7*m^2 + 11*m + 6)*a^7*x^7 + 3*(6*m^2 + 7*m + 3)*a^5*x^5 - (10*m^2 + 8*m + 1)*a^3*x^3 + (2*m^2 + m)*a*x)*sqrt(a*x + 1)*sqrt(a*x - 1)*x^m + ((m^2 + 2*m + 1)*a^10*x^10 - 4*(m^2 + 2*m + 1)*a^8*x^8 + 6*(m^2 + 2*m + 1)*a^6*x^6 - 4*(m^2 + 2*m + 1)*a^4*x^4 + (m^2 + 2*m + 1)*a^2*x^2)*x^m)/((a^10*x^10 + (a*x + 1)^2*(a*x - 1)^2*a^6*x^6 - 4*a^8*x^8 + 6*a^6*x^6 - 4*a^4*x^4 + 4*(a^7*x^7 - a^5*x^5)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + a^2*x^2 + 6*(a^8*x^8 - 2*a^6*x^6 + a^4*x^4)*(a*x + 1)*(a*x - 1) + 4*(a^9*x^9 - 3*a^7*x^7 + 3*a^5*x^5 - a^3*x^3)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
122,0,0,0,0.000000," ","integrate(x^m*arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int x^{m} \operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x^m*arccosh(a*x)^(3/2), x)","F",0
123,0,0,0,0.000000," ","integrate(x^m*arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int x^{m} \sqrt{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^m*sqrt(arccosh(a*x)), x)","F",0
124,0,0,0,0.000000," ","integrate(x^m/arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m}}{\sqrt{\operatorname{arcosh}\left(a x\right)}}\,{d x}"," ",0,"integrate(x^m/sqrt(arccosh(a*x)), x)","F",0
125,0,0,0,0.000000," ","integrate(x^m/arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{m}}{\operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m/arccosh(a*x)^(3/2), x)","F",0
126,0,0,0,0.000000," ","integrate((d*x)^m*arccosh(a*x)^n,x, algorithm=""maxima"")","\int \left(d x\right)^{m} \operatorname{arcosh}\left(a x\right)^{n}\,{d x}"," ",0,"integrate((d*x)^m*arccosh(a*x)^n, x)","F",0
127,0,0,0,0.000000," ","integrate(x^4*arccosh(a*x)^n,x, algorithm=""maxima"")","\int x^{4} \operatorname{arcosh}\left(a x\right)^{n}\,{d x}"," ",0,"integrate(x^4*arccosh(a*x)^n, x)","F",0
128,0,0,0,0.000000," ","integrate(x^3*arccosh(a*x)^n,x, algorithm=""maxima"")","\int x^{3} \operatorname{arcosh}\left(a x\right)^{n}\,{d x}"," ",0,"integrate(x^3*arccosh(a*x)^n, x)","F",0
129,0,0,0,0.000000," ","integrate(x^2*arccosh(a*x)^n,x, algorithm=""maxima"")","\int x^{2} \operatorname{arcosh}\left(a x\right)^{n}\,{d x}"," ",0,"integrate(x^2*arccosh(a*x)^n, x)","F",0
130,0,0,0,0.000000," ","integrate(x*arccosh(a*x)^n,x, algorithm=""maxima"")","\int x \operatorname{arcosh}\left(a x\right)^{n}\,{d x}"," ",0,"integrate(x*arccosh(a*x)^n, x)","F",0
131,0,0,0,0.000000," ","integrate(arccosh(a*x)^n,x, algorithm=""maxima"")","\int \operatorname{arcosh}\left(a x\right)^{n}\,{d x}"," ",0,"integrate(arccosh(a*x)^n, x)","F",0
132,0,0,0,0.000000," ","integrate(arccosh(a*x)^n/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{n}}{x}\,{d x}"," ",0,"integrate(arccosh(a*x)^n/x, x)","F",0
133,1,87,0,0.390167," ","integrate(x^3*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{32} \, {\left(8 \, x^{4} \operatorname{arcosh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} x}{c^{4}} + \frac{3 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} b"," ",0,"1/4*a*x^4 + 1/32*(8*x^4*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*b","A",0
134,1,58,0,0.419699," ","integrate(x^2*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b"," ",0,"1/3*a*x^3 + 1/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b","A",0
135,1,66,0,0.625559," ","integrate(x*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x}{c^{2}} + \frac{\log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}}\right)}\right)} b"," ",0,"1/2*a*x^2 + 1/4*(2*x^2*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x/c^2 + log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3))*b","A",0
136,1,30,0,0.535981," ","integrate(a+b*arccosh(c*x),x, algorithm=""maxima"")","a x + \frac{{\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b}{c}"," ",0,"a*x + (c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b/c","A",0
137,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x,x, algorithm=""maxima"")","b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x} + a \log\left(x\right)"," ",0,"b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x) + a*log(x)","F",0
