1,1,121,0,0.310592," ","integrate(x^3*(c*d*x+d)*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a c d x^{5} + \frac{1}{4} \, a d x^{4} + \frac{1}{20} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b c d + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b d"," ",0,"1/5*a*c*d*x^5 + 1/4*a*d*x^4 + 1/20*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*c*d + 1/24*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*d","A",0
2,1,110,0,0.320077," ","integrate(x^2*(c*d*x+d)*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a c d x^{4} + \frac{1}{3} \, a d x^{3} + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b c d + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b d"," ",0,"1/4*a*c*d*x^4 + 1/3*a*d*x^3 + 1/24*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*c*d + 1/6*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*d","A",0
3,1,99,0,0.306531," ","integrate(x*(c*d*x+d)*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a c d x^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b c d + \frac{1}{2} \, a d x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b d"," ",0,"1/3*a*c*d*x^3 + 1/6*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*c*d + 1/2*a*d*x^2 + 1/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*d","A",0
4,1,85,0,0.313776," ","integrate((c*d*x+d)*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, a c d x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b c d + a d x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d}{2 \, c}"," ",0,"1/2*a*c*d*x^2 + 1/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*c*d + a*d*x + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*d/c","B",0
5,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x,x, algorithm=""maxima"")","a c d x + \frac{1}{2} \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d + \frac{1}{2} \, b d \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{x}\,{d x} + a d \log\left(x\right)"," ",0,"a*c*d*x + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*d + 1/2*b*d*integrate((log(c*x + 1) - log(-c*x + 1))/x, x) + a*d*log(x)","F",0
6,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, b c d \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{x}\,{d x} + a c d \log\left(x\right) - \frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b d - \frac{a d}{x}"," ",0,"1/2*b*c*d*integrate((log(c*x + 1) - log(-c*x + 1))/x, x) + a*c*d*log(x) - 1/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*d - a*d/x","F",0
7,1,89,0,0.315428," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b c d + \frac{1}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b d - \frac{a c d}{x} - \frac{a d}{2 \, x^{2}}"," ",0,"-1/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*c*d + 1/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*d - a*c*d/x - 1/2*a*d/x^2","A",0
8,1,99,0,0.314333," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x^4,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b c d - \frac{1}{6} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b d - \frac{a c d}{2 \, x^{2}} - \frac{a d}{3 \, x^{3}}"," ",0,"1/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*c*d - 1/6*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*d - 1/2*a*c*d/x^2 - 1/3*a*d/x^3","A",0
9,1,114,0,0.314535," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x^5,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b c d + \frac{1}{24} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} b d - \frac{a c d}{3 \, x^{3}} - \frac{a d}{4 \, x^{4}}"," ",0,"-1/6*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*c*d + 1/24*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*b*d - 1/3*a*c*d/x^3 - 1/4*a*d/x^4","A",0
10,1,210,0,0.330499," ","integrate(x^3*(c*d*x+d)^2*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a c^{2} d^{2} x^{6} + \frac{2}{5} \, a c d^{2} x^{5} + \frac{1}{4} \, a d^{2} x^{4} + \frac{1}{180} \, {\left(30 \, x^{6} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} b c^{2} d^{2} + \frac{1}{10} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b c d^{2} + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b d^{2}"," ",0,"1/6*a*c^2*d^2*x^6 + 2/5*a*c*d^2*x^5 + 1/4*a*d^2*x^4 + 1/180*(30*x^6*arctanh(c*x) + c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*b*c^2*d^2 + 1/10*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*c*d^2 + 1/24*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*d^2","A",0
11,1,184,0,0.312119," ","integrate(x^2*(c*d*x+d)^2*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a c^{2} d^{2} x^{5} + \frac{1}{2} \, a c d^{2} x^{4} + \frac{1}{20} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b c^{2} d^{2} + \frac{1}{3} \, a d^{2} x^{3} + \frac{1}{12} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b c d^{2} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b d^{2}"," ",0,"1/5*a*c^2*d^2*x^5 + 1/2*a*c*d^2*x^4 + 1/20*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*c^2*d^2 + 1/3*a*d^2*x^3 + 1/12*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*c*d^2 + 1/6*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*d^2","A",0
12,1,179,0,0.313335," ","integrate(x*(c*d*x+d)^2*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a c^{2} d^{2} x^{4} + \frac{2}{3} \, a c d^{2} x^{3} + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b c^{2} d^{2} + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b c d^{2} + \frac{1}{2} \, a d^{2} x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b d^{2}"," ",0,"1/4*a*c^2*d^2*x^4 + 2/3*a*c*d^2*x^3 + 1/24*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*c^2*d^2 + 1/3*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*c*d^2 + 1/2*a*d^2*x^2 + 1/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*d^2","A",0
13,1,147,0,0.315275," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a c^{2} d^{2} x^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b c^{2} d^{2} + a c d^{2} x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b c d^{2} + a d^{2} x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d^{2}}{2 \, c}"," ",0,"1/3*a*c^2*d^2*x^3 + 1/6*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*c^2*d^2 + a*c*d^2*x^2 + 1/2*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*c*d^2 + a*d^2*x + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*d^2/c","B",0
14,1,173,0,0.472327," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x,x, algorithm=""maxima"")","\frac{1}{4} \, b c^{2} d^{2} x^{2} \log\left(c x + 1\right) - \frac{1}{4} \, b c^{2} d^{2} x^{2} \log\left(-c x + 1\right) + \frac{1}{2} \, a c^{2} d^{2} x^{2} + 2 \, a c d^{2} x + \frac{1}{2} \, b c d^{2} x + {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d^{2} - \frac{1}{2} \, {\left(\log\left(c x\right) \log\left(-c x + 1\right) + {\rm Li}_2\left(-c x + 1\right)\right)} b d^{2} + \frac{1}{2} \, {\left(\log\left(c x + 1\right) \log\left(-c x\right) + {\rm Li}_2\left(c x + 1\right)\right)} b d^{2} - \frac{1}{4} \, b d^{2} \log\left(c x + 1\right) + \frac{1}{4} \, b d^{2} \log\left(c x - 1\right) + a d^{2} \log\left(x\right)"," ",0,"1/4*b*c^2*d^2*x^2*log(c*x + 1) - 1/4*b*c^2*d^2*x^2*log(-c*x + 1) + 1/2*a*c^2*d^2*x^2 + 2*a*c*d^2*x + 1/2*b*c*d^2*x + (2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*d^2 - 1/2*(log(c*x)*log(-c*x + 1) + dilog(-c*x + 1))*b*d^2 + 1/2*(log(c*x + 1)*log(-c*x) + dilog(c*x + 1))*b*d^2 - 1/4*b*d^2*log(c*x + 1) + 1/4*b*d^2*log(c*x - 1) + a*d^2*log(x)","A",0
15,0,0,0,0.000000," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^2,x, algorithm=""maxima"")","a c^{2} d^{2} x + \frac{1}{2} \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b c d^{2} + b c d^{2} \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{x}\,{d x} + 2 \, a c d^{2} \log\left(x\right) - \frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b d^{2} - \frac{a d^{2}}{x}"," ",0,"a*c^2*d^2*x + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*c*d^2 + b*c*d^2*integrate((log(c*x + 1) - log(-c*x + 1))/x, x) + 2*a*c*d^2*log(x) - 1/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*d^2 - a*d^2/x","F",0
16,0,0,0,0.000000," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, b c^{2} d^{2} \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{x}\,{d x} + a c^{2} d^{2} \log\left(x\right) - {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b c d^{2} + \frac{1}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b d^{2} - \frac{2 \, a c d^{2}}{x} - \frac{a d^{2}}{2 \, x^{2}}"," ",0,"1/2*b*c^2*d^2*integrate((log(c*x + 1) - log(-c*x + 1))/x, x) + a*c^2*d^2*log(x) - (c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*c*d^2 + 1/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*d^2 - 2*a*c*d^2/x - 1/2*a*d^2/x^2","F",0
17,1,157,0,0.319777," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^4,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b c^{2} d^{2} + \frac{1}{2} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b c d^{2} - \frac{1}{6} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b d^{2} - \frac{a c^{2} d^{2}}{x} - \frac{a c d^{2}}{x^{2}} - \frac{a d^{2}}{3 \, x^{3}}"," ",0,"-1/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*c^2*d^2 + 1/2*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*c*d^2 - 1/6*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*d^2 - a*c^2*d^2/x - a*c*d^2/x^2 - 1/3*a*d^2/x^3","B",0
18,1,178,0,0.318795," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^5,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b c^{2} d^{2} - \frac{1}{3} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b c d^{2} + \frac{1}{24} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} b d^{2} - \frac{a c^{2} d^{2}}{2 \, x^{2}} - \frac{2 \, a c d^{2}}{3 \, x^{3}} - \frac{a d^{2}}{4 \, x^{4}}"," ",0,"1/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*c^2*d^2 - 1/3*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*c*d^2 + 1/24*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*b*d^2 - 1/2*a*c^2*d^2/x^2 - 2/3*a*c*d^2/x^3 - 1/4*a*d^2/x^4","A",0
19,1,194,0,0.319151," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^6,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b c^{2} d^{2} + \frac{1}{12} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} b c d^{2} - \frac{1}{20} \, {\left({\left(2 \, c^{4} \log\left(c^{2} x^{2} - 1\right) - 2 \, c^{4} \log\left(x^{2}\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} c + \frac{4 \, \operatorname{artanh}\left(c x\right)}{x^{5}}\right)} b d^{2} - \frac{a c^{2} d^{2}}{3 \, x^{3}} - \frac{a c d^{2}}{2 \, x^{4}} - \frac{a d^{2}}{5 \, x^{5}}"," ",0,"-1/6*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*c^2*d^2 + 1/12*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*b*c*d^2 - 1/20*((2*c^4*log(c^2*x^2 - 1) - 2*c^4*log(x^2) + (2*c^2*x^2 + 1)/x^4)*c + 4*arctanh(c*x)/x^5)*b*d^2 - 1/3*a*c^2*d^2/x^3 - 1/2*a*c*d^2/x^4 - 1/5*a*d^2/x^5","A",0
20,1,285,0,0.320031," ","integrate(x^3*(c*d*x+d)^3*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a c^{3} d^{3} x^{7} + \frac{1}{2} \, a c^{2} d^{3} x^{6} + \frac{3}{5} \, a c d^{3} x^{5} + \frac{1}{84} \, {\left(12 \, x^{7} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, c^{4} x^{6} + 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{6}} + \frac{6 \, \log\left(c^{2} x^{2} - 1\right)}{c^{8}}\right)}\right)} b c^{3} d^{3} + \frac{1}{4} \, a d^{3} x^{4} + \frac{1}{60} \, {\left(30 \, x^{6} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} b c^{2} d^{3} + \frac{3}{20} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b c d^{3} + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b d^{3}"," ",0,"1/7*a*c^3*d^3*x^7 + 1/2*a*c^2*d^3*x^6 + 3/5*a*c*d^3*x^5 + 1/84*(12*x^7*arctanh(c*x) + c*((2*c^4*x^6 + 3*c^2*x^4 + 6*x^2)/c^6 + 6*log(c^2*x^2 - 1)/c^8))*b*c^3*d^3 + 1/4*a*d^3*x^4 + 1/60*(30*x^6*arctanh(c*x) + c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*b*c^2*d^3 + 3/20*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*c*d^3 + 1/24*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*d^3","A",0
21,1,265,0,0.321007," ","integrate(x^2*(c*d*x+d)^3*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a c^{3} d^{3} x^{6} + \frac{3}{5} \, a c^{2} d^{3} x^{5} + \frac{3}{4} \, a c d^{3} x^{4} + \frac{1}{180} \, {\left(30 \, x^{6} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} b c^{3} d^{3} + \frac{3}{20} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b c^{2} d^{3} + \frac{1}{3} \, a d^{3} x^{3} + \frac{1}{8} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b c d^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b d^{3}"," ",0,"1/6*a*c^3*d^3*x^6 + 3/5*a*c^2*d^3*x^5 + 3/4*a*c*d^3*x^4 + 1/180*(30*x^6*arctanh(c*x) + c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*b*c^3*d^3 + 3/20*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*c^2*d^3 + 1/3*a*d^3*x^3 + 1/8*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*c*d^3 + 1/6*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*d^3","A",0
22,1,244,0,0.318275," ","integrate(x*(c*d*x+d)^3*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a c^{3} d^{3} x^{5} + \frac{3}{4} \, a c^{2} d^{3} x^{4} + \frac{1}{20} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b c^{3} d^{3} + a c d^{3} x^{3} + \frac{1}{8} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b c^{2} d^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b c d^{3} + \frac{1}{2} \, a d^{3} x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b d^{3}"," ",0,"1/5*a*c^3*d^3*x^5 + 3/4*a*c^2*d^3*x^4 + 1/20*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*c^3*d^3 + a*c*d^3*x^3 + 1/8*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*c^2*d^3 + 1/2*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*c*d^3 + 1/2*a*d^3*x^2 + 1/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*d^3","B",0
23,1,219,0,0.319706," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a c^{3} d^{3} x^{4} + a c^{2} d^{3} x^{3} + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b c^{3} d^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b c^{2} d^{3} + \frac{3}{2} \, a c d^{3} x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b c d^{3} + a d^{3} x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d^{3}}{2 \, c}"," ",0,"1/4*a*c^3*d^3*x^4 + a*c^2*d^3*x^3 + 1/24*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*c^3*d^3 + 1/2*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*c^2*d^3 + 3/2*a*c*d^3*x^2 + 3/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*c*d^3 + a*d^3*x + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*d^3/c","B",0
24,1,228,0,0.460343," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x,x, algorithm=""maxima"")","\frac{1}{3} \, a c^{3} d^{3} x^{3} + \frac{3}{2} \, a c^{2} d^{3} x^{2} + \frac{1}{6} \, b c^{2} d^{3} x^{2} + 3 \, a c d^{3} x + \frac{3}{2} \, b c d^{3} x + \frac{3}{2} \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d^{3} - \frac{1}{2} \, {\left(\log\left(c x\right) \log\left(-c x + 1\right) + {\rm Li}_2\left(-c x + 1\right)\right)} b d^{3} + \frac{1}{2} \, {\left(\log\left(c x + 1\right) \log\left(-c x\right) + {\rm Li}_2\left(c x + 1\right)\right)} b d^{3} - \frac{7}{12} \, b d^{3} \log\left(c x + 1\right) + \frac{11}{12} \, b d^{3} \log\left(c x - 1\right) + a d^{3} \log\left(x\right) + \frac{1}{12} \, {\left(2 \, b c^{3} d^{3} x^{3} + 9 \, b c^{2} d^{3} x^{2}\right)} \log\left(c x + 1\right) - \frac{1}{12} \, {\left(2 \, b c^{3} d^{3} x^{3} + 9 \, b c^{2} d^{3} x^{2}\right)} \log\left(-c x + 1\right)"," ",0,"1/3*a*c^3*d^3*x^3 + 3/2*a*c^2*d^3*x^2 + 1/6*b*c^2*d^3*x^2 + 3*a*c*d^3*x + 3/2*b*c*d^3*x + 3/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*d^3 - 1/2*(log(c*x)*log(-c*x + 1) + dilog(-c*x + 1))*b*d^3 + 1/2*(log(c*x + 1)*log(-c*x) + dilog(c*x + 1))*b*d^3 - 7/12*b*d^3*log(c*x + 1) + 11/12*b*d^3*log(c*x - 1) + a*d^3*log(x) + 1/12*(2*b*c^3*d^3*x^3 + 9*b*c^2*d^3*x^2)*log(c*x + 1) - 1/12*(2*b*c^3*d^3*x^3 + 9*b*c^2*d^3*x^2)*log(-c*x + 1)","A",0
25,1,229,0,0.487901," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, b c^{3} d^{3} x^{2} \log\left(c x + 1\right) - \frac{1}{4} \, b c^{3} d^{3} x^{2} \log\left(-c x + 1\right) + \frac{1}{2} \, a c^{3} d^{3} x^{2} + 3 \, a c^{2} d^{3} x + \frac{1}{2} \, b c^{2} d^{3} x + \frac{3}{2} \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b c d^{3} - \frac{3}{2} \, {\left(\log\left(c x\right) \log\left(-c x + 1\right) + {\rm Li}_2\left(-c x + 1\right)\right)} b c d^{3} + \frac{3}{2} \, {\left(\log\left(c x + 1\right) \log\left(-c x\right) + {\rm Li}_2\left(c x + 1\right)\right)} b c d^{3} - \frac{1}{4} \, b c d^{3} \log\left(c x + 1\right) + \frac{1}{4} \, b c d^{3} \log\left(c x - 1\right) + 3 \, a c d^{3} \log\left(x\right) - \frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b d^{3} - \frac{a d^{3}}{x}"," ",0,"1/4*b*c^3*d^3*x^2*log(c*x + 1) - 1/4*b*c^3*d^3*x^2*log(-c*x + 1) + 1/2*a*c^3*d^3*x^2 + 3*a*c^2*d^3*x + 1/2*b*c^2*d^3*x + 3/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*c*d^3 - 3/2*(log(c*x)*log(-c*x + 1) + dilog(-c*x + 1))*b*c*d^3 + 3/2*(log(c*x + 1)*log(-c*x) + dilog(c*x + 1))*b*c*d^3 - 1/4*b*c*d^3*log(c*x + 1) + 1/4*b*c*d^3*log(c*x - 1) + 3*a*c*d^3*log(x) - 1/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*d^3 - a*d^3/x","A",0
26,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^3,x, algorithm=""maxima"")","a c^{3} d^{3} x + \frac{1}{2} \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b c^{2} d^{3} + \frac{3}{2} \, b c^{2} d^{3} \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{x}\,{d x} + 3 \, a c^{2} d^{3} \log\left(x\right) - \frac{3}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b c d^{3} + \frac{1}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b d^{3} - \frac{3 \, a c d^{3}}{x} - \frac{a d^{3}}{2 \, x^{2}}"," ",0,"a*c^3*d^3*x + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*c^2*d^3 + 3/2*b*c^2*d^3*integrate((log(c*x + 1) - log(-c*x + 1))/x, x) + 3*a*c^2*d^3*log(x) - 3/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*c*d^3 + 1/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*d^3 - 3*a*c*d^3/x - 1/2*a*d^3/x^2","F",0
27,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^4,x, algorithm=""maxima"")","\frac{1}{2} \, b c^{3} d^{3} \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{x}\,{d x} + a c^{3} d^{3} \log\left(x\right) - \frac{3}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b c^{2} d^{3} + \frac{3}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b c d^{3} - \frac{1}{6} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b d^{3} - \frac{3 \, a c^{2} d^{3}}{x} - \frac{3 \, a c d^{3}}{2 \, x^{2}} - \frac{a d^{3}}{3 \, x^{3}}"," ",0,"1/2*b*c^3*d^3*integrate((log(c*x + 1) - log(-c*x + 1))/x, x) + a*c^3*d^3*log(x) - 3/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*c^2*d^3 + 3/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*c*d^3 - 1/6*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*d^3 - 3*a*c^2*d^3/x - 3/2*a*c*d^3/x^2 - 1/3*a*d^3/x^3","F",0
28,1,228,0,0.328068," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^5,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b c^{3} d^{3} + \frac{3}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b c^{2} d^{3} - \frac{1}{2} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b c d^{3} - \frac{a c^{3} d^{3}}{x} + \frac{1}{24} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} b d^{3} - \frac{3 \, a c^{2} d^{3}}{2 \, x^{2}} - \frac{a c d^{3}}{x^{3}} - \frac{a d^{3}}{4 \, x^{4}}"," ",0,"-1/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*c^3*d^3 + 3/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*c^2*d^3 - 1/2*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*c*d^3 - a*c^3*d^3/x + 1/24*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*b*d^3 - 3/2*a*c^2*d^3/x^2 - a*c*d^3/x^3 - 1/4*a*d^3/x^4","B",0
29,1,250,0,0.325664," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^6,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b c^{3} d^{3} - \frac{1}{2} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b c^{2} d^{3} + \frac{1}{8} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} b c d^{3} - \frac{1}{20} \, {\left({\left(2 \, c^{4} \log\left(c^{2} x^{2} - 1\right) - 2 \, c^{4} \log\left(x^{2}\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} c + \frac{4 \, \operatorname{artanh}\left(c x\right)}{x^{5}}\right)} b d^{3} - \frac{a c^{3} d^{3}}{2 \, x^{2}} - \frac{a c^{2} d^{3}}{x^{3}} - \frac{3 \, a c d^{3}}{4 \, x^{4}} - \frac{a d^{3}}{5 \, x^{5}}"," ",0,"1/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*c^3*d^3 - 1/2*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*c^2*d^3 + 1/8*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*b*c*d^3 - 1/20*((2*c^4*log(c^2*x^2 - 1) - 2*c^4*log(x^2) + (2*c^2*x^2 + 1)/x^4)*c + 4*arctanh(c*x)/x^5)*b*d^3 - 1/2*a*c^3*d^3/x^2 - a*c^2*d^3/x^3 - 3/4*a*c*d^3/x^4 - 1/5*a*d^3/x^5","B",0
30,1,273,0,0.328293," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^7,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b c^{3} d^{3} + \frac{1}{8} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} b c^{2} d^{3} - \frac{3}{20} \, {\left({\left(2 \, c^{4} \log\left(c^{2} x^{2} - 1\right) - 2 \, c^{4} \log\left(x^{2}\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} c + \frac{4 \, \operatorname{artanh}\left(c x\right)}{x^{5}}\right)} b c d^{3} + \frac{1}{180} \, {\left({\left(15 \, c^{5} \log\left(c x + 1\right) - 15 \, c^{5} \log\left(c x - 1\right) - \frac{2 \, {\left(15 \, c^{4} x^{4} + 5 \, c^{2} x^{2} + 3\right)}}{x^{5}}\right)} c - \frac{30 \, \operatorname{artanh}\left(c x\right)}{x^{6}}\right)} b d^{3} - \frac{a c^{3} d^{3}}{3 \, x^{3}} - \frac{3 \, a c^{2} d^{3}}{4 \, x^{4}} - \frac{3 \, a c d^{3}}{5 \, x^{5}} - \frac{a d^{3}}{6 \, x^{6}}"," ",0,"-1/6*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*c^3*d^3 + 1/8*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*b*c^2*d^3 - 3/20*((2*c^4*log(c^2*x^2 - 1) - 2*c^4*log(x^2) + (2*c^2*x^2 + 1)/x^4)*c + 4*arctanh(c*x)/x^5)*b*c*d^3 + 1/180*((15*c^5*log(c*x + 1) - 15*c^5*log(c*x - 1) - 2*(15*c^4*x^4 + 5*c^2*x^2 + 3)/x^5)*c - 30*arctanh(c*x)/x^6)*b*d^3 - 1/3*a*c^3*d^3/x^3 - 3/4*a*c^2*d^3/x^4 - 3/5*a*c*d^3/x^5 - 1/6*a*d^3/x^6","A",0
31,1,373,0,0.332578," ","integrate(x^3*(c*d*x+d)^4*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a c^{4} d^{4} x^{8} + \frac{4}{7} \, a c^{3} d^{4} x^{7} + a c^{2} d^{4} x^{6} + \frac{4}{5} \, a c d^{4} x^{5} + \frac{1}{1680} \, {\left(210 \, x^{8} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(15 \, c^{6} x^{7} + 21 \, c^{4} x^{5} + 35 \, c^{2} x^{3} + 105 \, x\right)}}{c^{8}} - \frac{105 \, \log\left(c x + 1\right)}{c^{9}} + \frac{105 \, \log\left(c x - 1\right)}{c^{9}}\right)}\right)} b c^{4} d^{4} + \frac{1}{21} \, {\left(12 \, x^{7} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, c^{4} x^{6} + 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{6}} + \frac{6 \, \log\left(c^{2} x^{2} - 1\right)}{c^{8}}\right)}\right)} b c^{3} d^{4} + \frac{1}{4} \, a d^{4} x^{4} + \frac{1}{30} \, {\left(30 \, x^{6} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} b c^{2} d^{4} + \frac{1}{5} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b c d^{4} + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b d^{4}"," ",0,"1/8*a*c^4*d^4*x^8 + 4/7*a*c^3*d^4*x^7 + a*c^2*d^4*x^6 + 4/5*a*c*d^4*x^5 + 1/1680*(210*x^8*arctanh(c*x) + c*(2*(15*c^6*x^7 + 21*c^4*x^5 + 35*c^2*x^3 + 105*x)/c^8 - 105*log(c*x + 1)/c^9 + 105*log(c*x - 1)/c^9))*b*c^4*d^4 + 1/21*(12*x^7*arctanh(c*x) + c*((2*c^4*x^6 + 3*c^2*x^4 + 6*x^2)/c^6 + 6*log(c^2*x^2 - 1)/c^8))*b*c^3*d^4 + 1/4*a*d^4*x^4 + 1/30*(30*x^6*arctanh(c*x) + c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*b*c^2*d^4 + 1/5*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*c*d^4 + 1/24*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*d^4","A",0
32,1,339,0,0.333023," ","integrate(x^2*(c*d*x+d)^4*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a c^{4} d^{4} x^{7} + \frac{2}{3} \, a c^{3} d^{4} x^{6} + \frac{6}{5} \, a c^{2} d^{4} x^{5} + \frac{1}{84} \, {\left(12 \, x^{7} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, c^{4} x^{6} + 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{6}} + \frac{6 \, \log\left(c^{2} x^{2} - 1\right)}{c^{8}}\right)}\right)} b c^{4} d^{4} + a c d^{4} x^{4} + \frac{1}{45} \, {\left(30 \, x^{6} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} b c^{3} d^{4} + \frac{3}{10} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b c^{2} d^{4} + \frac{1}{3} \, a d^{4} x^{3} + \frac{1}{6} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b c d^{4} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b d^{4}"," ",0,"1/7*a*c^4*d^4*x^7 + 2/3*a*c^3*d^4*x^6 + 6/5*a*c^2*d^4*x^5 + 1/84*(12*x^7*arctanh(c*x) + c*((2*c^4*x^6 + 3*c^2*x^4 + 6*x^2)/c^6 + 6*log(c^2*x^2 - 1)/c^8))*b*c^4*d^4 + a*c*d^4*x^4 + 1/45*(30*x^6*arctanh(c*x) + c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*b*c^3*d^4 + 3/10*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*c^2*d^4 + 1/3*a*d^4*x^3 + 1/6*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*c*d^4 + 1/6*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*d^4","B",0
33,1,326,0,0.336390," ","integrate(x*(c*d*x+d)^4*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a c^{4} d^{4} x^{6} + \frac{4}{5} \, a c^{3} d^{4} x^{5} + \frac{3}{2} \, a c^{2} d^{4} x^{4} + \frac{1}{180} \, {\left(30 \, x^{6} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} b c^{4} d^{4} + \frac{1}{5} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b c^{3} d^{4} + \frac{4}{3} \, a c d^{4} x^{3} + \frac{1}{4} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b c^{2} d^{4} + \frac{2}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b c d^{4} + \frac{1}{2} \, a d^{4} x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b d^{4}"," ",0,"1/6*a*c^4*d^4*x^6 + 4/5*a*c^3*d^4*x^5 + 3/2*a*c^2*d^4*x^4 + 1/180*(30*x^6*arctanh(c*x) + c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*b*c^4*d^4 + 1/5*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*c^3*d^4 + 4/3*a*c*d^4*x^3 + 1/4*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*c^2*d^4 + 2/3*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*c*d^4 + 1/2*a*d^4*x^2 + 1/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*d^4","B",0
34,1,283,0,0.334449," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a c^{4} d^{4} x^{5} + a c^{3} d^{4} x^{4} + \frac{1}{20} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b c^{4} d^{4} + 2 \, a c^{2} d^{4} x^{3} + \frac{1}{6} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b c^{3} d^{4} + {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b c^{2} d^{4} + 2 \, a c d^{4} x^{2} + {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b c d^{4} + a d^{4} x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d^{4}}{2 \, c}"," ",0,"1/5*a*c^4*d^4*x^5 + a*c^3*d^4*x^4 + 1/20*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*c^4*d^4 + 2*a*c^2*d^4*x^3 + 1/6*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*c^3*d^4 + (2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*c^2*d^4 + 2*a*c*d^4*x^2 + (2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*c*d^4 + a*d^4*x + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*d^4/c","B",0
35,1,276,0,0.471708," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x,x, algorithm=""maxima"")","\frac{1}{4} \, a c^{4} d^{4} x^{4} + \frac{4}{3} \, a c^{3} d^{4} x^{3} + \frac{1}{12} \, b c^{3} d^{4} x^{3} + 3 \, a c^{2} d^{4} x^{2} + \frac{2}{3} \, b c^{2} d^{4} x^{2} + 4 \, a c d^{4} x + \frac{13}{4} \, b c d^{4} x + 2 \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d^{4} - \frac{1}{2} \, {\left(\log\left(c x\right) \log\left(-c x + 1\right) + {\rm Li}_2\left(-c x + 1\right)\right)} b d^{4} + \frac{1}{2} \, {\left(\log\left(c x + 1\right) \log\left(-c x\right) + {\rm Li}_2\left(c x + 1\right)\right)} b d^{4} - \frac{23}{24} \, b d^{4} \log\left(c x + 1\right) + \frac{55}{24} \, b d^{4} \log\left(c x - 1\right) + a d^{4} \log\left(x\right) + \frac{1}{24} \, {\left(3 \, b c^{4} d^{4} x^{4} + 16 \, b c^{3} d^{4} x^{3} + 36 \, b c^{2} d^{4} x^{2}\right)} \log\left(c x + 1\right) - \frac{1}{24} \, {\left(3 \, b c^{4} d^{4} x^{4} + 16 \, b c^{3} d^{4} x^{3} + 36 \, b c^{2} d^{4} x^{2}\right)} \log\left(-c x + 1\right)"," ",0,"1/4*a*c^4*d^4*x^4 + 4/3*a*c^3*d^4*x^3 + 1/12*b*c^3*d^4*x^3 + 3*a*c^2*d^4*x^2 + 2/3*b*c^2*d^4*x^2 + 4*a*c*d^4*x + 13/4*b*c*d^4*x + 2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*d^4 - 1/2*(log(c*x)*log(-c*x + 1) + dilog(-c*x + 1))*b*d^4 + 1/2*(log(c*x + 1)*log(-c*x) + dilog(c*x + 1))*b*d^4 - 23/24*b*d^4*log(c*x + 1) + 55/24*b*d^4*log(c*x - 1) + a*d^4*log(x) + 1/24*(3*b*c^4*d^4*x^4 + 16*b*c^3*d^4*x^3 + 36*b*c^2*d^4*x^2)*log(c*x + 1) - 1/24*(3*b*c^4*d^4*x^4 + 16*b*c^3*d^4*x^3 + 36*b*c^2*d^4*x^2)*log(-c*x + 1)","A",0
36,1,281,0,0.473663," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, a c^{4} d^{4} x^{3} + 2 \, a c^{3} d^{4} x^{2} + \frac{1}{6} \, b c^{3} d^{4} x^{2} + 6 \, a c^{2} d^{4} x + 2 \, b c^{2} d^{4} x + 3 \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b c d^{4} - 2 \, {\left(\log\left(c x\right) \log\left(-c x + 1\right) + {\rm Li}_2\left(-c x + 1\right)\right)} b c d^{4} + 2 \, {\left(\log\left(c x + 1\right) \log\left(-c x\right) + {\rm Li}_2\left(c x + 1\right)\right)} b c d^{4} - \frac{5}{6} \, b c d^{4} \log\left(c x + 1\right) + \frac{7}{6} \, b c d^{4} \log\left(c x - 1\right) + 4 \, a c d^{4} \log\left(x\right) - \frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b d^{4} - \frac{a d^{4}}{x} + \frac{1}{6} \, {\left(b c^{4} d^{4} x^{3} + 6 \, b c^{3} d^{4} x^{2}\right)} \log\left(c x + 1\right) - \frac{1}{6} \, {\left(b c^{4} d^{4} x^{3} + 6 \, b c^{3} d^{4} x^{2}\right)} \log\left(-c x + 1\right)"," ",0,"1/3*a*c^4*d^4*x^3 + 2*a*c^3*d^4*x^2 + 1/6*b*c^3*d^4*x^2 + 6*a*c^2*d^4*x + 2*b*c^2*d^4*x + 3*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*c*d^4 - 2*(log(c*x)*log(-c*x + 1) + dilog(-c*x + 1))*b*c*d^4 + 2*(log(c*x + 1)*log(-c*x) + dilog(c*x + 1))*b*c*d^4 - 5/6*b*c*d^4*log(c*x + 1) + 7/6*b*c*d^4*log(c*x - 1) + 4*a*c*d^4*log(x) - 1/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*d^4 - a*d^4/x + 1/6*(b*c^4*d^4*x^3 + 6*b*c^3*d^4*x^2)*log(c*x + 1) - 1/6*(b*c^4*d^4*x^3 + 6*b*c^3*d^4*x^2)*log(-c*x + 1)","A",0
37,1,293,0,0.476640," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, b c^{4} d^{4} x^{2} \log\left(c x + 1\right) - \frac{1}{4} \, b c^{4} d^{4} x^{2} \log\left(-c x + 1\right) + \frac{1}{2} \, a c^{4} d^{4} x^{2} + 4 \, a c^{3} d^{4} x + \frac{1}{2} \, b c^{3} d^{4} x + 2 \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b c^{2} d^{4} - 3 \, {\left(\log\left(c x\right) \log\left(-c x + 1\right) + {\rm Li}_2\left(-c x + 1\right)\right)} b c^{2} d^{4} + 3 \, {\left(\log\left(c x + 1\right) \log\left(-c x\right) + {\rm Li}_2\left(c x + 1\right)\right)} b c^{2} d^{4} - \frac{1}{4} \, b c^{2} d^{4} \log\left(c x + 1\right) + \frac{1}{4} \, b c^{2} d^{4} \log\left(c x - 1\right) + 6 \, a c^{2} d^{4} \log\left(x\right) - 2 \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b c d^{4} + \frac{1}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b d^{4} - \frac{4 \, a c d^{4}}{x} - \frac{a d^{4}}{2 \, x^{2}}"," ",0,"1/4*b*c^4*d^4*x^2*log(c*x + 1) - 1/4*b*c^4*d^4*x^2*log(-c*x + 1) + 1/2*a*c^4*d^4*x^2 + 4*a*c^3*d^4*x + 1/2*b*c^3*d^4*x + 2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*c^2*d^4 - 3*(log(c*x)*log(-c*x + 1) + dilog(-c*x + 1))*b*c^2*d^4 + 3*(log(c*x + 1)*log(-c*x) + dilog(c*x + 1))*b*c^2*d^4 - 1/4*b*c^2*d^4*log(c*x + 1) + 1/4*b*c^2*d^4*log(c*x - 1) + 6*a*c^2*d^4*log(x) - 2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*c*d^4 + 1/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*d^4 - 4*a*c*d^4/x - 1/2*a*d^4/x^2","B",0
38,0,0,0,0.000000," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^4,x, algorithm=""maxima"")","a c^{4} d^{4} x + \frac{1}{2} \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b c^{3} d^{4} + 2 \, b c^{3} d^{4} \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{x}\,{d x} + 4 \, a c^{3} d^{4} \log\left(x\right) - 3 \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b c^{2} d^{4} + {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b c d^{4} - \frac{1}{6} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b d^{4} - \frac{6 \, a c^{2} d^{4}}{x} - \frac{2 \, a c d^{4}}{x^{2}} - \frac{a d^{4}}{3 \, x^{3}}"," ",0,"a*c^4*d^4*x + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*c^3*d^4 + 2*b*c^3*d^4*integrate((log(c*x + 1) - log(-c*x + 1))/x, x) + 4*a*c^3*d^4*log(x) - 3*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*c^2*d^4 + ((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*c*d^4 - 1/6*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*d^4 - 6*a*c^2*d^4/x - 2*a*c*d^4/x^2 - 1/3*a*d^4/x^3","F",0
39,0,0,0,0.000000," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^5,x, algorithm=""maxima"")","\frac{1}{2} \, b c^{4} d^{4} \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{x}\,{d x} + a c^{4} d^{4} \log\left(x\right) - 2 \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b c^{3} d^{4} + \frac{3}{2} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b c^{2} d^{4} - \frac{2}{3} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b c d^{4} - \frac{4 \, a c^{3} d^{4}}{x} + \frac{1}{24} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} b d^{4} - \frac{3 \, a c^{2} d^{4}}{x^{2}} - \frac{4 \, a c d^{4}}{3 \, x^{3}} - \frac{a d^{4}}{4 \, x^{4}}"," ",0,"1/2*b*c^4*d^4*integrate((log(c*x + 1) - log(-c*x + 1))/x, x) + a*c^4*d^4*log(x) - 2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*c^3*d^4 + 3/2*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*c^2*d^4 - 2/3*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*c*d^4 - 4*a*c^3*d^4/x + 1/24*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*b*d^4 - 3*a*c^2*d^4/x^2 - 4/3*a*c*d^4/x^3 - 1/4*a*d^4/x^4","F",0
40,1,299,0,0.328722," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^6,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b c^{4} d^{4} + {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b c^{3} d^{4} - {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b c^{2} d^{4} - \frac{a c^{4} d^{4}}{x} + \frac{1}{6} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} b c d^{4} - \frac{1}{20} \, {\left({\left(2 \, c^{4} \log\left(c^{2} x^{2} - 1\right) - 2 \, c^{4} \log\left(x^{2}\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} c + \frac{4 \, \operatorname{artanh}\left(c x\right)}{x^{5}}\right)} b d^{4} - \frac{2 \, a c^{3} d^{4}}{x^{2}} - \frac{2 \, a c^{2} d^{4}}{x^{3}} - \frac{a c d^{4}}{x^{4}} - \frac{a d^{4}}{5 \, x^{5}}"," ",0,"-1/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*c^4*d^4 + ((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*c^3*d^4 - ((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*c^2*d^4 - a*c^4*d^4/x + 1/6*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*b*c*d^4 - 1/20*((2*c^4*log(c^2*x^2 - 1) - 2*c^4*log(x^2) + (2*c^2*x^2 + 1)/x^4)*c + 4*arctanh(c*x)/x^5)*b*d^4 - 2*a*c^3*d^4/x^2 - 2*a*c^2*d^4/x^3 - a*c*d^4/x^4 - 1/5*a*d^4/x^5","B",0
41,1,329,0,0.326666," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^7,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b c^{4} d^{4} - \frac{2}{3} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b c^{3} d^{4} + \frac{1}{4} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} b c^{2} d^{4} - \frac{1}{5} \, {\left({\left(2 \, c^{4} \log\left(c^{2} x^{2} - 1\right) - 2 \, c^{4} \log\left(x^{2}\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} c + \frac{4 \, \operatorname{artanh}\left(c x\right)}{x^{5}}\right)} b c d^{4} - \frac{a c^{4} d^{4}}{2 \, x^{2}} + \frac{1}{180} \, {\left({\left(15 \, c^{5} \log\left(c x + 1\right) - 15 \, c^{5} \log\left(c x - 1\right) - \frac{2 \, {\left(15 \, c^{4} x^{4} + 5 \, c^{2} x^{2} + 3\right)}}{x^{5}}\right)} c - \frac{30 \, \operatorname{artanh}\left(c x\right)}{x^{6}}\right)} b d^{4} - \frac{4 \, a c^{3} d^{4}}{3 \, x^{3}} - \frac{3 \, a c^{2} d^{4}}{2 \, x^{4}} - \frac{4 \, a c d^{4}}{5 \, x^{5}} - \frac{a d^{4}}{6 \, x^{6}}"," ",0,"1/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*c^4*d^4 - 2/3*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*c^3*d^4 + 1/4*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*b*c^2*d^4 - 1/5*((2*c^4*log(c^2*x^2 - 1) - 2*c^4*log(x^2) + (2*c^2*x^2 + 1)/x^4)*c + 4*arctanh(c*x)/x^5)*b*c*d^4 - 1/2*a*c^4*d^4/x^2 + 1/180*((15*c^5*log(c*x + 1) - 15*c^5*log(c*x - 1) - 2*(15*c^4*x^4 + 5*c^2*x^2 + 3)/x^5)*c - 30*arctanh(c*x)/x^6)*b*d^4 - 4/3*a*c^3*d^4/x^3 - 3/2*a*c^2*d^4/x^4 - 4/5*a*c*d^4/x^5 - 1/6*a*d^4/x^6","B",0
42,1,353,0,0.327355," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^8,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b c^{4} d^{4} + \frac{1}{6} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} b c^{3} d^{4} - \frac{3}{10} \, {\left({\left(2 \, c^{4} \log\left(c^{2} x^{2} - 1\right) - 2 \, c^{4} \log\left(x^{2}\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} c + \frac{4 \, \operatorname{artanh}\left(c x\right)}{x^{5}}\right)} b c^{2} d^{4} + \frac{1}{45} \, {\left({\left(15 \, c^{5} \log\left(c x + 1\right) - 15 \, c^{5} \log\left(c x - 1\right) - \frac{2 \, {\left(15 \, c^{4} x^{4} + 5 \, c^{2} x^{2} + 3\right)}}{x^{5}}\right)} c - \frac{30 \, \operatorname{artanh}\left(c x\right)}{x^{6}}\right)} b c d^{4} - \frac{1}{84} \, {\left({\left(6 \, c^{6} \log\left(c^{2} x^{2} - 1\right) - 6 \, c^{6} \log\left(x^{2}\right) + \frac{6 \, c^{4} x^{4} + 3 \, c^{2} x^{2} + 2}{x^{6}}\right)} c + \frac{12 \, \operatorname{artanh}\left(c x\right)}{x^{7}}\right)} b d^{4} - \frac{a c^{4} d^{4}}{3 \, x^{3}} - \frac{a c^{3} d^{4}}{x^{4}} - \frac{6 \, a c^{2} d^{4}}{5 \, x^{5}} - \frac{2 \, a c d^{4}}{3 \, x^{6}} - \frac{a d^{4}}{7 \, x^{7}}"," ",0,"-1/6*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*c^4*d^4 + 1/6*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*b*c^3*d^4 - 3/10*((2*c^4*log(c^2*x^2 - 1) - 2*c^4*log(x^2) + (2*c^2*x^2 + 1)/x^4)*c + 4*arctanh(c*x)/x^5)*b*c^2*d^4 + 1/45*((15*c^5*log(c*x + 1) - 15*c^5*log(c*x - 1) - 2*(15*c^4*x^4 + 5*c^2*x^2 + 3)/x^5)*c - 30*arctanh(c*x)/x^6)*b*c*d^4 - 1/84*((6*c^6*log(c^2*x^2 - 1) - 6*c^6*log(x^2) + (6*c^4*x^4 + 3*c^2*x^2 + 2)/x^6)*c + 12*arctanh(c*x)/x^7)*b*d^4 - 1/3*a*c^4*d^4/x^3 - a*c^3*d^4/x^4 - 6/5*a*c^2*d^4/x^5 - 2/3*a*c*d^4/x^6 - 1/7*a*d^4/x^7","A",0
43,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x))/(c*d*x+d),x, algorithm=""maxima"")","\frac{1}{72} \, {\left(2 \, c^{4} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{7} d} - \frac{3 \, \log\left(c x + 1\right)}{c^{8} d} + \frac{3 \, \log\left(c x - 1\right)}{c^{8} d}\right)} + 216 \, c^{4} \int \frac{x^{4} \log\left(c x + 1\right)}{6 \, {\left(c^{5} d x^{2} - c^{3} d\right)}}\,{d x} - 3 \, c^{3} {\left(\frac{x^{2}}{c^{5} d} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{7} d}\right)} - 216 \, c^{3} \int \frac{x^{3} \log\left(c x + 1\right)}{6 \, {\left(c^{5} d x^{2} - c^{3} d\right)}}\,{d x} + 9 \, c^{2} {\left(\frac{2 \, x}{c^{5} d} - \frac{\log\left(c x + 1\right)}{c^{6} d} + \frac{\log\left(c x - 1\right)}{c^{6} d}\right)} - 216 \, c \int \frac{x \log\left(c x + 1\right)}{6 \, {\left(c^{5} d x^{2} - c^{3} d\right)}}\,{d x} - \frac{6 \, {\left(2 \, c^{3} x^{3} - 3 \, c^{2} x^{2} + 6 \, c x - 6 \, \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{c^{4} d} + \frac{18 \, \log\left(6 \, c^{5} d x^{2} - 6 \, c^{3} d\right)}{c^{4} d} - 216 \, \int \frac{\log\left(c x + 1\right)}{6 \, {\left(c^{5} d x^{2} - c^{3} d\right)}}\,{d x}\right)} b + \frac{1}{6} \, a {\left(\frac{2 \, c^{2} x^{3} - 3 \, c x^{2} + 6 \, x}{c^{3} d} - \frac{6 \, \log\left(c x + 1\right)}{c^{4} d}\right)}"," ",0,"1/72*(2*c^4*(2*(c^2*x^3 + 3*x)/(c^7*d) - 3*log(c*x + 1)/(c^8*d) + 3*log(c*x - 1)/(c^8*d)) + 216*c^4*integrate(1/6*x^4*log(c*x + 1)/(c^5*d*x^2 - c^3*d), x) - 3*c^3*(x^2/(c^5*d) + log(c^2*x^2 - 1)/(c^7*d)) - 216*c^3*integrate(1/6*x^3*log(c*x + 1)/(c^5*d*x^2 - c^3*d), x) + 9*c^2*(2*x/(c^5*d) - log(c*x + 1)/(c^6*d) + log(c*x - 1)/(c^6*d)) - 216*c*integrate(1/6*x*log(c*x + 1)/(c^5*d*x^2 - c^3*d), x) - 6*(2*c^3*x^3 - 3*c^2*x^2 + 6*c*x - 6*log(c*x + 1))*log(-c*x + 1)/(c^4*d) + 18*log(6*c^5*d*x^2 - 6*c^3*d)/(c^4*d) - 216*integrate(1/6*log(c*x + 1)/(c^5*d*x^2 - c^3*d), x))*b + 1/6*a*((2*c^2*x^3 - 3*c*x^2 + 6*x)/(c^3*d) - 6*log(c*x + 1)/(c^4*d))","F",0
44,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))/(c*d*x+d),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(c^{3} {\left(\frac{x^{2}}{c^{4} d} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{6} d}\right)} + 8 \, c^{3} \int \frac{x^{3} \log\left(c x + 1\right)}{2 \, {\left(c^{4} d x^{2} - c^{2} d\right)}}\,{d x} - c^{2} {\left(\frac{2 \, x}{c^{4} d} - \frac{\log\left(c x + 1\right)}{c^{5} d} + \frac{\log\left(c x - 1\right)}{c^{5} d}\right)} - 8 \, c^{2} \int \frac{x^{2} \log\left(c x + 1\right)}{2 \, {\left(c^{4} d x^{2} - c^{2} d\right)}}\,{d x} + 8 \, c \int \frac{x \log\left(c x + 1\right)}{2 \, {\left(c^{4} d x^{2} - c^{2} d\right)}}\,{d x} - \frac{2 \, {\left(c^{2} x^{2} - 2 \, c x + 2 \, \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{c^{3} d} - \frac{2 \, \log\left(2 \, c^{4} d x^{2} - 2 \, c^{2} d\right)}{c^{3} d} + 8 \, \int \frac{\log\left(c x + 1\right)}{2 \, {\left(c^{4} d x^{2} - c^{2} d\right)}}\,{d x}\right)} b + \frac{1}{2} \, a {\left(\frac{c x^{2} - 2 \, x}{c^{2} d} + \frac{2 \, \log\left(c x + 1\right)}{c^{3} d}\right)}"," ",0,"1/8*(c^3*(x^2/(c^4*d) + log(c^2*x^2 - 1)/(c^6*d)) + 8*c^3*integrate(1/2*x^3*log(c*x + 1)/(c^4*d*x^2 - c^2*d), x) - c^2*(2*x/(c^4*d) - log(c*x + 1)/(c^5*d) + log(c*x - 1)/(c^5*d)) - 8*c^2*integrate(1/2*x^2*log(c*x + 1)/(c^4*d*x^2 - c^2*d), x) + 8*c*integrate(1/2*x*log(c*x + 1)/(c^4*d*x^2 - c^2*d), x) - 2*(c^2*x^2 - 2*c*x + 2*log(c*x + 1))*log(-c*x + 1)/(c^3*d) - 2*log(2*c^4*d*x^2 - 2*c^2*d)/(c^3*d) + 8*integrate(1/2*log(c*x + 1)/(c^4*d*x^2 - c^2*d), x))*b + 1/2*a*((c*x^2 - 2*x)/(c^2*d) + 2*log(c*x + 1)/(c^3*d))","F",0
45,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))/(c*d*x+d),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(c^{2} {\left(\frac{2 \, x}{c^{3} d} - \frac{\log\left(c x + 1\right)}{c^{4} d} + \frac{\log\left(c x - 1\right)}{c^{4} d}\right)} + 2 \, c^{2} \int \frac{x^{2} \log\left(c x + 1\right)}{c^{3} d x^{2} - c d}\,{d x} - 4 \, c \int \frac{x \log\left(c x + 1\right)}{c^{3} d x^{2} - c d}\,{d x} - \frac{2 \, {\left(c x - \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{c^{2} d} + \frac{\log\left(c^{3} d x^{2} - c d\right)}{c^{2} d} - 2 \, \int \frac{\log\left(c x + 1\right)}{c^{3} d x^{2} - c d}\,{d x}\right)} b + a {\left(\frac{x}{c d} - \frac{\log\left(c x + 1\right)}{c^{2} d}\right)}"," ",0,"1/4*(c^2*(2*x/(c^3*d) - log(c*x + 1)/(c^4*d) + log(c*x - 1)/(c^4*d)) + 2*c^2*integrate(x^2*log(c*x + 1)/(c^3*d*x^2 - c*d), x) - 4*c*integrate(x*log(c*x + 1)/(c^3*d*x^2 - c*d), x) - 2*(c*x - log(c*x + 1))*log(-c*x + 1)/(c^2*d) + log(c^3*d*x^2 - c*d)/(c^2*d) - 2*integrate(log(c*x + 1)/(c^3*d*x^2 - c*d), x))*b + a*(x/(c*d) - log(c*x + 1)/(c^2*d))","F",0
46,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/(c*d*x+d),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(2 \, c \int \frac{x \log\left(c x + 1\right)}{c^{2} d x^{2} - d}\,{d x} - \frac{\log\left(c x + 1\right) \log\left(-c x + 1\right)}{c d}\right)} b + \frac{a \log\left(c d x + d\right)}{c d}"," ",0,"1/2*(2*c*integrate(x*log(c*x + 1)/(c^2*d*x^2 - d), x) - log(c*x + 1)*log(-c*x + 1)/(c*d))*b + a*log(c*d*x + d)/(c*d)","F",0
47,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x/(c*d*x+d),x, algorithm=""maxima"")","-a {\left(\frac{\log\left(c x + 1\right)}{d} - \frac{\log\left(x\right)}{d}\right)} + \frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{c d x^{2} + d x}\,{d x}"," ",0,"-a*(log(c*x + 1)/d - log(x)/d) + 1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(c*d*x^2 + d*x), x)","F",0
48,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x^2/(c*d*x+d),x, algorithm=""maxima"")","a {\left(\frac{c \log\left(c x + 1\right)}{d} - \frac{c \log\left(x\right)}{d} - \frac{1}{d x}\right)} + \frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{c d x^{3} + d x^{2}}\,{d x}"," ",0,"a*(c*log(c*x + 1)/d - c*log(x)/d - 1/(d*x)) + 1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(c*d*x^3 + d*x^2), x)","F",0
49,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x^3/(c*d*x+d),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{2 \, c^{2} \log\left(c x + 1\right)}{d} - \frac{2 \, c^{2} \log\left(x\right)}{d} - \frac{2 \, c x - 1}{d x^{2}}\right)} a + \frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{c d x^{4} + d x^{3}}\,{d x}"," ",0,"-1/2*(2*c^2*log(c*x + 1)/d - 2*c^2*log(x)/d - (2*c*x - 1)/(d*x^2))*a + 1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(c*d*x^4 + d*x^3), x)","F",0
50,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x^4/(c*d*x+d),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{6 \, c^{3} \log\left(c x + 1\right)}{d} - \frac{6 \, c^{3} \log\left(x\right)}{d} - \frac{6 \, c^{2} x^{2} - 3 \, c x + 2}{d x^{3}}\right)} a + \frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{c d x^{5} + d x^{4}}\,{d x}"," ",0,"1/6*(6*c^3*log(c*x + 1)/d - 6*c^3*log(x)/d - (6*c^2*x^2 - 3*c*x + 2)/(d*x^3))*a + 1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(c*d*x^5 + d*x^4), x)","F",0
51,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x))/(c*d*x+d)^2,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(c^{4} {\left(\frac{2}{c^{9} d^{2} x + c^{8} d^{2}} + \frac{2 \, {\left(c x^{2} - 2 \, x\right)}}{c^{7} d^{2}} + \frac{7 \, \log\left(c x + 1\right)}{c^{8} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{8} d^{2}}\right)} + 16 \, c^{4} \int \frac{x^{4} \log\left(c x + 1\right)}{2 \, {\left(c^{6} d^{2} x^{3} + c^{5} d^{2} x^{2} - c^{4} d^{2} x - c^{3} d^{2}\right)}}\,{d x} + 2 \, c^{3} {\left(\frac{2}{c^{8} d^{2} x + c^{7} d^{2}} - \frac{4 \, x}{c^{6} d^{2}} + \frac{5 \, \log\left(c x + 1\right)}{c^{7} d^{2}} - \frac{\log\left(c x - 1\right)}{c^{7} d^{2}}\right)} - 16 \, c^{3} \int \frac{x^{3} \log\left(c x + 1\right)}{2 \, {\left(c^{6} d^{2} x^{3} + c^{5} d^{2} x^{2} - c^{4} d^{2} x - c^{3} d^{2}\right)}}\,{d x} - 7 \, c^{2} {\left(\frac{2}{c^{7} d^{2} x + c^{6} d^{2}} + \frac{3 \, \log\left(c x + 1\right)}{c^{6} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{6} d^{2}}\right)} + 48 \, c^{2} \int \frac{x^{2} \log\left(c x + 1\right)}{2 \, {\left(c^{6} d^{2} x^{3} + c^{5} d^{2} x^{2} - c^{4} d^{2} x - c^{3} d^{2}\right)}}\,{d x} + 2 \, c {\left(\frac{2}{c^{6} d^{2} x + c^{5} d^{2}} + \frac{\log\left(c x + 1\right)}{c^{5} d^{2}} - \frac{\log\left(c x - 1\right)}{c^{5} d^{2}}\right)} + 96 \, c \int \frac{x \log\left(c x + 1\right)}{2 \, {\left(c^{6} d^{2} x^{3} + c^{5} d^{2} x^{2} - c^{4} d^{2} x - c^{3} d^{2}\right)}}\,{d x} - \frac{4 \, {\left(c^{3} x^{3} - 3 \, c^{2} x^{2} - 4 \, c x + 6 \, {\left(c x + 1\right)} \log\left(c x + 1\right) + 2\right)} \log\left(-c x + 1\right)}{c^{5} d^{2} x + c^{4} d^{2}} + \frac{4}{c^{5} d^{2} x + c^{4} d^{2}} - \frac{2 \, \log\left(c x + 1\right)}{c^{4} d^{2}} + \frac{2 \, \log\left(c x - 1\right)}{c^{4} d^{2}} + 48 \, \int \frac{\log\left(c x + 1\right)}{2 \, {\left(c^{6} d^{2} x^{3} + c^{5} d^{2} x^{2} - c^{4} d^{2} x - c^{3} d^{2}\right)}}\,{d x}\right)} b + \frac{1}{2} \, a {\left(\frac{2}{c^{5} d^{2} x + c^{4} d^{2}} + \frac{c x^{2} - 4 \, x}{c^{3} d^{2}} + \frac{6 \, \log\left(c x + 1\right)}{c^{4} d^{2}}\right)}"," ",0,"1/16*(c^4*(2/(c^9*d^2*x + c^8*d^2) + 2*(c*x^2 - 2*x)/(c^7*d^2) + 7*log(c*x + 1)/(c^8*d^2) + log(c*x - 1)/(c^8*d^2)) + 16*c^4*integrate(1/2*x^4*log(c*x + 1)/(c^6*d^2*x^3 + c^5*d^2*x^2 - c^4*d^2*x - c^3*d^2), x) + 2*c^3*(2/(c^8*d^2*x + c^7*d^2) - 4*x/(c^6*d^2) + 5*log(c*x + 1)/(c^7*d^2) - log(c*x - 1)/(c^7*d^2)) - 16*c^3*integrate(1/2*x^3*log(c*x + 1)/(c^6*d^2*x^3 + c^5*d^2*x^2 - c^4*d^2*x - c^3*d^2), x) - 7*c^2*(2/(c^7*d^2*x + c^6*d^2) + 3*log(c*x + 1)/(c^6*d^2) + log(c*x - 1)/(c^6*d^2)) + 48*c^2*integrate(1/2*x^2*log(c*x + 1)/(c^6*d^2*x^3 + c^5*d^2*x^2 - c^4*d^2*x - c^3*d^2), x) + 2*c*(2/(c^6*d^2*x + c^5*d^2) + log(c*x + 1)/(c^5*d^2) - log(c*x - 1)/(c^5*d^2)) + 96*c*integrate(1/2*x*log(c*x + 1)/(c^6*d^2*x^3 + c^5*d^2*x^2 - c^4*d^2*x - c^3*d^2), x) - 4*(c^3*x^3 - 3*c^2*x^2 - 4*c*x + 6*(c*x + 1)*log(c*x + 1) + 2)*log(-c*x + 1)/(c^5*d^2*x + c^4*d^2) + 4/(c^5*d^2*x + c^4*d^2) - 2*log(c*x + 1)/(c^4*d^2) + 2*log(c*x - 1)/(c^4*d^2) + 48*integrate(1/2*log(c*x + 1)/(c^6*d^2*x^3 + c^5*d^2*x^2 - c^4*d^2*x - c^3*d^2), x))*b + 1/2*a*(2/(c^5*d^2*x + c^4*d^2) + (c*x^2 - 4*x)/(c^3*d^2) + 6*log(c*x + 1)/(c^4*d^2))","F",0
52,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))/(c*d*x+d)^2,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(c^{3} {\left(\frac{2}{c^{7} d^{2} x + c^{6} d^{2}} - \frac{4 \, x}{c^{5} d^{2}} + \frac{5 \, \log\left(c x + 1\right)}{c^{6} d^{2}} - \frac{\log\left(c x - 1\right)}{c^{6} d^{2}}\right)} - 4 \, c^{3} \int \frac{x^{3} \log\left(c x + 1\right)}{c^{5} d^{2} x^{3} + c^{4} d^{2} x^{2} - c^{3} d^{2} x - c^{2} d^{2}}\,{d x} - 2 \, c^{2} {\left(\frac{2}{c^{6} d^{2} x + c^{5} d^{2}} + \frac{3 \, \log\left(c x + 1\right)}{c^{5} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{5} d^{2}}\right)} + 12 \, c^{2} \int \frac{x^{2} \log\left(c x + 1\right)}{c^{5} d^{2} x^{3} + c^{4} d^{2} x^{2} - c^{3} d^{2} x - c^{2} d^{2}}\,{d x} + 16 \, c \int \frac{x \log\left(c x + 1\right)}{c^{5} d^{2} x^{3} + c^{4} d^{2} x^{2} - c^{3} d^{2} x - c^{2} d^{2}}\,{d x} + \frac{4 \, {\left(c^{2} x^{2} + c x - 2 \, {\left(c x + 1\right)} \log\left(c x + 1\right) - 1\right)} \log\left(-c x + 1\right)}{c^{4} d^{2} x + c^{3} d^{2}} + \frac{2}{c^{4} d^{2} x + c^{3} d^{2}} - \frac{\log\left(c x + 1\right)}{c^{3} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{3} d^{2}} + 8 \, \int \frac{\log\left(c x + 1\right)}{c^{5} d^{2} x^{3} + c^{4} d^{2} x^{2} - c^{3} d^{2} x - c^{2} d^{2}}\,{d x}\right)} b - a {\left(\frac{1}{c^{4} d^{2} x + c^{3} d^{2}} - \frac{x}{c^{2} d^{2}} + \frac{2 \, \log\left(c x + 1\right)}{c^{3} d^{2}}\right)}"," ",0,"-1/8*(c^3*(2/(c^7*d^2*x + c^6*d^2) - 4*x/(c^5*d^2) + 5*log(c*x + 1)/(c^6*d^2) - log(c*x - 1)/(c^6*d^2)) - 4*c^3*integrate(x^3*log(c*x + 1)/(c^5*d^2*x^3 + c^4*d^2*x^2 - c^3*d^2*x - c^2*d^2), x) - 2*c^2*(2/(c^6*d^2*x + c^5*d^2) + 3*log(c*x + 1)/(c^5*d^2) + log(c*x - 1)/(c^5*d^2)) + 12*c^2*integrate(x^2*log(c*x + 1)/(c^5*d^2*x^3 + c^4*d^2*x^2 - c^3*d^2*x - c^2*d^2), x) + 16*c*integrate(x*log(c*x + 1)/(c^5*d^2*x^3 + c^4*d^2*x^2 - c^3*d^2*x - c^2*d^2), x) + 4*(c^2*x^2 + c*x - 2*(c*x + 1)*log(c*x + 1) - 1)*log(-c*x + 1)/(c^4*d^2*x + c^3*d^2) + 2/(c^4*d^2*x + c^3*d^2) - log(c*x + 1)/(c^3*d^2) + log(c*x - 1)/(c^3*d^2) + 8*integrate(log(c*x + 1)/(c^5*d^2*x^3 + c^4*d^2*x^2 - c^3*d^2*x - c^2*d^2), x))*b - a*(1/(c^4*d^2*x + c^3*d^2) - x/(c^2*d^2) + 2*log(c*x + 1)/(c^3*d^2))","F",0
53,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))/(c*d*x+d)^2,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(8 \, c^{2} \int \frac{x^{2} \log\left(c x + 1\right)}{c^{4} d^{2} x^{3} + c^{3} d^{2} x^{2} - c^{2} d^{2} x - c d^{2}}\,{d x} - c {\left(\frac{2}{c^{4} d^{2} x + c^{3} d^{2}} + \frac{\log\left(c x + 1\right)}{c^{3} d^{2}} - \frac{\log\left(c x - 1\right)}{c^{3} d^{2}}\right)} + 4 \, c \int \frac{x \log\left(c x + 1\right)}{c^{4} d^{2} x^{3} + c^{3} d^{2} x^{2} - c^{2} d^{2} x - c d^{2}}\,{d x} - \frac{4 \, {\left({\left(c x + 1\right)} \log\left(c x + 1\right) + 1\right)} \log\left(-c x + 1\right)}{c^{3} d^{2} x + c^{2} d^{2}} + \frac{2}{c^{3} d^{2} x + c^{2} d^{2}} - \frac{\log\left(c x + 1\right)}{c^{2} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{2} d^{2}} + 4 \, \int \frac{\log\left(c x + 1\right)}{c^{4} d^{2} x^{3} + c^{3} d^{2} x^{2} - c^{2} d^{2} x - c d^{2}}\,{d x}\right)} b + a {\left(\frac{1}{c^{3} d^{2} x + c^{2} d^{2}} + \frac{\log\left(c x + 1\right)}{c^{2} d^{2}}\right)}"," ",0,"1/8*(8*c^2*integrate(x^2*log(c*x + 1)/(c^4*d^2*x^3 + c^3*d^2*x^2 - c^2*d^2*x - c*d^2), x) - c*(2/(c^4*d^2*x + c^3*d^2) + log(c*x + 1)/(c^3*d^2) - log(c*x - 1)/(c^3*d^2)) + 4*c*integrate(x*log(c*x + 1)/(c^4*d^2*x^3 + c^3*d^2*x^2 - c^2*d^2*x - c*d^2), x) - 4*((c*x + 1)*log(c*x + 1) + 1)*log(-c*x + 1)/(c^3*d^2*x + c^2*d^2) + 2/(c^3*d^2*x + c^2*d^2) - log(c*x + 1)/(c^2*d^2) + log(c*x - 1)/(c^2*d^2) + 4*integrate(log(c*x + 1)/(c^4*d^2*x^3 + c^3*d^2*x^2 - c^2*d^2*x - c*d^2), x))*b + a*(1/(c^3*d^2*x + c^2*d^2) + log(c*x + 1)/(c^2*d^2))","F",0
54,1,96,0,0.304046," ","integrate((a+b*arctanh(c*x))/(c*d*x+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(c {\left(\frac{2}{c^{3} d^{2} x + c^{2} d^{2}} - \frac{\log\left(c x + 1\right)}{c^{2} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{2} d^{2}}\right)} + \frac{4 \, \operatorname{artanh}\left(c x\right)}{c^{2} d^{2} x + c d^{2}}\right)} b - \frac{a}{c^{2} d^{2} x + c d^{2}}"," ",0,"-1/4*(c*(2/(c^3*d^2*x + c^2*d^2) - log(c*x + 1)/(c^2*d^2) + log(c*x - 1)/(c^2*d^2)) + 4*arctanh(c*x)/(c^2*d^2*x + c*d^2))*b - a/(c^2*d^2*x + c*d^2)","A",0
55,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x/(c*d*x+d)^2,x, algorithm=""maxima"")","a {\left(\frac{1}{c d^{2} x + d^{2}} - \frac{\log\left(c x + 1\right)}{d^{2}} + \frac{\log\left(x\right)}{d^{2}}\right)} + \frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{c^{2} d^{2} x^{3} + 2 \, c d^{2} x^{2} + d^{2} x}\,{d x}"," ",0,"a*(1/(c*d^2*x + d^2) - log(c*x + 1)/d^2 + log(x)/d^2) + 1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(c^2*d^2*x^3 + 2*c*d^2*x^2 + d^2*x), x)","F",0
56,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x^2/(c*d*x+d)^2,x, algorithm=""maxima"")","-a {\left(\frac{2 \, c x + 1}{c d^{2} x^{2} + d^{2} x} - \frac{2 \, c \log\left(c x + 1\right)}{d^{2}} + \frac{2 \, c \log\left(x\right)}{d^{2}}\right)} + \frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{c^{2} d^{2} x^{4} + 2 \, c d^{2} x^{3} + d^{2} x^{2}}\,{d x}"," ",0,"-a*((2*c*x + 1)/(c*d^2*x^2 + d^2*x) - 2*c*log(c*x + 1)/d^2 + 2*c*log(x)/d^2) + 1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(c^2*d^2*x^4 + 2*c*d^2*x^3 + d^2*x^2), x)","F",0
57,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x^3/(c*d*x+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{6 \, c^{2} \log\left(c x + 1\right)}{d^{2}} - \frac{6 \, c^{2} \log\left(x\right)}{d^{2}} - \frac{6 \, c^{2} x^{2} + 3 \, c x - 1}{c d^{2} x^{3} + d^{2} x^{2}}\right)} + \frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{c^{2} d^{2} x^{5} + 2 \, c d^{2} x^{4} + d^{2} x^{3}}\,{d x}"," ",0,"-1/2*a*(6*c^2*log(c*x + 1)/d^2 - 6*c^2*log(x)/d^2 - (6*c^2*x^2 + 3*c*x - 1)/(c*d^2*x^3 + d^2*x^2)) + 1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(c^2*d^2*x^5 + 2*c*d^2*x^4 + d^2*x^3), x)","F",0
58,0,0,0,0.000000," ","integrate(x^4*(a+b*arctanh(c*x))/(c*d*x+d)^3,x, algorithm=""maxima"")","\frac{1}{32} \, {\left(c^{5} {\left(\frac{2 \, {\left(9 \, c x + 8\right)}}{c^{12} d^{3} x^{2} + 2 \, c^{11} d^{3} x + c^{10} d^{3}} + \frac{4 \, {\left(c x^{2} - 4 \, x\right)}}{c^{9} d^{3}} + \frac{31 \, \log\left(c x + 1\right)}{c^{10} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{10} d^{3}}\right)} + 32 \, c^{5} \int \frac{x^{5} \log\left(c x + 1\right)}{2 \, {\left(c^{8} d^{3} x^{4} + 2 \, c^{7} d^{3} x^{3} - 2 \, c^{5} d^{3} x - c^{4} d^{3}\right)}}\,{d x} + 3 \, c^{4} {\left(\frac{2 \, {\left(7 \, c x + 6\right)}}{c^{11} d^{3} x^{2} + 2 \, c^{10} d^{3} x + c^{9} d^{3}} - \frac{8 \, x}{c^{8} d^{3}} + \frac{17 \, \log\left(c x + 1\right)}{c^{9} d^{3}} - \frac{\log\left(c x - 1\right)}{c^{9} d^{3}}\right)} - 32 \, c^{4} \int \frac{x^{4} \log\left(c x + 1\right)}{2 \, {\left(c^{8} d^{3} x^{4} + 2 \, c^{7} d^{3} x^{3} - 2 \, c^{5} d^{3} x - c^{4} d^{3}\right)}}\,{d x} - 15 \, c^{3} {\left(\frac{2 \, {\left(5 \, c x + 4\right)}}{c^{10} d^{3} x^{2} + 2 \, c^{9} d^{3} x + c^{8} d^{3}} + \frac{7 \, \log\left(c x + 1\right)}{c^{8} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{8} d^{3}}\right)} + 192 \, c^{3} \int \frac{x^{3} \log\left(c x + 1\right)}{2 \, {\left(c^{8} d^{3} x^{4} + 2 \, c^{7} d^{3} x^{3} - 2 \, c^{5} d^{3} x - c^{4} d^{3}\right)}}\,{d x} + 9 \, c^{2} {\left(\frac{2 \, {\left(3 \, c x + 2\right)}}{c^{9} d^{3} x^{2} + 2 \, c^{8} d^{3} x + c^{7} d^{3}} + \frac{\log\left(c x + 1\right)}{c^{7} d^{3}} - \frac{\log\left(c x - 1\right)}{c^{7} d^{3}}\right)} + 576 \, c^{2} \int \frac{x^{2} \log\left(c x + 1\right)}{2 \, {\left(c^{8} d^{3} x^{4} + 2 \, c^{7} d^{3} x^{3} - 2 \, c^{5} d^{3} x - c^{4} d^{3}\right)}}\,{d x} + 9 \, c {\left(\frac{2 \, x}{c^{7} d^{3} x^{2} + 2 \, c^{6} d^{3} x + c^{5} d^{3}} - \frac{\log\left(c x + 1\right)}{c^{6} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{6} d^{3}}\right)} + 576 \, c \int \frac{x \log\left(c x + 1\right)}{2 \, {\left(c^{8} d^{3} x^{4} + 2 \, c^{7} d^{3} x^{3} - 2 \, c^{5} d^{3} x - c^{4} d^{3}\right)}}\,{d x} - \frac{8 \, {\left(c^{4} x^{4} - 4 \, c^{3} x^{3} - 11 \, c^{2} x^{2} + 2 \, c x + 12 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x + 1\right) + 7\right)} \log\left(-c x + 1\right)}{c^{7} d^{3} x^{2} + 2 \, c^{6} d^{3} x + c^{5} d^{3}} + \frac{14 \, {\left(c x + 2\right)}}{c^{7} d^{3} x^{2} + 2 \, c^{6} d^{3} x + c^{5} d^{3}} - \frac{7 \, \log\left(c x + 1\right)}{c^{5} d^{3}} + \frac{7 \, \log\left(c x - 1\right)}{c^{5} d^{3}} + 192 \, \int \frac{\log\left(c x + 1\right)}{2 \, {\left(c^{8} d^{3} x^{4} + 2 \, c^{7} d^{3} x^{3} - 2 \, c^{5} d^{3} x - c^{4} d^{3}\right)}}\,{d x}\right)} b + \frac{1}{2} \, a {\left(\frac{8 \, c x + 7}{c^{7} d^{3} x^{2} + 2 \, c^{6} d^{3} x + c^{5} d^{3}} + \frac{c x^{2} - 6 \, x}{c^{4} d^{3}} + \frac{12 \, \log\left(c x + 1\right)}{c^{5} d^{3}}\right)}"," ",0,"1/32*(c^5*(2*(9*c*x + 8)/(c^12*d^3*x^2 + 2*c^11*d^3*x + c^10*d^3) + 4*(c*x^2 - 4*x)/(c^9*d^3) + 31*log(c*x + 1)/(c^10*d^3) + log(c*x - 1)/(c^10*d^3)) + 32*c^5*integrate(1/2*x^5*log(c*x + 1)/(c^8*d^3*x^4 + 2*c^7*d^3*x^3 - 2*c^5*d^3*x - c^4*d^3), x) + 3*c^4*(2*(7*c*x + 6)/(c^11*d^3*x^2 + 2*c^10*d^3*x + c^9*d^3) - 8*x/(c^8*d^3) + 17*log(c*x + 1)/(c^9*d^3) - log(c*x - 1)/(c^9*d^3)) - 32*c^4*integrate(1/2*x^4*log(c*x + 1)/(c^8*d^3*x^4 + 2*c^7*d^3*x^3 - 2*c^5*d^3*x - c^4*d^3), x) - 15*c^3*(2*(5*c*x + 4)/(c^10*d^3*x^2 + 2*c^9*d^3*x + c^8*d^3) + 7*log(c*x + 1)/(c^8*d^3) + log(c*x - 1)/(c^8*d^3)) + 192*c^3*integrate(1/2*x^3*log(c*x + 1)/(c^8*d^3*x^4 + 2*c^7*d^3*x^3 - 2*c^5*d^3*x - c^4*d^3), x) + 9*c^2*(2*(3*c*x + 2)/(c^9*d^3*x^2 + 2*c^8*d^3*x + c^7*d^3) + log(c*x + 1)/(c^7*d^3) - log(c*x - 1)/(c^7*d^3)) + 576*c^2*integrate(1/2*x^2*log(c*x + 1)/(c^8*d^3*x^4 + 2*c^7*d^3*x^3 - 2*c^5*d^3*x - c^4*d^3), x) + 9*c*(2*x/(c^7*d^3*x^2 + 2*c^6*d^3*x + c^5*d^3) - log(c*x + 1)/(c^6*d^3) + log(c*x - 1)/(c^6*d^3)) + 576*c*integrate(1/2*x*log(c*x + 1)/(c^8*d^3*x^4 + 2*c^7*d^3*x^3 - 2*c^5*d^3*x - c^4*d^3), x) - 8*(c^4*x^4 - 4*c^3*x^3 - 11*c^2*x^2 + 2*c*x + 12*(c^2*x^2 + 2*c*x + 1)*log(c*x + 1) + 7)*log(-c*x + 1)/(c^7*d^3*x^2 + 2*c^6*d^3*x + c^5*d^3) + 14*(c*x + 2)/(c^7*d^3*x^2 + 2*c^6*d^3*x + c^5*d^3) - 7*log(c*x + 1)/(c^5*d^3) + 7*log(c*x - 1)/(c^5*d^3) + 192*integrate(1/2*log(c*x + 1)/(c^8*d^3*x^4 + 2*c^7*d^3*x^3 - 2*c^5*d^3*x - c^4*d^3), x))*b + 1/2*a*((8*c*x + 7)/(c^7*d^3*x^2 + 2*c^6*d^3*x + c^5*d^3) + (c*x^2 - 6*x)/(c^4*d^3) + 12*log(c*x + 1)/(c^5*d^3))","F",0