138,1,30,0,0.836985," ","integrate((a+b*arccosh(c*x))/x^2,x, algorithm=""maxima"")","-{\left(c \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arcosh}\left(c x\right)}{x}\right)} b - \frac{a}{x}"," ",0,"-(c*arcsin(1/(c*abs(x))) + arccosh(c*x)/x)*b - a/x","A",0
139,1,36,0,0.533382," ","integrate((a+b*arccosh(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, b {\left(\frac{\sqrt{c^{2} x^{2} - 1} c}{x} - \frac{\operatorname{arcosh}\left(c x\right)}{x^{2}}\right)} - \frac{a}{2 \, x^{2}}"," ",0,"1/2*b*(sqrt(c^2*x^2 - 1)*c/x - arccosh(c*x)/x^2) - 1/2*a/x^2","A",0
140,1,52,0,0.735703," ","integrate((a+b*arccosh(c*x))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(c^{2} \arcsin\left(\frac{1}{c {\left| x \right|}}\right) - \frac{\sqrt{c^{2} x^{2} - 1}}{x^{2}}\right)} c + \frac{2 \, \operatorname{arcosh}\left(c x\right)}{x^{3}}\right)} b - \frac{a}{3 \, x^{3}}"," ",0,"-1/6*((c^2*arcsin(1/(c*abs(x))) - sqrt(c^2*x^2 - 1)/x^2)*c + 2*arccosh(c*x)/x^3)*b - 1/3*a/x^3","A",0
141,1,57,0,0.680652," ","integrate((a+b*arccosh(c*x))/x^5,x, algorithm=""maxima"")","\frac{1}{12} \, {\left({\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} c^{2}}{x} + \frac{\sqrt{c^{2} x^{2} - 1}}{x^{3}}\right)} c - \frac{3 \, \operatorname{arcosh}\left(c x\right)}{x^{4}}\right)} b - \frac{a}{4 \, x^{4}}"," ",0,"1/12*((2*sqrt(c^2*x^2 - 1)*c^2/x + sqrt(c^2*x^2 - 1)/x^3)*c - 3*arccosh(c*x)/x^4)*b - 1/4*a/x^4","A",0
142,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{arcosh}\left(c x\right) + a} x^{2}\,{d x}"," ",0,"integrate(sqrt(b*arccosh(c*x) + a)*x^2, x)","F",0
143,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{arcosh}\left(c x\right) + a} x\,{d x}"," ",0,"integrate(sqrt(b*arccosh(c*x) + a)*x, x)","F",0
144,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*arccosh(c*x) + a), x)","F",0
145,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}} x^{2}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^(3/2)*x^2, x)","F",0
146,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}} x\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^(3/2)*x, x)","F",0
147,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^(3/2), x)","F",0
148,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))^(5/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{5}{2}} x^{2}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^(5/2)*x^2, x)","F",0
149,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))^(5/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{5}{2}} x\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^(5/2)*x, x)","F",0
150,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^(5/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^(5/2), x)","F",0
151,0,0,0,0.000000," ","integrate(x^2/(a+b*arccosh(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{b \operatorname{arcosh}\left(c x\right) + a}}\,{d x}"," ",0,"integrate(x^2/sqrt(b*arccosh(c*x) + a), x)","F",0
152,0,0,0,0.000000," ","integrate(x/(a+b*arccosh(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{b \operatorname{arcosh}\left(c x\right) + a}}\,{d x}"," ",0,"integrate(x/sqrt(b*arccosh(c*x) + a), x)","F",0
153,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \operatorname{arcosh}\left(c x\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arccosh(c*x) + a), x)","F",0
154,0,0,0,0.000000," ","integrate(x^2/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(b*arccosh(c*x) + a)^(3/2), x)","F",0
155,0,0,0,0.000000," ","integrate(x/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{x}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(b*arccosh(c*x) + a)^(3/2), x)","F",0
156,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^(-3/2), x)","F",0
157,0,0,0,0.000000," ","integrate(x^2/(a+b*arccosh(c*x))^(5/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^2/(b*arccosh(c*x) + a)^(5/2), x)","F",0
158,0,0,0,0.000000," ","integrate(x/(a+b*arccosh(c*x))^(5/2),x, algorithm=""maxima"")","\int \frac{x}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x/(b*arccosh(c*x) + a)^(5/2), x)","F",0