59,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x))/(c*d*x+d)^3,x, algorithm=""maxima"")","-\frac{1}{32} \, {\left(2 \, c^{4} {\left(\frac{2 \, {\left(7 \, c x + 6\right)}}{c^{10} d^{3} x^{2} + 2 \, c^{9} d^{3} x + c^{8} d^{3}} - \frac{8 \, x}{c^{7} d^{3}} + \frac{17 \, \log\left(c x + 1\right)}{c^{8} d^{3}} - \frac{\log\left(c x - 1\right)}{c^{8} d^{3}}\right)} - 32 \, c^{4} \int \frac{x^{4} \log\left(c x + 1\right)}{2 \, {\left(c^{7} d^{3} x^{4} + 2 \, c^{6} d^{3} x^{3} - 2 \, c^{4} d^{3} x - c^{3} d^{3}\right)}}\,{d x} - 6 \, c^{3} {\left(\frac{2 \, {\left(5 \, c x + 4\right)}}{c^{9} d^{3} x^{2} + 2 \, c^{8} d^{3} x + c^{7} d^{3}} + \frac{7 \, \log\left(c x + 1\right)}{c^{7} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{7} d^{3}}\right)} + 128 \, c^{3} \int \frac{x^{3} \log\left(c x + 1\right)}{2 \, {\left(c^{7} d^{3} x^{4} + 2 \, c^{6} d^{3} x^{3} - 2 \, c^{4} d^{3} x - c^{3} d^{3}\right)}}\,{d x} + 288 \, c^{2} \int \frac{x^{2} \log\left(c x + 1\right)}{2 \, {\left(c^{7} d^{3} x^{4} + 2 \, c^{6} d^{3} x^{3} - 2 \, c^{4} d^{3} x - c^{3} d^{3}\right)}}\,{d x} + 9 \, c {\left(\frac{2 \, x}{c^{6} d^{3} x^{2} + 2 \, c^{5} d^{3} x + c^{4} d^{3}} - \frac{\log\left(c x + 1\right)}{c^{5} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{5} d^{3}}\right)} + 288 \, c \int \frac{x \log\left(c x + 1\right)}{2 \, {\left(c^{7} d^{3} x^{4} + 2 \, c^{6} d^{3} x^{3} - 2 \, c^{4} d^{3} x - c^{3} d^{3}\right)}}\,{d x} + \frac{8 \, {\left(2 \, c^{3} x^{3} + 4 \, c^{2} x^{2} - 4 \, c x - 6 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x + 1\right) - 5\right)} \log\left(-c x + 1\right)}{c^{6} d^{3} x^{2} + 2 \, c^{5} d^{3} x + c^{4} d^{3}} + \frac{10 \, {\left(c x + 2\right)}}{c^{6} d^{3} x^{2} + 2 \, c^{5} d^{3} x + c^{4} d^{3}} - \frac{5 \, \log\left(c x + 1\right)}{c^{4} d^{3}} + \frac{5 \, \log\left(c x - 1\right)}{c^{4} d^{3}} + 96 \, \int \frac{\log\left(c x + 1\right)}{2 \, {\left(c^{7} d^{3} x^{4} + 2 \, c^{6} d^{3} x^{3} - 2 \, c^{4} d^{3} x - c^{3} d^{3}\right)}}\,{d x}\right)} b - \frac{1}{2} \, a {\left(\frac{6 \, c x + 5}{c^{6} d^{3} x^{2} + 2 \, c^{5} d^{3} x + c^{4} d^{3}} - \frac{2 \, x}{c^{3} d^{3}} + \frac{6 \, \log\left(c x + 1\right)}{c^{4} d^{3}}\right)}"," ",0,"-1/32*(2*c^4*(2*(7*c*x + 6)/(c^10*d^3*x^2 + 2*c^9*d^3*x + c^8*d^3) - 8*x/(c^7*d^3) + 17*log(c*x + 1)/(c^8*d^3) - log(c*x - 1)/(c^8*d^3)) - 32*c^4*integrate(1/2*x^4*log(c*x + 1)/(c^7*d^3*x^4 + 2*c^6*d^3*x^3 - 2*c^4*d^3*x - c^3*d^3), x) - 6*c^3*(2*(5*c*x + 4)/(c^9*d^3*x^2 + 2*c^8*d^3*x + c^7*d^3) + 7*log(c*x + 1)/(c^7*d^3) + log(c*x - 1)/(c^7*d^3)) + 128*c^3*integrate(1/2*x^3*log(c*x + 1)/(c^7*d^3*x^4 + 2*c^6*d^3*x^3 - 2*c^4*d^3*x - c^3*d^3), x) + 288*c^2*integrate(1/2*x^2*log(c*x + 1)/(c^7*d^3*x^4 + 2*c^6*d^3*x^3 - 2*c^4*d^3*x - c^3*d^3), x) + 9*c*(2*x/(c^6*d^3*x^2 + 2*c^5*d^3*x + c^4*d^3) - log(c*x + 1)/(c^5*d^3) + log(c*x - 1)/(c^5*d^3)) + 288*c*integrate(1/2*x*log(c*x + 1)/(c^7*d^3*x^4 + 2*c^6*d^3*x^3 - 2*c^4*d^3*x - c^3*d^3), x) + 8*(2*c^3*x^3 + 4*c^2*x^2 - 4*c*x - 6*(c^2*x^2 + 2*c*x + 1)*log(c*x + 1) - 5)*log(-c*x + 1)/(c^6*d^3*x^2 + 2*c^5*d^3*x + c^4*d^3) + 10*(c*x + 2)/(c^6*d^3*x^2 + 2*c^5*d^3*x + c^4*d^3) - 5*log(c*x + 1)/(c^4*d^3) + 5*log(c*x - 1)/(c^4*d^3) + 96*integrate(1/2*log(c*x + 1)/(c^7*d^3*x^4 + 2*c^6*d^3*x^3 - 2*c^4*d^3*x - c^3*d^3), x))*b - 1/2*a*((6*c*x + 5)/(c^6*d^3*x^2 + 2*c^5*d^3*x + c^4*d^3) - 2*x/(c^3*d^3) + 6*log(c*x + 1)/(c^4*d^3))","F",0
60,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))/(c*d*x+d)^3,x, algorithm=""maxima"")","\frac{1}{32} \, {\left(64 \, c^{3} \int \frac{x^{3} \log\left(c x + 1\right)}{2 \, {\left(c^{6} d^{3} x^{4} + 2 \, c^{5} d^{3} x^{3} - 2 \, c^{3} d^{3} x - c^{2} d^{3}\right)}}\,{d x} - 4 \, c^{2} {\left(\frac{2 \, {\left(3 \, c x + 2\right)}}{c^{7} d^{3} x^{2} + 2 \, c^{6} d^{3} x + c^{5} d^{3}} + \frac{\log\left(c x + 1\right)}{c^{5} d^{3}} - \frac{\log\left(c x - 1\right)}{c^{5} d^{3}}\right)} + 64 \, c^{2} \int \frac{x^{2} \log\left(c x + 1\right)}{2 \, {\left(c^{6} d^{3} x^{4} + 2 \, c^{5} d^{3} x^{3} - 2 \, c^{3} d^{3} x - c^{2} d^{3}\right)}}\,{d x} + 7 \, c {\left(\frac{2 \, x}{c^{5} d^{3} x^{2} + 2 \, c^{4} d^{3} x + c^{3} d^{3}} - \frac{\log\left(c x + 1\right)}{c^{4} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{4} d^{3}}\right)} + 96 \, c \int \frac{x \log\left(c x + 1\right)}{2 \, {\left(c^{6} d^{3} x^{4} + 2 \, c^{5} d^{3} x^{3} - 2 \, c^{3} d^{3} x - c^{2} d^{3}\right)}}\,{d x} - \frac{8 \, {\left(4 \, c x + 2 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x + 1\right) + 3\right)} \log\left(-c x + 1\right)}{c^{5} d^{3} x^{2} + 2 \, c^{4} d^{3} x + c^{3} d^{3}} + \frac{6 \, {\left(c x + 2\right)}}{c^{5} d^{3} x^{2} + 2 \, c^{4} d^{3} x + c^{3} d^{3}} - \frac{3 \, \log\left(c x + 1\right)}{c^{3} d^{3}} + \frac{3 \, \log\left(c x - 1\right)}{c^{3} d^{3}} + 32 \, \int \frac{\log\left(c x + 1\right)}{2 \, {\left(c^{6} d^{3} x^{4} + 2 \, c^{5} d^{3} x^{3} - 2 \, c^{3} d^{3} x - c^{2} d^{3}\right)}}\,{d x}\right)} b + \frac{1}{2} \, a {\left(\frac{4 \, c x + 3}{c^{5} d^{3} x^{2} + 2 \, c^{4} d^{3} x + c^{3} d^{3}} + \frac{2 \, \log\left(c x + 1\right)}{c^{3} d^{3}}\right)}"," ",0,"1/32*(64*c^3*integrate(1/2*x^3*log(c*x + 1)/(c^6*d^3*x^4 + 2*c^5*d^3*x^3 - 2*c^3*d^3*x - c^2*d^3), x) - 4*c^2*(2*(3*c*x + 2)/(c^7*d^3*x^2 + 2*c^6*d^3*x + c^5*d^3) + log(c*x + 1)/(c^5*d^3) - log(c*x - 1)/(c^5*d^3)) + 64*c^2*integrate(1/2*x^2*log(c*x + 1)/(c^6*d^3*x^4 + 2*c^5*d^3*x^3 - 2*c^3*d^3*x - c^2*d^3), x) + 7*c*(2*x/(c^5*d^3*x^2 + 2*c^4*d^3*x + c^3*d^3) - log(c*x + 1)/(c^4*d^3) + log(c*x - 1)/(c^4*d^3)) + 96*c*integrate(1/2*x*log(c*x + 1)/(c^6*d^3*x^4 + 2*c^5*d^3*x^3 - 2*c^3*d^3*x - c^2*d^3), x) - 8*(4*c*x + 2*(c^2*x^2 + 2*c*x + 1)*log(c*x + 1) + 3)*log(-c*x + 1)/(c^5*d^3*x^2 + 2*c^4*d^3*x + c^3*d^3) + 6*(c*x + 2)/(c^5*d^3*x^2 + 2*c^4*d^3*x + c^3*d^3) - 3*log(c*x + 1)/(c^3*d^3) + 3*log(c*x - 1)/(c^3*d^3) + 32*integrate(1/2*log(c*x + 1)/(c^6*d^3*x^4 + 2*c^5*d^3*x^3 - 2*c^3*d^3*x - c^2*d^3), x))*b + 1/2*a*((4*c*x + 3)/(c^5*d^3*x^2 + 2*c^4*d^3*x + c^3*d^3) + 2*log(c*x + 1)/(c^3*d^3))","F",0
61,1,152,0,0.327713," ","integrate(x*(a+b*arctanh(c*x))/(c*d*x+d)^3,x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(c {\left(\frac{2 \, {\left(3 \, c x + 2\right)}}{c^{5} d^{3} x^{2} + 2 \, c^{4} d^{3} x + c^{3} d^{3}} - \frac{3 \, \log\left(c x + 1\right)}{c^{3} d^{3}} + \frac{3 \, \log\left(c x - 1\right)}{c^{3} d^{3}}\right)} + \frac{8 \, {\left(2 \, c x + 1\right)} \operatorname{artanh}\left(c x\right)}{c^{4} d^{3} x^{2} + 2 \, c^{3} d^{3} x + c^{2} d^{3}}\right)} b - \frac{{\left(2 \, c x + 1\right)} a}{2 \, {\left(c^{4} d^{3} x^{2} + 2 \, c^{3} d^{3} x + c^{2} d^{3}\right)}}"," ",0,"-1/16*(c*(2*(3*c*x + 2)/(c^5*d^3*x^2 + 2*c^4*d^3*x + c^3*d^3) - 3*log(c*x + 1)/(c^3*d^3) + 3*log(c*x - 1)/(c^3*d^3)) + 8*(2*c*x + 1)*arctanh(c*x)/(c^4*d^3*x^2 + 2*c^3*d^3*x + c^2*d^3))*b - 1/2*(2*c*x + 1)*a/(c^4*d^3*x^2 + 2*c^3*d^3*x + c^2*d^3)","B",0
62,1,134,0,0.317813," ","integrate((a+b*arctanh(c*x))/(c*d*x+d)^3,x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(c {\left(\frac{2 \, {\left(c x + 2\right)}}{c^{4} d^{3} x^{2} + 2 \, c^{3} d^{3} x + c^{2} d^{3}} - \frac{\log\left(c x + 1\right)}{c^{2} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{2} d^{3}}\right)} + \frac{8 \, \operatorname{artanh}\left(c x\right)}{c^{3} d^{3} x^{2} + 2 \, c^{2} d^{3} x + c d^{3}}\right)} b - \frac{a}{2 \, {\left(c^{3} d^{3} x^{2} + 2 \, c^{2} d^{3} x + c d^{3}\right)}}"," ",0,"-1/16*(c*(2*(c*x + 2)/(c^4*d^3*x^2 + 2*c^3*d^3*x + c^2*d^3) - log(c*x + 1)/(c^2*d^3) + log(c*x - 1)/(c^2*d^3)) + 8*arctanh(c*x)/(c^3*d^3*x^2 + 2*c^2*d^3*x + c*d^3))*b - 1/2*a/(c^3*d^3*x^2 + 2*c^2*d^3*x + c*d^3)","A",0
63,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x/(c*d*x+d)^3,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{2 \, c x + 3}{c^{2} d^{3} x^{2} + 2 \, c d^{3} x + d^{3}} - \frac{2 \, \log\left(c x + 1\right)}{d^{3}} + \frac{2 \, \log\left(x\right)}{d^{3}}\right)} + \frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{c^{3} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{3} + 3 \, c d^{3} x^{2} + d^{3} x}\,{d x}"," ",0,"1/2*a*((2*c*x + 3)/(c^2*d^3*x^2 + 2*c*d^3*x + d^3) - 2*log(c*x + 1)/d^3 + 2*log(x)/d^3) + 1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(c^3*d^3*x^4 + 3*c^2*d^3*x^3 + 3*c*d^3*x^2 + d^3*x), x)","F",0
64,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x^2/(c*d*x+d)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{6 \, c^{2} x^{2} + 9 \, c x + 2}{c^{2} d^{3} x^{3} + 2 \, c d^{3} x^{2} + d^{3} x} - \frac{6 \, c \log\left(c x + 1\right)}{d^{3}} + \frac{6 \, c \log\left(x\right)}{d^{3}}\right)} + \frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{c^{3} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{4} + 3 \, c d^{3} x^{3} + d^{3} x^{2}}\,{d x}"," ",0,"-1/2*a*((6*c^2*x^2 + 9*c*x + 2)/(c^2*d^3*x^3 + 2*c*d^3*x^2 + d^3*x) - 6*c*log(c*x + 1)/d^3 + 6*c*log(x)/d^3) + 1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(c^3*d^3*x^5 + 3*c^2*d^3*x^4 + 3*c*d^3*x^3 + d^3*x^2), x)","F",0
65,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x^3/(c*d*x+d)^3,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{12 \, c^{3} x^{3} + 18 \, c^{2} x^{2} + 4 \, c x - 1}{c^{2} d^{3} x^{4} + 2 \, c d^{3} x^{3} + d^{3} x^{2}} - \frac{12 \, c^{2} \log\left(c x + 1\right)}{d^{3}} + \frac{12 \, c^{2} \log\left(x\right)}{d^{3}}\right)} + \frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{c^{3} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{5} + 3 \, c d^{3} x^{4} + d^{3} x^{3}}\,{d x}"," ",0,"1/2*a*((12*c^3*x^3 + 18*c^2*x^2 + 4*c*x - 1)/(c^2*d^3*x^4 + 2*c*d^3*x^3 + d^3*x^2) - 12*c^2*log(c*x + 1)/d^3 + 12*c^2*log(x)/d^3) + 1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(c^3*d^3*x^6 + 3*c^2*d^3*x^5 + 3*c*d^3*x^4 + d^3*x^3), x)","F",0
66,1,132,0,0.311180," ","integrate((a+b*arctanh(c*x))/(c*x+1)^4,x, algorithm=""maxima"")","-\frac{1}{144} \, {\left(c {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} + 9 \, c x + 10\right)}}{c^{5} x^{3} + 3 \, c^{4} x^{2} + 3 \, c^{3} x + c^{2}} - \frac{3 \, \log\left(c x + 1\right)}{c^{2}} + \frac{3 \, \log\left(c x - 1\right)}{c^{2}}\right)} + \frac{48 \, \operatorname{artanh}\left(c x\right)}{c^{4} x^{3} + 3 \, c^{3} x^{2} + 3 \, c^{2} x + c}\right)} b - \frac{a}{3 \, {\left(c^{4} x^{3} + 3 \, c^{3} x^{2} + 3 \, c^{2} x + c\right)}}"," ",0,"-1/144*(c*(2*(3*c^2*x^2 + 9*c*x + 10)/(c^5*x^3 + 3*c^4*x^2 + 3*c^3*x + c^2) - 3*log(c*x + 1)/c^2 + 3*log(c*x - 1)/c^2) + 48*arctanh(c*x)/(c^4*x^3 + 3*c^3*x^2 + 3*c^2*x + c))*b - 1/3*a/(c^4*x^3 + 3*c^3*x^2 + 3*c^2*x + c)","A",0
67,1,120,0,0.315080," ","integrate(arctanh(a*x)/(a*c*x^2+c*x),x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\frac{\log\left(a x + 1\right)^{2}}{a c} - \frac{2 \, {\left(\log\left(a x + 1\right) \log\left(-\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a c} - \frac{2 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)}}{a c} + \frac{2 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)}}{a c}\right)} - {\left(\frac{\log\left(a x + 1\right)}{c} - \frac{\log\left(x\right)}{c}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/4*a*(log(a*x + 1)^2/(a*c) - 2*(log(a*x + 1)*log(-1/2*a*x + 1/2) + dilog(1/2*a*x + 1/2))/(a*c) - 2*(log(a*x + 1)*log(x) + dilog(-a*x))/(a*c) + 2*(log(-a*x + 1)*log(x) + dilog(a*x))/(a*c)) - (log(a*x + 1)/c - log(x)/c)*arctanh(a*x)","B",0
68,0,0,0,0.000000," ","integrate(x^3*(c*d*x+d)*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} c d x^{5} + \frac{1}{4} \, b^{2} d x^{4} \operatorname{artanh}\left(c x\right)^{2} + \frac{1}{4} \, a^{2} d x^{4} + \frac{1}{10} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} a b c d - \frac{1}{36000} \, {\left(24 \, c^{6} {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{10}} - \frac{15 \, \log\left(c x + 1\right)}{c^{11}} + \frac{15 \, \log\left(c x - 1\right)}{c^{11}}\right)} - 45 \, c^{5} {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{8}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{10}}\right)} - 1080000 \, c^{5} \int \frac{x^{5} \log\left(c x + 1\right)}{150 \, {\left(c^{6} x^{2} - c^{4}\right)}}\,{d x} + 50 \, c^{4} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{8}} - \frac{3 \, \log\left(c x + 1\right)}{c^{9}} + \frac{3 \, \log\left(c x - 1\right)}{c^{9}}\right)} - 300 \, c^{3} {\left(\frac{x^{2}}{c^{6}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{8}}\right)} + 900 \, c^{2} {\left(\frac{2 \, x}{c^{6}} - \frac{\log\left(c x + 1\right)}{c^{7}} + \frac{\log\left(c x - 1\right)}{c^{7}}\right)} - 540000 \, c \int \frac{x \log\left(c x + 1\right)}{150 \, {\left(c^{6} x^{2} - c^{4}\right)}}\,{d x} - \frac{60 \, {\left(30 \, c^{5} x^{5} \log\left(c x + 1\right)^{2} + {\left(12 \, c^{5} x^{5} - 15 \, c^{4} x^{4} + 20 \, c^{3} x^{3} - 30 \, c^{2} x^{2} + 60 \, c x - 60 \, {\left(c^{5} x^{5} + 1\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)\right)}}{c^{5}} - \frac{72 \, {\left(c x - 1\right)}^{5} {\left(25 \, \log\left(-c x + 1\right)^{2} - 10 \, \log\left(-c x + 1\right) + 2\right)} + 1125 \, {\left(c x - 1\right)}^{4} {\left(8 \, \log\left(-c x + 1\right)^{2} - 4 \, \log\left(-c x + 1\right) + 1\right)} + 2000 \, {\left(c x - 1\right)}^{3} {\left(9 \, \log\left(-c x + 1\right)^{2} - 6 \, \log\left(-c x + 1\right) + 2\right)} + 9000 \, {\left(c x - 1\right)}^{2} {\left(2 \, \log\left(-c x + 1\right)^{2} - 2 \, \log\left(-c x + 1\right) + 1\right)} + 9000 \, {\left(c x - 1\right)} {\left(\log\left(-c x + 1\right)^{2} - 2 \, \log\left(-c x + 1\right) + 2\right)}}{c^{5}} + \frac{1800 \, \log\left(150 \, c^{6} x^{2} - 150 \, c^{4}\right)}{c^{5}} - 540000 \, \int \frac{\log\left(c x + 1\right)}{150 \, {\left(c^{6} x^{2} - c^{4}\right)}}\,{d x}\right)} b^{2} c d + \frac{1}{12} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a b d + \frac{1}{48} \, {\left(4 \, c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)} \operatorname{artanh}\left(c x\right) + \frac{4 \, c^{2} x^{2} - 2 \, {\left(3 \, \log\left(c x - 1\right) - 8\right)} \log\left(c x + 1\right) + 3 \, \log\left(c x + 1\right)^{2} + 3 \, \log\left(c x - 1\right)^{2} + 16 \, \log\left(c x - 1\right)}{c^{4}}\right)} b^{2} d"," ",0,"1/5*a^2*c*d*x^5 + 1/4*b^2*d*x^4*arctanh(c*x)^2 + 1/4*a^2*d*x^4 + 1/10*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*a*b*c*d - 1/36000*(24*c^6*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^10 - 15*log(c*x + 1)/c^11 + 15*log(c*x - 1)/c^11) - 45*c^5*((c^2*x^4 + 2*x^2)/c^8 + 2*log(c^2*x^2 - 1)/c^10) - 1080000*c^5*integrate(1/150*x^5*log(c*x + 1)/(c^6*x^2 - c^4), x) + 50*c^4*(2*(c^2*x^3 + 3*x)/c^8 - 3*log(c*x + 1)/c^9 + 3*log(c*x - 1)/c^9) - 300*c^3*(x^2/c^6 + log(c^2*x^2 - 1)/c^8) + 900*c^2*(2*x/c^6 - log(c*x + 1)/c^7 + log(c*x - 1)/c^7) - 540000*c*integrate(1/150*x*log(c*x + 1)/(c^6*x^2 - c^4), x) - 60*(30*c^5*x^5*log(c*x + 1)^2 + (12*c^5*x^5 - 15*c^4*x^4 + 20*c^3*x^3 - 30*c^2*x^2 + 60*c*x - 60*(c^5*x^5 + 1)*log(c*x + 1))*log(-c*x + 1))/c^5 - (72*(c*x - 1)^5*(25*log(-c*x + 1)^2 - 10*log(-c*x + 1) + 2) + 1125*(c*x - 1)^4*(8*log(-c*x + 1)^2 - 4*log(-c*x + 1) + 1) + 2000*(c*x - 1)^3*(9*log(-c*x + 1)^2 - 6*log(-c*x + 1) + 2) + 9000*(c*x - 1)^2*(2*log(-c*x + 1)^2 - 2*log(-c*x + 1) + 1) + 9000*(c*x - 1)*(log(-c*x + 1)^2 - 2*log(-c*x + 1) + 2))/c^5 + 1800*log(150*c^6*x^2 - 150*c^4)/c^5 - 540000*integrate(1/150*log(c*x + 1)/(c^6*x^2 - c^4), x))*b^2*c*d + 1/12*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a*b*d + 1/48*(4*c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5)*arctanh(c*x) + (4*c^2*x^2 - 2*(3*log(c*x - 1) - 8)*log(c*x + 1) + 3*log(c*x + 1)^2 + 3*log(c*x - 1)^2 + 16*log(c*x - 1))/c^4)*b^2*d","F",0
69,1,402,0,0.658737," ","integrate(x^2*(c*d*x+d)*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} c d x^{4} + \frac{1}{3} \, a^{2} d x^{3} + \frac{1}{12} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a b c d + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a b d + \frac{{\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} d}{3 \, c^{3}} + \frac{b^{2} d \log\left(c x + 1\right)}{6 \, c^{3}} + \frac{b^{2} d \log\left(c x - 1\right)}{2 \, c^{3}} + \frac{4 \, b^{2} c^{2} d x^{2} + 16 \, b^{2} c d x + {\left(3 \, b^{2} c^{4} d x^{4} + 4 \, b^{2} c^{3} d x^{3} + b^{2} d\right)} \log\left(c x + 1\right)^{2} + {\left(3 \, b^{2} c^{4} d x^{4} + 4 \, b^{2} c^{3} d x^{3} - 7 \, b^{2} d\right)} \log\left(-c x + 1\right)^{2} + 4 \, {\left(b^{2} c^{3} d x^{3} + 2 \, b^{2} c^{2} d x^{2} + 3 \, b^{2} c d x\right)} \log\left(c x + 1\right) - 2 \, {\left(2 \, b^{2} c^{3} d x^{3} + 4 \, b^{2} c^{2} d x^{2} + 6 \, b^{2} c d x + {\left(3 \, b^{2} c^{4} d x^{4} + 4 \, b^{2} c^{3} d x^{3} + b^{2} d\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{48 \, c^{3}}"," ",0,"1/4*a^2*c*d*x^4 + 1/3*a^2*d*x^3 + 1/12*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a*b*c*d + 1/3*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a*b*d + 1/3*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*d/c^3 + 1/6*b^2*d*log(c*x + 1)/c^3 + 1/2*b^2*d*log(c*x - 1)/c^3 + 1/48*(4*b^2*c^2*d*x^2 + 16*b^2*c*d*x + (3*b^2*c^4*d*x^4 + 4*b^2*c^3*d*x^3 + b^2*d)*log(c*x + 1)^2 + (3*b^2*c^4*d*x^4 + 4*b^2*c^3*d*x^3 - 7*b^2*d)*log(-c*x + 1)^2 + 4*(b^2*c^3*d*x^3 + 2*b^2*c^2*d*x^2 + 3*b^2*c*d*x)*log(c*x + 1) - 2*(2*b^2*c^3*d*x^3 + 4*b^2*c^2*d*x^2 + 6*b^2*c*d*x + (3*b^2*c^4*d*x^4 + 4*b^2*c^3*d*x^3 + b^2*d)*log(c*x + 1))*log(-c*x + 1))/c^3","A",0
70,0,0,0,0.000000," ","integrate(x*(c*d*x+d)*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} c d x^{3} + \frac{1}{2} \, b^{2} d x^{2} \operatorname{artanh}\left(c x\right)^{2} + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a b c d - \frac{1}{216} \, {\left(2 \, c^{4} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{6}} - \frac{3 \, \log\left(c x + 1\right)}{c^{7}} + \frac{3 \, \log\left(c x - 1\right)}{c^{7}}\right)} - 3 \, c^{3} {\left(\frac{x^{2}}{c^{4}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)} - 648 \, c^{3} \int \frac{x^{3} \log\left(c x + 1\right)}{9 \, {\left(c^{4} x^{2} - c^{2}\right)}}\,{d x} + 9 \, c^{2} {\left(\frac{2 \, x}{c^{4}} - \frac{\log\left(c x + 1\right)}{c^{5}} + \frac{\log\left(c x - 1\right)}{c^{5}}\right)} - 324 \, c \int \frac{x \log\left(c x + 1\right)}{9 \, {\left(c^{4} x^{2} - c^{2}\right)}}\,{d x} - \frac{6 \, {\left(3 \, c^{3} x^{3} \log\left(c x + 1\right)^{2} + {\left(2 \, c^{3} x^{3} - 3 \, c^{2} x^{2} + 6 \, c x - 6 \, {\left(c^{3} x^{3} + 1\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)\right)}}{c^{3}} - \frac{2 \, {\left(c x - 1\right)}^{3} {\left(9 \, \log\left(-c x + 1\right)^{2} - 6 \, \log\left(-c x + 1\right) + 2\right)} + 27 \, {\left(c x - 1\right)}^{2} {\left(2 \, \log\left(-c x + 1\right)^{2} - 2 \, \log\left(-c x + 1\right) + 1\right)} + 54 \, {\left(c x - 1\right)} {\left(\log\left(-c x + 1\right)^{2} - 2 \, \log\left(-c x + 1\right) + 2\right)}}{c^{3}} + \frac{18 \, \log\left(9 \, c^{4} x^{2} - 9 \, c^{2}\right)}{c^{3}} - 324 \, \int \frac{\log\left(c x + 1\right)}{9 \, {\left(c^{4} x^{2} - c^{2}\right)}}\,{d x}\right)} b^{2} c d + \frac{1}{2} \, a^{2} d x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a b d + \frac{1}{8} \, {\left(4 \, c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} \operatorname{artanh}\left(c x\right) - \frac{2 \, {\left(\log\left(c x - 1\right) - 2\right)} \log\left(c x + 1\right) - \log\left(c x + 1\right)^{2} - \log\left(c x - 1\right)^{2} - 4 \, \log\left(c x - 1\right)}{c^{2}}\right)} b^{2} d"," ",0,"1/3*a^2*c*d*x^3 + 1/2*b^2*d*x^2*arctanh(c*x)^2 + 1/3*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a*b*c*d - 1/216*(2*c^4*(2*(c^2*x^3 + 3*x)/c^6 - 3*log(c*x + 1)/c^7 + 3*log(c*x - 1)/c^7) - 3*c^3*(x^2/c^4 + log(c^2*x^2 - 1)/c^6) - 648*c^3*integrate(1/9*x^3*log(c*x + 1)/(c^4*x^2 - c^2), x) + 9*c^2*(2*x/c^4 - log(c*x + 1)/c^5 + log(c*x - 1)/c^5) - 324*c*integrate(1/9*x*log(c*x + 1)/(c^4*x^2 - c^2), x) - 6*(3*c^3*x^3*log(c*x + 1)^2 + (2*c^3*x^3 - 3*c^2*x^2 + 6*c*x - 6*(c^3*x^3 + 1)*log(c*x + 1))*log(-c*x + 1))/c^3 - (2*(c*x - 1)^3*(9*log(-c*x + 1)^2 - 6*log(-c*x + 1) + 2) + 27*(c*x - 1)^2*(2*log(-c*x + 1)^2 - 2*log(-c*x + 1) + 1) + 54*(c*x - 1)*(log(-c*x + 1)^2 - 2*log(-c*x + 1) + 2))/c^3 + 18*log(9*c^4*x^2 - 9*c^2)/c^3 - 324*integrate(1/9*log(c*x + 1)/(c^4*x^2 - c^2), x))*b^2*c*d + 1/2*a^2*d*x^2 + 1/2*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a*b*d + 1/8*(4*c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3)*arctanh(c*x) - (2*(log(c*x - 1) - 2)*log(c*x + 1) - log(c*x + 1)^2 - log(c*x - 1)^2 - 4*log(c*x - 1))/c^2)*b^2*d","F",0
71,1,290,0,0.563534," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} c d x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a b c d + a^{2} d x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a b d}{c} + \frac{{\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} d}{c} + \frac{b^{2} d \log\left(c x + 1\right)}{2 \, c} + \frac{b^{2} d \log\left(c x - 1\right)}{2 \, c} + \frac{4 \, b^{2} c d x \log\left(c x + 1\right) + {\left(b^{2} c^{2} d x^{2} + 2 \, b^{2} c d x + b^{2} d\right)} \log\left(c x + 1\right)^{2} + {\left(b^{2} c^{2} d x^{2} + 2 \, b^{2} c d x - 3 \, b^{2} d\right)} \log\left(-c x + 1\right)^{2} - 2 \, {\left(2 \, b^{2} c d x + {\left(b^{2} c^{2} d x^{2} + 2 \, b^{2} c d x + b^{2} d\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{8 \, c}"," ",0,"1/2*a^2*c*d*x^2 + 1/2*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a*b*c*d + a^2*d*x + (2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a*b*d/c + (log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*d/c + 1/2*b^2*d*log(c*x + 1)/c + 1/2*b^2*d*log(c*x - 1)/c + 1/8*(4*b^2*c*d*x*log(c*x + 1) + (b^2*c^2*d*x^2 + 2*b^2*c*d*x + b^2*d)*log(c*x + 1)^2 + (b^2*c^2*d*x^2 + 2*b^2*c*d*x - 3*b^2*d)*log(-c*x + 1)^2 - 2*(2*b^2*c*d*x + (b^2*c^2*d*x^2 + 2*b^2*c*d*x + b^2*d)*log(c*x + 1))*log(-c*x + 1))/c","B",0
72,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))^2/x,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} c d x \log\left(-c x + 1\right)^{2} + a^{2} c d x + {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a b d + a^{2} d \log\left(x\right) - \int -\frac{{\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c d x - a b d\right)} \log\left(c x + 1\right) - 2 \, {\left(b^{2} c^{2} d x^{2} + 2 \, a b c d x - 2 \, a b d + {\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c x^{2} - x\right)}}\,{d x}"," ",0,"1/4*b^2*c*d*x*log(-c*x + 1)^2 + a^2*c*d*x + (2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a*b*d + a^2*d*log(x) - integrate(-1/4*((b^2*c^2*d*x^2 - b^2*d)*log(c*x + 1)^2 + 4*(a*b*c*d*x - a*b*d)*log(c*x + 1) - 2*(b^2*c^2*d*x^2 + 2*a*b*c*d*x - 2*a*b*d + (b^2*c^2*d*x^2 - b^2*d)*log(c*x + 1))*log(-c*x + 1))/(c*x^2 - x), x)","F",0
73,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))^2/x^2,x, algorithm=""maxima"")","a^{2} c d \log\left(x\right) - {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} a b d - \frac{b^{2} d \log\left(-c x + 1\right)^{2}}{4 \, x} - \frac{a^{2} d}{x} - \int -\frac{{\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c^{2} d x^{2} - a b c d x\right)} \log\left(c x + 1\right) - 2 \, {\left(2 \, a b c^{2} d x^{2} - {\left(2 \, a b c d + b^{2} c d\right)} x + {\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c x^{3} - x^{2}\right)}}\,{d x}"," ",0,"a^2*c*d*log(x) - (c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*a*b*d - 1/4*b^2*d*log(-c*x + 1)^2/x - a^2*d/x - integrate(-1/4*((b^2*c^2*d*x^2 - b^2*d)*log(c*x + 1)^2 + 4*(a*b*c^2*d*x^2 - a*b*c*d*x)*log(c*x + 1) - 2*(2*a*b*c^2*d*x^2 - (2*a*b*c*d + b^2*c*d)*x + (b^2*c^2*d*x^2 - b^2*d)*log(c*x + 1))*log(-c*x + 1))/(c*x^3 - x^2), x)","F",0
74,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))^2/x^3,x, algorithm=""maxima"")","-{\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} a b c d - \frac{1}{4} \, b^{2} c d {\left(\frac{\log\left(-c x + 1\right)^{2}}{x} + \int -\frac{{\left(c x - 1\right)} \log\left(c x + 1\right)^{2} + 2 \, {\left(c x - {\left(c x - 1\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{c x^{3} - x^{2}}\,{d x}\right)} + \frac{1}{2} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} a b d + \frac{1}{8} \, {\left({\left(2 \, {\left(\log\left(c x - 1\right) - 2\right)} \log\left(c x + 1\right) - \log\left(c x + 1\right)^{2} - \log\left(c x - 1\right)^{2} - 4 \, \log\left(c x - 1\right) + 8 \, \log\left(x\right)\right)} c^{2} + 4 \, {\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c \operatorname{artanh}\left(c x\right)\right)} b^{2} d - \frac{a^{2} c d}{x} - \frac{b^{2} d \operatorname{artanh}\left(c x\right)^{2}}{2 \, x^{2}} - \frac{a^{2} d}{2 \, x^{2}}"," ",0,"-(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*a*b*c*d - 1/4*b^2*c*d*(log(-c*x + 1)^2/x + integrate(-((c*x - 1)*log(c*x + 1)^2 + 2*(c*x - (c*x - 1)*log(c*x + 1))*log(-c*x + 1))/(c*x^3 - x^2), x)) + 1/2*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*a*b*d + 1/8*((2*(log(c*x - 1) - 2)*log(c*x + 1) - log(c*x + 1)^2 - log(c*x - 1)^2 - 4*log(c*x - 1) + 8*log(x))*c^2 + 4*(c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c*arctanh(c*x))*b^2*d - a^2*c*d/x - 1/2*b^2*d*arctanh(c*x)^2/x^2 - 1/2*a^2*d/x^2","F",0
75,1,417,0,0.924340," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))^2/x^4,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} c^{3} d - \frac{1}{3} \, {\left(\log\left(c x\right) \log\left(-c x + 1\right) + {\rm Li}_2\left(-c x + 1\right)\right)} b^{2} c^{3} d + \frac{1}{3} \, {\left(\log\left(c x + 1\right) \log\left(-c x\right) + {\rm Li}_2\left(c x + 1\right)\right)} b^{2} c^{3} d - \frac{1}{3} \, b^{2} c^{3} d \log\left(c x + 1\right) - \frac{2}{3} \, b^{2} c^{3} d \log\left(c x - 1\right) + b^{2} c^{3} d \log\left(x\right) + \frac{1}{2} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} a b c d - \frac{1}{3} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} a b d - \frac{a^{2} c d}{2 \, x^{2}} - \frac{a^{2} d}{3 \, x^{3}} - \frac{8 \, b^{2} c^{2} d x^{2} - {\left(b^{2} c^{3} d x^{3} - 3 \, b^{2} c d x - 2 \, b^{2} d\right)} \log\left(c x + 1\right)^{2} - {\left(5 \, b^{2} c^{3} d x^{3} - 3 \, b^{2} c d x - 2 \, b^{2} d\right)} \log\left(-c x + 1\right)^{2} + 4 \, {\left(3 \, b^{2} c^{2} d x^{2} + b^{2} c d x\right)} \log\left(c x + 1\right) - 2 \, {\left(6 \, b^{2} c^{2} d x^{2} + 2 \, b^{2} c d x - {\left(b^{2} c^{3} d x^{3} - 3 \, b^{2} c d x - 2 \, b^{2} d\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{24 \, x^{3}}"," ",0,"-1/3*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*c^3*d - 1/3*(log(c*x)*log(-c*x + 1) + dilog(-c*x + 1))*b^2*c^3*d + 1/3*(log(c*x + 1)*log(-c*x) + dilog(c*x + 1))*b^2*c^3*d - 1/3*b^2*c^3*d*log(c*x + 1) - 2/3*b^2*c^3*d*log(c*x - 1) + b^2*c^3*d*log(x) + 1/2*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*a*b*c*d - 1/3*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*a*b*d - 1/2*a^2*c*d/x^2 - 1/3*a^2*d/x^3 - 1/24*(8*b^2*c^2*d*x^2 - (b^2*c^3*d*x^3 - 3*b^2*c*d*x - 2*b^2*d)*log(c*x + 1)^2 - (5*b^2*c^3*d*x^3 - 3*b^2*c*d*x - 2*b^2*d)*log(-c*x + 1)^2 + 4*(3*b^2*c^2*d*x^2 + b^2*c*d*x)*log(c*x + 1) - 2*(6*b^2*c^2*d*x^2 + 2*b^2*c*d*x - (b^2*c^3*d*x^3 - 3*b^2*c*d*x - 2*b^2*d)*log(c*x + 1))*log(-c*x + 1))/x^3","B",0
76,1,766,0,0.688033," ","integrate(x^3*(c*d*x+d)^2*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} c^{2} d^{2} x^{6} + \frac{2}{5} \, a^{2} c d^{2} x^{5} + \frac{1}{4} \, b^{2} d^{2} x^{4} \operatorname{artanh}\left(c x\right)^{2} + \frac{1}{4} \, a^{2} d^{2} x^{4} + \frac{1}{90} \, {\left(30 \, x^{6} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} a b c^{2} d^{2} + \frac{1}{5} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} a b c d^{2} + \frac{1}{12} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a b d^{2} + \frac{1}{48} \, {\left(4 \, c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)} \operatorname{artanh}\left(c x\right) + \frac{4 \, c^{2} x^{2} - 2 \, {\left(3 \, \log\left(c x - 1\right) - 8\right)} \log\left(c x + 1\right) + 3 \, \log\left(c x + 1\right)^{2} + 3 \, \log\left(c x - 1\right)^{2} + 16 \, \log\left(c x - 1\right)}{c^{4}}\right)} b^{2} d^{2} + \frac{2 \, {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} d^{2}}{5 \, c^{4}} - \frac{2 \, b^{2} d^{2} \log\left(c x + 1\right)}{45 \, c^{4}} + \frac{5 \, b^{2} d^{2} \log\left(c x - 1\right)}{9 \, c^{4}} + \frac{6 \, b^{2} c^{4} d^{2} x^{4} + 24 \, b^{2} c^{3} d^{2} x^{3} + 32 \, b^{2} c^{2} d^{2} x^{2} + 216 \, b^{2} c d^{2} x + 3 \, {\left(5 \, b^{2} c^{6} d^{2} x^{6} + 12 \, b^{2} c^{5} d^{2} x^{5} + 7 \, b^{2} d^{2}\right)} \log\left(c x + 1\right)^{2} + 3 \, {\left(5 \, b^{2} c^{6} d^{2} x^{6} + 12 \, b^{2} c^{5} d^{2} x^{5} - 17 \, b^{2} d^{2}\right)} \log\left(-c x + 1\right)^{2} + 4 \, {\left(3 \, b^{2} c^{5} d^{2} x^{5} + 9 \, b^{2} c^{4} d^{2} x^{4} + 5 \, b^{2} c^{3} d^{2} x^{3} + 18 \, b^{2} c^{2} d^{2} x^{2} + 15 \, b^{2} c d^{2} x\right)} \log\left(c x + 1\right) - 2 \, {\left(6 \, b^{2} c^{5} d^{2} x^{5} + 18 \, b^{2} c^{4} d^{2} x^{4} + 10 \, b^{2} c^{3} d^{2} x^{3} + 36 \, b^{2} c^{2} d^{2} x^{2} + 30 \, b^{2} c d^{2} x + 3 \, {\left(5 \, b^{2} c^{6} d^{2} x^{6} + 12 \, b^{2} c^{5} d^{2} x^{5} + 7 \, b^{2} d^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{360 \, c^{4}}"," ",0,"1/6*a^2*c^2*d^2*x^6 + 2/5*a^2*c*d^2*x^5 + 1/4*b^2*d^2*x^4*arctanh(c*x)^2 + 1/4*a^2*d^2*x^4 + 1/90*(30*x^6*arctanh(c*x) + c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*a*b*c^2*d^2 + 1/5*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*a*b*c*d^2 + 1/12*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a*b*d^2 + 1/48*(4*c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5)*arctanh(c*x) + (4*c^2*x^2 - 2*(3*log(c*x - 1) - 8)*log(c*x + 1) + 3*log(c*x + 1)^2 + 3*log(c*x - 1)^2 + 16*log(c*x - 1))/c^4)*b^2*d^2 + 2/5*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*d^2/c^4 - 2/45*b^2*d^2*log(c*x + 1)/c^4 + 5/9*b^2*d^2*log(c*x - 1)/c^4 + 1/360*(6*b^2*c^4*d^2*x^4 + 24*b^2*c^3*d^2*x^3 + 32*b^2*c^2*d^2*x^2 + 216*b^2*c*d^2*x + 3*(5*b^2*c^6*d^2*x^6 + 12*b^2*c^5*d^2*x^5 + 7*b^2*d^2)*log(c*x + 1)^2 + 3*(5*b^2*c^6*d^2*x^6 + 12*b^2*c^5*d^2*x^5 - 17*b^2*d^2)*log(-c*x + 1)^2 + 4*(3*b^2*c^5*d^2*x^5 + 9*b^2*c^4*d^2*x^4 + 5*b^2*c^3*d^2*x^3 + 18*b^2*c^2*d^2*x^2 + 15*b^2*c*d^2*x)*log(c*x + 1) - 2*(6*b^2*c^5*d^2*x^5 + 18*b^2*c^4*d^2*x^4 + 10*b^2*c^3*d^2*x^3 + 36*b^2*c^2*d^2*x^2 + 30*b^2*c*d^2*x + 3*(5*b^2*c^6*d^2*x^6 + 12*b^2*c^5*d^2*x^5 + 7*b^2*d^2)*log(c*x + 1))*log(-c*x + 1))/c^4","B",0
77,1,604,0,0.658423," ","integrate(x^2*(c*d*x+d)^2*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} c^{2} d^{2} x^{5} + \frac{1}{2} \, a^{2} c d^{2} x^{4} + \frac{1}{10} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} a b c^{2} d^{2} + \frac{1}{3} \, a^{2} d^{2} x^{3} + \frac{1}{6} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a b c d^{2} + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a b d^{2} + \frac{8 \, {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} d^{2}}{15 \, c^{3}} + \frac{7 \, b^{2} d^{2} \log\left(c x + 1\right)}{20 \, c^{3}} + \frac{59 \, b^{2} d^{2} \log\left(c x - 1\right)}{60 \, c^{3}} + \frac{4 \, b^{2} c^{3} d^{2} x^{3} + 20 \, b^{2} c^{2} d^{2} x^{2} + 76 \, b^{2} c d^{2} x + {\left(6 \, b^{2} c^{5} d^{2} x^{5} + 15 \, b^{2} c^{4} d^{2} x^{4} + 10 \, b^{2} c^{3} d^{2} x^{3} + b^{2} d^{2}\right)} \log\left(c x + 1\right)^{2} + {\left(6 \, b^{2} c^{5} d^{2} x^{5} + 15 \, b^{2} c^{4} d^{2} x^{4} + 10 \, b^{2} c^{3} d^{2} x^{3} - 31 \, b^{2} d^{2}\right)} \log\left(-c x + 1\right)^{2} + 2 \, {\left(3 \, b^{2} c^{4} d^{2} x^{4} + 10 \, b^{2} c^{3} d^{2} x^{3} + 16 \, b^{2} c^{2} d^{2} x^{2} + 30 \, b^{2} c d^{2} x\right)} \log\left(c x + 1\right) - 2 \, {\left(3 \, b^{2} c^{4} d^{2} x^{4} + 10 \, b^{2} c^{3} d^{2} x^{3} + 16 \, b^{2} c^{2} d^{2} x^{2} + 30 \, b^{2} c d^{2} x + {\left(6 \, b^{2} c^{5} d^{2} x^{5} + 15 \, b^{2} c^{4} d^{2} x^{4} + 10 \, b^{2} c^{3} d^{2} x^{3} + b^{2} d^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{120 \, c^{3}}"," ",0,"1/5*a^2*c^2*d^2*x^5 + 1/2*a^2*c*d^2*x^4 + 1/10*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*a*b*c^2*d^2 + 1/3*a^2*d^2*x^3 + 1/6*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a*b*c*d^2 + 1/3*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a*b*d^2 + 8/15*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*d^2/c^3 + 7/20*b^2*d^2*log(c*x + 1)/c^3 + 59/60*b^2*d^2*log(c*x - 1)/c^3 + 1/120*(4*b^2*c^3*d^2*x^3 + 20*b^2*c^2*d^2*x^2 + 76*b^2*c*d^2*x + (6*b^2*c^5*d^2*x^5 + 15*b^2*c^4*d^2*x^4 + 10*b^2*c^3*d^2*x^3 + b^2*d^2)*log(c*x + 1)^2 + (6*b^2*c^5*d^2*x^5 + 15*b^2*c^4*d^2*x^4 + 10*b^2*c^3*d^2*x^3 - 31*b^2*d^2)*log(-c*x + 1)^2 + 2*(3*b^2*c^4*d^2*x^4 + 10*b^2*c^3*d^2*x^3 + 16*b^2*c^2*d^2*x^2 + 30*b^2*c*d^2*x)*log(c*x + 1) - 2*(3*b^2*c^4*d^2*x^4 + 10*b^2*c^3*d^2*x^3 + 16*b^2*c^2*d^2*x^2 + 30*b^2*c*d^2*x + (6*b^2*c^5*d^2*x^5 + 15*b^2*c^4*d^2*x^4 + 10*b^2*c^3*d^2*x^3 + b^2*d^2)*log(c*x + 1))*log(-c*x + 1))/c^3","B",0
78,1,610,0,0.672649," ","integrate(x*(c*d*x+d)^2*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} c^{2} d^{2} x^{4} + \frac{2}{3} \, a^{2} c d^{2} x^{3} + \frac{1}{2} \, b^{2} d^{2} x^{2} \operatorname{artanh}\left(c x\right)^{2} + \frac{1}{12} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a b c^{2} d^{2} + \frac{2}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a b c d^{2} + \frac{1}{2} \, a^{2} d^{2} x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a b d^{2} + \frac{1}{8} \, {\left(4 \, c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} \operatorname{artanh}\left(c x\right) - \frac{2 \, {\left(\log\left(c x - 1\right) - 2\right)} \log\left(c x + 1\right) - \log\left(c x + 1\right)^{2} - \log\left(c x - 1\right)^{2} - 4 \, \log\left(c x - 1\right)}{c^{2}}\right)} b^{2} d^{2} + \frac{2 \, {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} d^{2}}{3 \, c^{2}} + \frac{2 \, b^{2} d^{2} \log\left(c x - 1\right)}{3 \, c^{2}} + \frac{4 \, b^{2} c^{2} d^{2} x^{2} + 32 \, b^{2} c d^{2} x + {\left(3 \, b^{2} c^{4} d^{2} x^{4} + 8 \, b^{2} c^{3} d^{2} x^{3} + 5 \, b^{2} d^{2}\right)} \log\left(c x + 1\right)^{2} + {\left(3 \, b^{2} c^{4} d^{2} x^{4} + 8 \, b^{2} c^{3} d^{2} x^{3} - 11 \, b^{2} d^{2}\right)} \log\left(-c x + 1\right)^{2} + 4 \, {\left(b^{2} c^{3} d^{2} x^{3} + 4 \, b^{2} c^{2} d^{2} x^{2} + 3 \, b^{2} c d^{2} x\right)} \log\left(c x + 1\right) - 2 \, {\left(2 \, b^{2} c^{3} d^{2} x^{3} + 8 \, b^{2} c^{2} d^{2} x^{2} + 6 \, b^{2} c d^{2} x + {\left(3 \, b^{2} c^{4} d^{2} x^{4} + 8 \, b^{2} c^{3} d^{2} x^{3} + 5 \, b^{2} d^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{48 \, c^{2}}"," ",0,"1/4*a^2*c^2*d^2*x^4 + 2/3*a^2*c*d^2*x^3 + 1/2*b^2*d^2*x^2*arctanh(c*x)^2 + 1/12*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a*b*c^2*d^2 + 2/3*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a*b*c*d^2 + 1/2*a^2*d^2*x^2 + 1/2*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a*b*d^2 + 1/8*(4*c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3)*arctanh(c*x) - (2*(log(c*x - 1) - 2)*log(c*x + 1) - log(c*x + 1)^2 - log(c*x - 1)^2 - 4*log(c*x - 1))/c^2)*b^2*d^2 + 2/3*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*d^2/c^2 + 2/3*b^2*d^2*log(c*x - 1)/c^2 + 1/48*(4*b^2*c^2*d^2*x^2 + 32*b^2*c*d^2*x + (3*b^2*c^4*d^2*x^4 + 8*b^2*c^3*d^2*x^3 + 5*b^2*d^2)*log(c*x + 1)^2 + (3*b^2*c^4*d^2*x^4 + 8*b^2*c^3*d^2*x^3 - 11*b^2*d^2)*log(-c*x + 1)^2 + 4*(b^2*c^3*d^2*x^3 + 4*b^2*c^2*d^2*x^2 + 3*b^2*c*d^2*x)*log(c*x + 1) - 2*(2*b^2*c^3*d^2*x^3 + 8*b^2*c^2*d^2*x^2 + 6*b^2*c*d^2*x + (3*b^2*c^4*d^2*x^4 + 8*b^2*c^3*d^2*x^3 + 5*b^2*d^2)*log(c*x + 1))*log(-c*x + 1))/c^2","B",0
79,1,464,0,0.553275," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} c^{2} d^{2} x^{3} + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a b c^{2} d^{2} + a^{2} c d^{2} x^{2} + {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a b c d^{2} + a^{2} d^{2} x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a b d^{2}}{c} + \frac{4 \, {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} d^{2}}{3 \, c} + \frac{5 \, b^{2} d^{2} \log\left(c x + 1\right)}{6 \, c} + \frac{7 \, b^{2} d^{2} \log\left(c x - 1\right)}{6 \, c} + \frac{4 \, b^{2} c d^{2} x + {\left(b^{2} c^{3} d^{2} x^{3} + 3 \, b^{2} c^{2} d^{2} x^{2} + 3 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \log\left(c x + 1\right)^{2} + {\left(b^{2} c^{3} d^{2} x^{3} + 3 \, b^{2} c^{2} d^{2} x^{2} + 3 \, b^{2} c d^{2} x - 7 \, b^{2} d^{2}\right)} \log\left(-c x + 1\right)^{2} + 2 \, {\left(b^{2} c^{2} d^{2} x^{2} + 6 \, b^{2} c d^{2} x\right)} \log\left(c x + 1\right) - 2 \, {\left(b^{2} c^{2} d^{2} x^{2} + 6 \, b^{2} c d^{2} x + {\left(b^{2} c^{3} d^{2} x^{3} + 3 \, b^{2} c^{2} d^{2} x^{2} + 3 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{12 \, c}"," ",0,"1/3*a^2*c^2*d^2*x^3 + 1/3*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a*b*c^2*d^2 + a^2*c*d^2*x^2 + (2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a*b*c*d^2 + a^2*d^2*x + (2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a*b*d^2/c + 4/3*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*d^2/c + 5/6*b^2*d^2*log(c*x + 1)/c + 7/6*b^2*d^2*log(c*x - 1)/c + 1/12*(4*b^2*c*d^2*x + (b^2*c^3*d^2*x^3 + 3*b^2*c^2*d^2*x^2 + 3*b^2*c*d^2*x + b^2*d^2)*log(c*x + 1)^2 + (b^2*c^3*d^2*x^3 + 3*b^2*c^2*d^2*x^2 + 3*b^2*c*d^2*x - 7*b^2*d^2)*log(-c*x + 1)^2 + 2*(b^2*c^2*d^2*x^2 + 6*b^2*c*d^2*x)*log(c*x + 1) - 2*(b^2*c^2*d^2*x^2 + 6*b^2*c*d^2*x + (b^2*c^3*d^2*x^3 + 3*b^2*c^2*d^2*x^2 + 3*b^2*c*d^2*x + b^2*d^2)*log(c*x + 1))*log(-c*x + 1))/c","B",0
80,0,0,0,0.000000," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))^2/x,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} c^{2} d^{2} x^{2} + 2 \, a^{2} c d^{2} x + 2 \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a b d^{2} + a^{2} d^{2} \log\left(x\right) + \frac{1}{8} \, {\left(b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c d^{2} x\right)} \log\left(-c x + 1\right)^{2} - \int -\frac{{\left(b^{2} c^{3} d^{2} x^{3} + b^{2} c^{2} d^{2} x^{2} - b^{2} c d^{2} x - b^{2} d^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c^{3} d^{2} x^{3} - a b c^{2} d^{2} x^{2} + a b c d^{2} x - a b d^{2}\right)} \log\left(c x + 1\right) - {\left(4 \, a b c d^{2} x - 4 \, a b d^{2} + {\left(4 \, a b c^{3} d^{2} + b^{2} c^{3} d^{2}\right)} x^{3} - 4 \, {\left(a b c^{2} d^{2} - b^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} x^{3} + b^{2} c^{2} d^{2} x^{2} - b^{2} c d^{2} x - b^{2} d^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c x^{2} - x\right)}}\,{d x}"," ",0,"1/2*a^2*c^2*d^2*x^2 + 2*a^2*c*d^2*x + 2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a*b*d^2 + a^2*d^2*log(x) + 1/8*(b^2*c^2*d^2*x^2 + 4*b^2*c*d^2*x)*log(-c*x + 1)^2 - integrate(-1/4*((b^2*c^3*d^2*x^3 + b^2*c^2*d^2*x^2 - b^2*c*d^2*x - b^2*d^2)*log(c*x + 1)^2 + 4*(a*b*c^3*d^2*x^3 - a*b*c^2*d^2*x^2 + a*b*c*d^2*x - a*b*d^2)*log(c*x + 1) - (4*a*b*c*d^2*x - 4*a*b*d^2 + (4*a*b*c^3*d^2 + b^2*c^3*d^2)*x^3 - 4*(a*b*c^2*d^2 - b^2*c^2*d^2)*x^2 + 2*(b^2*c^3*d^2*x^3 + b^2*c^2*d^2*x^2 - b^2*c*d^2*x - b^2*d^2)*log(c*x + 1))*log(-c*x + 1))/(c*x^2 - x), x)","F",0
81,0,0,0,0.000000," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))^2/x^2,x, algorithm=""maxima"")","a^{2} c^{2} d^{2} x - \frac{1}{2} \, b^{2} c^{2} d^{2} \int \log\left(c x + 1\right) \log\left(-c x + 1\right)\,{d x} + \frac{1}{4} \, b^{2} c^{2} d^{2} \int \frac{\log\left(c x + 1\right)^{2}}{c^{2} x^{2}}\,{d x} + {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a b c d^{2} + \frac{1}{2} \, {\left(c x - {\left(c x - 1\right)} \log\left(-c x + 1\right) - 1\right)} b^{2} c d^{2} + \frac{1}{4} \, b^{2} c d^{2} \Gamma\left(3, -\log\left(c x + 1\right)\right) + \frac{1}{2} \, b^{2} c d^{2} \int \frac{\log\left(c x + 1\right)^{2}}{x}\,{d x} - b^{2} c d^{2} \int \frac{\log\left(c x + 1\right) \log\left(-c x + 1\right)}{x}\,{d x} + 2 \, a b c d^{2} \int \frac{\log\left(c x + 1\right)}{x}\,{d x} - 2 \, a b c d^{2} \int \frac{\log\left(-c x + 1\right)}{x}\,{d x} - \frac{1}{2} \, b^{2} c d^{2} \int \frac{\log\left(-c x + 1\right)}{x}\,{d x} + 2 \, a^{2} c d^{2} \log\left(x\right) - {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} a b d^{2} - \frac{1}{2} \, b^{2} d^{2} \int \frac{\log\left(c x + 1\right) \log\left(-c x + 1\right)}{x^{2}}\,{d x} - \frac{a^{2} d^{2}}{x} + \frac{{\left(b^{2} c^{2} d^{2} x^{2} - b^{2} d^{2}\right)} \log\left(-c x + 1\right)^{2}}{4 \, x}"," ",0,"a^2*c^2*d^2*x - 1/2*b^2*c^2*d^2*integrate(log(c*x + 1)*log(-c*x + 1), x) + 1/4*b^2*c^2*d^2*integrate(log(c*x + 1)^2/(c^2*x^2), x) + (2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a*b*c*d^2 + 1/2*(c*x - (c*x - 1)*log(-c*x + 1) - 1)*b^2*c*d^2 + 1/4*b^2*c*d^2*gamma(3, -log(c*x + 1)) + 1/2*b^2*c*d^2*integrate(log(c*x + 1)^2/x, x) - b^2*c*d^2*integrate(log(c*x + 1)*log(-c*x + 1)/x, x) + 2*a*b*c*d^2*integrate(log(c*x + 1)/x, x) - 2*a*b*c*d^2*integrate(log(-c*x + 1)/x, x) - 1/2*b^2*c*d^2*integrate(log(-c*x + 1)/x, x) + 2*a^2*c*d^2*log(x) - (c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*a*b*d^2 - 1/2*b^2*d^2*integrate(log(c*x + 1)*log(-c*x + 1)/x^2, x) - a^2*d^2/x + 1/4*(b^2*c^2*d^2*x^2 - b^2*d^2)*log(-c*x + 1)^2/x","F",0
82,0,0,0,0.000000," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))^2/x^3,x, algorithm=""maxima"")","a^{2} c^{2} d^{2} \log\left(x\right) - 2 \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} a b c d^{2} + \frac{1}{2} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} a b d^{2} - \frac{2 \, a^{2} c d^{2}}{x} - \frac{a^{2} d^{2}}{2 \, x^{2}} - \frac{{\left(4 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \log\left(-c x + 1\right)^{2}}{8 \, x^{2}} - \int -\frac{{\left(b^{2} c^{3} d^{2} x^{3} + b^{2} c^{2} d^{2} x^{2} - b^{2} c d^{2} x - b^{2} d^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c^{3} d^{2} x^{3} - a b c^{2} d^{2} x^{2}\right)} \log\left(c x + 1\right) - {\left(4 \, a b c^{3} d^{2} x^{3} - b^{2} c d^{2} x - 4 \, {\left(a b c^{2} d^{2} + b^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} x^{3} + b^{2} c^{2} d^{2} x^{2} - b^{2} c d^{2} x - b^{2} d^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c x^{4} - x^{3}\right)}}\,{d x}"," ",0,"a^2*c^2*d^2*log(x) - 2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*a*b*c*d^2 + 1/2*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*a*b*d^2 - 2*a^2*c*d^2/x - 1/2*a^2*d^2/x^2 - 1/8*(4*b^2*c*d^2*x + b^2*d^2)*log(-c*x + 1)^2/x^2 - integrate(-1/4*((b^2*c^3*d^2*x^3 + b^2*c^2*d^2*x^2 - b^2*c*d^2*x - b^2*d^2)*log(c*x + 1)^2 + 4*(a*b*c^3*d^2*x^3 - a*b*c^2*d^2*x^2)*log(c*x + 1) - (4*a*b*c^3*d^2*x^3 - b^2*c*d^2*x - 4*(a*b*c^2*d^2 + b^2*c^2*d^2)*x^2 + 2*(b^2*c^3*d^2*x^3 + b^2*c^2*d^2*x^2 - b^2*c*d^2*x - b^2*d^2)*log(c*x + 1))*log(-c*x + 1))/(c*x^4 - x^3), x)","F",0
83,1,555,0,0.936416," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))^2/x^4,x, algorithm=""maxima"")","-\frac{4}{3} \, {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} c^{3} d^{2} - \frac{4}{3} \, {\left(\log\left(c x\right) \log\left(-c x + 1\right) + {\rm Li}_2\left(-c x + 1\right)\right)} b^{2} c^{3} d^{2} + \frac{4}{3} \, {\left(\log\left(c x + 1\right) \log\left(-c x\right) + {\rm Li}_2\left(c x + 1\right)\right)} b^{2} c^{3} d^{2} - \frac{5}{6} \, b^{2} c^{3} d^{2} \log\left(c x + 1\right) - \frac{7}{6} \, b^{2} c^{3} d^{2} \log\left(c x - 1\right) + 2 \, b^{2} c^{3} d^{2} \log\left(x\right) - {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} a b c^{2} d^{2} + {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} a b c d^{2} - \frac{1}{3} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} a b d^{2} - \frac{a^{2} c^{2} d^{2}}{x} - \frac{a^{2} c d^{2}}{x^{2}} - \frac{a^{2} d^{2}}{3 \, x^{3}} - \frac{4 \, b^{2} c^{2} d^{2} x^{2} + {\left(b^{2} c^{3} d^{2} x^{3} + 3 \, b^{2} c^{2} d^{2} x^{2} + 3 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \log\left(c x + 1\right)^{2} - {\left(7 \, b^{2} c^{3} d^{2} x^{3} - 3 \, b^{2} c^{2} d^{2} x^{2} - 3 \, b^{2} c d^{2} x - b^{2} d^{2}\right)} \log\left(-c x + 1\right)^{2} + 2 \, {\left(6 \, b^{2} c^{2} d^{2} x^{2} + b^{2} c d^{2} x\right)} \log\left(c x + 1\right) - 2 \, {\left(6 \, b^{2} c^{2} d^{2} x^{2} + b^{2} c d^{2} x + {\left(b^{2} c^{3} d^{2} x^{3} + 3 \, b^{2} c^{2} d^{2} x^{2} + 3 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{12 \, x^{3}}"," ",0,"-4/3*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*c^3*d^2 - 4/3*(log(c*x)*log(-c*x + 1) + dilog(-c*x + 1))*b^2*c^3*d^2 + 4/3*(log(c*x + 1)*log(-c*x) + dilog(c*x + 1))*b^2*c^3*d^2 - 5/6*b^2*c^3*d^2*log(c*x + 1) - 7/6*b^2*c^3*d^2*log(c*x - 1) + 2*b^2*c^3*d^2*log(x) - (c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*a*b*c^2*d^2 + ((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*a*b*c*d^2 - 1/3*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*a*b*d^2 - a^2*c^2*d^2/x - a^2*c*d^2/x^2 - 1/3*a^2*d^2/x^3 - 1/12*(4*b^2*c^2*d^2*x^2 + (b^2*c^3*d^2*x^3 + 3*b^2*c^2*d^2*x^2 + 3*b^2*c*d^2*x + b^2*d^2)*log(c*x + 1)^2 - (7*b^2*c^3*d^2*x^3 - 3*b^2*c^2*d^2*x^2 - 3*b^2*c*d^2*x - b^2*d^2)*log(-c*x + 1)^2 + 2*(6*b^2*c^2*d^2*x^2 + b^2*c*d^2*x)*log(c*x + 1) - 2*(6*b^2*c^2*d^2*x^2 + b^2*c*d^2*x + (b^2*c^3*d^2*x^3 + 3*b^2*c^2*d^2*x^2 + 3*b^2*c*d^2*x + b^2*d^2)*log(c*x + 1))*log(-c*x + 1))/x^3","B",0
84,1,928,0,0.702883," ","integrate(x^3*(c*d*x+d)^3*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{7} \, a^{2} c^{3} d^{3} x^{7} + \frac{1}{2} \, a^{2} c^{2} d^{3} x^{6} + \frac{3}{5} \, a^{2} c d^{3} x^{5} + \frac{1}{4} \, b^{2} d^{3} x^{4} \operatorname{artanh}\left(c x\right)^{2} + \frac{1}{42} \, {\left(12 \, x^{7} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, c^{4} x^{6} + 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{6}} + \frac{6 \, \log\left(c^{2} x^{2} - 1\right)}{c^{8}}\right)}\right)} a b c^{3} d^{3} + \frac{1}{4} \, a^{2} d^{3} x^{4} + \frac{1}{30} \, {\left(30 \, x^{6} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} a b c^{2} d^{3} + \frac{3}{10} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} a b c d^{3} + \frac{1}{12} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a b d^{3} + \frac{1}{48} \, {\left(4 \, c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)} \operatorname{artanh}\left(c x\right) + \frac{4 \, c^{2} x^{2} - 2 \, {\left(3 \, \log\left(c x - 1\right) - 8\right)} \log\left(c x + 1\right) + 3 \, \log\left(c x + 1\right)^{2} + 3 \, \log\left(c x - 1\right)^{2} + 16 \, \log\left(c x - 1\right)}{c^{4}}\right)} b^{2} d^{3} + \frac{26 \, {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} d^{3}}{35 \, c^{4}} + \frac{13 \, b^{2} d^{3} \log\left(c x + 1\right)}{70 \, c^{4}} + \frac{283 \, b^{2} d^{3} \log\left(c x - 1\right)}{210 \, c^{4}} + \frac{24 \, b^{2} c^{5} d^{3} x^{5} + 126 \, b^{2} c^{4} d^{3} x^{4} + 352 \, b^{2} c^{3} d^{3} x^{3} + 672 \, b^{2} c^{2} d^{3} x^{2} + 2928 \, b^{2} c d^{3} x + 9 \, {\left(10 \, b^{2} c^{7} d^{3} x^{7} + 35 \, b^{2} c^{6} d^{3} x^{6} + 42 \, b^{2} c^{5} d^{3} x^{5} + 17 \, b^{2} d^{3}\right)} \log\left(c x + 1\right)^{2} + 9 \, {\left(10 \, b^{2} c^{7} d^{3} x^{7} + 35 \, b^{2} c^{6} d^{3} x^{6} + 42 \, b^{2} c^{5} d^{3} x^{5} - 87 \, b^{2} d^{3}\right)} \log\left(-c x + 1\right)^{2} + 12 \, {\left(5 \, b^{2} c^{6} d^{3} x^{6} + 21 \, b^{2} c^{5} d^{3} x^{5} + 39 \, b^{2} c^{4} d^{3} x^{4} + 35 \, b^{2} c^{3} d^{3} x^{3} + 78 \, b^{2} c^{2} d^{3} x^{2} + 105 \, b^{2} c d^{3} x\right)} \log\left(c x + 1\right) - 6 \, {\left(10 \, b^{2} c^{6} d^{3} x^{6} + 42 \, b^{2} c^{5} d^{3} x^{5} + 78 \, b^{2} c^{4} d^{3} x^{4} + 70 \, b^{2} c^{3} d^{3} x^{3} + 156 \, b^{2} c^{2} d^{3} x^{2} + 210 \, b^{2} c d^{3} x + 3 \, {\left(10 \, b^{2} c^{7} d^{3} x^{7} + 35 \, b^{2} c^{6} d^{3} x^{6} + 42 \, b^{2} c^{5} d^{3} x^{5} + 17 \, b^{2} d^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{2520 \, c^{4}}"," ",0,"1/7*a^2*c^3*d^3*x^7 + 1/2*a^2*c^2*d^3*x^6 + 3/5*a^2*c*d^3*x^5 + 1/4*b^2*d^3*x^4*arctanh(c*x)^2 + 1/42*(12*x^7*arctanh(c*x) + c*((2*c^4*x^6 + 3*c^2*x^4 + 6*x^2)/c^6 + 6*log(c^2*x^2 - 1)/c^8))*a*b*c^3*d^3 + 1/4*a^2*d^3*x^4 + 1/30*(30*x^6*arctanh(c*x) + c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*a*b*c^2*d^3 + 3/10*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*a*b*c*d^3 + 1/12*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a*b*d^3 + 1/48*(4*c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5)*arctanh(c*x) + (4*c^2*x^2 - 2*(3*log(c*x - 1) - 8)*log(c*x + 1) + 3*log(c*x + 1)^2 + 3*log(c*x - 1)^2 + 16*log(c*x - 1))/c^4)*b^2*d^3 + 26/35*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*d^3/c^4 + 13/70*b^2*d^3*log(c*x + 1)/c^4 + 283/210*b^2*d^3*log(c*x - 1)/c^4 + 1/2520*(24*b^2*c^5*d^3*x^5 + 126*b^2*c^4*d^3*x^4 + 352*b^2*c^3*d^3*x^3 + 672*b^2*c^2*d^3*x^2 + 2928*b^2*c*d^3*x + 9*(10*b^2*c^7*d^3*x^7 + 35*b^2*c^6*d^3*x^6 + 42*b^2*c^5*d^3*x^5 + 17*b^2*d^3)*log(c*x + 1)^2 + 9*(10*b^2*c^7*d^3*x^7 + 35*b^2*c^6*d^3*x^6 + 42*b^2*c^5*d^3*x^5 - 87*b^2*d^3)*log(-c*x + 1)^2 + 12*(5*b^2*c^6*d^3*x^6 + 21*b^2*c^5*d^3*x^5 + 39*b^2*c^4*d^3*x^4 + 35*b^2*c^3*d^3*x^3 + 78*b^2*c^2*d^3*x^2 + 105*b^2*c*d^3*x)*log(c*x + 1) - 6*(10*b^2*c^6*d^3*x^6 + 42*b^2*c^5*d^3*x^5 + 78*b^2*c^4*d^3*x^4 + 70*b^2*c^3*d^3*x^3 + 156*b^2*c^2*d^3*x^2 + 210*b^2*c*d^3*x + 3*(10*b^2*c^7*d^3*x^7 + 35*b^2*c^6*d^3*x^6 + 42*b^2*c^5*d^3*x^5 + 17*b^2*d^3)*log(c*x + 1))*log(-c*x + 1))/c^4","B",0
85,1,775,0,0.700124," ","integrate(x^2*(c*d*x+d)^3*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} c^{3} d^{3} x^{6} + \frac{3}{5} \, a^{2} c^{2} d^{3} x^{5} + \frac{3}{4} \, a^{2} c d^{3} x^{4} + \frac{1}{90} \, {\left(30 \, x^{6} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} a b c^{3} d^{3} + \frac{3}{10} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} a b c^{2} d^{3} + \frac{1}{3} \, a^{2} d^{3} x^{3} + \frac{1}{4} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a b c d^{3} + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a b d^{3} + \frac{14 \, {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} d^{3}}{15 \, c^{3}} + \frac{23 \, b^{2} d^{3} \log\left(c x + 1\right)}{36 \, c^{3}} + \frac{337 \, b^{2} d^{3} \log\left(c x - 1\right)}{180 \, c^{3}} + \frac{12 \, b^{2} c^{4} d^{3} x^{4} + 72 \, b^{2} c^{3} d^{3} x^{3} + 244 \, b^{2} c^{2} d^{3} x^{2} + 888 \, b^{2} c d^{3} x + 3 \, {\left(10 \, b^{2} c^{6} d^{3} x^{6} + 36 \, b^{2} c^{5} d^{3} x^{5} + 45 \, b^{2} c^{4} d^{3} x^{4} + 20 \, b^{2} c^{3} d^{3} x^{3} + b^{2} d^{3}\right)} \log\left(c x + 1\right)^{2} + 3 \, {\left(10 \, b^{2} c^{6} d^{3} x^{6} + 36 \, b^{2} c^{5} d^{3} x^{5} + 45 \, b^{2} c^{4} d^{3} x^{4} + 20 \, b^{2} c^{3} d^{3} x^{3} - 111 \, b^{2} d^{3}\right)} \log\left(-c x + 1\right)^{2} + 4 \, {\left(6 \, b^{2} c^{5} d^{3} x^{5} + 27 \, b^{2} c^{4} d^{3} x^{4} + 55 \, b^{2} c^{3} d^{3} x^{3} + 84 \, b^{2} c^{2} d^{3} x^{2} + 165 \, b^{2} c d^{3} x\right)} \log\left(c x + 1\right) - 2 \, {\left(12 \, b^{2} c^{5} d^{3} x^{5} + 54 \, b^{2} c^{4} d^{3} x^{4} + 110 \, b^{2} c^{3} d^{3} x^{3} + 168 \, b^{2} c^{2} d^{3} x^{2} + 330 \, b^{2} c d^{3} x + 3 \, {\left(10 \, b^{2} c^{6} d^{3} x^{6} + 36 \, b^{2} c^{5} d^{3} x^{5} + 45 \, b^{2} c^{4} d^{3} x^{4} + 20 \, b^{2} c^{3} d^{3} x^{3} + b^{2} d^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{720 \, c^{3}}"," ",0,"1/6*a^2*c^3*d^3*x^6 + 3/5*a^2*c^2*d^3*x^5 + 3/4*a^2*c*d^3*x^4 + 1/90*(30*x^6*arctanh(c*x) + c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*a*b*c^3*d^3 + 3/10*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*a*b*c^2*d^3 + 1/3*a^2*d^3*x^3 + 1/4*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a*b*c*d^3 + 1/3*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a*b*d^3 + 14/15*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*d^3/c^3 + 23/36*b^2*d^3*log(c*x + 1)/c^3 + 337/180*b^2*d^3*log(c*x - 1)/c^3 + 1/720*(12*b^2*c^4*d^3*x^4 + 72*b^2*c^3*d^3*x^3 + 244*b^2*c^2*d^3*x^2 + 888*b^2*c*d^3*x + 3*(10*b^2*c^6*d^3*x^6 + 36*b^2*c^5*d^3*x^5 + 45*b^2*c^4*d^3*x^4 + 20*b^2*c^3*d^3*x^3 + b^2*d^3)*log(c*x + 1)^2 + 3*(10*b^2*c^6*d^3*x^6 + 36*b^2*c^5*d^3*x^5 + 45*b^2*c^4*d^3*x^4 + 20*b^2*c^3*d^3*x^3 - 111*b^2*d^3)*log(-c*x + 1)^2 + 4*(6*b^2*c^5*d^3*x^5 + 27*b^2*c^4*d^3*x^4 + 55*b^2*c^3*d^3*x^3 + 84*b^2*c^2*d^3*x^2 + 165*b^2*c*d^3*x)*log(c*x + 1) - 2*(12*b^2*c^5*d^3*x^5 + 54*b^2*c^4*d^3*x^4 + 110*b^2*c^3*d^3*x^3 + 168*b^2*c^2*d^3*x^2 + 330*b^2*c*d^3*x + 3*(10*b^2*c^6*d^3*x^6 + 36*b^2*c^5*d^3*x^5 + 45*b^2*c^4*d^3*x^4 + 20*b^2*c^3*d^3*x^3 + b^2*d^3)*log(c*x + 1))*log(-c*x + 1))/c^3","B",0
86,1,780,0,0.695988," ","integrate(x*(c*d*x+d)^3*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} c^{3} d^{3} x^{5} + \frac{3}{4} \, a^{2} c^{2} d^{3} x^{4} + \frac{1}{10} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} a b c^{3} d^{3} + a^{2} c d^{3} x^{3} + \frac{1}{2} \, b^{2} d^{3} x^{2} \operatorname{artanh}\left(c x\right)^{2} + \frac{1}{4} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a b c^{2} d^{3} + {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a b c d^{3} + \frac{1}{2} \, a^{2} d^{3} x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a b d^{3} + \frac{1}{8} \, {\left(4 \, c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} \operatorname{artanh}\left(c x\right) - \frac{2 \, {\left(\log\left(c x - 1\right) - 2\right)} \log\left(c x + 1\right) - \log\left(c x + 1\right)^{2} - \log\left(c x - 1\right)^{2} - 4 \, \log\left(c x - 1\right)}{c^{2}}\right)} b^{2} d^{3} + \frac{6 \, {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} d^{3}}{5 \, c^{2}} + \frac{7 \, b^{2} d^{3} \log\left(c x + 1\right)}{20 \, c^{2}} + \frac{33 \, b^{2} d^{3} \log\left(c x - 1\right)}{20 \, c^{2}} + \frac{8 \, b^{2} c^{3} d^{3} x^{3} + 60 \, b^{2} c^{2} d^{3} x^{2} + 312 \, b^{2} c d^{3} x + 3 \, {\left(4 \, b^{2} c^{5} d^{3} x^{5} + 15 \, b^{2} c^{4} d^{3} x^{4} + 20 \, b^{2} c^{3} d^{3} x^{3} + 9 \, b^{2} d^{3}\right)} \log\left(c x + 1\right)^{2} + 3 \, {\left(4 \, b^{2} c^{5} d^{3} x^{5} + 15 \, b^{2} c^{4} d^{3} x^{4} + 20 \, b^{2} c^{3} d^{3} x^{3} - 39 \, b^{2} d^{3}\right)} \log\left(-c x + 1\right)^{2} + 12 \, {\left(b^{2} c^{4} d^{3} x^{4} + 5 \, b^{2} c^{3} d^{3} x^{3} + 12 \, b^{2} c^{2} d^{3} x^{2} + 15 \, b^{2} c d^{3} x\right)} \log\left(c x + 1\right) - 6 \, {\left(2 \, b^{2} c^{4} d^{3} x^{4} + 10 \, b^{2} c^{3} d^{3} x^{3} + 24 \, b^{2} c^{2} d^{3} x^{2} + 30 \, b^{2} c d^{3} x + {\left(4 \, b^{2} c^{5} d^{3} x^{5} + 15 \, b^{2} c^{4} d^{3} x^{4} + 20 \, b^{2} c^{3} d^{3} x^{3} + 9 \, b^{2} d^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{240 \, c^{2}}"," ",0,"1/5*a^2*c^3*d^3*x^5 + 3/4*a^2*c^2*d^3*x^4 + 1/10*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*a*b*c^3*d^3 + a^2*c*d^3*x^3 + 1/2*b^2*d^3*x^2*arctanh(c*x)^2 + 1/4*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a*b*c^2*d^3 + (2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a*b*c*d^3 + 1/2*a^2*d^3*x^2 + 1/2*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a*b*d^3 + 1/8*(4*c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3)*arctanh(c*x) - (2*(log(c*x - 1) - 2)*log(c*x + 1) - log(c*x + 1)^2 - log(c*x - 1)^2 - 4*log(c*x - 1))/c^2)*b^2*d^3 + 6/5*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*d^3/c^2 + 7/20*b^2*d^3*log(c*x + 1)/c^2 + 33/20*b^2*d^3*log(c*x - 1)/c^2 + 1/240*(8*b^2*c^3*d^3*x^3 + 60*b^2*c^2*d^3*x^2 + 312*b^2*c*d^3*x + 3*(4*b^2*c^5*d^3*x^5 + 15*b^2*c^4*d^3*x^4 + 20*b^2*c^3*d^3*x^3 + 9*b^2*d^3)*log(c*x + 1)^2 + 3*(4*b^2*c^5*d^3*x^5 + 15*b^2*c^4*d^3*x^4 + 20*b^2*c^3*d^3*x^3 - 39*b^2*d^3)*log(-c*x + 1)^2 + 12*(b^2*c^4*d^3*x^4 + 5*b^2*c^3*d^3*x^3 + 12*b^2*c^2*d^3*x^2 + 15*b^2*c*d^3*x)*log(c*x + 1) - 6*(2*b^2*c^4*d^3*x^4 + 10*b^2*c^3*d^3*x^3 + 24*b^2*c^2*d^3*x^2 + 30*b^2*c*d^3*x + (4*b^2*c^5*d^3*x^5 + 15*b^2*c^4*d^3*x^4 + 20*b^2*c^3*d^3*x^3 + 9*b^2*d^3)*log(c*x + 1))*log(-c*x + 1))/c^2","B",0
87,1,627,0,0.562887," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} c^{3} d^{3} x^{4} + a^{2} c^{2} d^{3} x^{3} + \frac{1}{12} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a b c^{3} d^{3} + {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a b c^{2} d^{3} + \frac{3}{2} \, a^{2} c d^{3} x^{2} + \frac{3}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a b c d^{3} + a^{2} d^{3} x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a b d^{3}}{c} + \frac{2 \, {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} d^{3}}{c} + \frac{4 \, b^{2} d^{3} \log\left(c x + 1\right)}{3 \, c} + \frac{7 \, b^{2} d^{3} \log\left(c x - 1\right)}{3 \, c} + \frac{4 \, b^{2} c^{2} d^{3} x^{2} + 48 \, b^{2} c d^{3} x + 3 \, {\left(b^{2} c^{4} d^{3} x^{4} + 4 \, b^{2} c^{3} d^{3} x^{3} + 6 \, b^{2} c^{2} d^{3} x^{2} + 4 \, b^{2} c d^{3} x + b^{2} d^{3}\right)} \log\left(c x + 1\right)^{2} + 3 \, {\left(b^{2} c^{4} d^{3} x^{4} + 4 \, b^{2} c^{3} d^{3} x^{3} + 6 \, b^{2} c^{2} d^{3} x^{2} + 4 \, b^{2} c d^{3} x - 15 \, b^{2} d^{3}\right)} \log\left(-c x + 1\right)^{2} + 4 \, {\left(b^{2} c^{3} d^{3} x^{3} + 6 \, b^{2} c^{2} d^{3} x^{2} + 21 \, b^{2} c d^{3} x\right)} \log\left(c x + 1\right) - 2 \, {\left(2 \, b^{2} c^{3} d^{3} x^{3} + 12 \, b^{2} c^{2} d^{3} x^{2} + 42 \, b^{2} c d^{3} x + 3 \, {\left(b^{2} c^{4} d^{3} x^{4} + 4 \, b^{2} c^{3} d^{3} x^{3} + 6 \, b^{2} c^{2} d^{3} x^{2} + 4 \, b^{2} c d^{3} x + b^{2} d^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{48 \, c}"," ",0,"1/4*a^2*c^3*d^3*x^4 + a^2*c^2*d^3*x^3 + 1/12*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a*b*c^3*d^3 + (2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a*b*c^2*d^3 + 3/2*a^2*c*d^3*x^2 + 3/2*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a*b*c*d^3 + a^2*d^3*x + (2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a*b*d^3/c + 2*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*d^3/c + 4/3*b^2*d^3*log(c*x + 1)/c + 7/3*b^2*d^3*log(c*x - 1)/c + 1/48*(4*b^2*c^2*d^3*x^2 + 48*b^2*c*d^3*x + 3*(b^2*c^4*d^3*x^4 + 4*b^2*c^3*d^3*x^3 + 6*b^2*c^2*d^3*x^2 + 4*b^2*c*d^3*x + b^2*d^3)*log(c*x + 1)^2 + 3*(b^2*c^4*d^3*x^4 + 4*b^2*c^3*d^3*x^3 + 6*b^2*c^2*d^3*x^2 + 4*b^2*c*d^3*x - 15*b^2*d^3)*log(-c*x + 1)^2 + 4*(b^2*c^3*d^3*x^3 + 6*b^2*c^2*d^3*x^2 + 21*b^2*c*d^3*x)*log(c*x + 1) - 2*(2*b^2*c^3*d^3*x^3 + 12*b^2*c^2*d^3*x^2 + 42*b^2*c*d^3*x + 3*(b^2*c^4*d^3*x^4 + 4*b^2*c^3*d^3*x^3 + 6*b^2*c^2*d^3*x^2 + 4*b^2*c*d^3*x + b^2*d^3)*log(c*x + 1))*log(-c*x + 1))/c","B",0
88,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} c^{3} d^{3} x^{3} + \frac{3}{2} \, a^{2} c^{2} d^{3} x^{2} + 3 \, a^{2} c d^{3} x + 3 \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a b d^{3} + a^{2} d^{3} \log\left(x\right) + \frac{1}{24} \, {\left(2 \, b^{2} c^{3} d^{3} x^{3} + 9 \, b^{2} c^{2} d^{3} x^{2} + 18 \, b^{2} c d^{3} x\right)} \log\left(-c x + 1\right)^{2} - \int -\frac{3 \, {\left(b^{2} c^{4} d^{3} x^{4} + 2 \, b^{2} c^{3} d^{3} x^{3} - 2 \, b^{2} c d^{3} x - b^{2} d^{3}\right)} \log\left(c x + 1\right)^{2} + 12 \, {\left(a b c^{4} d^{3} x^{4} + 2 \, a b c^{3} d^{3} x^{3} - 3 \, a b c^{2} d^{3} x^{2} + a b c d^{3} x - a b d^{3}\right)} \log\left(c x + 1\right) - {\left(12 \, a b c d^{3} x - 12 \, a b d^{3} + 2 \, {\left(6 \, a b c^{4} d^{3} + b^{2} c^{4} d^{3}\right)} x^{4} + 3 \, {\left(8 \, a b c^{3} d^{3} + 3 \, b^{2} c^{3} d^{3}\right)} x^{3} - 18 \, {\left(2 \, a b c^{2} d^{3} - b^{2} c^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{2} c^{4} d^{3} x^{4} + 2 \, b^{2} c^{3} d^{3} x^{3} - 2 \, b^{2} c d^{3} x - b^{2} d^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{12 \, {\left(c x^{2} - x\right)}}\,{d x}"," ",0,"1/3*a^2*c^3*d^3*x^3 + 3/2*a^2*c^2*d^3*x^2 + 3*a^2*c*d^3*x + 3*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a*b*d^3 + a^2*d^3*log(x) + 1/24*(2*b^2*c^3*d^3*x^3 + 9*b^2*c^2*d^3*x^2 + 18*b^2*c*d^3*x)*log(-c*x + 1)^2 - integrate(-1/12*(3*(b^2*c^4*d^3*x^4 + 2*b^2*c^3*d^3*x^3 - 2*b^2*c*d^3*x - b^2*d^3)*log(c*x + 1)^2 + 12*(a*b*c^4*d^3*x^4 + 2*a*b*c^3*d^3*x^3 - 3*a*b*c^2*d^3*x^2 + a*b*c*d^3*x - a*b*d^3)*log(c*x + 1) - (12*a*b*c*d^3*x - 12*a*b*d^3 + 2*(6*a*b*c^4*d^3 + b^2*c^4*d^3)*x^4 + 3*(8*a*b*c^3*d^3 + 3*b^2*c^3*d^3)*x^3 - 18*(2*a*b*c^2*d^3 - b^2*c^2*d^3)*x^2 + 6*(b^2*c^4*d^3*x^4 + 2*b^2*c^3*d^3*x^3 - 2*b^2*c*d^3*x - b^2*d^3)*log(c*x + 1))*log(-c*x + 1))/(c*x^2 - x), x)","F",0
89,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} c^{3} d^{3} x^{2} + 3 \, a^{2} c^{2} d^{3} x + 3 \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a b c d^{3} + 3 \, a^{2} c d^{3} \log\left(x\right) - {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} a b d^{3} - \frac{a^{2} d^{3}}{x} + \frac{{\left(b^{2} c^{3} d^{3} x^{3} + 6 \, b^{2} c^{2} d^{3} x^{2} - 2 \, b^{2} d^{3}\right)} \log\left(-c x + 1\right)^{2}}{8 \, x} - \int -\frac{{\left(b^{2} c^{4} d^{3} x^{4} + 2 \, b^{2} c^{3} d^{3} x^{3} - 2 \, b^{2} c d^{3} x - b^{2} d^{3}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c^{4} d^{3} x^{4} - a b c^{3} d^{3} x^{3} + 3 \, a b c^{2} d^{3} x^{2} - 3 \, a b c d^{3} x\right)} \log\left(c x + 1\right) - {\left(12 \, a b c^{2} d^{3} x^{2} + {\left(4 \, a b c^{4} d^{3} + b^{2} c^{4} d^{3}\right)} x^{4} - 2 \, {\left(2 \, a b c^{3} d^{3} - 3 \, b^{2} c^{3} d^{3}\right)} x^{3} - 2 \, {\left(6 \, a b c d^{3} + b^{2} c d^{3}\right)} x + 2 \, {\left(b^{2} c^{4} d^{3} x^{4} + 2 \, b^{2} c^{3} d^{3} x^{3} - 2 \, b^{2} c d^{3} x - b^{2} d^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c x^{3} - x^{2}\right)}}\,{d x}"," ",0,"1/2*a^2*c^3*d^3*x^2 + 3*a^2*c^2*d^3*x + 3*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a*b*c*d^3 + 3*a^2*c*d^3*log(x) - (c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*a*b*d^3 - a^2*d^3/x + 1/8*(b^2*c^3*d^3*x^3 + 6*b^2*c^2*d^3*x^2 - 2*b^2*d^3)*log(-c*x + 1)^2/x - integrate(-1/4*((b^2*c^4*d^3*x^4 + 2*b^2*c^3*d^3*x^3 - 2*b^2*c*d^3*x - b^2*d^3)*log(c*x + 1)^2 + 4*(a*b*c^4*d^3*x^4 - a*b*c^3*d^3*x^3 + 3*a*b*c^2*d^3*x^2 - 3*a*b*c*d^3*x)*log(c*x + 1) - (12*a*b*c^2*d^3*x^2 + (4*a*b*c^4*d^3 + b^2*c^4*d^3)*x^4 - 2*(2*a*b*c^3*d^3 - 3*b^2*c^3*d^3)*x^3 - 2*(6*a*b*c*d^3 + b^2*c*d^3)*x + 2*(b^2*c^4*d^3*x^4 + 2*b^2*c^3*d^3*x^3 - 2*b^2*c*d^3*x - b^2*d^3)*log(c*x + 1))*log(-c*x + 1))/(c*x^3 - x^2), x)","F",0