159,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(c*x))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^(-5/2), x)","F",0
160,0,0,0,0.000000," ","integrate(x^2/(a+b*arccosh(c*x))^(7/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(x^2/(b*arccosh(c*x) + a)^(7/2), x)","F",0
161,0,0,0,0.000000," ","integrate(x/(a+b*arccosh(c*x))^(7/2),x, algorithm=""maxima"")","\int \frac{x}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(x/(b*arccosh(c*x) + a)^(7/2), x)","F",0
162,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(c*x))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^(-7/2), x)","F",0
163,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2*(f*x)^(1/2),x, algorithm=""maxima"")","\frac{2}{3} \, b^{2} \sqrt{f} x^{\frac{3}{2}} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + \frac{2 \, \left(f x\right)^{\frac{3}{2}} a^{2}}{3 \, f} + \int \frac{2 \, {\left({\left({\left(3 \, a b c^{2} \sqrt{f} - 2 \, b^{2} c^{2} \sqrt{f}\right)} x^{2} - 3 \, a b \sqrt{f}\right)} \sqrt{c x + 1} \sqrt{c x - 1} \sqrt{x} + {\left({\left(3 \, a b c^{3} \sqrt{f} - 2 \, b^{2} c^{3} \sqrt{f}\right)} x^{3} - {\left(3 \, a b c \sqrt{f} - 2 \, b^{2} c \sqrt{f}\right)} x\right)} \sqrt{x}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{3 \, {\left(c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x\right)}}\,{d x}"," ",0,"2/3*b^2*sqrt(f)*x^(3/2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 2/3*(f*x)^(3/2)*a^2/f + integrate(2/3*(((3*a*b*c^2*sqrt(f) - 2*b^2*c^2*sqrt(f))*x^2 - 3*a*b*sqrt(f))*sqrt(c*x + 1)*sqrt(c*x - 1)*sqrt(x) + ((3*a*b*c^3*sqrt(f) - 2*b^2*c^3*sqrt(f))*x^3 - (3*a*b*c*sqrt(f) - 2*b^2*c*sqrt(f))*x)*sqrt(x))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x), x)","F",0
164,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{b^{2} d^{m} x x^{m} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{m + 1} + \frac{\left(d x\right)^{m + 1} a^{2}}{d {\left(m + 1\right)}} + \int -\frac{2 \, {\left({\left(a b d^{m} {\left(m + 1\right)} - {\left(a b c^{2} d^{m} {\left(m + 1\right)} - b^{2} c^{2} d^{m}\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1} x^{m} - {\left({\left(a b c^{3} d^{m} {\left(m + 1\right)} - b^{2} c^{3} d^{m}\right)} x^{3} - {\left(a b c d^{m} {\left(m + 1\right)} - b^{2} c d^{m}\right)} x\right)} x^{m}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{3} {\left(m + 1\right)} x^{3} - c {\left(m + 1\right)} x + {\left(c^{2} {\left(m + 1\right)} x^{2} - m - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1}}\,{d x}"," ",0,"b^2*d^m*x*x^m*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(m + 1) + (d*x)^(m + 1)*a^2/(d*(m + 1)) + integrate(-2*((a*b*d^m*(m + 1) - (a*b*c^2*d^m*(m + 1) - b^2*c^2*d^m)*x^2)*sqrt(c*x + 1)*sqrt(c*x - 1)*x^m - ((a*b*c^3*d^m*(m + 1) - b^2*c^3*d^m)*x^3 - (a*b*c*d^m*(m + 1) - b^2*c*d^m)*x)*x^m)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^3*(m + 1)*x^3 - c*(m + 1)*x + (c^2*(m + 1)*x^2 - m - 1)*sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
165,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-{\left(c^{2} d^{m} \int \frac{x^{2} x^{m}}{c^{2} {\left(m + 1\right)} x^{2} - m - 1}\,{d x} - c d^{m} \int \frac{x x^{m}}{c^{3} {\left(m + 1\right)} x^{3} - c {\left(m + 1\right)} x + {\left(c^{2} {\left(m + 1\right)} x^{2} - m - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1}}\,{d x} - \frac{d^{m} x x^{m} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{m + 1}\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 - m - 1), x) - c*d^m*integrate(x*x^m/(c^3*(m + 1)*x^3 - c*(m + 1)*x + (c^2*(m + 1)*x^2 - m - 1)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) - d^m*x*x^m*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(m + 1))*b + (d*x)^(m + 1)*a/(d*(m + 1))","F",0
166,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{\left(d x\right)^{m}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((d*x)^m/(b*arccosh(c*x) + a), x)","F",0