90,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^3,x, algorithm=""maxima"")","a^{2} c^{3} d^{3} x + {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a b c^{2} d^{3} + 3 \, a^{2} c^{2} d^{3} \log\left(x\right) - 3 \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} a b c d^{3} + \frac{1}{2} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} a b d^{3} - \frac{3 \, a^{2} c d^{3}}{x} - \frac{a^{2} d^{3}}{2 \, x^{2}} + \frac{{\left(2 \, b^{2} c^{3} d^{3} x^{3} - 6 \, b^{2} c d^{3} x - b^{2} d^{3}\right)} \log\left(-c x + 1\right)^{2}}{8 \, x^{2}} - \int -\frac{{\left(b^{2} c^{4} d^{3} x^{4} + 2 \, b^{2} c^{3} d^{3} x^{3} - 2 \, b^{2} c d^{3} x - b^{2} d^{3}\right)} \log\left(c x + 1\right)^{2} + 12 \, {\left(a b c^{3} d^{3} x^{3} - a b c^{2} d^{3} x^{2}\right)} \log\left(c x + 1\right) - {\left(2 \, b^{2} c^{4} d^{3} x^{4} + 12 \, a b c^{3} d^{3} x^{3} - b^{2} c d^{3} x - 6 \, {\left(2 \, a b c^{2} d^{3} + b^{2} c^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{4} d^{3} x^{4} + 2 \, b^{2} c^{3} d^{3} x^{3} - 2 \, b^{2} c d^{3} x - b^{2} d^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c x^{4} - x^{3}\right)}}\,{d x}"," ",0,"a^2*c^3*d^3*x + (2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a*b*c^2*d^3 + 3*a^2*c^2*d^3*log(x) - 3*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*a*b*c*d^3 + 1/2*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*a*b*d^3 - 3*a^2*c*d^3/x - 1/2*a^2*d^3/x^2 + 1/8*(2*b^2*c^3*d^3*x^3 - 6*b^2*c*d^3*x - b^2*d^3)*log(-c*x + 1)^2/x^2 - integrate(-1/4*((b^2*c^4*d^3*x^4 + 2*b^2*c^3*d^3*x^3 - 2*b^2*c*d^3*x - b^2*d^3)*log(c*x + 1)^2 + 12*(a*b*c^3*d^3*x^3 - a*b*c^2*d^3*x^2)*log(c*x + 1) - (2*b^2*c^4*d^3*x^4 + 12*a*b*c^3*d^3*x^3 - b^2*c*d^3*x - 6*(2*a*b*c^2*d^3 + b^2*c^2*d^3)*x^2 + 2*(b^2*c^4*d^3*x^4 + 2*b^2*c^3*d^3*x^3 - 2*b^2*c*d^3*x - b^2*d^3)*log(c*x + 1))*log(-c*x + 1))/(c*x^4 - x^3), x)","F",0
91,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^4,x, algorithm=""maxima"")","a^{2} c^{3} d^{3} \log\left(x\right) - 3 \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} a b c^{2} d^{3} + \frac{3}{2} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} a b c d^{3} - \frac{1}{3} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} a b d^{3} - \frac{3 \, a^{2} c^{2} d^{3}}{x} - \frac{3 \, a^{2} c d^{3}}{2 \, x^{2}} - \frac{a^{2} d^{3}}{3 \, x^{3}} - \frac{{\left(18 \, b^{2} c^{2} d^{3} x^{2} + 9 \, b^{2} c d^{3} x + 2 \, b^{2} d^{3}\right)} \log\left(-c x + 1\right)^{2}}{24 \, x^{3}} - \int -\frac{3 \, {\left(b^{2} c^{4} d^{3} x^{4} + 2 \, b^{2} c^{3} d^{3} x^{3} - 2 \, b^{2} c d^{3} x - b^{2} d^{3}\right)} \log\left(c x + 1\right)^{2} + 12 \, {\left(a b c^{4} d^{3} x^{4} - a b c^{3} d^{3} x^{3}\right)} \log\left(c x + 1\right) - {\left(12 \, a b c^{4} d^{3} x^{4} - 9 \, b^{2} c^{2} d^{3} x^{2} - 2 \, b^{2} c d^{3} x - 6 \, {\left(2 \, a b c^{3} d^{3} + 3 \, b^{2} c^{3} d^{3}\right)} x^{3} + 6 \, {\left(b^{2} c^{4} d^{3} x^{4} + 2 \, b^{2} c^{3} d^{3} x^{3} - 2 \, b^{2} c d^{3} x - b^{2} d^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{12 \, {\left(c x^{5} - x^{4}\right)}}\,{d x}"," ",0,"a^2*c^3*d^3*log(x) - 3*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*a*b*c^2*d^3 + 3/2*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*a*b*c*d^3 - 1/3*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*a*b*d^3 - 3*a^2*c^2*d^3/x - 3/2*a^2*c*d^3/x^2 - 1/3*a^2*d^3/x^3 - 1/24*(18*b^2*c^2*d^3*x^2 + 9*b^2*c*d^3*x + 2*b^2*d^3)*log(-c*x + 1)^2/x^3 - integrate(-1/12*(3*(b^2*c^4*d^3*x^4 + 2*b^2*c^3*d^3*x^3 - 2*b^2*c*d^3*x - b^2*d^3)*log(c*x + 1)^2 + 12*(a*b*c^4*d^3*x^4 - a*b*c^3*d^3*x^3)*log(c*x + 1) - (12*a*b*c^4*d^3*x^4 - 9*b^2*c^2*d^3*x^2 - 2*b^2*c*d^3*x - 6*(2*a*b*c^3*d^3 + 3*b^2*c^3*d^3)*x^3 + 6*(b^2*c^4*d^3*x^4 + 2*b^2*c^3*d^3*x^3 - 2*b^2*c*d^3*x - b^2*d^3)*log(c*x + 1))*log(-c*x + 1))/(c*x^5 - x^4), x)","F",0
92,1,813,0,0.963798," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^5,x, algorithm=""maxima"")","-2 \, {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} c^{4} d^{3} - 2 \, {\left(\log\left(c x\right) \log\left(-c x + 1\right) + {\rm Li}_2\left(-c x + 1\right)\right)} b^{2} c^{4} d^{3} + 2 \, {\left(\log\left(c x + 1\right) \log\left(-c x\right) + {\rm Li}_2\left(c x + 1\right)\right)} b^{2} c^{4} d^{3} - b^{2} c^{4} d^{3} \log\left(c x + 1\right) - 2 \, b^{2} c^{4} d^{3} \log\left(c x - 1\right) + 3 \, b^{2} c^{4} d^{3} \log\left(x\right) - {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} a b c^{3} d^{3} + \frac{3}{2} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} a b c^{2} d^{3} - {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} a b c d^{3} - \frac{a^{2} c^{3} d^{3}}{x} + \frac{1}{12} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} a b d^{3} + \frac{1}{48} \, {\left({\left(32 \, c^{2} \log\left(x\right) - \frac{3 \, c^{2} x^{2} \log\left(c x + 1\right)^{2} + 3 \, c^{2} x^{2} \log\left(c x - 1\right)^{2} + 16 \, c^{2} x^{2} \log\left(c x - 1\right) - 2 \, {\left(3 \, c^{2} x^{2} \log\left(c x - 1\right) - 8 \, c^{2} x^{2}\right)} \log\left(c x + 1\right) + 4}{x^{2}}\right)} c^{2} + 4 \, {\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c \operatorname{artanh}\left(c x\right)\right)} b^{2} d^{3} - \frac{3 \, a^{2} c^{2} d^{3}}{2 \, x^{2}} - \frac{a^{2} c d^{3}}{x^{3}} - \frac{b^{2} d^{3} \operatorname{artanh}\left(c x\right)^{2}}{4 \, x^{4}} - \frac{a^{2} d^{3}}{4 \, x^{4}} - \frac{8 \, b^{2} c^{3} d^{3} x^{2} + {\left(b^{2} c^{4} d^{3} x^{3} + 2 \, b^{2} c^{3} d^{3} x^{2} + 3 \, b^{2} c^{2} d^{3} x + 2 \, b^{2} c d^{3}\right)} \log\left(c x + 1\right)^{2} - {\left(7 \, b^{2} c^{4} d^{3} x^{3} - 2 \, b^{2} c^{3} d^{3} x^{2} - 3 \, b^{2} c^{2} d^{3} x - 2 \, b^{2} c d^{3}\right)} \log\left(-c x + 1\right)^{2} + 4 \, {\left(3 \, b^{2} c^{3} d^{3} x^{2} + b^{2} c^{2} d^{3} x\right)} \log\left(c x + 1\right) - 2 \, {\left(6 \, b^{2} c^{3} d^{3} x^{2} + 2 \, b^{2} c^{2} d^{3} x + {\left(b^{2} c^{4} d^{3} x^{3} + 2 \, b^{2} c^{3} d^{3} x^{2} + 3 \, b^{2} c^{2} d^{3} x + 2 \, b^{2} c d^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{8 \, x^{3}}"," ",0,"-2*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*c^4*d^3 - 2*(log(c*x)*log(-c*x + 1) + dilog(-c*x + 1))*b^2*c^4*d^3 + 2*(log(c*x + 1)*log(-c*x) + dilog(c*x + 1))*b^2*c^4*d^3 - b^2*c^4*d^3*log(c*x + 1) - 2*b^2*c^4*d^3*log(c*x - 1) + 3*b^2*c^4*d^3*log(x) - (c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*a*b*c^3*d^3 + 3/2*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*a*b*c^2*d^3 - ((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*a*b*c*d^3 - a^2*c^3*d^3/x + 1/12*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*a*b*d^3 + 1/48*((32*c^2*log(x) - (3*c^2*x^2*log(c*x + 1)^2 + 3*c^2*x^2*log(c*x - 1)^2 + 16*c^2*x^2*log(c*x - 1) - 2*(3*c^2*x^2*log(c*x - 1) - 8*c^2*x^2)*log(c*x + 1) + 4)/x^2)*c^2 + 4*(3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c*arctanh(c*x))*b^2*d^3 - 3/2*a^2*c^2*d^3/x^2 - a^2*c*d^3/x^3 - 1/4*b^2*d^3*arctanh(c*x)^2/x^4 - 1/4*a^2*d^3/x^4 - 1/8*(8*b^2*c^3*d^3*x^2 + (b^2*c^4*d^3*x^3 + 2*b^2*c^3*d^3*x^2 + 3*b^2*c^2*d^3*x + 2*b^2*c*d^3)*log(c*x + 1)^2 - (7*b^2*c^4*d^3*x^3 - 2*b^2*c^3*d^3*x^2 - 3*b^2*c^2*d^3*x - 2*b^2*c*d^3)*log(-c*x + 1)^2 + 4*(3*b^2*c^3*d^3*x^2 + b^2*c^2*d^3*x)*log(c*x + 1) - 2*(6*b^2*c^3*d^3*x^2 + 2*b^2*c^2*d^3*x + (b^2*c^4*d^3*x^3 + 2*b^2*c^3*d^3*x^2 + 3*b^2*c^2*d^3*x + 2*b^2*c*d^3)*log(c*x + 1))*log(-c*x + 1))/x^3","B",0
93,1,783,0,0.952946," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^6,x, algorithm=""maxima"")","-\frac{6}{5} \, {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} c^{5} d^{3} - \frac{6}{5} \, {\left(\log\left(c x\right) \log\left(-c x + 1\right) + {\rm Li}_2\left(-c x + 1\right)\right)} b^{2} c^{5} d^{3} + \frac{6}{5} \, {\left(\log\left(c x + 1\right) \log\left(-c x\right) + {\rm Li}_2\left(c x + 1\right)\right)} b^{2} c^{5} d^{3} - \frac{17}{20} \, b^{2} c^{5} d^{3} \log\left(c x + 1\right) - \frac{43}{20} \, b^{2} c^{5} d^{3} \log\left(c x - 1\right) + 3 \, b^{2} c^{5} d^{3} \log\left(x\right) + \frac{1}{2} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} a b c^{3} d^{3} - {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} a b c^{2} d^{3} + \frac{1}{4} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} a b c d^{3} - \frac{1}{10} \, {\left({\left(2 \, c^{4} \log\left(c^{2} x^{2} - 1\right) - 2 \, c^{4} \log\left(x^{2}\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} c + \frac{4 \, \operatorname{artanh}\left(c x\right)}{x^{5}}\right)} a b d^{3} - \frac{a^{2} c^{3} d^{3}}{2 \, x^{2}} - \frac{a^{2} c^{2} d^{3}}{x^{3}} - \frac{3 \, a^{2} c d^{3}}{4 \, x^{4}} - \frac{a^{2} d^{3}}{5 \, x^{5}} - \frac{312 \, b^{2} c^{4} d^{3} x^{4} + 60 \, b^{2} c^{3} d^{3} x^{3} + 8 \, b^{2} c^{2} d^{3} x^{2} - 3 \, {\left(b^{2} c^{5} d^{3} x^{5} - 10 \, b^{2} c^{3} d^{3} x^{3} - 20 \, b^{2} c^{2} d^{3} x^{2} - 15 \, b^{2} c d^{3} x - 4 \, b^{2} d^{3}\right)} \log\left(c x + 1\right)^{2} - 3 \, {\left(49 \, b^{2} c^{5} d^{3} x^{5} - 10 \, b^{2} c^{3} d^{3} x^{3} - 20 \, b^{2} c^{2} d^{3} x^{2} - 15 \, b^{2} c d^{3} x - 4 \, b^{2} d^{3}\right)} \log\left(-c x + 1\right)^{2} + 12 \, {\left(25 \, b^{2} c^{4} d^{3} x^{4} + 12 \, b^{2} c^{3} d^{3} x^{3} + 5 \, b^{2} c^{2} d^{3} x^{2} + b^{2} c d^{3} x\right)} \log\left(c x + 1\right) - 6 \, {\left(50 \, b^{2} c^{4} d^{3} x^{4} + 24 \, b^{2} c^{3} d^{3} x^{3} + 10 \, b^{2} c^{2} d^{3} x^{2} + 2 \, b^{2} c d^{3} x - {\left(b^{2} c^{5} d^{3} x^{5} - 10 \, b^{2} c^{3} d^{3} x^{3} - 20 \, b^{2} c^{2} d^{3} x^{2} - 15 \, b^{2} c d^{3} x - 4 \, b^{2} d^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{240 \, x^{5}}"," ",0,"-6/5*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*c^5*d^3 - 6/5*(log(c*x)*log(-c*x + 1) + dilog(-c*x + 1))*b^2*c^5*d^3 + 6/5*(log(c*x + 1)*log(-c*x) + dilog(c*x + 1))*b^2*c^5*d^3 - 17/20*b^2*c^5*d^3*log(c*x + 1) - 43/20*b^2*c^5*d^3*log(c*x - 1) + 3*b^2*c^5*d^3*log(x) + 1/2*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*a*b*c^3*d^3 - ((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*a*b*c^2*d^3 + 1/4*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*a*b*c*d^3 - 1/10*((2*c^4*log(c^2*x^2 - 1) - 2*c^4*log(x^2) + (2*c^2*x^2 + 1)/x^4)*c + 4*arctanh(c*x)/x^5)*a*b*d^3 - 1/2*a^2*c^3*d^3/x^2 - a^2*c^2*d^3/x^3 - 3/4*a^2*c*d^3/x^4 - 1/5*a^2*d^3/x^5 - 1/240*(312*b^2*c^4*d^3*x^4 + 60*b^2*c^3*d^3*x^3 + 8*b^2*c^2*d^3*x^2 - 3*(b^2*c^5*d^3*x^5 - 10*b^2*c^3*d^3*x^3 - 20*b^2*c^2*d^3*x^2 - 15*b^2*c*d^3*x - 4*b^2*d^3)*log(c*x + 1)^2 - 3*(49*b^2*c^5*d^3*x^5 - 10*b^2*c^3*d^3*x^3 - 20*b^2*c^2*d^3*x^2 - 15*b^2*c*d^3*x - 4*b^2*d^3)*log(-c*x + 1)^2 + 12*(25*b^2*c^4*d^3*x^4 + 12*b^2*c^3*d^3*x^3 + 5*b^2*c^2*d^3*x^2 + b^2*c*d^3*x)*log(c*x + 1) - 6*(50*b^2*c^4*d^3*x^4 + 24*b^2*c^3*d^3*x^3 + 10*b^2*c^2*d^3*x^2 + 2*b^2*c*d^3*x - (b^2*c^5*d^3*x^5 - 10*b^2*c^3*d^3*x^3 - 20*b^2*c^2*d^3*x^2 - 15*b^2*c*d^3*x - 4*b^2*d^3)*log(c*x + 1))*log(-c*x + 1))/x^5","B",0
94,1,961,0,0.977803," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^7,x, algorithm=""maxima"")","-\frac{14}{15} \, {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} c^{6} d^{3} - \frac{14}{15} \, {\left(\log\left(c x\right) \log\left(-c x + 1\right) + {\rm Li}_2\left(-c x + 1\right)\right)} b^{2} c^{6} d^{3} + \frac{14}{15} \, {\left(\log\left(c x + 1\right) \log\left(-c x\right) + {\rm Li}_2\left(c x + 1\right)\right)} b^{2} c^{6} d^{3} - \frac{23}{60} \, b^{2} c^{6} d^{3} \log\left(c x + 1\right) - \frac{97}{60} \, b^{2} c^{6} d^{3} \log\left(c x - 1\right) + 2 \, b^{2} c^{6} d^{3} \log\left(x\right) - \frac{1}{3} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} a b c^{3} d^{3} + \frac{1}{4} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} a b c^{2} d^{3} - \frac{3}{10} \, {\left({\left(2 \, c^{4} \log\left(c^{2} x^{2} - 1\right) - 2 \, c^{4} \log\left(x^{2}\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} c + \frac{4 \, \operatorname{artanh}\left(c x\right)}{x^{5}}\right)} a b c d^{3} + \frac{1}{90} \, {\left({\left(15 \, c^{5} \log\left(c x + 1\right) - 15 \, c^{5} \log\left(c x - 1\right) - \frac{2 \, {\left(15 \, c^{4} x^{4} + 5 \, c^{2} x^{2} + 3\right)}}{x^{5}}\right)} c - \frac{30 \, \operatorname{artanh}\left(c x\right)}{x^{6}}\right)} a b d^{3} + \frac{1}{360} \, {\left({\left(184 \, c^{4} \log\left(x\right) - \frac{15 \, c^{4} x^{4} \log\left(c x + 1\right)^{2} + 15 \, c^{4} x^{4} \log\left(c x - 1\right)^{2} + 92 \, c^{4} x^{4} \log\left(c x - 1\right) + 32 \, c^{2} x^{2} - 2 \, {\left(15 \, c^{4} x^{4} \log\left(c x - 1\right) - 46 \, c^{4} x^{4}\right)} \log\left(c x + 1\right) + 6}{x^{4}}\right)} c^{2} + 4 \, {\left(15 \, c^{5} \log\left(c x + 1\right) - 15 \, c^{5} \log\left(c x - 1\right) - \frac{2 \, {\left(15 \, c^{4} x^{4} + 5 \, c^{2} x^{2} + 3\right)}}{x^{5}}\right)} c \operatorname{artanh}\left(c x\right)\right)} b^{2} d^{3} - \frac{a^{2} c^{3} d^{3}}{3 \, x^{3}} - \frac{3 \, a^{2} c^{2} d^{3}}{4 \, x^{4}} - \frac{3 \, a^{2} c d^{3}}{5 \, x^{5}} - \frac{b^{2} d^{3} \operatorname{artanh}\left(c x\right)^{2}}{6 \, x^{6}} - \frac{a^{2} d^{3}}{6 \, x^{6}} - \frac{296 \, b^{2} c^{5} d^{3} x^{4} + 60 \, b^{2} c^{4} d^{3} x^{3} + 24 \, b^{2} c^{3} d^{3} x^{2} + {\left(11 \, b^{2} c^{6} d^{3} x^{5} + 20 \, b^{2} c^{3} d^{3} x^{2} + 45 \, b^{2} c^{2} d^{3} x + 36 \, b^{2} c d^{3}\right)} \log\left(c x + 1\right)^{2} - {\left(101 \, b^{2} c^{6} d^{3} x^{5} - 20 \, b^{2} c^{3} d^{3} x^{2} - 45 \, b^{2} c^{2} d^{3} x - 36 \, b^{2} c d^{3}\right)} \log\left(-c x + 1\right)^{2} + 4 \, {\left(45 \, b^{2} c^{5} d^{3} x^{4} + 28 \, b^{2} c^{4} d^{3} x^{3} + 15 \, b^{2} c^{3} d^{3} x^{2} + 9 \, b^{2} c^{2} d^{3} x\right)} \log\left(c x + 1\right) - 2 \, {\left(90 \, b^{2} c^{5} d^{3} x^{4} + 56 \, b^{2} c^{4} d^{3} x^{3} + 30 \, b^{2} c^{3} d^{3} x^{2} + 18 \, b^{2} c^{2} d^{3} x + {\left(11 \, b^{2} c^{6} d^{3} x^{5} + 20 \, b^{2} c^{3} d^{3} x^{2} + 45 \, b^{2} c^{2} d^{3} x + 36 \, b^{2} c d^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{240 \, x^{5}}"," ",0,"-14/15*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*c^6*d^3 - 14/15*(log(c*x)*log(-c*x + 1) + dilog(-c*x + 1))*b^2*c^6*d^3 + 14/15*(log(c*x + 1)*log(-c*x) + dilog(c*x + 1))*b^2*c^6*d^3 - 23/60*b^2*c^6*d^3*log(c*x + 1) - 97/60*b^2*c^6*d^3*log(c*x - 1) + 2*b^2*c^6*d^3*log(x) - 1/3*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*a*b*c^3*d^3 + 1/4*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*a*b*c^2*d^3 - 3/10*((2*c^4*log(c^2*x^2 - 1) - 2*c^4*log(x^2) + (2*c^2*x^2 + 1)/x^4)*c + 4*arctanh(c*x)/x^5)*a*b*c*d^3 + 1/90*((15*c^5*log(c*x + 1) - 15*c^5*log(c*x - 1) - 2*(15*c^4*x^4 + 5*c^2*x^2 + 3)/x^5)*c - 30*arctanh(c*x)/x^6)*a*b*d^3 + 1/360*((184*c^4*log(x) - (15*c^4*x^4*log(c*x + 1)^2 + 15*c^4*x^4*log(c*x - 1)^2 + 92*c^4*x^4*log(c*x - 1) + 32*c^2*x^2 - 2*(15*c^4*x^4*log(c*x - 1) - 46*c^4*x^4)*log(c*x + 1) + 6)/x^4)*c^2 + 4*(15*c^5*log(c*x + 1) - 15*c^5*log(c*x - 1) - 2*(15*c^4*x^4 + 5*c^2*x^2 + 3)/x^5)*c*arctanh(c*x))*b^2*d^3 - 1/3*a^2*c^3*d^3/x^3 - 3/4*a^2*c^2*d^3/x^4 - 3/5*a^2*c*d^3/x^5 - 1/6*b^2*d^3*arctanh(c*x)^2/x^6 - 1/6*a^2*d^3/x^6 - 1/240*(296*b^2*c^5*d^3*x^4 + 60*b^2*c^4*d^3*x^3 + 24*b^2*c^3*d^3*x^2 + (11*b^2*c^6*d^3*x^5 + 20*b^2*c^3*d^3*x^2 + 45*b^2*c^2*d^3*x + 36*b^2*c*d^3)*log(c*x + 1)^2 - (101*b^2*c^6*d^3*x^5 - 20*b^2*c^3*d^3*x^2 - 45*b^2*c^2*d^3*x - 36*b^2*c*d^3)*log(-c*x + 1)^2 + 4*(45*b^2*c^5*d^3*x^4 + 28*b^2*c^4*d^3*x^3 + 15*b^2*c^3*d^3*x^2 + 9*b^2*c^2*d^3*x)*log(c*x + 1) - 2*(90*b^2*c^5*d^3*x^4 + 56*b^2*c^4*d^3*x^3 + 30*b^2*c^3*d^3*x^2 + 18*b^2*c^2*d^3*x + (11*b^2*c^6*d^3*x^5 + 20*b^2*c^3*d^3*x^2 + 45*b^2*c^2*d^3*x + 36*b^2*c*d^3)*log(c*x + 1))*log(-c*x + 1))/x^5","B",0
95,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x))^2/(c*d*x+d),x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} {\left(\frac{2 \, c^{2} x^{3} - 3 \, c x^{2} + 6 \, x}{c^{3} d} - \frac{6 \, \log\left(c x + 1\right)}{c^{4} d}\right)} + \frac{{\left(2 \, b^{2} c^{3} x^{3} - 3 \, b^{2} c^{2} x^{2} + 6 \, b^{2} c x - 6 \, b^{2} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{24 \, c^{4} d} - \int -\frac{3 \, {\left(b^{2} c^{4} x^{4} - b^{2} c^{3} x^{3}\right)} \log\left(c x + 1\right)^{2} + 12 \, {\left(a b c^{4} x^{4} - a b c^{3} x^{3}\right)} \log\left(c x + 1\right) - {\left(3 \, b^{2} c^{2} x^{2} + 2 \, {\left(6 \, a b c^{4} + b^{2} c^{4}\right)} x^{4} + 6 \, b^{2} c x - {\left(12 \, a b c^{3} + b^{2} c^{3}\right)} x^{3} + 6 \, {\left(b^{2} c^{4} x^{4} - b^{2} c^{3} x^{3} - b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{12 \, {\left(c^{5} d x^{2} - c^{3} d\right)}}\,{d x}"," ",0,"1/6*a^2*((2*c^2*x^3 - 3*c*x^2 + 6*x)/(c^3*d) - 6*log(c*x + 1)/(c^4*d)) + 1/24*(2*b^2*c^3*x^3 - 3*b^2*c^2*x^2 + 6*b^2*c*x - 6*b^2*log(c*x + 1))*log(-c*x + 1)^2/(c^4*d) - integrate(-1/12*(3*(b^2*c^4*x^4 - b^2*c^3*x^3)*log(c*x + 1)^2 + 12*(a*b*c^4*x^4 - a*b*c^3*x^3)*log(c*x + 1) - (3*b^2*c^2*x^2 + 2*(6*a*b*c^4 + b^2*c^4)*x^4 + 6*b^2*c*x - (12*a*b*c^3 + b^2*c^3)*x^3 + 6*(b^2*c^4*x^4 - b^2*c^3*x^3 - b^2*c*x - b^2)*log(c*x + 1))*log(-c*x + 1))/(c^5*d*x^2 - c^3*d), x)","F",0
96,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))^2/(c*d*x+d),x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{c x^{2} - 2 \, x}{c^{2} d} + \frac{2 \, \log\left(c x + 1\right)}{c^{3} d}\right)} + \frac{{\left(b^{2} c^{2} x^{2} - 2 \, b^{2} c x + 2 \, b^{2} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{8 \, c^{3} d} - \int -\frac{{\left(b^{2} c^{3} x^{3} - b^{2} c^{2} x^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c^{3} x^{3} - a b c^{2} x^{2}\right)} \log\left(c x + 1\right) + {\left(2 \, b^{2} c x - {\left(4 \, a b c^{3} + b^{2} c^{3}\right)} x^{3} + {\left(4 \, a b c^{2} + b^{2} c^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{3} x^{3} - b^{2} c^{2} x^{2} + b^{2} c x + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{4} d x^{2} - c^{2} d\right)}}\,{d x}"," ",0,"1/2*a^2*((c*x^2 - 2*x)/(c^2*d) + 2*log(c*x + 1)/(c^3*d)) + 1/8*(b^2*c^2*x^2 - 2*b^2*c*x + 2*b^2*log(c*x + 1))*log(-c*x + 1)^2/(c^3*d) - integrate(-1/4*((b^2*c^3*x^3 - b^2*c^2*x^2)*log(c*x + 1)^2 + 4*(a*b*c^3*x^3 - a*b*c^2*x^2)*log(c*x + 1) + (2*b^2*c*x - (4*a*b*c^3 + b^2*c^3)*x^3 + (4*a*b*c^2 + b^2*c^2)*x^2 - 2*(b^2*c^3*x^3 - b^2*c^2*x^2 + b^2*c*x + b^2)*log(c*x + 1))*log(-c*x + 1))/(c^4*d*x^2 - c^2*d), x)","F",0
97,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))^2/(c*d*x+d),x, algorithm=""maxima"")","a^{2} {\left(\frac{x}{c d} - \frac{\log\left(c x + 1\right)}{c^{2} d}\right)} + \frac{{\left(b^{2} c x - b^{2} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{4 \, c^{2} d} - \int -\frac{{\left(b^{2} c^{2} x^{2} - b^{2} c x\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c^{2} x^{2} - a b c x\right)} \log\left(c x + 1\right) - 2 \, {\left({\left(2 \, a b c^{2} + b^{2} c^{2}\right)} x^{2} - {\left(2 \, a b c - b^{2} c\right)} x + {\left(b^{2} c^{2} x^{2} - 2 \, b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{3} d x^{2} - c d\right)}}\,{d x}"," ",0,"a^2*(x/(c*d) - log(c*x + 1)/(c^2*d)) + 1/4*(b^2*c*x - b^2*log(c*x + 1))*log(-c*x + 1)^2/(c^2*d) - integrate(-1/4*((b^2*c^2*x^2 - b^2*c*x)*log(c*x + 1)^2 + 4*(a*b*c^2*x^2 - a*b*c*x)*log(c*x + 1) - 2*((2*a*b*c^2 + b^2*c^2)*x^2 - (2*a*b*c - b^2*c)*x + (b^2*c^2*x^2 - 2*b^2*c*x - b^2)*log(c*x + 1))*log(-c*x + 1))/(c^3*d*x^2 - c*d), x)","F",0
98,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/(c*d*x+d),x, algorithm=""maxima"")","\frac{b^{2} \log\left(c x + 1\right) \log\left(-c x + 1\right)^{2}}{4 \, c d} + \frac{a^{2} \log\left(c d x + d\right)}{c d} - \int -\frac{{\left(b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c x - a b\right)} \log\left(c x + 1\right) - 4 \, {\left(b^{2} c x \log\left(c x + 1\right) + a b c x - a b\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{2} d x^{2} - d\right)}}\,{d x}"," ",0,"1/4*b^2*log(c*x + 1)*log(-c*x + 1)^2/(c*d) + a^2*log(c*d*x + d)/(c*d) - integrate(-1/4*((b^2*c*x - b^2)*log(c*x + 1)^2 + 4*(a*b*c*x - a*b)*log(c*x + 1) - 4*(b^2*c*x*log(c*x + 1) + a*b*c*x - a*b)*log(-c*x + 1))/(c^2*d*x^2 - d), x)","F",0
99,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x/(c*d*x+d),x, algorithm=""maxima"")","-\frac{b^{2} \log\left(c x + 1\right) \log\left(-c x + 1\right)^{2}}{4 \, d} - a^{2} {\left(\frac{\log\left(c x + 1\right)}{d} - \frac{\log\left(x\right)}{d}\right)} + \int \frac{{\left(b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c x - a b\right)} \log\left(c x + 1\right) - 2 \, {\left(2 \, a b c x - 2 \, a b - {\left(b^{2} c^{2} x^{2} + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{2} d x^{3} - d x\right)}}\,{d x}"," ",0,"-1/4*b^2*log(c*x + 1)*log(-c*x + 1)^2/d - a^2*(log(c*x + 1)/d - log(x)/d) + integrate(1/4*((b^2*c*x - b^2)*log(c*x + 1)^2 + 4*(a*b*c*x - a*b)*log(c*x + 1) - 2*(2*a*b*c*x - 2*a*b - (b^2*c^2*x^2 + b^2)*log(c*x + 1))*log(-c*x + 1))/(c^2*d*x^3 - d*x), x)","F",0
100,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x^2/(c*d*x+d),x, algorithm=""maxima"")","a^{2} {\left(\frac{c \log\left(c x + 1\right)}{d} - \frac{c \log\left(x\right)}{d} - \frac{1}{d x}\right)} + \frac{{\left(b^{2} c x \log\left(c x + 1\right) - b^{2}\right)} \log\left(-c x + 1\right)^{2}}{4 \, d x} - \int -\frac{{\left(b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c x - a b\right)} \log\left(c x + 1\right) + 2 \, {\left(b^{2} c^{2} x^{2} + 2 \, a b - {\left(2 \, a b c - b^{2} c\right)} x - {\left(b^{2} c^{3} x^{3} + b^{2} c^{2} x^{2} + b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{2} d x^{4} - d x^{2}\right)}}\,{d x}"," ",0,"a^2*(c*log(c*x + 1)/d - c*log(x)/d - 1/(d*x)) + 1/4*(b^2*c*x*log(c*x + 1) - b^2)*log(-c*x + 1)^2/(d*x) - integrate(-1/4*((b^2*c*x - b^2)*log(c*x + 1)^2 + 4*(a*b*c*x - a*b)*log(c*x + 1) + 2*(b^2*c^2*x^2 + 2*a*b - (2*a*b*c - b^2*c)*x - (b^2*c^3*x^3 + b^2*c^2*x^2 + b^2*c*x - b^2)*log(c*x + 1))*log(-c*x + 1))/(c^2*d*x^4 - d*x^2), x)","F",0
101,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x^3/(c*d*x+d),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{2 \, c^{2} \log\left(c x + 1\right)}{d} - \frac{2 \, c^{2} \log\left(x\right)}{d} - \frac{2 \, c x - 1}{d x^{2}}\right)} a^{2} - \frac{{\left(2 \, b^{2} c^{2} x^{2} \log\left(c x + 1\right) - 2 \, b^{2} c x + b^{2}\right)} \log\left(-c x + 1\right)^{2}}{8 \, d x^{2}} + \int \frac{{\left(b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c x - a b\right)} \log\left(c x + 1\right) - {\left(2 \, b^{2} c^{3} x^{3} + b^{2} c^{2} x^{2} - 4 \, a b + {\left(4 \, a b c - b^{2} c\right)} x - 2 \, {\left(b^{2} c^{4} x^{4} + b^{2} c^{3} x^{3} - b^{2} c x + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{2} d x^{5} - d x^{3}\right)}}\,{d x}"," ",0,"-1/2*(2*c^2*log(c*x + 1)/d - 2*c^2*log(x)/d - (2*c*x - 1)/(d*x^2))*a^2 - 1/8*(2*b^2*c^2*x^2*log(c*x + 1) - 2*b^2*c*x + b^2)*log(-c*x + 1)^2/(d*x^2) + integrate(1/4*((b^2*c*x - b^2)*log(c*x + 1)^2 + 4*(a*b*c*x - a*b)*log(c*x + 1) - (2*b^2*c^3*x^3 + b^2*c^2*x^2 - 4*a*b + (4*a*b*c - b^2*c)*x - 2*(b^2*c^4*x^4 + b^2*c^3*x^3 - b^2*c*x + b^2)*log(c*x + 1))*log(-c*x + 1))/(c^2*d*x^5 - d*x^3), x)","F",0
102,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x^4/(c*d*x+d),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{6 \, c^{3} \log\left(c x + 1\right)}{d} - \frac{6 \, c^{3} \log\left(x\right)}{d} - \frac{6 \, c^{2} x^{2} - 3 \, c x + 2}{d x^{3}}\right)} a^{2} + \frac{{\left(6 \, b^{2} c^{3} x^{3} \log\left(c x + 1\right) - 6 \, b^{2} c^{2} x^{2} + 3 \, b^{2} c x - 2 \, b^{2}\right)} \log\left(-c x + 1\right)^{2}}{24 \, d x^{3}} - \int -\frac{3 \, {\left(b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)^{2} + 12 \, {\left(a b c x - a b\right)} \log\left(c x + 1\right) + {\left(6 \, b^{2} c^{4} x^{4} + 3 \, b^{2} c^{3} x^{3} - b^{2} c^{2} x^{2} + 12 \, a b - 2 \, {\left(6 \, a b c - b^{2} c\right)} x - 6 \, {\left(b^{2} c^{5} x^{5} + b^{2} c^{4} x^{4} + b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{12 \, {\left(c^{2} d x^{6} - d x^{4}\right)}}\,{d x}"," ",0,"1/6*(6*c^3*log(c*x + 1)/d - 6*c^3*log(x)/d - (6*c^2*x^2 - 3*c*x + 2)/(d*x^3))*a^2 + 1/24*(6*b^2*c^3*x^3*log(c*x + 1) - 6*b^2*c^2*x^2 + 3*b^2*c*x - 2*b^2)*log(-c*x + 1)^2/(d*x^3) - integrate(-1/12*(3*(b^2*c*x - b^2)*log(c*x + 1)^2 + 12*(a*b*c*x - a*b)*log(c*x + 1) + (6*b^2*c^4*x^4 + 3*b^2*c^3*x^3 - b^2*c^2*x^2 + 12*a*b - 2*(6*a*b*c - b^2*c)*x - 6*(b^2*c^5*x^5 + b^2*c^4*x^4 + b^2*c*x - b^2)*log(c*x + 1))*log(-c*x + 1))/(c^2*d*x^6 - d*x^4), x)","F",0
103,0,0,0,0.000000," ","integrate(x^4*(a+b*arctanh(c*x))^2/(c*d*x+d)^2,x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} {\left(\frac{3}{c^{6} d^{2} x + c^{5} d^{2}} - \frac{c^{2} x^{3} - 3 \, c x^{2} + 9 \, x}{c^{4} d^{2}} + \frac{12 \, \log\left(c x + 1\right)}{c^{5} d^{2}}\right)} + \frac{{\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{3} x^{3} + 6 \, b^{2} c^{2} x^{2} + 9 \, b^{2} c x - 3 \, b^{2} - 12 \, {\left(b^{2} c x + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{12 \, {\left(c^{6} d^{2} x + c^{5} d^{2}\right)}} - \int -\frac{3 \, {\left(b^{2} c^{5} x^{5} - b^{2} c^{4} x^{4}\right)} \log\left(c x + 1\right)^{2} + 12 \, {\left(a b c^{5} x^{5} - a b c^{4} x^{4}\right)} \log\left(c x + 1\right) - 2 \, {\left(4 \, b^{2} c^{3} x^{3} + 15 \, b^{2} c^{2} x^{2} + {\left(6 \, a b c^{5} + b^{2} c^{5}\right)} x^{5} - {\left(6 \, a b c^{4} + b^{2} c^{4}\right)} x^{4} + 6 \, b^{2} c x - 3 \, b^{2} + 3 \, {\left(b^{2} c^{5} x^{5} - b^{2} c^{4} x^{4} - 4 \, b^{2} c^{2} x^{2} - 8 \, b^{2} c x - 4 \, b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{12 \, {\left(c^{7} d^{2} x^{3} + c^{6} d^{2} x^{2} - c^{5} d^{2} x - c^{4} d^{2}\right)}}\,{d x}"," ",0,"-1/3*a^2*(3/(c^6*d^2*x + c^5*d^2) - (c^2*x^3 - 3*c*x^2 + 9*x)/(c^4*d^2) + 12*log(c*x + 1)/(c^5*d^2)) + 1/12*(b^2*c^4*x^4 - 2*b^2*c^3*x^3 + 6*b^2*c^2*x^2 + 9*b^2*c*x - 3*b^2 - 12*(b^2*c*x + b^2)*log(c*x + 1))*log(-c*x + 1)^2/(c^6*d^2*x + c^5*d^2) - integrate(-1/12*(3*(b^2*c^5*x^5 - b^2*c^4*x^4)*log(c*x + 1)^2 + 12*(a*b*c^5*x^5 - a*b*c^4*x^4)*log(c*x + 1) - 2*(4*b^2*c^3*x^3 + 15*b^2*c^2*x^2 + (6*a*b*c^5 + b^2*c^5)*x^5 - (6*a*b*c^4 + b^2*c^4)*x^4 + 6*b^2*c*x - 3*b^2 + 3*(b^2*c^5*x^5 - b^2*c^4*x^4 - 4*b^2*c^2*x^2 - 8*b^2*c*x - 4*b^2)*log(c*x + 1))*log(-c*x + 1))/(c^7*d^2*x^3 + c^6*d^2*x^2 - c^5*d^2*x - c^4*d^2), x)","F",0
104,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x))^2/(c*d*x+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{2}{c^{5} d^{2} x + c^{4} d^{2}} + \frac{c x^{2} - 4 \, x}{c^{3} d^{2}} + \frac{6 \, \log\left(c x + 1\right)}{c^{4} d^{2}}\right)} + \frac{{\left(b^{2} c^{3} x^{3} - 3 \, b^{2} c^{2} x^{2} - 4 \, b^{2} c x + 2 \, b^{2} + 6 \, {\left(b^{2} c x + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{8 \, {\left(c^{5} d^{2} x + c^{4} d^{2}\right)}} - \int -\frac{{\left(b^{2} c^{4} x^{4} - b^{2} c^{3} x^{3}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c^{4} x^{4} - a b c^{3} x^{3}\right)} \log\left(c x + 1\right) + {\left(7 \, b^{2} c^{2} x^{2} - {\left(4 \, a b c^{4} + b^{2} c^{4}\right)} x^{4} + 2 \, b^{2} c x + 2 \, {\left(2 \, a b c^{3} + b^{2} c^{3}\right)} x^{3} - 2 \, b^{2} - 2 \, {\left(b^{2} c^{4} x^{4} - b^{2} c^{3} x^{3} + 3 \, b^{2} c^{2} x^{2} + 6 \, b^{2} c x + 3 \, b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{6} d^{2} x^{3} + c^{5} d^{2} x^{2} - c^{4} d^{2} x - c^{3} d^{2}\right)}}\,{d x}"," ",0,"1/2*a^2*(2/(c^5*d^2*x + c^4*d^2) + (c*x^2 - 4*x)/(c^3*d^2) + 6*log(c*x + 1)/(c^4*d^2)) + 1/8*(b^2*c^3*x^3 - 3*b^2*c^2*x^2 - 4*b^2*c*x + 2*b^2 + 6*(b^2*c*x + b^2)*log(c*x + 1))*log(-c*x + 1)^2/(c^5*d^2*x + c^4*d^2) - integrate(-1/4*((b^2*c^4*x^4 - b^2*c^3*x^3)*log(c*x + 1)^2 + 4*(a*b*c^4*x^4 - a*b*c^3*x^3)*log(c*x + 1) + (7*b^2*c^2*x^2 - (4*a*b*c^4 + b^2*c^4)*x^4 + 2*b^2*c*x + 2*(2*a*b*c^3 + b^2*c^3)*x^3 - 2*b^2 - 2*(b^2*c^4*x^4 - b^2*c^3*x^3 + 3*b^2*c^2*x^2 + 6*b^2*c*x + 3*b^2)*log(c*x + 1))*log(-c*x + 1))/(c^6*d^2*x^3 + c^5*d^2*x^2 - c^4*d^2*x - c^3*d^2), x)","F",0
105,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))^2/(c*d*x+d)^2,x, algorithm=""maxima"")","-a^{2} {\left(\frac{1}{c^{4} d^{2} x + c^{3} d^{2}} - \frac{x}{c^{2} d^{2}} + \frac{2 \, \log\left(c x + 1\right)}{c^{3} d^{2}}\right)} + \frac{{\left(b^{2} c^{2} x^{2} + b^{2} c x - b^{2} - 2 \, {\left(b^{2} c x + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{4 \, {\left(c^{4} d^{2} x + c^{3} d^{2}\right)}} - \int -\frac{{\left(b^{2} c^{3} x^{3} - b^{2} c^{2} x^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c^{3} x^{3} - a b c^{2} x^{2}\right)} \log\left(c x + 1\right) - 2 \, {\left({\left(2 \, a b c^{3} + b^{2} c^{3}\right)} x^{3} - 2 \, {\left(a b c^{2} - b^{2} c^{2}\right)} x^{2} - b^{2} + {\left(b^{2} c^{3} x^{3} - 3 \, b^{2} c^{2} x^{2} - 4 \, b^{2} c x - 2 \, b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{5} d^{2} x^{3} + c^{4} d^{2} x^{2} - c^{3} d^{2} x - c^{2} d^{2}\right)}}\,{d x}"," ",0,"-a^2*(1/(c^4*d^2*x + c^3*d^2) - x/(c^2*d^2) + 2*log(c*x + 1)/(c^3*d^2)) + 1/4*(b^2*c^2*x^2 + b^2*c*x - b^2 - 2*(b^2*c*x + b^2)*log(c*x + 1))*log(-c*x + 1)^2/(c^4*d^2*x + c^3*d^2) - integrate(-1/4*((b^2*c^3*x^3 - b^2*c^2*x^2)*log(c*x + 1)^2 + 4*(a*b*c^3*x^3 - a*b*c^2*x^2)*log(c*x + 1) - 2*((2*a*b*c^3 + b^2*c^3)*x^3 - 2*(a*b*c^2 - b^2*c^2)*x^2 - b^2 + (b^2*c^3*x^3 - 3*b^2*c^2*x^2 - 4*b^2*c*x - 2*b^2)*log(c*x + 1))*log(-c*x + 1))/(c^5*d^2*x^3 + c^4*d^2*x^2 - c^3*d^2*x - c^2*d^2), x)","F",0
106,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))^2/(c*d*x+d)^2,x, algorithm=""maxima"")","a^{2} {\left(\frac{1}{c^{3} d^{2} x + c^{2} d^{2}} + \frac{\log\left(c x + 1\right)}{c^{2} d^{2}}\right)} + \frac{{\left(b^{2} + {\left(b^{2} c x + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{4 \, {\left(c^{3} d^{2} x + c^{2} d^{2}\right)}} - \int -\frac{{\left(b^{2} c^{2} x^{2} - b^{2} c x\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c^{2} x^{2} - a b c x\right)} \log\left(c x + 1\right) - 2 \, {\left(2 \, a b c^{2} x^{2} + b^{2} - {\left(2 \, a b c - b^{2} c\right)} x + {\left(2 \, b^{2} c^{2} x^{2} + b^{2} c x + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{4} d^{2} x^{3} + c^{3} d^{2} x^{2} - c^{2} d^{2} x - c d^{2}\right)}}\,{d x}"," ",0,"a^2*(1/(c^3*d^2*x + c^2*d^2) + log(c*x + 1)/(c^2*d^2)) + 1/4*(b^2 + (b^2*c*x + b^2)*log(c*x + 1))*log(-c*x + 1)^2/(c^3*d^2*x + c^2*d^2) - integrate(-1/4*((b^2*c^2*x^2 - b^2*c*x)*log(c*x + 1)^2 + 4*(a*b*c^2*x^2 - a*b*c*x)*log(c*x + 1) - 2*(2*a*b*c^2*x^2 + b^2 - (2*a*b*c - b^2*c)*x + (2*b^2*c^2*x^2 + b^2*c*x + b^2)*log(c*x + 1))*log(-c*x + 1))/(c^4*d^2*x^3 + c^3*d^2*x^2 - c^2*d^2*x - c*d^2), x)","F",0
107,1,277,0,0.333947," ","integrate((a+b*arctanh(c*x))^2/(c*d*x+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\frac{2}{c^{3} d^{2} x + c^{2} d^{2}} - \frac{\log\left(c x + 1\right)}{c^{2} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{2} d^{2}}\right)} + \frac{4 \, \operatorname{artanh}\left(c x\right)}{c^{2} d^{2} x + c d^{2}}\right)} a b - \frac{1}{8} \, {\left(4 \, c {\left(\frac{2}{c^{3} d^{2} x + c^{2} d^{2}} - \frac{\log\left(c x + 1\right)}{c^{2} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{2} d^{2}}\right)} \operatorname{artanh}\left(c x\right) + \frac{{\left({\left(c x + 1\right)} \log\left(c x + 1\right)^{2} + {\left(c x + 1\right)} \log\left(c x - 1\right)^{2} - 2 \, {\left(c x + {\left(c x + 1\right)} \log\left(c x - 1\right) + 1\right)} \log\left(c x + 1\right) + 2 \, {\left(c x + 1\right)} \log\left(c x - 1\right) + 4\right)} c^{2}}{c^{4} d^{2} x + c^{3} d^{2}}\right)} b^{2} - \frac{b^{2} \operatorname{artanh}\left(c x\right)^{2}}{c^{2} d^{2} x + c d^{2}} - \frac{a^{2}}{c^{2} d^{2} x + c d^{2}}"," ",0,"-1/2*(c*(2/(c^3*d^2*x + c^2*d^2) - log(c*x + 1)/(c^2*d^2) + log(c*x - 1)/(c^2*d^2)) + 4*arctanh(c*x)/(c^2*d^2*x + c*d^2))*a*b - 1/8*(4*c*(2/(c^3*d^2*x + c^2*d^2) - log(c*x + 1)/(c^2*d^2) + log(c*x - 1)/(c^2*d^2))*arctanh(c*x) + ((c*x + 1)*log(c*x + 1)^2 + (c*x + 1)*log(c*x - 1)^2 - 2*(c*x + (c*x + 1)*log(c*x - 1) + 1)*log(c*x + 1) + 2*(c*x + 1)*log(c*x - 1) + 4)*c^2/(c^4*d^2*x + c^3*d^2))*b^2 - b^2*arctanh(c*x)^2/(c^2*d^2*x + c*d^2) - a^2/(c^2*d^2*x + c*d^2)","B",0
108,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x/(c*d*x+d)^2,x, algorithm=""maxima"")","a^{2} {\left(\frac{1}{c d^{2} x + d^{2}} - \frac{\log\left(c x + 1\right)}{d^{2}} + \frac{\log\left(x\right)}{d^{2}}\right)} + \frac{{\left(b^{2} - {\left(b^{2} c x + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{4 \, {\left(c d^{2} x + d^{2}\right)}} + \int \frac{{\left(b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c x - a b\right)} \log\left(c x + 1\right) - 2 \, {\left(b^{2} c^{2} x^{2} - 2 \, a b + {\left(2 \, a b c + b^{2} c\right)} x - {\left(b^{2} c^{3} x^{3} + 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{3} d^{2} x^{4} + c^{2} d^{2} x^{3} - c d^{2} x^{2} - d^{2} x\right)}}\,{d x}"," ",0,"a^2*(1/(c*d^2*x + d^2) - log(c*x + 1)/d^2 + log(x)/d^2) + 1/4*(b^2 - (b^2*c*x + b^2)*log(c*x + 1))*log(-c*x + 1)^2/(c*d^2*x + d^2) + integrate(1/4*((b^2*c*x - b^2)*log(c*x + 1)^2 + 4*(a*b*c*x - a*b)*log(c*x + 1) - 2*(b^2*c^2*x^2 - 2*a*b + (2*a*b*c + b^2*c)*x - (b^2*c^3*x^3 + 2*b^2*c^2*x^2 + b^2)*log(c*x + 1))*log(-c*x + 1))/(c^3*d^2*x^4 + c^2*d^2*x^3 - c*d^2*x^2 - d^2*x), x)","F",0
109,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x^2/(c*d*x+d)^2,x, algorithm=""maxima"")","-a^{2} {\left(\frac{2 \, c x + 1}{c d^{2} x^{2} + d^{2} x} - \frac{2 \, c \log\left(c x + 1\right)}{d^{2}} + \frac{2 \, c \log\left(x\right)}{d^{2}}\right)} - \frac{{\left(2 \, b^{2} c x + b^{2} - 2 \, {\left(b^{2} c^{2} x^{2} + b^{2} c x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{4 \, {\left(c d^{2} x^{2} + d^{2} x\right)}} - \int -\frac{{\left(b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c x - a b\right)} \log\left(c x + 1\right) + 2 \, {\left(2 \, b^{2} c^{3} x^{3} + 3 \, b^{2} c^{2} x^{2} + 2 \, a b - {\left(2 \, a b c - b^{2} c\right)} x - {\left(2 \, b^{2} c^{4} x^{4} + 4 \, b^{2} c^{3} x^{3} + 2 \, b^{2} c^{2} x^{2} + b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{3} d^{2} x^{5} + c^{2} d^{2} x^{4} - c d^{2} x^{3} - d^{2} x^{2}\right)}}\,{d x}"," ",0,"-a^2*((2*c*x + 1)/(c*d^2*x^2 + d^2*x) - 2*c*log(c*x + 1)/d^2 + 2*c*log(x)/d^2) - 1/4*(2*b^2*c*x + b^2 - 2*(b^2*c^2*x^2 + b^2*c*x)*log(c*x + 1))*log(-c*x + 1)^2/(c*d^2*x^2 + d^2*x) - integrate(-1/4*((b^2*c*x - b^2)*log(c*x + 1)^2 + 4*(a*b*c*x - a*b)*log(c*x + 1) + 2*(2*b^2*c^3*x^3 + 3*b^2*c^2*x^2 + 2*a*b - (2*a*b*c - b^2*c)*x - (2*b^2*c^4*x^4 + 4*b^2*c^3*x^3 + 2*b^2*c^2*x^2 + b^2*c*x - b^2)*log(c*x + 1))*log(-c*x + 1))/(c^3*d^2*x^5 + c^2*d^2*x^4 - c*d^2*x^3 - d^2*x^2), x)","F",0
110,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x^3/(c*d*x+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{6 \, c^{2} \log\left(c x + 1\right)}{d^{2}} - \frac{6 \, c^{2} \log\left(x\right)}{d^{2}} - \frac{6 \, c^{2} x^{2} + 3 \, c x - 1}{c d^{2} x^{3} + d^{2} x^{2}}\right)} + \frac{{\left(6 \, b^{2} c^{2} x^{2} + 3 \, b^{2} c x - b^{2} - 6 \, {\left(b^{2} c^{3} x^{3} + b^{2} c^{2} x^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{8 \, {\left(c d^{2} x^{3} + d^{2} x^{2}\right)}} + \int \frac{{\left(b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c x - a b\right)} \log\left(c x + 1\right) - {\left(6 \, b^{2} c^{4} x^{4} + 9 \, b^{2} c^{3} x^{3} + 2 \, b^{2} c^{2} x^{2} - 4 \, a b + {\left(4 \, a b c - b^{2} c\right)} x - 2 \, {\left(3 \, b^{2} c^{5} x^{5} + 6 \, b^{2} c^{4} x^{4} + 3 \, b^{2} c^{3} x^{3} - b^{2} c x + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{3} d^{2} x^{6} + c^{2} d^{2} x^{5} - c d^{2} x^{4} - d^{2} x^{3}\right)}}\,{d x}"," ",0,"-1/2*a^2*(6*c^2*log(c*x + 1)/d^2 - 6*c^2*log(x)/d^2 - (6*c^2*x^2 + 3*c*x - 1)/(c*d^2*x^3 + d^2*x^2)) + 1/8*(6*b^2*c^2*x^2 + 3*b^2*c*x - b^2 - 6*(b^2*c^3*x^3 + b^2*c^2*x^2)*log(c*x + 1))*log(-c*x + 1)^2/(c*d^2*x^3 + d^2*x^2) + integrate(1/4*((b^2*c*x - b^2)*log(c*x + 1)^2 + 4*(a*b*c*x - a*b)*log(c*x + 1) - (6*b^2*c^4*x^4 + 9*b^2*c^3*x^3 + 2*b^2*c^2*x^2 - 4*a*b + (4*a*b*c - b^2*c)*x - 2*(3*b^2*c^5*x^5 + 6*b^2*c^4*x^4 + 3*b^2*c^3*x^3 - b^2*c*x + b^2)*log(c*x + 1))*log(-c*x + 1))/(c^3*d^2*x^6 + c^2*d^2*x^5 - c*d^2*x^4 - d^2*x^3), x)","F",0
111,0,0,0,0.000000," ","integrate(x^4*(a+b*arctanh(c*x))^2/(c*d*x+d)^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{8 \, c x + 7}{c^{7} d^{3} x^{2} + 2 \, c^{6} d^{3} x + c^{5} d^{3}} + \frac{c x^{2} - 6 \, x}{c^{4} d^{3}} + \frac{12 \, \log\left(c x + 1\right)}{c^{5} d^{3}}\right)} + \frac{{\left(b^{2} c^{4} x^{4} - 4 \, b^{2} c^{3} x^{3} - 11 \, b^{2} c^{2} x^{2} + 2 \, b^{2} c x + 7 \, b^{2} + 12 \, {\left(b^{2} c^{2} x^{2} + 2 \, b^{2} c x + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{8 \, {\left(c^{7} d^{3} x^{2} + 2 \, c^{6} d^{3} x + c^{5} d^{3}\right)}} - \int -\frac{{\left(b^{2} c^{5} x^{5} - b^{2} c^{4} x^{4}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c^{5} x^{5} - a b c^{4} x^{4}\right)} \log\left(c x + 1\right) + {\left(15 \, b^{2} c^{3} x^{3} + 9 \, b^{2} c^{2} x^{2} - {\left(4 \, a b c^{5} + b^{2} c^{5}\right)} x^{5} + {\left(4 \, a b c^{4} + 3 \, b^{2} c^{4}\right)} x^{4} - 9 \, b^{2} c x - 7 \, b^{2} - 2 \, {\left(b^{2} c^{5} x^{5} - b^{2} c^{4} x^{4} + 6 \, b^{2} c^{3} x^{3} + 18 \, b^{2} c^{2} x^{2} + 18 \, b^{2} c x + 6 \, b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{8} d^{3} x^{4} + 2 \, c^{7} d^{3} x^{3} - 2 \, c^{5} d^{3} x - c^{4} d^{3}\right)}}\,{d x}"," ",0,"1/2*a^2*((8*c*x + 7)/(c^7*d^3*x^2 + 2*c^6*d^3*x + c^5*d^3) + (c*x^2 - 6*x)/(c^4*d^3) + 12*log(c*x + 1)/(c^5*d^3)) + 1/8*(b^2*c^4*x^4 - 4*b^2*c^3*x^3 - 11*b^2*c^2*x^2 + 2*b^2*c*x + 7*b^2 + 12*(b^2*c^2*x^2 + 2*b^2*c*x + b^2)*log(c*x + 1))*log(-c*x + 1)^2/(c^7*d^3*x^2 + 2*c^6*d^3*x + c^5*d^3) - integrate(-1/4*((b^2*c^5*x^5 - b^2*c^4*x^4)*log(c*x + 1)^2 + 4*(a*b*c^5*x^5 - a*b*c^4*x^4)*log(c*x + 1) + (15*b^2*c^3*x^3 + 9*b^2*c^2*x^2 - (4*a*b*c^5 + b^2*c^5)*x^5 + (4*a*b*c^4 + 3*b^2*c^4)*x^4 - 9*b^2*c*x - 7*b^2 - 2*(b^2*c^5*x^5 - b^2*c^4*x^4 + 6*b^2*c^3*x^3 + 18*b^2*c^2*x^2 + 18*b^2*c*x + 6*b^2)*log(c*x + 1))*log(-c*x + 1))/(c^8*d^3*x^4 + 2*c^7*d^3*x^3 - 2*c^5*d^3*x - c^4*d^3), x)","F",0
112,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x))^2/(c*d*x+d)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{6 \, c x + 5}{c^{6} d^{3} x^{2} + 2 \, c^{5} d^{3} x + c^{4} d^{3}} - \frac{2 \, x}{c^{3} d^{3}} + \frac{6 \, \log\left(c x + 1\right)}{c^{4} d^{3}}\right)} + \frac{{\left(2 \, b^{2} c^{3} x^{3} + 4 \, b^{2} c^{2} x^{2} - 4 \, b^{2} c x - 5 \, b^{2} - 6 \, {\left(b^{2} c^{2} x^{2} + 2 \, b^{2} c x + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{8 \, {\left(c^{6} d^{3} x^{2} + 2 \, c^{5} d^{3} x + c^{4} d^{3}\right)}} - \int -\frac{{\left(b^{2} c^{4} x^{4} - b^{2} c^{3} x^{3}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c^{4} x^{4} - a b c^{3} x^{3}\right)} \log\left(c x + 1\right) - {\left(2 \, {\left(2 \, a b c^{4} + b^{2} c^{4}\right)} x^{4} - 9 \, b^{2} c x - 2 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{3}\right)} x^{3} - 5 \, b^{2} + 2 \, {\left(b^{2} c^{4} x^{4} - 4 \, b^{2} c^{3} x^{3} - 9 \, b^{2} c^{2} x^{2} - 9 \, b^{2} c x - 3 \, b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{7} d^{3} x^{4} + 2 \, c^{6} d^{3} x^{3} - 2 \, c^{4} d^{3} x - c^{3} d^{3}\right)}}\,{d x}"," ",0,"-1/2*a^2*((6*c*x + 5)/(c^6*d^3*x^2 + 2*c^5*d^3*x + c^4*d^3) - 2*x/(c^3*d^3) + 6*log(c*x + 1)/(c^4*d^3)) + 1/8*(2*b^2*c^3*x^3 + 4*b^2*c^2*x^2 - 4*b^2*c*x - 5*b^2 - 6*(b^2*c^2*x^2 + 2*b^2*c*x + b^2)*log(c*x + 1))*log(-c*x + 1)^2/(c^6*d^3*x^2 + 2*c^5*d^3*x + c^4*d^3) - integrate(-1/4*((b^2*c^4*x^4 - b^2*c^3*x^3)*log(c*x + 1)^2 + 4*(a*b*c^4*x^4 - a*b*c^3*x^3)*log(c*x + 1) - (2*(2*a*b*c^4 + b^2*c^4)*x^4 - 9*b^2*c*x - 2*(2*a*b*c^3 - 3*b^2*c^3)*x^3 - 5*b^2 + 2*(b^2*c^4*x^4 - 4*b^2*c^3*x^3 - 9*b^2*c^2*x^2 - 9*b^2*c*x - 3*b^2)*log(c*x + 1))*log(-c*x + 1))/(c^7*d^3*x^4 + 2*c^6*d^3*x^3 - 2*c^4*d^3*x - c^3*d^3), x)","F",0
113,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))^2/(c*d*x+d)^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{4 \, c x + 3}{c^{5} d^{3} x^{2} + 2 \, c^{4} d^{3} x + c^{3} d^{3}} + \frac{2 \, \log\left(c x + 1\right)}{c^{3} d^{3}}\right)} + \frac{{\left(4 \, b^{2} c x + 3 \, b^{2} + 2 \, {\left(b^{2} c^{2} x^{2} + 2 \, b^{2} c x + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{8 \, {\left(c^{5} d^{3} x^{2} + 2 \, c^{4} d^{3} x + c^{3} d^{3}\right)}} - \int -\frac{{\left(b^{2} c^{3} x^{3} - b^{2} c^{2} x^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c^{3} x^{3} - a b c^{2} x^{2}\right)} \log\left(c x + 1\right) - {\left(4 \, a b c^{3} x^{3} + 7 \, b^{2} c x - 4 \, {\left(a b c^{2} - b^{2} c^{2}\right)} x^{2} + 3 \, b^{2} + 2 \, {\left(2 \, b^{2} c^{3} x^{3} + 2 \, b^{2} c^{2} x^{2} + 3 \, b^{2} c x + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{6} d^{3} x^{4} + 2 \, c^{5} d^{3} x^{3} - 2 \, c^{3} d^{3} x - c^{2} d^{3}\right)}}\,{d x}"," ",0,"1/2*a^2*((4*c*x + 3)/(c^5*d^3*x^2 + 2*c^4*d^3*x + c^3*d^3) + 2*log(c*x + 1)/(c^3*d^3)) + 1/8*(4*b^2*c*x + 3*b^2 + 2*(b^2*c^2*x^2 + 2*b^2*c*x + b^2)*log(c*x + 1))*log(-c*x + 1)^2/(c^5*d^3*x^2 + 2*c^4*d^3*x + c^3*d^3) - integrate(-1/4*((b^2*c^3*x^3 - b^2*c^2*x^2)*log(c*x + 1)^2 + 4*(a*b*c^3*x^3 - a*b*c^2*x^2)*log(c*x + 1) - (4*a*b*c^3*x^3 + 7*b^2*c*x - 4*(a*b*c^2 - b^2*c^2)*x^2 + 3*b^2 + 2*(2*b^2*c^3*x^3 + 2*b^2*c^2*x^2 + 3*b^2*c*x + b^2)*log(c*x + 1))*log(-c*x + 1))/(c^6*d^3*x^4 + 2*c^5*d^3*x^3 - 2*c^3*d^3*x - c^2*d^3), x)","F",0
114,1,429,0,0.339901," ","integrate(x*(a+b*arctanh(c*x))^2/(c*d*x+d)^3,x, algorithm=""maxima"")","-\frac{{\left(2 \, c x + 1\right)} b^{2} \operatorname{artanh}\left(c x\right)^{2}}{2 \, {\left(c^{4} d^{3} x^{2} + 2 \, c^{3} d^{3} x + c^{2} d^{3}\right)}} - \frac{1}{8} \, {\left(c {\left(\frac{2 \, {\left(3 \, c x + 2\right)}}{c^{5} d^{3} x^{2} + 2 \, c^{4} d^{3} x + c^{3} d^{3}} - \frac{3 \, \log\left(c x + 1\right)}{c^{3} d^{3}} + \frac{3 \, \log\left(c x - 1\right)}{c^{3} d^{3}}\right)} + \frac{8 \, {\left(2 \, c x + 1\right)} \operatorname{artanh}\left(c x\right)}{c^{4} d^{3} x^{2} + 2 \, c^{3} d^{3} x + c^{2} d^{3}}\right)} a b - \frac{1}{32} \, {\left(4 \, c {\left(\frac{2 \, {\left(3 \, c x + 2\right)}}{c^{5} d^{3} x^{2} + 2 \, c^{4} d^{3} x + c^{3} d^{3}} - \frac{3 \, \log\left(c x + 1\right)}{c^{3} d^{3}} + \frac{3 \, \log\left(c x - 1\right)}{c^{3} d^{3}}\right)} \operatorname{artanh}\left(c x\right) + \frac{{\left(3 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x + 1\right)^{2} + 3 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right)^{2} + 10 \, c x - {\left(5 \, c^{2} x^{2} + 10 \, c x + 6 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right) + 5\right)} \log\left(c x + 1\right) + 5 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right) + 8\right)} c^{2}}{c^{6} d^{3} x^{2} + 2 \, c^{5} d^{3} x + c^{4} d^{3}}\right)} b^{2} - \frac{{\left(2 \, c x + 1\right)} a^{2}}{2 \, {\left(c^{4} d^{3} x^{2} + 2 \, c^{3} d^{3} x + c^{2} d^{3}\right)}}"," ",0,"-1/2*(2*c*x + 1)*b^2*arctanh(c*x)^2/(c^4*d^3*x^2 + 2*c^3*d^3*x + c^2*d^3) - 1/8*(c*(2*(3*c*x + 2)/(c^5*d^3*x^2 + 2*c^4*d^3*x + c^3*d^3) - 3*log(c*x + 1)/(c^3*d^3) + 3*log(c*x - 1)/(c^3*d^3)) + 8*(2*c*x + 1)*arctanh(c*x)/(c^4*d^3*x^2 + 2*c^3*d^3*x + c^2*d^3))*a*b - 1/32*(4*c*(2*(3*c*x + 2)/(c^5*d^3*x^2 + 2*c^4*d^3*x + c^3*d^3) - 3*log(c*x + 1)/(c^3*d^3) + 3*log(c*x - 1)/(c^3*d^3))*arctanh(c*x) + (3*(c^2*x^2 + 2*c*x + 1)*log(c*x + 1)^2 + 3*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1)^2 + 10*c*x - (5*c^2*x^2 + 10*c*x + 6*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1) + 5)*log(c*x + 1) + 5*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1) + 8)*c^2/(c^6*d^3*x^2 + 2*c^5*d^3*x + c^4*d^3))*b^2 - 1/2*(2*c*x + 1)*a^2/(c^4*d^3*x^2 + 2*c^3*d^3*x + c^2*d^3)","B",0
115,1,399,0,0.344200," ","integrate((a+b*arctanh(c*x))^2/(c*d*x+d)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(c {\left(\frac{2 \, {\left(c x + 2\right)}}{c^{4} d^{3} x^{2} + 2 \, c^{3} d^{3} x + c^{2} d^{3}} - \frac{\log\left(c x + 1\right)}{c^{2} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{2} d^{3}}\right)} + \frac{8 \, \operatorname{artanh}\left(c x\right)}{c^{3} d^{3} x^{2} + 2 \, c^{2} d^{3} x + c d^{3}}\right)} a b - \frac{1}{32} \, {\left(4 \, c {\left(\frac{2 \, {\left(c x + 2\right)}}{c^{4} d^{3} x^{2} + 2 \, c^{3} d^{3} x + c^{2} d^{3}} - \frac{\log\left(c x + 1\right)}{c^{2} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{2} d^{3}}\right)} \operatorname{artanh}\left(c x\right) + \frac{{\left({\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x + 1\right)^{2} + {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right)^{2} + 6 \, c x - {\left(3 \, c^{2} x^{2} + 6 \, c x + 2 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right) + 3\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right) + 8\right)} c^{2}}{c^{5} d^{3} x^{2} + 2 \, c^{4} d^{3} x + c^{3} d^{3}}\right)} b^{2} - \frac{b^{2} \operatorname{artanh}\left(c x\right)^{2}}{2 \, {\left(c^{3} d^{3} x^{2} + 2 \, c^{2} d^{3} x + c d^{3}\right)}} - \frac{a^{2}}{2 \, {\left(c^{3} d^{3} x^{2} + 2 \, c^{2} d^{3} x + c d^{3}\right)}}"," ",0,"-1/8*(c*(2*(c*x + 2)/(c^4*d^3*x^2 + 2*c^3*d^3*x + c^2*d^3) - log(c*x + 1)/(c^2*d^3) + log(c*x - 1)/(c^2*d^3)) + 8*arctanh(c*x)/(c^3*d^3*x^2 + 2*c^2*d^3*x + c*d^3))*a*b - 1/32*(4*c*(2*(c*x + 2)/(c^4*d^3*x^2 + 2*c^3*d^3*x + c^2*d^3) - log(c*x + 1)/(c^2*d^3) + log(c*x - 1)/(c^2*d^3))*arctanh(c*x) + ((c^2*x^2 + 2*c*x + 1)*log(c*x + 1)^2 + (c^2*x^2 + 2*c*x + 1)*log(c*x - 1)^2 + 6*c*x - (3*c^2*x^2 + 6*c*x + 2*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1) + 3)*log(c*x + 1) + 3*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1) + 8)*c^2/(c^5*d^3*x^2 + 2*c^4*d^3*x + c^3*d^3))*b^2 - 1/2*b^2*arctanh(c*x)^2/(c^3*d^3*x^2 + 2*c^2*d^3*x + c*d^3) - 1/2*a^2/(c^3*d^3*x^2 + 2*c^2*d^3*x + c*d^3)","B",0
116,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x/(c*d*x+d)^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{2 \, c x + 3}{c^{2} d^{3} x^{2} + 2 \, c d^{3} x + d^{3}} - \frac{2 \, \log\left(c x + 1\right)}{d^{3}} + \frac{2 \, \log\left(x\right)}{d^{3}}\right)} + \frac{{\left(2 \, b^{2} c x + 3 \, b^{2} - 2 \, {\left(b^{2} c^{2} x^{2} + 2 \, b^{2} c x + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{8 \, {\left(c^{2} d^{3} x^{2} + 2 \, c d^{3} x + d^{3}\right)}} + \int \frac{{\left(b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c x - a b\right)} \log\left(c x + 1\right) - {\left(2 \, b^{2} c^{3} x^{3} + 5 \, b^{2} c^{2} x^{2} - 4 \, a b + {\left(4 \, a b c + 3 \, b^{2} c\right)} x - 2 \, {\left(b^{2} c^{4} x^{4} + 3 \, b^{2} c^{3} x^{3} + 3 \, b^{2} c^{2} x^{2} + b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{4} d^{3} x^{5} + 2 \, c^{3} d^{3} x^{4} - 2 \, c d^{3} x^{2} - d^{3} x\right)}}\,{d x}"," ",0,"1/2*a^2*((2*c*x + 3)/(c^2*d^3*x^2 + 2*c*d^3*x + d^3) - 2*log(c*x + 1)/d^3 + 2*log(x)/d^3) + 1/8*(2*b^2*c*x + 3*b^2 - 2*(b^2*c^2*x^2 + 2*b^2*c*x + b^2)*log(c*x + 1))*log(-c*x + 1)^2/(c^2*d^3*x^2 + 2*c*d^3*x + d^3) + integrate(1/4*((b^2*c*x - b^2)*log(c*x + 1)^2 + 4*(a*b*c*x - a*b)*log(c*x + 1) - (2*b^2*c^3*x^3 + 5*b^2*c^2*x^2 - 4*a*b + (4*a*b*c + 3*b^2*c)*x - 2*(b^2*c^4*x^4 + 3*b^2*c^3*x^3 + 3*b^2*c^2*x^2 + b^2)*log(c*x + 1))*log(-c*x + 1))/(c^4*d^3*x^5 + 2*c^3*d^3*x^4 - 2*c*d^3*x^2 - d^3*x), x)","F",0
117,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x^2/(c*d*x+d)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{6 \, c^{2} x^{2} + 9 \, c x + 2}{c^{2} d^{3} x^{3} + 2 \, c d^{3} x^{2} + d^{3} x} - \frac{6 \, c \log\left(c x + 1\right)}{d^{3}} + \frac{6 \, c \log\left(x\right)}{d^{3}}\right)} - \frac{{\left(6 \, b^{2} c^{2} x^{2} + 9 \, b^{2} c x + 2 \, b^{2} - 6 \, {\left(b^{2} c^{3} x^{3} + 2 \, b^{2} c^{2} x^{2} + b^{2} c x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{8 \, {\left(c^{2} d^{3} x^{3} + 2 \, c d^{3} x^{2} + d^{3} x\right)}} - \int -\frac{{\left(b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c x - a b\right)} \log\left(c x + 1\right) + {\left(6 \, b^{2} c^{4} x^{4} + 15 \, b^{2} c^{3} x^{3} + 11 \, b^{2} c^{2} x^{2} + 4 \, a b - 2 \, {\left(2 \, a b c - b^{2} c\right)} x - 2 \, {\left(3 \, b^{2} c^{5} x^{5} + 9 \, b^{2} c^{4} x^{4} + 9 \, b^{2} c^{3} x^{3} + 3 \, b^{2} c^{2} x^{2} + b^{2} c x - b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{4} d^{3} x^{6} + 2 \, c^{3} d^{3} x^{5} - 2 \, c d^{3} x^{3} - d^{3} x^{2}\right)}}\,{d x}"," ",0,"-1/2*a^2*((6*c^2*x^2 + 9*c*x + 2)/(c^2*d^3*x^3 + 2*c*d^3*x^2 + d^3*x) - 6*c*log(c*x + 1)/d^3 + 6*c*log(x)/d^3) - 1/8*(6*b^2*c^2*x^2 + 9*b^2*c*x + 2*b^2 - 6*(b^2*c^3*x^3 + 2*b^2*c^2*x^2 + b^2*c*x)*log(c*x + 1))*log(-c*x + 1)^2/(c^2*d^3*x^3 + 2*c*d^3*x^2 + d^3*x) - integrate(-1/4*((b^2*c*x - b^2)*log(c*x + 1)^2 + 4*(a*b*c*x - a*b)*log(c*x + 1) + (6*b^2*c^4*x^4 + 15*b^2*c^3*x^3 + 11*b^2*c^2*x^2 + 4*a*b - 2*(2*a*b*c - b^2*c)*x - 2*(3*b^2*c^5*x^5 + 9*b^2*c^4*x^4 + 9*b^2*c^3*x^3 + 3*b^2*c^2*x^2 + b^2*c*x - b^2)*log(c*x + 1))*log(-c*x + 1))/(c^4*d^3*x^6 + 2*c^3*d^3*x^5 - 2*c*d^3*x^3 - d^3*x^2), x)","F",0
118,1,445,0,0.348467," ","integrate((a+b*arctanh(c*x))^2/(c*x+1)^4,x, algorithm=""maxima"")","-\frac{1}{72} \, {\left(c {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} + 9 \, c x + 10\right)}}{c^{5} x^{3} + 3 \, c^{4} x^{2} + 3 \, c^{3} x + c^{2}} - \frac{3 \, \log\left(c x + 1\right)}{c^{2}} + \frac{3 \, \log\left(c x - 1\right)}{c^{2}}\right)} + \frac{48 \, \operatorname{artanh}\left(c x\right)}{c^{4} x^{3} + 3 \, c^{3} x^{2} + 3 \, c^{2} x + c}\right)} a b - \frac{1}{864} \, {\left(12 \, c {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} + 9 \, c x + 10\right)}}{c^{5} x^{3} + 3 \, c^{4} x^{2} + 3 \, c^{3} x + c^{2}} - \frac{3 \, \log\left(c x + 1\right)}{c^{2}} + \frac{3 \, \log\left(c x - 1\right)}{c^{2}}\right)} \operatorname{artanh}\left(c x\right) + \frac{{\left(66 \, c^{2} x^{2} + 9 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x + 1\right)^{2} + 9 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right)^{2} + 162 \, c x - 3 \, {\left(11 \, c^{3} x^{3} + 33 \, c^{2} x^{2} + 33 \, c x + 6 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right) + 11\right)} \log\left(c x + 1\right) + 33 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right) + 112\right)} c^{2}}{c^{6} x^{3} + 3 \, c^{5} x^{2} + 3 \, c^{4} x + c^{3}}\right)} b^{2} - \frac{b^{2} \operatorname{artanh}\left(c x\right)^{2}}{3 \, {\left(c^{4} x^{3} + 3 \, c^{3} x^{2} + 3 \, c^{2} x + c\right)}} - \frac{a^{2}}{3 \, {\left(c^{4} x^{3} + 3 \, c^{3} x^{2} + 3 \, c^{2} x + c\right)}}"," ",0,"-1/72*(c*(2*(3*c^2*x^2 + 9*c*x + 10)/(c^5*x^3 + 3*c^4*x^2 + 3*c^3*x + c^2) - 3*log(c*x + 1)/c^2 + 3*log(c*x - 1)/c^2) + 48*arctanh(c*x)/(c^4*x^3 + 3*c^3*x^2 + 3*c^2*x + c))*a*b - 1/864*(12*c*(2*(3*c^2*x^2 + 9*c*x + 10)/(c^5*x^3 + 3*c^4*x^2 + 3*c^3*x + c^2) - 3*log(c*x + 1)/c^2 + 3*log(c*x - 1)/c^2)*arctanh(c*x) + (66*c^2*x^2 + 9*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x + 1)^2 + 9*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1)^2 + 162*c*x - 3*(11*c^3*x^3 + 33*c^2*x^2 + 33*c*x + 6*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1) + 11)*log(c*x + 1) + 33*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1) + 112)*c^2/(c^6*x^3 + 3*c^5*x^2 + 3*c^4*x + c^3))*b^2 - 1/3*b^2*arctanh(c*x)^2/(c^4*x^3 + 3*c^3*x^2 + 3*c^2*x + c) - 1/3*a^2/(c^4*x^3 + 3*c^3*x^2 + 3*c^2*x + c)","B",0
119,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/(-a*c*x^2+c*x),x, algorithm=""maxima"")","-\frac{\log\left(-a x + 1\right)^{3}}{12 \, c} + \frac{1}{4} \, \int -\frac{\log\left(a x + 1\right)^{2} - 2 \, \log\left(a x + 1\right) \log\left(-a x + 1\right)}{a c x^{2} - c x}\,{d x}"," ",0,"-1/12*log(-a*x + 1)^3/c + 1/4*integrate(-(log(a*x + 1)^2 - 2*log(a*x + 1)*log(-a*x + 1))/(a*c*x^2 - c*x), x)","F",0
120,0,0,0,0.000000," ","integrate((c*x+1)^3*(a+b*arctanh(c*x))^3,x, algorithm=""maxima"")","\frac{1}{4} \, a^{3} c^{3} x^{4} + a^{3} c^{2} x^{3} + \frac{1}{8} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a^{2} b c^{3} + \frac{3}{2} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a^{2} b c^{2} + \frac{3}{2} \, a^{3} c x^{2} + \frac{9}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a^{2} b c + a^{3} x + \frac{3 \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a^{2} b}{2 \, c} - \frac{{\left(b^{3} c^{4} x^{4} + 4 \, b^{3} c^{3} x^{3} + 6 \, b^{3} c^{2} x^{2} + 4 \, b^{3} c x - 15 \, b^{3}\right)} \log\left(-c x + 1\right)^{3} - {\left(6 \, a b^{2} c^{4} x^{4} + 2 \, {\left(12 \, a b^{2} c^{3} + b^{3} c^{3}\right)} x^{3} + 12 \, {\left(3 \, a b^{2} c^{2} + b^{3} c^{2}\right)} x^{2} + 6 \, {\left(4 \, a b^{2} c + 7 \, b^{3} c\right)} x + 3 \, {\left(b^{3} c^{4} x^{4} + 4 \, b^{3} c^{3} x^{3} + 6 \, b^{3} c^{2} x^{2} + 4 \, b^{3} c x + b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{32 \, c} - \int -\frac{2 \, {\left(b^{3} c^{4} x^{4} + 2 \, b^{3} c^{3} x^{3} - 2 \, b^{3} c x - b^{3}\right)} \log\left(c x + 1\right)^{3} + 12 \, {\left(a b^{2} c^{4} x^{4} + 2 \, a b^{2} c^{3} x^{3} - 2 \, a b^{2} c x - a b^{2}\right)} \log\left(c x + 1\right)^{2} - {\left(6 \, a b^{2} c^{4} x^{4} + 2 \, {\left(12 \, a b^{2} c^{3} + b^{3} c^{3}\right)} x^{3} + 12 \, {\left(3 \, a b^{2} c^{2} + b^{3} c^{2}\right)} x^{2} + 6 \, {\left(b^{3} c^{4} x^{4} + 2 \, b^{3} c^{3} x^{3} - 2 \, b^{3} c x - b^{3}\right)} \log\left(c x + 1\right)^{2} + 6 \, {\left(4 \, a b^{2} c + 7 \, b^{3} c\right)} x + 3 \, {\left(6 \, b^{3} c^{2} x^{2} + {\left(8 \, a b^{2} c^{4} + b^{3} c^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{2} c^{3} + b^{3} c^{3}\right)} x^{3} - 8 \, a b^{2} + b^{3} - 4 \, {\left(4 \, a b^{2} c - b^{3} c\right)} x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{16 \, {\left(c x - 1\right)}}\,{d x}"," ",0,"1/4*a^3*c^3*x^4 + a^3*c^2*x^3 + 1/8*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a^2*b*c^3 + 3/2*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a^2*b*c^2 + 3/2*a^3*c*x^2 + 9/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a^2*b*c + a^3*x + 3/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a^2*b/c - 1/32*((b^3*c^4*x^4 + 4*b^3*c^3*x^3 + 6*b^3*c^2*x^2 + 4*b^3*c*x - 15*b^3)*log(-c*x + 1)^3 - (6*a*b^2*c^4*x^4 + 2*(12*a*b^2*c^3 + b^3*c^3)*x^3 + 12*(3*a*b^2*c^2 + b^3*c^2)*x^2 + 6*(4*a*b^2*c + 7*b^3*c)*x + 3*(b^3*c^4*x^4 + 4*b^3*c^3*x^3 + 6*b^3*c^2*x^2 + 4*b^3*c*x + b^3)*log(c*x + 1))*log(-c*x + 1)^2)/c - integrate(-1/16*(2*(b^3*c^4*x^4 + 2*b^3*c^3*x^3 - 2*b^3*c*x - b^3)*log(c*x + 1)^3 + 12*(a*b^2*c^4*x^4 + 2*a*b^2*c^3*x^3 - 2*a*b^2*c*x - a*b^2)*log(c*x + 1)^2 - (6*a*b^2*c^4*x^4 + 2*(12*a*b^2*c^3 + b^3*c^3)*x^3 + 12*(3*a*b^2*c^2 + b^3*c^2)*x^2 + 6*(b^3*c^4*x^4 + 2*b^3*c^3*x^3 - 2*b^3*c*x - b^3)*log(c*x + 1)^2 + 6*(4*a*b^2*c + 7*b^3*c)*x + 3*(6*b^3*c^2*x^2 + (8*a*b^2*c^4 + b^3*c^4)*x^4 + 4*(4*a*b^2*c^3 + b^3*c^3)*x^3 - 8*a*b^2 + b^3 - 4*(4*a*b^2*c - b^3*c)*x)*log(c*x + 1))*log(-c*x + 1))/(c*x - 1), x)","F",0
121,0,0,0,0.000000," ","integrate((c*x+1)^2*(a+b*arctanh(c*x))^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} c^{2} x^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a^{2} b c^{2} + a^{3} c x^{2} + \frac{3}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a^{2} b c + a^{3} x + \frac{3 \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a^{2} b}{2 \, c} - \frac{{\left(b^{3} c^{3} x^{3} + 3 \, b^{3} c^{2} x^{2} + 3 \, b^{3} c x - 7 \, b^{3}\right)} \log\left(-c x + 1\right)^{3} - 3 \, {\left(2 \, a b^{2} c^{3} x^{3} + {\left(6 \, a b^{2} c^{2} + b^{3} c^{2}\right)} x^{2} + 6 \, {\left(a b^{2} c + b^{3} c\right)} x + {\left(b^{3} c^{3} x^{3} + 3 \, b^{3} c^{2} x^{2} + 3 \, b^{3} c x + b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{24 \, c} - \int -\frac{{\left(b^{3} c^{3} x^{3} + b^{3} c^{2} x^{2} - b^{3} c x - b^{3}\right)} \log\left(c x + 1\right)^{3} + 6 \, {\left(a b^{2} c^{3} x^{3} + a b^{2} c^{2} x^{2} - a b^{2} c x - a b^{2}\right)} \log\left(c x + 1\right)^{2} - {\left(4 \, a b^{2} c^{3} x^{3} + 2 \, {\left(6 \, a b^{2} c^{2} + b^{3} c^{2}\right)} x^{2} + 3 \, {\left(b^{3} c^{3} x^{3} + b^{3} c^{2} x^{2} - b^{3} c x - b^{3}\right)} \log\left(c x + 1\right)^{2} + 12 \, {\left(a b^{2} c + b^{3} c\right)} x + 2 \, {\left({\left(6 \, a b^{2} c^{3} + b^{3} c^{3}\right)} x^{3} - 6 \, a b^{2} + b^{3} + 3 \, {\left(2 \, a b^{2} c^{2} + b^{3} c^{2}\right)} x^{2} - 3 \, {\left(2 \, a b^{2} c - b^{3} c\right)} x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{8 \, {\left(c x - 1\right)}}\,{d x}"," ",0,"1/3*a^3*c^2*x^3 + 1/2*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a^2*b*c^2 + a^3*c*x^2 + 3/2*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a^2*b*c + a^3*x + 3/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a^2*b/c - 1/24*((b^3*c^3*x^3 + 3*b^3*c^2*x^2 + 3*b^3*c*x - 7*b^3)*log(-c*x + 1)^3 - 3*(2*a*b^2*c^3*x^3 + (6*a*b^2*c^2 + b^3*c^2)*x^2 + 6*(a*b^2*c + b^3*c)*x + (b^3*c^3*x^3 + 3*b^3*c^2*x^2 + 3*b^3*c*x + b^3)*log(c*x + 1))*log(-c*x + 1)^2)/c - integrate(-1/8*((b^3*c^3*x^3 + b^3*c^2*x^2 - b^3*c*x - b^3)*log(c*x + 1)^3 + 6*(a*b^2*c^3*x^3 + a*b^2*c^2*x^2 - a*b^2*c*x - a*b^2)*log(c*x + 1)^2 - (4*a*b^2*c^3*x^3 + 2*(6*a*b^2*c^2 + b^3*c^2)*x^2 + 3*(b^3*c^3*x^3 + b^3*c^2*x^2 - b^3*c*x - b^3)*log(c*x + 1)^2 + 12*(a*b^2*c + b^3*c)*x + 2*((6*a*b^2*c^3 + b^3*c^3)*x^3 - 6*a*b^2 + b^3 + 3*(2*a*b^2*c^2 + b^3*c^2)*x^2 - 3*(2*a*b^2*c - b^3*c)*x)*log(c*x + 1))*log(-c*x + 1))/(c*x - 1), x)","F",0
122,0,0,0,0.000000," ","integrate((c*x+1)*(a+b*arctanh(c*x))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} c x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a^{2} b c + a^{3} x + \frac{3 \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a^{2} b}{2 \, c} - \frac{{\left(b^{3} c^{2} x^{2} + 2 \, b^{3} c x - 3 \, b^{3}\right)} \log\left(-c x + 1\right)^{3} - 3 \, {\left(2 \, a b^{2} c^{2} x^{2} + 2 \, {\left(2 \, a b^{2} c + b^{3} c\right)} x + {\left(b^{3} c^{2} x^{2} + 2 \, b^{3} c x + b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{16 \, c} - \int -\frac{{\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(c x + 1\right)^{3} + 6 \, {\left(a b^{2} c^{2} x^{2} - a b^{2}\right)} \log\left(c x + 1\right)^{2} - 3 \, {\left(2 \, a b^{2} c^{2} x^{2} + {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(c x + 1\right)^{2} + 2 \, {\left(2 \, a b^{2} c + b^{3} c\right)} x + {\left(2 \, b^{3} c x - 4 \, a b^{2} + b^{3} + {\left(4 \, a b^{2} c^{2} + b^{3} c^{2}\right)} x^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{8 \, {\left(c x - 1\right)}}\,{d x}"," ",0,"1/2*a^3*c*x^2 + 3/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a^2*b*c + a^3*x + 3/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a^2*b/c - 1/16*((b^3*c^2*x^2 + 2*b^3*c*x - 3*b^3)*log(-c*x + 1)^3 - 3*(2*a*b^2*c^2*x^2 + 2*(2*a*b^2*c + b^3*c)*x + (b^3*c^2*x^2 + 2*b^3*c*x + b^3)*log(c*x + 1))*log(-c*x + 1)^2)/c - integrate(-1/8*((b^3*c^2*x^2 - b^3)*log(c*x + 1)^3 + 6*(a*b^2*c^2*x^2 - a*b^2)*log(c*x + 1)^2 - 3*(2*a*b^2*c^2*x^2 + (b^3*c^2*x^2 - b^3)*log(c*x + 1)^2 + 2*(2*a*b^2*c + b^3*c)*x + (2*b^3*c*x - 4*a*b^2 + b^3 + (4*a*b^2*c^2 + b^3*c^2)*x^2)*log(c*x + 1))*log(-c*x + 1))/(c*x - 1), x)","F",0
123,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/(c*x+1),x, algorithm=""maxima"")","-\frac{b^{3} \log\left(c x + 1\right) \log\left(-c x + 1\right)^{3}}{8 \, c} + \frac{a^{3} \log\left(c x + 1\right)}{c} + \int \frac{{\left(b^{3} c x - b^{3}\right)} \log\left(c x + 1\right)^{3} + 6 \, {\left(a b^{2} c x - a b^{2}\right)} \log\left(c x + 1\right)^{2} + 6 \, {\left(b^{3} c x \log\left(c x + 1\right) + a b^{2} c x - a b^{2}\right)} \log\left(-c x + 1\right)^{2} + 12 \, {\left(a^{2} b c x - a^{2} b\right)} \log\left(c x + 1\right) - 3 \, {\left(4 \, a^{2} b c x - 4 \, a^{2} b + {\left(b^{3} c x - b^{3}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b^{2} c x - a b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{8 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"-1/8*b^3*log(c*x + 1)*log(-c*x + 1)^3/c + a^3*log(c*x + 1)/c + integrate(1/8*((b^3*c*x - b^3)*log(c*x + 1)^3 + 6*(a*b^2*c*x - a*b^2)*log(c*x + 1)^2 + 6*(b^3*c*x*log(c*x + 1) + a*b^2*c*x - a*b^2)*log(-c*x + 1)^2 + 12*(a^2*b*c*x - a^2*b)*log(c*x + 1) - 3*(4*a^2*b*c*x - 4*a^2*b + (b^3*c*x - b^3)*log(c*x + 1)^2 + 4*(a*b^2*c*x - a*b^2)*log(c*x + 1))*log(-c*x + 1))/(c^2*x^2 - 1), x)","F",0
124,1,529,0,0.346852," ","integrate((a+b*arctanh(c*x))^3/(c*x+1)^2,x, algorithm=""maxima"")","-\frac{b^{3} \operatorname{artanh}\left(c x\right)^{3}}{c^{2} x + c} - \frac{3}{4} \, {\left(c {\left(\frac{2}{c^{3} x + c^{2}} - \frac{\log\left(c x + 1\right)}{c^{2}} + \frac{\log\left(c x - 1\right)}{c^{2}}\right)} + \frac{4 \, \operatorname{artanh}\left(c x\right)}{c^{2} x + c}\right)} a^{2} b - \frac{3}{8} \, {\left(4 \, c {\left(\frac{2}{c^{3} x + c^{2}} - \frac{\log\left(c x + 1\right)}{c^{2}} + \frac{\log\left(c x - 1\right)}{c^{2}}\right)} \operatorname{artanh}\left(c x\right) + \frac{{\left({\left(c x + 1\right)} \log\left(c x + 1\right)^{2} + {\left(c x + 1\right)} \log\left(c x - 1\right)^{2} - 2 \, {\left(c x + {\left(c x + 1\right)} \log\left(c x - 1\right) + 1\right)} \log\left(c x + 1\right) + 2 \, {\left(c x + 1\right)} \log\left(c x - 1\right) + 4\right)} c^{2}}{c^{4} x + c^{3}}\right)} a b^{2} - \frac{1}{16} \, {\left(12 \, c {\left(\frac{2}{c^{3} x + c^{2}} - \frac{\log\left(c x + 1\right)}{c^{2}} + \frac{\log\left(c x - 1\right)}{c^{2}}\right)} \operatorname{artanh}\left(c x\right)^{2} - {\left(\frac{{\left({\left(c x + 1\right)} \log\left(c x + 1\right)^{3} - {\left(c x + 1\right)} \log\left(c x - 1\right)^{3} - 3 \, {\left(c x + {\left(c x + 1\right)} \log\left(c x - 1\right) + 1\right)} \log\left(c x + 1\right)^{2} - 3 \, {\left(c x + 1\right)} \log\left(c x - 1\right)^{2} + 3 \, {\left({\left(c x + 1\right)} \log\left(c x - 1\right)^{2} + 2 \, c x + 2 \, {\left(c x + 1\right)} \log\left(c x - 1\right) + 2\right)} \log\left(c x + 1\right) - 6 \, {\left(c x + 1\right)} \log\left(c x - 1\right) - 12\right)} c^{2}}{c^{5} x + c^{4}} - \frac{6 \, {\left({\left(c x + 1\right)} \log\left(c x + 1\right)^{2} + {\left(c x + 1\right)} \log\left(c x - 1\right)^{2} - 2 \, {\left(c x + {\left(c x + 1\right)} \log\left(c x - 1\right) + 1\right)} \log\left(c x + 1\right) + 2 \, {\left(c x + 1\right)} \log\left(c x - 1\right) + 4\right)} c \operatorname{artanh}\left(c x\right)}{c^{4} x + c^{3}}\right)} c\right)} b^{3} - \frac{3 \, a b^{2} \operatorname{artanh}\left(c x\right)^{2}}{c^{2} x + c} - \frac{a^{3}}{c^{2} x + c}"," ",0,"-b^3*arctanh(c*x)^3/(c^2*x + c) - 3/4*(c*(2/(c^3*x + c^2) - log(c*x + 1)/c^2 + log(c*x - 1)/c^2) + 4*arctanh(c*x)/(c^2*x + c))*a^2*b - 3/8*(4*c*(2/(c^3*x + c^2) - log(c*x + 1)/c^2 + log(c*x - 1)/c^2)*arctanh(c*x) + ((c*x + 1)*log(c*x + 1)^2 + (c*x + 1)*log(c*x - 1)^2 - 2*(c*x + (c*x + 1)*log(c*x - 1) + 1)*log(c*x + 1) + 2*(c*x + 1)*log(c*x - 1) + 4)*c^2/(c^4*x + c^3))*a*b^2 - 1/16*(12*c*(2/(c^3*x + c^2) - log(c*x + 1)/c^2 + log(c*x - 1)/c^2)*arctanh(c*x)^2 - (((c*x + 1)*log(c*x + 1)^3 - (c*x + 1)*log(c*x - 1)^3 - 3*(c*x + (c*x + 1)*log(c*x - 1) + 1)*log(c*x + 1)^2 - 3*(c*x + 1)*log(c*x - 1)^2 + 3*((c*x + 1)*log(c*x - 1)^2 + 2*c*x + 2*(c*x + 1)*log(c*x - 1) + 2)*log(c*x + 1) - 6*(c*x + 1)*log(c*x - 1) - 12)*c^2/(c^5*x + c^4) - 6*((c*x + 1)*log(c*x + 1)^2 + (c*x + 1)*log(c*x - 1)^2 - 2*(c*x + (c*x + 1)*log(c*x - 1) + 1)*log(c*x + 1) + 2*(c*x + 1)*log(c*x - 1) + 4)*c*arctanh(c*x)/(c^4*x + c^3))*c)*b^3 - 3*a*b^2*arctanh(c*x)^2/(c^2*x + c) - a^3/(c^2*x + c)","B",0
125,1,796,0,0.355819," ","integrate((a+b*arctanh(c*x))^3/(c*x+1)^3,x, algorithm=""maxima"")","-\frac{b^{3} \operatorname{artanh}\left(c x\right)^{3}}{2 \, {\left(c^{3} x^{2} + 2 \, c^{2} x + c\right)}} - \frac{3}{16} \, {\left(c {\left(\frac{2 \, {\left(c x + 2\right)}}{c^{4} x^{2} + 2 \, c^{3} x + c^{2}} - \frac{\log\left(c x + 1\right)}{c^{2}} + \frac{\log\left(c x - 1\right)}{c^{2}}\right)} + \frac{8 \, \operatorname{artanh}\left(c x\right)}{c^{3} x^{2} + 2 \, c^{2} x + c}\right)} a^{2} b - \frac{3}{32} \, {\left(4 \, c {\left(\frac{2 \, {\left(c x + 2\right)}}{c^{4} x^{2} + 2 \, c^{3} x + c^{2}} - \frac{\log\left(c x + 1\right)}{c^{2}} + \frac{\log\left(c x - 1\right)}{c^{2}}\right)} \operatorname{artanh}\left(c x\right) + \frac{{\left({\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x + 1\right)^{2} + {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right)^{2} + 6 \, c x - {\left(3 \, c^{2} x^{2} + 6 \, c x + 2 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right) + 3\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right) + 8\right)} c^{2}}{c^{5} x^{2} + 2 \, c^{4} x + c^{3}}\right)} a b^{2} - \frac{1}{128} \, {\left(24 \, c {\left(\frac{2 \, {\left(c x + 2\right)}}{c^{4} x^{2} + 2 \, c^{3} x + c^{2}} - \frac{\log\left(c x + 1\right)}{c^{2}} + \frac{\log\left(c x - 1\right)}{c^{2}}\right)} \operatorname{artanh}\left(c x\right)^{2} - {\left(\frac{{\left(2 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x + 1\right)^{3} - 2 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right)^{3} - 3 \, {\left(3 \, c^{2} x^{2} + 6 \, c x + 2 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right) + 3\right)} \log\left(c x + 1\right)^{2} - 9 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right)^{2} - 42 \, c x + 3 \, {\left(7 \, c^{2} x^{2} + 2 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right)^{2} + 14 \, c x + 6 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right) + 7\right)} \log\left(c x + 1\right) - 21 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right) - 48\right)} c^{2}}{c^{6} x^{2} + 2 \, c^{5} x + c^{4}} - \frac{12 \, {\left({\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x + 1\right)^{2} + {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right)^{2} + 6 \, c x - {\left(3 \, c^{2} x^{2} + 6 \, c x + 2 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right) + 3\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{2} x^{2} + 2 \, c x + 1\right)} \log\left(c x - 1\right) + 8\right)} c \operatorname{artanh}\left(c x\right)}{c^{5} x^{2} + 2 \, c^{4} x + c^{3}}\right)} c\right)} b^{3} - \frac{3 \, a b^{2} \operatorname{artanh}\left(c x\right)^{2}}{2 \, {\left(c^{3} x^{2} + 2 \, c^{2} x + c\right)}} - \frac{a^{3}}{2 \, {\left(c^{3} x^{2} + 2 \, c^{2} x + c\right)}}"," ",0,"-1/2*b^3*arctanh(c*x)^3/(c^3*x^2 + 2*c^2*x + c) - 3/16*(c*(2*(c*x + 2)/(c^4*x^2 + 2*c^3*x + c^2) - log(c*x + 1)/c^2 + log(c*x - 1)/c^2) + 8*arctanh(c*x)/(c^3*x^2 + 2*c^2*x + c))*a^2*b - 3/32*(4*c*(2*(c*x + 2)/(c^4*x^2 + 2*c^3*x + c^2) - log(c*x + 1)/c^2 + log(c*x - 1)/c^2)*arctanh(c*x) + ((c^2*x^2 + 2*c*x + 1)*log(c*x + 1)^2 + (c^2*x^2 + 2*c*x + 1)*log(c*x - 1)^2 + 6*c*x - (3*c^2*x^2 + 6*c*x + 2*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1) + 3)*log(c*x + 1) + 3*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1) + 8)*c^2/(c^5*x^2 + 2*c^4*x + c^3))*a*b^2 - 1/128*(24*c*(2*(c*x + 2)/(c^4*x^2 + 2*c^3*x + c^2) - log(c*x + 1)/c^2 + log(c*x - 1)/c^2)*arctanh(c*x)^2 - ((2*(c^2*x^2 + 2*c*x + 1)*log(c*x + 1)^3 - 2*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1)^3 - 3*(3*c^2*x^2 + 6*c*x + 2*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1) + 3)*log(c*x + 1)^2 - 9*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1)^2 - 42*c*x + 3*(7*c^2*x^2 + 2*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1)^2 + 14*c*x + 6*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1) + 7)*log(c*x + 1) - 21*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1) - 48)*c^2/(c^6*x^2 + 2*c^5*x + c^4) - 12*((c^2*x^2 + 2*c*x + 1)*log(c*x + 1)^2 + (c^2*x^2 + 2*c*x + 1)*log(c*x - 1)^2 + 6*c*x - (3*c^2*x^2 + 6*c*x + 2*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1) + 3)*log(c*x + 1) + 3*(c^2*x^2 + 2*c*x + 1)*log(c*x - 1) + 8)*c*arctanh(c*x)/(c^5*x^2 + 2*c^4*x + c^3))*c)*b^3 - 3/2*a*b^2*arctanh(c*x)^2/(c^3*x^2 + 2*c^2*x + c) - 1/2*a^3/(c^3*x^2 + 2*c^2*x + c)","B",0
126,1,1085,0,0.391463," ","integrate((a+b*arctanh(c*x))^3/(c*x+1)^4,x, algorithm=""maxima"")","-\frac{b^{3} \operatorname{artanh}\left(c x\right)^{3}}{3 \, {\left(c^{4} x^{3} + 3 \, c^{3} x^{2} + 3 \, c^{2} x + c\right)}} - \frac{1}{48} \, {\left(c {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} + 9 \, c x + 10\right)}}{c^{5} x^{3} + 3 \, c^{4} x^{2} + 3 \, c^{3} x + c^{2}} - \frac{3 \, \log\left(c x + 1\right)}{c^{2}} + \frac{3 \, \log\left(c x - 1\right)}{c^{2}}\right)} + \frac{48 \, \operatorname{artanh}\left(c x\right)}{c^{4} x^{3} + 3 \, c^{3} x^{2} + 3 \, c^{2} x + c}\right)} a^{2} b - \frac{1}{288} \, {\left(12 \, c {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} + 9 \, c x + 10\right)}}{c^{5} x^{3} + 3 \, c^{4} x^{2} + 3 \, c^{3} x + c^{2}} - \frac{3 \, \log\left(c x + 1\right)}{c^{2}} + \frac{3 \, \log\left(c x - 1\right)}{c^{2}}\right)} \operatorname{artanh}\left(c x\right) + \frac{{\left(66 \, c^{2} x^{2} + 9 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x + 1\right)^{2} + 9 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right)^{2} + 162 \, c x - 3 \, {\left(11 \, c^{3} x^{3} + 33 \, c^{2} x^{2} + 33 \, c x + 6 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right) + 11\right)} \log\left(c x + 1\right) + 33 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right) + 112\right)} c^{2}}{c^{6} x^{3} + 3 \, c^{5} x^{2} + 3 \, c^{4} x + c^{3}}\right)} a b^{2} - \frac{1}{3456} \, {\left(72 \, c {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} + 9 \, c x + 10\right)}}{c^{5} x^{3} + 3 \, c^{4} x^{2} + 3 \, c^{3} x + c^{2}} - \frac{3 \, \log\left(c x + 1\right)}{c^{2}} + \frac{3 \, \log\left(c x - 1\right)}{c^{2}}\right)} \operatorname{artanh}\left(c x\right)^{2} + {\left(\frac{{\left(510 \, c^{2} x^{2} - 18 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x + 1\right)^{3} + 18 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right)^{3} + 9 \, {\left(11 \, c^{3} x^{3} + 33 \, c^{2} x^{2} + 33 \, c x + 6 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right) + 11\right)} \log\left(c x + 1\right)^{2} + 99 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right)^{2} + 1134 \, c x - 3 \, {\left(85 \, c^{3} x^{3} + 255 \, c^{2} x^{2} + 18 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right)^{2} + 255 \, c x + 66 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right) + 85\right)} \log\left(c x + 1\right) + 255 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right) + 656\right)} c^{2}}{c^{7} x^{3} + 3 \, c^{6} x^{2} + 3 \, c^{5} x + c^{4}} + \frac{12 \, {\left(66 \, c^{2} x^{2} + 9 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x + 1\right)^{2} + 9 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right)^{2} + 162 \, c x - 3 \, {\left(11 \, c^{3} x^{3} + 33 \, c^{2} x^{2} + 33 \, c x + 6 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right) + 11\right)} \log\left(c x + 1\right) + 33 \, {\left(c^{3} x^{3} + 3 \, c^{2} x^{2} + 3 \, c x + 1\right)} \log\left(c x - 1\right) + 112\right)} c \operatorname{artanh}\left(c x\right)}{c^{6} x^{3} + 3 \, c^{5} x^{2} + 3 \, c^{4} x + c^{3}}\right)} c\right)} b^{3} - \frac{a b^{2} \operatorname{artanh}\left(c x\right)^{2}}{c^{4} x^{3} + 3 \, c^{3} x^{2} + 3 \, c^{2} x + c} - \frac{a^{3}}{3 \, {\left(c^{4} x^{3} + 3 \, c^{3} x^{2} + 3 \, c^{2} x + c\right)}}"," ",0,"-1/3*b^3*arctanh(c*x)^3/(c^4*x^3 + 3*c^3*x^2 + 3*c^2*x + c) - 1/48*(c*(2*(3*c^2*x^2 + 9*c*x + 10)/(c^5*x^3 + 3*c^4*x^2 + 3*c^3*x + c^2) - 3*log(c*x + 1)/c^2 + 3*log(c*x - 1)/c^2) + 48*arctanh(c*x)/(c^4*x^3 + 3*c^3*x^2 + 3*c^2*x + c))*a^2*b - 1/288*(12*c*(2*(3*c^2*x^2 + 9*c*x + 10)/(c^5*x^3 + 3*c^4*x^2 + 3*c^3*x + c^2) - 3*log(c*x + 1)/c^2 + 3*log(c*x - 1)/c^2)*arctanh(c*x) + (66*c^2*x^2 + 9*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x + 1)^2 + 9*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1)^2 + 162*c*x - 3*(11*c^3*x^3 + 33*c^2*x^2 + 33*c*x + 6*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1) + 11)*log(c*x + 1) + 33*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1) + 112)*c^2/(c^6*x^3 + 3*c^5*x^2 + 3*c^4*x + c^3))*a*b^2 - 1/3456*(72*c*(2*(3*c^2*x^2 + 9*c*x + 10)/(c^5*x^3 + 3*c^4*x^2 + 3*c^3*x + c^2) - 3*log(c*x + 1)/c^2 + 3*log(c*x - 1)/c^2)*arctanh(c*x)^2 + ((510*c^2*x^2 - 18*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x + 1)^3 + 18*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1)^3 + 9*(11*c^3*x^3 + 33*c^2*x^2 + 33*c*x + 6*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1) + 11)*log(c*x + 1)^2 + 99*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1)^2 + 1134*c*x - 3*(85*c^3*x^3 + 255*c^2*x^2 + 18*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1)^2 + 255*c*x + 66*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1) + 85)*log(c*x + 1) + 255*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1) + 656)*c^2/(c^7*x^3 + 3*c^6*x^2 + 3*c^5*x + c^4) + 12*(66*c^2*x^2 + 9*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x + 1)^2 + 9*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1)^2 + 162*c*x - 3*(11*c^3*x^3 + 33*c^2*x^2 + 33*c*x + 6*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1) + 11)*log(c*x + 1) + 33*(c^3*x^3 + 3*c^2*x^2 + 3*c*x + 1)*log(c*x - 1) + 112)*c*arctanh(c*x)/(c^6*x^3 + 3*c^5*x^2 + 3*c^4*x + c^3))*c)*b^3 - a*b^2*arctanh(c*x)^2/(c^4*x^3 + 3*c^3*x^2 + 3*c^2*x + c) - 1/3*a^3/(c^4*x^3 + 3*c^3*x^2 + 3*c^2*x + c)","B",0
127,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^3/(a*c*x+c),x, algorithm=""maxima"")","-\frac{{\left(a^{2} x^{2} - 2 \, a x + 2 \, \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{3}}{16 \, a^{3} c} + \frac{1}{8} \, \int \frac{2 \, {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \log\left(a x + 1\right)^{3} - 6 \, {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) + 3 \, {\left(a^{3} x^{3} - a^{2} x^{2} - 2 \, a x + 2 \, {\left(a^{3} x^{3} - a^{2} x^{2} + a x + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{2}}{2 \, {\left(a^{4} c x^{2} - a^{2} c\right)}}\,{d x}"," ",0,"-1/16*(a^2*x^2 - 2*a*x + 2*log(a*x + 1))*log(-a*x + 1)^3/(a^3*c) + 1/8*integrate(1/2*(2*(a^3*x^3 - a^2*x^2)*log(a*x + 1)^3 - 6*(a^3*x^3 - a^2*x^2)*log(a*x + 1)^2*log(-a*x + 1) + 3*(a^3*x^3 - a^2*x^2 - 2*a*x + 2*(a^3*x^3 - a^2*x^2 + a*x + 1)*log(a*x + 1))*log(-a*x + 1)^2)/(a^4*c*x^2 - a^2*c), x)","F",0
128,0,0,0,0.000000," ","integrate(x*arctanh(a*x)^3/(a*c*x+c),x, algorithm=""maxima"")","-\frac{{\left(a x - \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{3}}{8 \, a^{2} c} + \frac{1}{8} \, \int \frac{{\left(a^{2} x^{2} - a x\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(a^{2} x^{2} - a x\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) + 3 \, {\left(a^{2} x^{2} + a x + {\left(a^{2} x^{2} - 2 \, a x - 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{2}}{a^{3} c x^{2} - a c}\,{d x}"," ",0,"-1/8*(a*x - log(a*x + 1))*log(-a*x + 1)^3/(a^2*c) + 1/8*integrate(((a^2*x^2 - a*x)*log(a*x + 1)^3 - 3*(a^2*x^2 - a*x)*log(a*x + 1)^2*log(-a*x + 1) + 3*(a^2*x^2 + a*x + (a^2*x^2 - 2*a*x - 1)*log(a*x + 1))*log(-a*x + 1)^2)/(a^3*c*x^2 - a*c), x)","F",0
129,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/(a*c*x+c),x, algorithm=""maxima"")","-\frac{\log\left(a x + 1\right) \log\left(-a x + 1\right)^{3}}{8 \, a c} + \frac{1}{8} \, \int \frac{6 \, a x \log\left(a x + 1\right) \log\left(-a x + 1\right)^{2} + {\left(a x - 1\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(a x - 1\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)}{a^{2} c x^{2} - c}\,{d x}"," ",0,"-1/8*log(a*x + 1)*log(-a*x + 1)^3/(a*c) + 1/8*integrate((6*a*x*log(a*x + 1)*log(-a*x + 1)^2 + (a*x - 1)*log(a*x + 1)^3 - 3*(a*x - 1)*log(a*x + 1)^2*log(-a*x + 1))/(a^2*c*x^2 - c), x)","F",0
130,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x/(a*c*x+c),x, algorithm=""maxima"")","\frac{\log\left(a x + 1\right) \log\left(-a x + 1\right)^{3}}{8 \, c} - \frac{1}{8} \, \int -\frac{{\left(a x - 1\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(a x - 1\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) - 3 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right)^{2}}{a^{2} c x^{3} - c x}\,{d x}"," ",0,"1/8*log(a*x + 1)*log(-a*x + 1)^3/c - 1/8*integrate(-((a*x - 1)*log(a*x + 1)^3 - 3*(a*x - 1)*log(a*x + 1)^2*log(-a*x + 1) - 3*(a^2*x^2 + 1)*log(a*x + 1)*log(-a*x + 1)^2)/(a^2*c*x^3 - c*x), x)","F",0
131,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/(a*c*x^2+c*x),x, algorithm=""maxima"")","\frac{\log\left(a x + 1\right) \log\left(-a x + 1\right)^{3}}{8 \, c} - \frac{1}{8} \, \int -\frac{{\left(a x - 1\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(a x - 1\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) - 3 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right)^{2}}{a^{2} c x^{3} - c x}\,{d x}"," ",0,"1/8*log(a*x + 1)*log(-a*x + 1)^3/c - 1/8*integrate(-((a*x - 1)*log(a*x + 1)^3 - 3*(a*x - 1)*log(a*x + 1)^2*log(-a*x + 1) - 3*(a^2*x^2 + 1)*log(a*x + 1)*log(-a*x + 1)^2)/(a^2*c*x^3 - c*x), x)","F",0
132,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^2/(a*c*x+c),x, algorithm=""maxima"")","-\frac{{\left(a x \log\left(a x + 1\right) - 1\right)} \log\left(-a x + 1\right)^{3}}{8 \, c x} + \frac{1}{8} \, \int \frac{{\left(a x - 1\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(a x - 1\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) - 3 \, {\left(a^{2} x^{2} + a x - {\left(a^{3} x^{3} + a^{2} x^{2} + a x - 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{2}}{a^{2} c x^{4} - c x^{2}}\,{d x}"," ",0,"-1/8*(a*x*log(a*x + 1) - 1)*log(-a*x + 1)^3/(c*x) + 1/8*integrate(((a*x - 1)*log(a*x + 1)^3 - 3*(a*x - 1)*log(a*x + 1)^2*log(-a*x + 1) - 3*(a^2*x^2 + a*x - (a^3*x^3 + a^2*x^2 + a*x - 1)*log(a*x + 1))*log(-a*x + 1)^2)/(a^2*c*x^4 - c*x^2), x)","F",0
133,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^3/(a*c*x+c),x, algorithm=""maxima"")","\frac{{\left(2 \, a^{2} x^{2} \log\left(a x + 1\right) - 2 \, a x + 1\right)} \log\left(-a x + 1\right)^{3}}{16 \, c x^{2}} - \frac{1}{8} \, \int -\frac{2 \, {\left(a x - 1\right)} \log\left(a x + 1\right)^{3} - 6 \, {\left(a x - 1\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) + 3 \, {\left(2 \, a^{3} x^{3} + a^{2} x^{2} - a x - 2 \, {\left(a^{4} x^{4} + a^{3} x^{3} - a x + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{2}}{2 \, {\left(a^{2} c x^{5} - c x^{3}\right)}}\,{d x}"," ",0,"1/16*(2*a^2*x^2*log(a*x + 1) - 2*a*x + 1)*log(-a*x + 1)^3/(c*x^2) - 1/8*integrate(-1/2*(2*(a*x - 1)*log(a*x + 1)^3 - 6*(a*x - 1)*log(a*x + 1)^2*log(-a*x + 1) + 3*(2*a^3*x^3 + a^2*x^2 - a*x - 2*(a^4*x^4 + a^3*x^3 - a*x + 1)*log(a*x + 1))*log(-a*x + 1)^2)/(a^2*c*x^5 - c*x^3), x)","F",0
134,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^4/(-a*c*x+c),x, algorithm=""maxima"")","-\frac{4 \, \log\left(-a x + 1\right)^{5} + 5 \, {\left(2 \, \log\left(-a x + 1\right)^{4} - 4 \, \log\left(-a x + 1\right)^{3} + 6 \, \log\left(-a x + 1\right)^{2} - 6 \, \log\left(-a x + 1\right) + 3\right)} {\left(a x - 1\right)}^{2} + 40 \, {\left(\log\left(-a x + 1\right)^{4} - 4 \, \log\left(-a x + 1\right)^{3} + 12 \, \log\left(-a x + 1\right)^{2} - 24 \, \log\left(-a x + 1\right) + 24\right)} {\left(a x - 1\right)}}{320 \, a^{3} c} + \frac{1}{16} \, \int -\frac{x^{2} \log\left(a x + 1\right)^{4} - 4 \, x^{2} \log\left(a x + 1\right)^{3} \log\left(-a x + 1\right) + 6 \, x^{2} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)^{2} - 4 \, x^{2} \log\left(a x + 1\right) \log\left(-a x + 1\right)^{3}}{a c x - c}\,{d x}"," ",0,"-1/320*(4*log(-a*x + 1)^5 + 5*(2*log(-a*x + 1)^4 - 4*log(-a*x + 1)^3 + 6*log(-a*x + 1)^2 - 6*log(-a*x + 1) + 3)*(a*x - 1)^2 + 40*(log(-a*x + 1)^4 - 4*log(-a*x + 1)^3 + 12*log(-a*x + 1)^2 - 24*log(-a*x + 1) + 24)*(a*x - 1))/(a^3*c) + 1/16*integrate(-(x^2*log(a*x + 1)^4 - 4*x^2*log(a*x + 1)^3*log(-a*x + 1) + 6*x^2*log(a*x + 1)^2*log(-a*x + 1)^2 - 4*x^2*log(a*x + 1)*log(-a*x + 1)^3)/(a*c*x - c), x)","F",0
135,0,0,0,0.000000," ","integrate(x*arctanh(a*x)^4/(-a*c*x+c),x, algorithm=""maxima"")","-\frac{\log\left(-a x + 1\right)^{5} + 5 \, {\left(\log\left(-a x + 1\right)^{4} - 4 \, \log\left(-a x + 1\right)^{3} + 12 \, \log\left(-a x + 1\right)^{2} - 24 \, \log\left(-a x + 1\right) + 24\right)} {\left(a x - 1\right)}}{80 \, a^{2} c} + \frac{1}{16} \, \int -\frac{x \log\left(a x + 1\right)^{4} - 4 \, x \log\left(a x + 1\right)^{3} \log\left(-a x + 1\right) + 6 \, x \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)^{2} - 4 \, x \log\left(a x + 1\right) \log\left(-a x + 1\right)^{3}}{a c x - c}\,{d x}"," ",0,"-1/80*(log(-a*x + 1)^5 + 5*(log(-a*x + 1)^4 - 4*log(-a*x + 1)^3 + 12*log(-a*x + 1)^2 - 24*log(-a*x + 1) + 24)*(a*x - 1))/(a^2*c) + 1/16*integrate(-(x*log(a*x + 1)^4 - 4*x*log(a*x + 1)^3*log(-a*x + 1) + 6*x*log(a*x + 1)^2*log(-a*x + 1)^2 - 4*x*log(a*x + 1)*log(-a*x + 1)^3)/(a*c*x - c), x)","F",0
136,0,0,0,0.000000," ","integrate(arctanh(a*x)^4/(-a*c*x+c),x, algorithm=""maxima"")","-\frac{\log\left(-a x + 1\right)^{5}}{80 \, a c} + \frac{1}{16} \, \int -\frac{\log\left(a x + 1\right)^{4} - 4 \, \log\left(a x + 1\right)^{3} \log\left(-a x + 1\right) + 6 \, \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)^{2} - 4 \, \log\left(a x + 1\right) \log\left(-a x + 1\right)^{3}}{a c x - c}\,{d x}"," ",0,"-1/80*log(-a*x + 1)^5/(a*c) + 1/16*integrate(-(log(a*x + 1)^4 - 4*log(a*x + 1)^3*log(-a*x + 1) + 6*log(a*x + 1)^2*log(-a*x + 1)^2 - 4*log(a*x + 1)*log(-a*x + 1)^3)/(a*c*x - c), x)","F",0
137,0,0,0,0.000000," ","integrate(arctanh(a*x)^4/x/(-a*c*x+c),x, algorithm=""maxima"")","-\frac{\log\left(-a x + 1\right)^{5}}{80 \, c} + \frac{1}{16} \, \int -\frac{\log\left(a x + 1\right)^{4} - 4 \, \log\left(a x + 1\right)^{3} \log\left(-a x + 1\right) + 6 \, \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)^{2} - 4 \, \log\left(a x + 1\right) \log\left(-a x + 1\right)^{3}}{a c x^{2} - c x}\,{d x}"," ",0,"-1/80*log(-a*x + 1)^5/c + 1/16*integrate(-(log(a*x + 1)^4 - 4*log(a*x + 1)^3*log(-a*x + 1) + 6*log(a*x + 1)^2*log(-a*x + 1)^2 - 4*log(a*x + 1)*log(-a*x + 1)^3)/(a*c*x^2 - c*x), x)","F",0
138,0,0,0,0.000000," ","integrate(arctanh(a*x)^4/(-a*c*x^2+c*x),x, algorithm=""maxima"")","-\frac{\log\left(-a x + 1\right)^{5}}{80 \, c} + \frac{1}{16} \, \int -\frac{\log\left(a x + 1\right)^{4} - 4 \, \log\left(a x + 1\right)^{3} \log\left(-a x + 1\right) + 6 \, \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)^{2} - 4 \, \log\left(a x + 1\right) \log\left(-a x + 1\right)^{3}}{a c x^{2} - c x}\,{d x}"," ",0,"-1/80*log(-a*x + 1)^5/c + 1/16*integrate(-(log(a*x + 1)^4 - 4*log(a*x + 1)^3*log(-a*x + 1) + 6*log(a*x + 1)^2*log(-a*x + 1)^2 - 4*log(a*x + 1)*log(-a*x + 1)^3)/(a*c*x^2 - c*x), x)","F",0
139,0,0,0,0.000000," ","integrate(arctanh(a*x)^4/x^2/(-a*c*x+c),x, algorithm=""maxima"")","-\frac{a x \log\left(-a x + 1\right)^{5} + 5 \, \log\left(-a x + 1\right)^{4}}{80 \, c x} + \frac{1}{16} \, \int -\frac{\log\left(a x + 1\right)^{4} - 4 \, \log\left(a x + 1\right)^{3} \log\left(-a x + 1\right) + 6 \, \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)^{2} - 4 \, {\left(a x + \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{3}}{a c x^{3} - c x^{2}}\,{d x}"," ",0,"-1/80*(a*x*log(-a*x + 1)^5 + 5*log(-a*x + 1)^4)/(c*x) + 1/16*integrate(-(log(a*x + 1)^4 - 4*log(a*x + 1)^3*log(-a*x + 1) + 6*log(a*x + 1)^2*log(-a*x + 1)^2 - 4*(a*x + log(a*x + 1))*log(-a*x + 1)^3)/(a*c*x^3 - c*x^2), x)","F",0
140,0,0,0,0.000000," ","integrate(arctanh(a*x)^4/x^3/(-a*c*x+c),x, algorithm=""maxima"")","-\frac{2 \, a^{2} x^{2} \log\left(-a x + 1\right)^{5} + 5 \, {\left(2 \, a x + 1\right)} \log\left(-a x + 1\right)^{4}}{160 \, c x^{2}} + \frac{1}{16} \, \int -\frac{\log\left(a x + 1\right)^{4} - 4 \, \log\left(a x + 1\right)^{3} \log\left(-a x + 1\right) + 6 \, \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)^{2} - 2 \, {\left(2 \, a^{2} x^{2} + a x + 2 \, \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{3}}{a c x^{4} - c x^{3}}\,{d x}"," ",0,"-1/160*(2*a^2*x^2*log(-a*x + 1)^5 + 5*(2*a*x + 1)*log(-a*x + 1)^4)/(c*x^2) + 1/16*integrate(-(log(a*x + 1)^4 - 4*log(a*x + 1)^3*log(-a*x + 1) + 6*log(a*x + 1)^2*log(-a*x + 1)^2 - 2*(2*a^2*x^2 + a*x + 2*log(a*x + 1))*log(-a*x + 1)^3)/(a*c*x^4 - c*x^3), x)","F",0
141,0,0,0,0.000000," ","integrate(x/(a*c*x+c)/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x}{{\left(a c x + c\right)} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x/((a*c*x + c)*arctanh(a*x)), x)","F",0
142,0,0,0,0.000000," ","integrate(1/(a*c*x+c)/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a c x + c\right)} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a*c*x + c)*arctanh(a*x)), x)","F",0
143,0,0,0,0.000000," ","integrate(1/x/(a*c*x+c)/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a c x + c\right)} x \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a*c*x + c)*x*arctanh(a*x)), x)","F",0
144,0,0,0,0.000000," ","integrate(x/(a*c*x+c)/arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a x^{2} - x\right)}}{a c \log\left(a x + 1\right) - a c \log\left(-a x + 1\right)} + \int -\frac{2 \, {\left(2 \, a x - 1\right)}}{a c \log\left(a x + 1\right) - a c \log\left(-a x + 1\right)}\,{d x}"," ",0,"2*(a*x^2 - x)/(a*c*log(a*x + 1) - a*c*log(-a*x + 1)) + integrate(-2*(2*a*x - 1)/(a*c*log(a*x + 1) - a*c*log(-a*x + 1)), x)","F",0
145,0,0,0,0.000000," ","integrate(1/(a*c*x+c)/arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a x - 1\right)}}{a c \log\left(a x + 1\right) - a c \log\left(-a x + 1\right)} + 2 \, \int -\frac{1}{c \log\left(a x + 1\right) - c \log\left(-a x + 1\right)}\,{d x}"," ",0,"2*(a*x - 1)/(a*c*log(a*x + 1) - a*c*log(-a*x + 1)) + 2*integrate(-1/(c*log(a*x + 1) - c*log(-a*x + 1)), x)","F",0
146,0,0,0,0.000000," ","integrate(1/x/(a*c*x+c)/arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a x - 1\right)}}{a c x \log\left(a x + 1\right) - a c x \log\left(-a x + 1\right)} + 2 \, \int -\frac{1}{a c x^{2} \log\left(a x + 1\right) - a c x^{2} \log\left(-a x + 1\right)}\,{d x}"," ",0,"2*(a*x - 1)/(a*c*x*log(a*x + 1) - a*c*x*log(-a*x + 1)) + 2*integrate(-1/(a*c*x^2*log(a*x + 1) - a*c*x^2*log(-a*x + 1)), x)","F",0
147,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x))/(e*x+d),x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{6 \, d^{3} \log\left(e x + d\right)}{e^{4}} - \frac{2 \, e^{2} x^{3} - 3 \, d e x^{2} + 6 \, d^{2} x}{e^{3}}\right)} + \frac{1}{2} \, b \int \frac{x^{3} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{e x + d}\,{d x}"," ",0,"-1/6*a*(6*d^3*log(e*x + d)/e^4 - (2*e^2*x^3 - 3*d*e*x^2 + 6*d^2*x)/e^3) + 1/2*b*integrate(x^3*(log(c*x + 1) - log(-c*x + 1))/(e*x + d), x)","F",0
148,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))/(e*x+d),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{2 \, d^{2} \log\left(e x + d\right)}{e^{3}} + \frac{e x^{2} - 2 \, d x}{e^{2}}\right)} + \frac{1}{2} \, b \int \frac{x^{2} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{e x + d}\,{d x}"," ",0,"1/2*a*(2*d^2*log(e*x + d)/e^3 + (e*x^2 - 2*d*x)/e^2) + 1/2*b*integrate(x^2*(log(c*x + 1) - log(-c*x + 1))/(e*x + d), x)","F",0
149,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))/(e*x+d),x, algorithm=""maxima"")","a {\left(\frac{x}{e} - \frac{d \log\left(e x + d\right)}{e^{2}}\right)} + \frac{1}{2} \, b \int \frac{x {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{e x + d}\,{d x}"," ",0,"a*(x/e - d*log(e*x + d)/e^2) + 1/2*b*integrate(x*(log(c*x + 1) - log(-c*x + 1))/(e*x + d), x)","F",0
150,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/(e*x+d),x, algorithm=""maxima"")","\frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{e x + d}\,{d x} + \frac{a \log\left(e x + d\right)}{e}"," ",0,"1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(e*x + d), x) + a*log(e*x + d)/e","F",0
151,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x/(e*x+d),x, algorithm=""maxima"")","-a {\left(\frac{\log\left(e x + d\right)}{d} - \frac{\log\left(x\right)}{d}\right)} + \frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{e x^{2} + d x}\,{d x}"," ",0,"-a*(log(e*x + d)/d - log(x)/d) + 1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(e*x^2 + d*x), x)","F",0
152,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x^2/(e*x+d),x, algorithm=""maxima"")","a {\left(\frac{e \log\left(e x + d\right)}{d^{2}} - \frac{e \log\left(x\right)}{d^{2}} - \frac{1}{d x}\right)} + \frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{e x^{3} + d x^{2}}\,{d x}"," ",0,"a*(e*log(e*x + d)/d^2 - e*log(x)/d^2 - 1/(d*x)) + 1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(e*x^3 + d*x^2), x)","F",0
153,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x^3/(e*x+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, e^{2} \log\left(e x + d\right)}{d^{3}} - \frac{2 \, e^{2} \log\left(x\right)}{d^{3}} - \frac{2 \, e x - d}{d^{2} x^{2}}\right)} + \frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{e x^{4} + d x^{3}}\,{d x}"," ",0,"-1/2*a*(2*e^2*log(e*x + d)/d^3 - 2*e^2*log(x)/d^3 - (2*e*x - d)/(d^2*x^2)) + 1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(e*x^4 + d*x^3), x)","F",0
154,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))^2/(e*x+d),x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{2 \, d^{2} \log\left(e x + d\right)}{e^{3}} + \frac{e x^{2} - 2 \, d x}{e^{2}}\right)} + \frac{{\left(b^{2} e x^{2} - 2 \, b^{2} d x\right)} \log\left(-c x + 1\right)^{2}}{8 \, e^{2}} - \int -\frac{{\left(b^{2} c e^{2} x^{3} - b^{2} e^{2} x^{2}\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c e^{2} x^{3} - a b e^{2} x^{2}\right)} \log\left(c x + 1\right) + {\left(2 \, b^{2} c d^{2} x - {\left(4 \, a b c e^{2} + b^{2} c e^{2}\right)} x^{3} + {\left(b^{2} c d e + 4 \, a b e^{2}\right)} x^{2} - 2 \, {\left(b^{2} c e^{2} x^{3} - b^{2} e^{2} x^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c e^{3} x^{2} - d e^{2} + {\left(c d e^{2} - e^{3}\right)} x\right)}}\,{d x}"," ",0,"1/2*a^2*(2*d^2*log(e*x + d)/e^3 + (e*x^2 - 2*d*x)/e^2) + 1/8*(b^2*e*x^2 - 2*b^2*d*x)*log(-c*x + 1)^2/e^2 - integrate(-1/4*((b^2*c*e^2*x^3 - b^2*e^2*x^2)*log(c*x + 1)^2 + 4*(a*b*c*e^2*x^3 - a*b*e^2*x^2)*log(c*x + 1) + (2*b^2*c*d^2*x - (4*a*b*c*e^2 + b^2*c*e^2)*x^3 + (b^2*c*d*e + 4*a*b*e^2)*x^2 - 2*(b^2*c*e^2*x^3 - b^2*e^2*x^2)*log(c*x + 1))*log(-c*x + 1))/(c*e^3*x^2 - d*e^2 + (c*d*e^2 - e^3)*x), x)","F",0
155,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))^2/(e*x+d),x, algorithm=""maxima"")","\frac{b^{2} x \log\left(-c x + 1\right)^{2}}{4 \, e} + a^{2} {\left(\frac{x}{e} - \frac{d \log\left(e x + d\right)}{e^{2}}\right)} - \int -\frac{{\left(b^{2} c e x^{2} - b^{2} e x\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c e x^{2} - a b e x\right)} \log\left(c x + 1\right) - 2 \, {\left({\left(2 \, a b c e + b^{2} c e\right)} x^{2} + {\left(b^{2} c d - 2 \, a b e\right)} x + {\left(b^{2} c e x^{2} - b^{2} e x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c e^{2} x^{2} - d e + {\left(c d e - e^{2}\right)} x\right)}}\,{d x}"," ",0,"1/4*b^2*x*log(-c*x + 1)^2/e + a^2*(x/e - d*log(e*x + d)/e^2) - integrate(-1/4*((b^2*c*e*x^2 - b^2*e*x)*log(c*x + 1)^2 + 4*(a*b*c*e*x^2 - a*b*e*x)*log(c*x + 1) - 2*((2*a*b*c*e + b^2*c*e)*x^2 + (b^2*c*d - 2*a*b*e)*x + (b^2*c*e*x^2 - b^2*e*x)*log(c*x + 1))*log(-c*x + 1))/(c*e^2*x^2 - d*e + (c*d*e - e^2)*x), x)","F",0
156,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/(e*x+d),x, algorithm=""maxima"")","\frac{a^{2} \log\left(e x + d\right)}{e} + \int \frac{b^{2} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}^{2}}{4 \, {\left(e x + d\right)}} + \frac{a b {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{e x + d}\,{d x}"," ",0,"a^2*log(e*x + d)/e + integrate(1/4*b^2*(log(c*x + 1) - log(-c*x + 1))^2/(e*x + d) + a*b*(log(c*x + 1) - log(-c*x + 1))/(e*x + d), x)","F",0
157,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x/(e*x+d),x, algorithm=""maxima"")","-a^{2} {\left(\frac{\log\left(e x + d\right)}{d} - \frac{\log\left(x\right)}{d}\right)} + \int \frac{b^{2} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}^{2}}{4 \, {\left(e x^{2} + d x\right)}} + \frac{a b {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{e x^{2} + d x}\,{d x}"," ",0,"-a^2*(log(e*x + d)/d - log(x)/d) + integrate(1/4*b^2*(log(c*x + 1) - log(-c*x + 1))^2/(e*x^2 + d*x) + a*b*(log(c*x + 1) - log(-c*x + 1))/(e*x^2 + d*x), x)","F",0
158,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x^2/(e*x+d),x, algorithm=""maxima"")","a^{2} {\left(\frac{e \log\left(e x + d\right)}{d^{2}} - \frac{e \log\left(x\right)}{d^{2}} - \frac{1}{d x}\right)} - \frac{b^{2} \log\left(-c x + 1\right)^{2}}{4 \, d x} - \int -\frac{{\left(b^{2} c d x - b^{2} d\right)} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c d x - a b d\right)} \log\left(c x + 1\right) + 2 \, {\left(b^{2} c e x^{2} + 2 \, a b d - {\left(2 \, a b c d - b^{2} c d\right)} x - {\left(b^{2} c d x - b^{2} d\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c d e x^{4} - d^{2} x^{2} + {\left(c d^{2} - d e\right)} x^{3}\right)}}\,{d x}"," ",0,"a^2*(e*log(e*x + d)/d^2 - e*log(x)/d^2 - 1/(d*x)) - 1/4*b^2*log(-c*x + 1)^2/(d*x) - integrate(-1/4*((b^2*c*d*x - b^2*d)*log(c*x + 1)^2 + 4*(a*b*c*d*x - a*b*d)*log(c*x + 1) + 2*(b^2*c*e*x^2 + 2*a*b*d - (2*a*b*c*d - b^2*c*d)*x - (b^2*c*d*x - b^2*d)*log(c*x + 1))*log(-c*x + 1))/(c*d*e*x^4 - d^2*x^2 + (c*d^2 - d*e)*x^3), x)","F",0
159,0,0,0,0.000000," ","integrate(arctanh(c*x)^2/x/(e*x+d),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(c x\right)^{2}}{{\left(e x + d\right)} x}\,{d x}"," ",0,"integrate(arctanh(c*x)^2/((e*x + d)*x), x)","F",0
160,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*arctan(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x + d\right)} {\left(b \arctan\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x + d)*(b*arctan(c*x) + a)), x)","F",0
161,1,73,0,0.305963," ","integrate(x^4*(-a^2*x^2+1)*arctanh(a*x),x, algorithm=""maxima"")","-\frac{1}{210} \, a {\left(\frac{5 \, a^{4} x^{6} - 3 \, a^{2} x^{4} - 6 \, x^{2}}{a^{4}} - \frac{6 \, \log\left(a x + 1\right)}{a^{6}} - \frac{6 \, \log\left(a x - 1\right)}{a^{6}}\right)} - \frac{1}{35} \, {\left(5 \, a^{2} x^{7} - 7 \, x^{5}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/210*a*((5*a^4*x^6 - 3*a^2*x^4 - 6*x^2)/a^4 - 6*log(a*x + 1)/a^6 - 6*log(a*x - 1)/a^6) - 1/35*(5*a^2*x^7 - 7*x^5)*arctanh(a*x)","A",0
162,1,72,0,0.305588," ","integrate(x^3*(-a^2*x^2+1)*arctanh(a*x),x, algorithm=""maxima"")","-\frac{1}{360} \, a {\left(\frac{2 \, {\left(6 \, a^{4} x^{5} - 5 \, a^{2} x^{3} - 15 \, x\right)}}{a^{4}} + \frac{15 \, \log\left(a x + 1\right)}{a^{5}} - \frac{15 \, \log\left(a x - 1\right)}{a^{5}}\right)} - \frac{1}{12} \, {\left(2 \, a^{2} x^{6} - 3 \, x^{4}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/360*a*(2*(6*a^4*x^5 - 5*a^2*x^3 - 15*x)/a^4 + 15*log(a*x + 1)/a^5 - 15*log(a*x - 1)/a^5) - 1/12*(2*a^2*x^6 - 3*x^4)*arctanh(a*x)","A",0
163,1,65,0,0.305181," ","integrate(x^2*(-a^2*x^2+1)*arctanh(a*x),x, algorithm=""maxima"")","-\frac{1}{60} \, a {\left(\frac{3 \, a^{2} x^{4} - 4 \, x^{2}}{a^{2}} - \frac{4 \, \log\left(a x + 1\right)}{a^{4}} - \frac{4 \, \log\left(a x - 1\right)}{a^{4}}\right)} - \frac{1}{15} \, {\left(3 \, a^{2} x^{5} - 5 \, x^{3}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/60*a*((3*a^2*x^4 - 4*x^2)/a^2 - 4*log(a*x + 1)/a^4 - 4*log(a*x - 1)/a^4) - 1/15*(3*a^2*x^5 - 5*x^3)*arctanh(a*x)","A",0
164,1,37,0,0.303223," ","integrate(x*(-a^2*x^2+1)*arctanh(a*x),x, algorithm=""maxima"")","-\frac{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)}{4 \, a^{2}} - \frac{a^{2} x^{3} - 3 \, x}{12 \, a}"," ",0,"-1/4*(a^2*x^2 - 1)^2*arctanh(a*x)/a^2 - 1/12*(a^2*x^3 - 3*x)/a","A",0
165,1,47,0,0.307145," ","integrate((-a^2*x^2+1)*arctanh(a*x),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(x^{2} - \frac{2 \, \log\left(a x + 1\right)}{a^{2}} - \frac{2 \, \log\left(a x - 1\right)}{a^{2}}\right)} a - \frac{1}{3} \, {\left(a^{2} x^{3} - 3 \, x\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/6*(x^2 - 2*log(a*x + 1)/a^2 - 2*log(a*x - 1)/a^2)*a - 1/3*(a^2*x^3 - 3*x)*arctanh(a*x)","A",0
166,1,89,0,0.309660," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(2 \, x + \frac{2 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)}}{a} - \frac{2 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)}}{a} - \frac{\log\left(a x + 1\right)}{a} + \frac{\log\left(a x - 1\right)}{a}\right)} - \frac{1}{2} \, {\left(a^{2} x^{2} - \log\left(x^{2}\right)\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/4*a*(2*x + 2*(log(a*x + 1)*log(x) + dilog(-a*x))/a - 2*(log(-a*x + 1)*log(x) + dilog(a*x))/a - log(a*x + 1)/a + log(a*x - 1)/a) - 1/2*(a^2*x^2 - log(x^2))*arctanh(a*x)","B",0
167,1,36,0,0.307855," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^2,x, algorithm=""maxima"")","-a {\left(\log\left(a x + 1\right) + \log\left(a x - 1\right) - \log\left(x\right)\right)} - {\left(a^{2} x + \frac{1}{x}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-a*(log(a*x + 1) + log(a*x - 1) - log(x)) - (a^2*x + 1/x)*arctanh(a*x)","A",0
168,1,81,0,0.315969," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(2 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)} a - 2 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)} a + a \log\left(a x + 1\right) - a \log\left(a x - 1\right) - \frac{2}{x}\right)} a - \frac{1}{2} \, {\left(a^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/4*(2*(log(a*x + 1)*log(x) + dilog(-a*x))*a - 2*(log(-a*x + 1)*log(x) + dilog(a*x))*a + a*log(a*x + 1) - a*log(a*x - 1) - 2/x)*a - 1/2*(a^2*log(x^2) + 1/x^2)*arctanh(a*x)","A",0
169,1,53,0,0.306736," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(2 \, a^{2} \log\left(a^{2} x^{2} - 1\right) - 2 \, a^{2} \log\left(x^{2}\right) - \frac{1}{x^{2}}\right)} a + \frac{{\left(3 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)}{3 \, x^{3}}"," ",0,"1/6*(2*a^2*log(a^2*x^2 - 1) - 2*a^2*log(x^2) - 1/x^2)*a + 1/3*(3*a^2*x^2 - 1)*arctanh(a*x)/x^3","A",0
170,1,61,0,0.302453," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^5,x, algorithm=""maxima"")","-\frac{1}{24} \, {\left(3 \, a^{3} \log\left(a x + 1\right) - 3 \, a^{3} \log\left(a x - 1\right) - \frac{2 \, {\left(3 \, a^{2} x^{2} - 1\right)}}{x^{3}}\right)} a + \frac{{\left(2 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)}{4 \, x^{4}}"," ",0,"-1/24*(3*a^3*log(a*x + 1) - 3*a^3*log(a*x - 1) - 2*(3*a^2*x^2 - 1)/x^3)*a + 1/4*(2*a^2*x^2 - 1)*arctanh(a*x)/x^4","A",0
171,1,62,0,0.315102," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^6,x, algorithm=""maxima"")","\frac{1}{60} \, {\left(4 \, a^{4} \log\left(a^{2} x^{2} - 1\right) - 4 \, a^{4} \log\left(x^{2}\right) + \frac{4 \, a^{2} x^{2} - 3}{x^{4}}\right)} a + \frac{{\left(5 \, a^{2} x^{2} - 3\right)} \operatorname{artanh}\left(a x\right)}{15 \, x^{5}}"," ",0,"1/60*(4*a^4*log(a^2*x^2 - 1) - 4*a^4*log(x^2) + (4*a^2*x^2 - 3)/x^4)*a + 1/15*(5*a^2*x^2 - 3)*arctanh(a*x)/x^5","A",0
172,1,190,0,0.319921," ","integrate(x^4*(-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{1}{630} \, a^{2} {\left(\frac{6 \, a^{5} x^{5} + 4 \, a^{3} x^{3} - 24 \, a x + 9 \, \log\left(a x + 1\right)^{2} - 18 \, \log\left(a x + 1\right) \log\left(a x - 1\right) - 9 \, \log\left(a x - 1\right)^{2} - 12 \, \log\left(a x - 1\right)}{a^{7}} + \frac{36 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a^{7}} + \frac{12 \, \log\left(a x + 1\right)}{a^{7}}\right)} - \frac{1}{105} \, a {\left(\frac{5 \, a^{4} x^{6} - 3 \, a^{2} x^{4} - 6 \, x^{2}}{a^{4}} - \frac{6 \, \log\left(a x + 1\right)}{a^{6}} - \frac{6 \, \log\left(a x - 1\right)}{a^{6}}\right)} \operatorname{artanh}\left(a x\right) - \frac{1}{35} \, {\left(5 \, a^{2} x^{7} - 7 \, x^{5}\right)} \operatorname{artanh}\left(a x\right)^{2}"," ",0,"-1/630*a^2*((6*a^5*x^5 + 4*a^3*x^3 - 24*a*x + 9*log(a*x + 1)^2 - 18*log(a*x + 1)*log(a*x - 1) - 9*log(a*x - 1)^2 - 12*log(a*x - 1))/a^7 + 36*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a^7 + 12*log(a*x + 1)/a^7) - 1/105*a*((5*a^4*x^6 - 3*a^2*x^4 - 6*x^2)/a^4 - 6*log(a*x + 1)/a^6 - 6*log(a*x - 1)/a^6)*arctanh(a*x) - 1/35*(5*a^2*x^7 - 7*x^5)*arctanh(a*x)^2","A",0
173,1,146,0,0.330422," ","integrate(x^3*(-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{1}{180} \, a {\left(\frac{2 \, {\left(6 \, a^{4} x^{5} - 5 \, a^{2} x^{3} - 15 \, x\right)}}{a^{4}} + \frac{15 \, \log\left(a x + 1\right)}{a^{5}} - \frac{15 \, \log\left(a x - 1\right)}{a^{5}}\right)} \operatorname{artanh}\left(a x\right) - \frac{1}{12} \, {\left(2 \, a^{2} x^{6} - 3 \, x^{4}\right)} \operatorname{artanh}\left(a x\right)^{2} - \frac{12 \, a^{4} x^{4} + 4 \, a^{2} x^{2} + 2 \, {\left(15 \, \log\left(a x - 1\right) - 28\right)} \log\left(a x + 1\right) - 15 \, \log\left(a x + 1\right)^{2} - 15 \, \log\left(a x - 1\right)^{2} - 56 \, \log\left(a x - 1\right)}{720 \, a^{4}}"," ",0,"-1/180*a*(2*(6*a^4*x^5 - 5*a^2*x^3 - 15*x)/a^4 + 15*log(a*x + 1)/a^5 - 15*log(a*x - 1)/a^5)*arctanh(a*x) - 1/12*(2*a^2*x^6 - 3*x^4)*arctanh(a*x)^2 - 1/720*(12*a^4*x^4 + 4*a^2*x^2 + 2*(15*log(a*x - 1) - 28)*log(a*x + 1) - 15*log(a*x + 1)^2 - 15*log(a*x - 1)^2 - 56*log(a*x - 1))/a^4","A",0
174,1,173,0,0.319571," ","integrate(x^2*(-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{1}{60} \, a^{2} {\left(\frac{2 \, a^{3} x^{3} - 2 \, a x + 2 \, \log\left(a x + 1\right)^{2} - 4 \, \log\left(a x + 1\right) \log\left(a x - 1\right) - 2 \, \log\left(a x - 1\right)^{2} - \log\left(a x - 1\right)}{a^{5}} + \frac{8 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a^{5}} + \frac{\log\left(a x + 1\right)}{a^{5}}\right)} - \frac{1}{30} \, a {\left(\frac{3 \, a^{2} x^{4} - 4 \, x^{2}}{a^{2}} - \frac{4 \, \log\left(a x + 1\right)}{a^{4}} - \frac{4 \, \log\left(a x - 1\right)}{a^{4}}\right)} \operatorname{artanh}\left(a x\right) - \frac{1}{15} \, {\left(3 \, a^{2} x^{5} - 5 \, x^{3}\right)} \operatorname{artanh}\left(a x\right)^{2}"," ",0,"-1/60*a^2*((2*a^3*x^3 - 2*a*x + 2*log(a*x + 1)^2 - 4*log(a*x + 1)*log(a*x - 1) - 2*log(a*x - 1)^2 - log(a*x - 1))/a^5 + 8*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a^5 + log(a*x + 1)/a^5) - 1/30*a*((3*a^2*x^4 - 4*x^2)/a^2 - 4*log(a*x + 1)/a^4 - 4*log(a*x - 1)/a^4)*arctanh(a*x) - 1/15*(3*a^2*x^5 - 5*x^3)*arctanh(a*x)^2","A",0
175,1,74,0,0.308485," ","integrate(x*(-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{2}}{4 \, a^{2}} - \frac{{\left(x^{2} - \frac{2 \, \log\left(a x + 1\right)}{a^{2}} - \frac{2 \, \log\left(a x - 1\right)}{a^{2}}\right)} a + 2 \, {\left(a^{2} x^{3} - 3 \, x\right)} \operatorname{artanh}\left(a x\right)}{12 \, a}"," ",0,"-1/4*(a^2*x^2 - 1)^2*arctanh(a*x)^2/a^2 - 1/12*((x^2 - 2*log(a*x + 1)/a^2 - 2*log(a*x - 1)/a^2)*a + 2*(a^2*x^3 - 3*x)*arctanh(a*x))/a","A",0
176,1,144,0,0.329897," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{1}{6} \, a^{2} {\left(\frac{2 \, a x + \log\left(a x + 1\right)^{2} - 2 \, \log\left(a x + 1\right) \log\left(a x - 1\right) - \log\left(a x - 1\right)^{2} + \log\left(a x - 1\right)}{a^{3}} + \frac{4 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a^{3}} - \frac{\log\left(a x + 1\right)}{a^{3}}\right)} - \frac{1}{3} \, {\left(x^{2} - \frac{2 \, \log\left(a x + 1\right)}{a^{2}} - \frac{2 \, \log\left(a x - 1\right)}{a^{2}}\right)} a \operatorname{artanh}\left(a x\right) - \frac{1}{3} \, {\left(a^{2} x^{3} - 3 \, x\right)} \operatorname{artanh}\left(a x\right)^{2}"," ",0,"-1/6*a^2*((2*a*x + log(a*x + 1)^2 - 2*log(a*x + 1)*log(a*x - 1) - log(a*x - 1)^2 + log(a*x - 1))/a^3 + 4*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a^3 - log(a*x + 1)/a^3) - 1/3*(x^2 - 2*log(a*x + 1)/a^2 - 2*log(a*x - 1)/a^2)*a*arctanh(a*x) - 1/3*(a^2*x^3 - 3*x)*arctanh(a*x)^2","A",0
177,0,0,0,0.000000," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x,x, algorithm=""maxima"")","-\frac{1}{8} \, a^{2} x^{2} \log\left(-a x + 1\right)^{2} + \frac{1}{4} \, \int -\frac{{\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(a x + 1\right)^{2} - {\left(a^{3} x^{3} + 2 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)}{a x^{2} - x}\,{d x}"," ",0,"-1/8*a^2*x^2*log(-a*x + 1)^2 + 1/4*integrate(-((a^3*x^3 - a^2*x^2 - a*x + 1)*log(a*x + 1)^2 - (a^3*x^3 + 2*(a^3*x^3 - a^2*x^2 - a*x + 1)*log(a*x + 1))*log(-a*x + 1))/(a*x^2 - x), x)","F",0
178,1,152,0,0.323695," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{\log\left(a x + 1\right)^{2} - 2 \, \log\left(a x + 1\right) \log\left(a x - 1\right) - \log\left(a x - 1\right)^{2}}{a} + \frac{4 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a} - \frac{2 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)}}{a} + \frac{2 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)}}{a}\right)} - 2 \, a {\left(\log\left(a x + 1\right) + \log\left(a x - 1\right) - \log\left(x\right)\right)} \operatorname{artanh}\left(a x\right) - {\left(a^{2} x + \frac{1}{x}\right)} \operatorname{artanh}\left(a x\right)^{2}"," ",0,"1/2*a^2*((log(a*x + 1)^2 - 2*log(a*x + 1)*log(a*x - 1) - log(a*x - 1)^2)/a + 4*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a - 2*(log(a*x + 1)*log(x) + dilog(-a*x))/a + 2*(log(-a*x + 1)*log(x) + dilog(a*x))/a) - 2*a*(log(a*x + 1) + log(a*x - 1) - log(x))*arctanh(a*x) - (a^2*x + 1/x)*arctanh(a*x)^2","A",0
179,0,0,0,0.000000," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^3,x, algorithm=""maxima"")","-\frac{\log\left(-a x + 1\right)^{2}}{8 \, x^{2}} + \frac{1}{4} \, \int -\frac{{\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(a x + 1\right)^{2} - {\left(a x + 2 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)}{a x^{4} - x^{3}}\,{d x}"," ",0,"-1/8*log(-a*x + 1)^2/x^2 + 1/4*integrate(-((a^3*x^3 - a^2*x^2 - a*x + 1)*log(a*x + 1)^2 - (a*x + 2*(a^3*x^3 - a^2*x^2 - a*x + 1)*log(a*x + 1))*log(-a*x + 1))/(a*x^4 - x^3), x)","F",0
180,1,188,0,0.330450," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(4 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)} a - 4 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)} a + 4 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)} a - a \log\left(a x + 1\right) + a \log\left(a x - 1\right) + \frac{a x \log\left(a x + 1\right)^{2} - 2 \, a x \log\left(a x + 1\right) \log\left(a x - 1\right) - a x \log\left(a x - 1\right)^{2} + 2}{x}\right)} a^{2} + \frac{1}{3} \, {\left(2 \, a^{2} \log\left(a^{2} x^{2} - 1\right) - 2 \, a^{2} \log\left(x^{2}\right) - \frac{1}{x^{2}}\right)} a \operatorname{artanh}\left(a x\right) + \frac{{\left(3 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{3 \, x^{3}}"," ",0,"-1/6*(4*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))*a - 4*(log(a*x + 1)*log(x) + dilog(-a*x))*a + 4*(log(-a*x + 1)*log(x) + dilog(a*x))*a - a*log(a*x + 1) + a*log(a*x - 1) + (a*x*log(a*x + 1)^2 - 2*a*x*log(a*x + 1)*log(a*x - 1) - a*x*log(a*x - 1)^2 + 2)/x)*a^2 + 1/3*(2*a^2*log(a^2*x^2 - 1) - 2*a^2*log(x^2) - 1/x^2)*a*arctanh(a*x) + 1/3*(3*a^2*x^2 - 1)*arctanh(a*x)^2/x^3","A",0
181,1,164,0,0.326486," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^5,x, algorithm=""maxima"")","-\frac{1}{48} \, {\left(16 \, a^{2} \log\left(x\right) - \frac{3 \, a^{2} x^{2} \log\left(a x + 1\right)^{2} + 3 \, a^{2} x^{2} \log\left(a x - 1\right)^{2} + 8 \, a^{2} x^{2} \log\left(a x - 1\right) - 2 \, {\left(3 \, a^{2} x^{2} \log\left(a x - 1\right) - 4 \, a^{2} x^{2}\right)} \log\left(a x + 1\right) - 4}{x^{2}}\right)} a^{2} - \frac{1}{12} \, {\left(3 \, a^{3} \log\left(a x + 1\right) - 3 \, a^{3} \log\left(a x - 1\right) - \frac{2 \, {\left(3 \, a^{2} x^{2} - 1\right)}}{x^{3}}\right)} a \operatorname{artanh}\left(a x\right) + \frac{{\left(2 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{4 \, x^{4}}"," ",0,"-1/48*(16*a^2*log(x) - (3*a^2*x^2*log(a*x + 1)^2 + 3*a^2*x^2*log(a*x - 1)^2 + 8*a^2*x^2*log(a*x - 1) - 2*(3*a^2*x^2*log(a*x - 1) - 4*a^2*x^2)*log(a*x + 1) - 4)/x^2)*a^2 - 1/12*(3*a^3*log(a*x + 1) - 3*a^3*log(a*x - 1) - 2*(3*a^2*x^2 - 1)/x^3)*a*arctanh(a*x) + 1/4*(2*a^2*x^2 - 1)*arctanh(a*x)^2/x^4","B",0
182,1,228,0,0.322482," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^6,x, algorithm=""maxima"")","-\frac{1}{60} \, {\left(8 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)} a^{3} - 8 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)} a^{3} + 8 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)} a^{3} + a^{3} \log\left(a x + 1\right) - a^{3} \log\left(a x - 1\right) + \frac{2 \, {\left(a^{3} x^{3} \log\left(a x + 1\right)^{2} - 2 \, a^{3} x^{3} \log\left(a x + 1\right) \log\left(a x - 1\right) - a^{3} x^{3} \log\left(a x - 1\right)^{2} - a^{2} x^{2} + 1\right)}}{x^{3}}\right)} a^{2} + \frac{1}{30} \, {\left(4 \, a^{4} \log\left(a^{2} x^{2} - 1\right) - 4 \, a^{4} \log\left(x^{2}\right) + \frac{4 \, a^{2} x^{2} - 3}{x^{4}}\right)} a \operatorname{artanh}\left(a x\right) + \frac{{\left(5 \, a^{2} x^{2} - 3\right)} \operatorname{artanh}\left(a x\right)^{2}}{15 \, x^{5}}"," ",0,"-1/60*(8*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))*a^3 - 8*(log(a*x + 1)*log(x) + dilog(-a*x))*a^3 + 8*(log(-a*x + 1)*log(x) + dilog(a*x))*a^3 + a^3*log(a*x + 1) - a^3*log(a*x - 1) + 2*(a^3*x^3*log(a*x + 1)^2 - 2*a^3*x^3*log(a*x + 1)*log(a*x - 1) - a^3*x^3*log(a*x - 1)^2 - a^2*x^2 + 1)/x^3)*a^2 + 1/30*(4*a^4*log(a^2*x^2 - 1) - 4*a^4*log(x^2) + (4*a^2*x^2 - 3)/x^4)*a*arctanh(a*x) + 1/15*(5*a^2*x^2 - 3)*arctanh(a*x)^2/x^5","A",0
183,0,0,0,0.000000," ","integrate((-a^2*x^2+1)*arctanh(a*x)^3,x, algorithm=""maxima"")","\frac{{\left(2 \, a^{3} x^{3} - 3 \, a^{2} x^{2} - 12 \, a x - 6 \, {\left(a^{3} x^{3} - 3 \, a x - 2\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{2}}{48 \, a} - \frac{{\left(\log\left(-a x + 1\right)^{3} - 3 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 6\right)} {\left(a x - 1\right)}}{8 \, a} + \frac{4 \, {\left(9 \, \log\left(-a x + 1\right)^{3} - 9 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 2\right)} {\left(a x - 1\right)}^{3} + 27 \, {\left(4 \, \log\left(-a x + 1\right)^{3} - 6 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 3\right)} {\left(a x - 1\right)}^{2} + 108 \, {\left(\log\left(-a x + 1\right)^{3} - 3 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 6\right)} {\left(a x - 1\right)}}{864 \, a} + \frac{1}{8} \, \int -\frac{3 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(a x + 1\right)^{3} + {\left(2 \, a^{3} x^{3} - 3 \, a^{2} x^{2} - 9 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(a x + 1\right)^{2} - 12 \, a x - 6 \, {\left(a^{3} x^{3} - 3 \, a x - 2\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)}{3 \, {\left(a x - 1\right)}}\,{d x}"," ",0,"1/48*(2*a^3*x^3 - 3*a^2*x^2 - 12*a*x - 6*(a^3*x^3 - 3*a*x - 2)*log(a*x + 1))*log(-a*x + 1)^2/a - 1/8*(log(-a*x + 1)^3 - 3*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 6)*(a*x - 1)/a + 1/864*(4*(9*log(-a*x + 1)^3 - 9*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 2)*(a*x - 1)^3 + 27*(4*log(-a*x + 1)^3 - 6*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 3)*(a*x - 1)^2 + 108*(log(-a*x + 1)^3 - 3*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 6)*(a*x - 1))/a + 1/8*integrate(-1/3*(3*(a^3*x^3 - a^2*x^2 - a*x + 1)*log(a*x + 1)^3 + (2*a^3*x^3 - 3*a^2*x^2 - 9*(a^3*x^3 - a^2*x^2 - a*x + 1)*log(a*x + 1)^2 - 12*a*x - 6*(a^3*x^3 - 3*a*x - 2)*log(a*x + 1))*log(-a*x + 1))/(a*x - 1), x)","F",0
184,1,277,0,0.431751," ","integrate(x*arctanh(1/2*x*2^(1/2))/(-x^2+1),x, algorithm=""maxima"")","-\frac{1}{2} \, \operatorname{artanh}\left(\frac{1}{2} \, \sqrt{2} x\right) \log\left(x^{2} - 1\right) - \frac{1}{4} \, \log\left(x^{2} - 1\right) \log\left(\frac{x - \sqrt{2}}{x + \sqrt{2}}\right) + \frac{1}{8} \, \sqrt{2} {\left(\sqrt{2} \log\left(x^{2} - 1\right) \log\left(\frac{x - \sqrt{2}}{x + \sqrt{2}}\right) + \sqrt{2} {\left({\left(\log\left(2 \, x + 2 \, \sqrt{2}\right) - \log\left(2 \, x - 2 \, \sqrt{2}\right)\right)} \log\left(x^{2} - 1\right) - \log\left(x + \sqrt{2}\right) \log\left(-\frac{x + \sqrt{2}}{\sqrt{2} + 1} + 1\right) + \log\left(x - \sqrt{2}\right) \log\left(\frac{x - \sqrt{2}}{\sqrt{2} + 1} + 1\right) - \log\left(x + \sqrt{2}\right) \log\left(-\frac{x + \sqrt{2}}{\sqrt{2} - 1} + 1\right) + \log\left(x - \sqrt{2}\right) \log\left(\frac{x - \sqrt{2}}{\sqrt{2} - 1} + 1\right) - {\rm Li}_2\left(\frac{x + \sqrt{2}}{\sqrt{2} + 1}\right) + {\rm Li}_2\left(-\frac{x - \sqrt{2}}{\sqrt{2} + 1}\right) - {\rm Li}_2\left(\frac{x + \sqrt{2}}{\sqrt{2} - 1}\right) + {\rm Li}_2\left(-\frac{x - \sqrt{2}}{\sqrt{2} - 1}\right)\right)}\right)}"," ",0,"-1/2*arctanh(1/2*sqrt(2)*x)*log(x^2 - 1) - 1/4*log(x^2 - 1)*log((x - sqrt(2))/(x + sqrt(2))) + 1/8*sqrt(2)*(sqrt(2)*log(x^2 - 1)*log((x - sqrt(2))/(x + sqrt(2))) + sqrt(2)*((log(2*x + 2*sqrt(2)) - log(2*x - 2*sqrt(2)))*log(x^2 - 1) - log(x + sqrt(2))*log(-(x + sqrt(2))/(sqrt(2) + 1) + 1) + log(x - sqrt(2))*log((x - sqrt(2))/(sqrt(2) + 1) + 1) - log(x + sqrt(2))*log(-(x + sqrt(2))/(sqrt(2) - 1) + 1) + log(x - sqrt(2))*log((x - sqrt(2))/(sqrt(2) - 1) + 1) - dilog((x + sqrt(2))/(sqrt(2) + 1)) + dilog(-(x - sqrt(2))/(sqrt(2) + 1)) - dilog((x + sqrt(2))/(sqrt(2) - 1)) + dilog(-(x - sqrt(2))/(sqrt(2) - 1))))","A",0
185,0,0,0,0.000000," ","integrate(x*(-a^2*x^2+1)/arctanh(a*x),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} x}{\operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*x/arctanh(a*x), x)","F",0
186,0,0,0,0.000000," ","integrate((-a^2*x^2+1)/arctanh(a*x),x, algorithm=""maxima"")","-\int \frac{a^{2} x^{2} - 1}{\operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)/arctanh(a*x), x)","F",0
187,0,0,0,0.000000," ","integrate((-a^2*x^2+1)/x/arctanh(a*x),x, algorithm=""maxima"")","-\int \frac{a^{2} x^{2} - 1}{x \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)/(x*arctanh(a*x)), x)","F",0
188,0,0,0,0.000000," ","integrate(x*(-a^2*x^2+1)/arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{4} x^{5} - 2 \, a^{2} x^{3} + x\right)}}{a \log\left(a x + 1\right) - a \log\left(-a x + 1\right)} - \int -\frac{2 \, {\left(5 \, a^{4} x^{4} - 6 \, a^{2} x^{2} + 1\right)}}{a \log\left(a x + 1\right) - a \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2*(a^4*x^5 - 2*a^2*x^3 + x)/(a*log(a*x + 1) - a*log(-a*x + 1)) - integrate(-2*(5*a^4*x^4 - 6*a^2*x^2 + 1)/(a*log(a*x + 1) - a*log(-a*x + 1)), x)","F",0
189,0,0,0,0.000000," ","integrate((-a^2*x^2+1)/arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)}}{a \log\left(a x + 1\right) - a \log\left(-a x + 1\right)} - \int -\frac{8 \, {\left(a^{3} x^{3} - a x\right)}}{\log\left(a x + 1\right) - \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2*(a^4*x^4 - 2*a^2*x^2 + 1)/(a*log(a*x + 1) - a*log(-a*x + 1)) - integrate(-8*(a^3*x^3 - a*x)/(log(a*x + 1) - log(-a*x + 1)), x)","F",0
190,0,0,0,0.000000," ","integrate((-a^2*x^2+1)/x/arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)}}{a x \log\left(a x + 1\right) - a x \log\left(-a x + 1\right)} - \int -\frac{2 \, {\left(3 \, a^{4} x^{4} - 2 \, a^{2} x^{2} - 1\right)}}{a x^{2} \log\left(a x + 1\right) - a x^{2} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2*(a^4*x^4 - 2*a^2*x^2 + 1)/(a*x*log(a*x + 1) - a*x*log(-a*x + 1)) - integrate(-2*(3*a^4*x^4 - 2*a^2*x^2 - 1)/(a*x^2*log(a*x + 1) - a*x^2*log(-a*x + 1)), x)","F",0
191,0,0,0,0.000000," ","integrate((-a^2*x^2+1)/arctanh(a*x)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} - 2 \, {\left(a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right)} \log\left(a x + 1\right) + 2 \, {\left(a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right)} \log\left(-a x + 1\right) + 1\right)}}{a \log\left(a x + 1\right)^{2} - 2 \, a \log\left(a x + 1\right) \log\left(-a x + 1\right) + a \log\left(-a x + 1\right)^{2}} + \int -\frac{4 \, {\left(5 \, a^{4} x^{4} - 6 \, a^{2} x^{2} + 1\right)}}{\log\left(a x + 1\right) - \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2*(a^4*x^4 - 2*a^2*x^2 - 2*(a^5*x^5 - 2*a^3*x^3 + a*x)*log(a*x + 1) + 2*(a^5*x^5 - 2*a^3*x^3 + a*x)*log(-a*x + 1) + 1)/(a*log(a*x + 1)^2 - 2*a*log(a*x + 1)*log(-a*x + 1) + a*log(-a*x + 1)^2) + integrate(-4*(5*a^4*x^4 - 6*a^2*x^2 + 1)/(log(a*x + 1) - log(-a*x + 1)), x)","F",0
192,1,89,0,0.303737," ","integrate(x^4*(-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""maxima"")","\frac{1}{7560} \, a {\left(\frac{105 \, a^{6} x^{8} - 220 \, a^{4} x^{6} + 48 \, a^{2} x^{4} + 96 \, x^{2}}{a^{4}} + \frac{96 \, \log\left(a x + 1\right)}{a^{6}} + \frac{96 \, \log\left(a x - 1\right)}{a^{6}}\right)} + \frac{1}{315} \, {\left(35 \, a^{4} x^{9} - 90 \, a^{2} x^{7} + 63 \, x^{5}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/7560*a*((105*a^6*x^8 - 220*a^4*x^6 + 48*a^2*x^4 + 96*x^2)/a^4 + 96*log(a*x + 1)/a^6 + 96*log(a*x - 1)/a^6) + 1/315*(35*a^4*x^9 - 90*a^2*x^7 + 63*x^5)*arctanh(a*x)","A",0
193,1,88,0,0.302692," ","integrate(x^3*(-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""maxima"")","\frac{1}{1008} \, a {\left(\frac{2 \, {\left(9 \, a^{6} x^{7} - 21 \, a^{4} x^{5} + 7 \, a^{2} x^{3} + 21 \, x\right)}}{a^{4}} - \frac{21 \, \log\left(a x + 1\right)}{a^{5}} + \frac{21 \, \log\left(a x - 1\right)}{a^{5}}\right)} + \frac{1}{24} \, {\left(3 \, a^{4} x^{8} - 8 \, a^{2} x^{6} + 6 \, x^{4}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/1008*a*(2*(9*a^6*x^7 - 21*a^4*x^5 + 7*a^2*x^3 + 21*x)/a^4 - 21*log(a*x + 1)/a^5 + 21*log(a*x - 1)/a^5) + 1/24*(3*a^4*x^8 - 8*a^2*x^6 + 6*x^4)*arctanh(a*x)","A",0
194,1,81,0,0.303304," ","integrate(x^2*(-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""maxima"")","\frac{1}{420} \, a {\left(\frac{10 \, a^{4} x^{6} - 27 \, a^{2} x^{4} + 16 \, x^{2}}{a^{2}} + \frac{16 \, \log\left(a x + 1\right)}{a^{4}} + \frac{16 \, \log\left(a x - 1\right)}{a^{4}}\right)} + \frac{1}{105} \, {\left(15 \, a^{4} x^{7} - 42 \, a^{2} x^{5} + 35 \, x^{3}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/420*a*((10*a^4*x^6 - 27*a^2*x^4 + 16*x^2)/a^2 + 16*log(a*x + 1)/a^4 + 16*log(a*x - 1)/a^4) + 1/105*(15*a^4*x^7 - 42*a^2*x^5 + 35*x^3)*arctanh(a*x)","A",0
195,1,46,0,0.301217," ","integrate(x*(-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""maxima"")","\frac{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)}{6 \, a^{2}} + \frac{3 \, a^{4} x^{5} - 10 \, a^{2} x^{3} + 15 \, x}{90 \, a}"," ",0,"1/6*(a^2*x^2 - 1)^3*arctanh(a*x)/a^2 + 1/90*(3*a^4*x^5 - 10*a^2*x^3 + 15*x)/a","A",0
196,1,66,0,0.302236," ","integrate((-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""maxima"")","\frac{1}{60} \, {\left(3 \, a^{2} x^{4} - 14 \, x^{2} + \frac{16 \, \log\left(a x + 1\right)}{a^{2}} + \frac{16 \, \log\left(a x - 1\right)}{a^{2}}\right)} a + \frac{1}{15} \, {\left(3 \, a^{4} x^{5} - 10 \, a^{2} x^{3} + 15 \, x\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/60*(3*a^2*x^4 - 14*x^2 + 16*log(a*x + 1)/a^2 + 16*log(a*x - 1)/a^2)*a + 1/15*(3*a^4*x^5 - 10*a^2*x^3 + 15*x)*arctanh(a*x)","A",0
197,1,106,0,0.311140," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x,x, algorithm=""maxima"")","\frac{1}{24} \, {\left(2 \, a^{2} x^{3} - 18 \, x - \frac{12 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)}}{a} + \frac{12 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)}}{a} + \frac{9 \, \log\left(a x + 1\right)}{a} - \frac{9 \, \log\left(a x - 1\right)}{a}\right)} a + \frac{1}{4} \, {\left(a^{4} x^{4} - 4 \, a^{2} x^{2} + 2 \, \log\left(x^{2}\right)\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/24*(2*a^2*x^3 - 18*x - 12*(log(a*x + 1)*log(x) + dilog(-a*x))/a + 12*(log(-a*x + 1)*log(x) + dilog(a*x))/a + 9*log(a*x + 1)/a - 9*log(a*x - 1)/a)*a + 1/4*(a^4*x^4 - 4*a^2*x^2 + 2*log(x^2))*arctanh(a*x)","A",0
198,1,57,0,0.311654," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^2,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(a^{2} x^{2} - 8 \, \log\left(a x + 1\right) - 8 \, \log\left(a x - 1\right) + 6 \, \log\left(x\right)\right)} a + \frac{1}{3} \, {\left(a^{4} x^{3} - 6 \, a^{2} x - \frac{3}{x}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/6*(a^2*x^2 - 8*log(a*x + 1) - 8*log(a*x - 1) + 6*log(x))*a + 1/3*(a^4*x^3 - 6*a^2*x - 3/x)*arctanh(a*x)","A",0
199,1,82,0,0.308062," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(2 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)} a - 2 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)} a + \frac{a^{2} x^{2} - 1}{x}\right)} a + \frac{1}{2} \, {\left(a^{4} x^{2} - 2 \, a^{2} \log\left(x^{2}\right) - \frac{1}{x^{2}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/2*(2*(log(a*x + 1)*log(x) + dilog(-a*x))*a - 2*(log(-a*x + 1)*log(x) + dilog(a*x))*a + (a^2*x^2 - 1)/x)*a + 1/2*(a^4*x^2 - 2*a^2*log(x^2) - 1/x^2)*arctanh(a*x)","A",0
200,1,66,0,0.301683," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(8 \, a^{2} \log\left(a x + 1\right) + 8 \, a^{2} \log\left(a x - 1\right) - 10 \, a^{2} \log\left(x\right) - \frac{1}{x^{2}}\right)} a + \frac{1}{3} \, {\left(3 \, a^{4} x + \frac{6 \, a^{2} x^{2} - 1}{x^{3}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/6*(8*a^2*log(a*x + 1) + 8*a^2*log(a*x - 1) - 10*a^2*log(x) - 1/x^2)*a + 1/3*(3*a^4*x + (6*a^2*x^2 - 1)/x^3)*arctanh(a*x)","A",0
201,1,112,0,0.304912," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^5,x, algorithm=""maxima"")","-\frac{1}{24} \, {\left(12 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)} a^{3} - 12 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)} a^{3} + 9 \, a^{3} \log\left(a x + 1\right) - 9 \, a^{3} \log\left(a x - 1\right) - \frac{2 \, {\left(9 \, a^{2} x^{2} - 1\right)}}{x^{3}}\right)} a + \frac{1}{4} \, {\left(2 \, a^{4} \log\left(x^{2}\right) + \frac{4 \, a^{2} x^{2} - 1}{x^{4}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/24*(12*(log(a*x + 1)*log(x) + dilog(-a*x))*a^3 - 12*(log(-a*x + 1)*log(x) + dilog(a*x))*a^3 + 9*a^3*log(a*x + 1) - 9*a^3*log(a*x - 1) - 2*(9*a^2*x^2 - 1)/x^3)*a + 1/4*(2*a^4*log(x^2) + (4*a^2*x^2 - 1)/x^4)*arctanh(a*x)","A",0
202,1,71,0,0.307269," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^6,x, algorithm=""maxima"")","-\frac{1}{60} \, {\left(16 \, a^{4} \log\left(a^{2} x^{2} - 1\right) - 16 \, a^{4} \log\left(x^{2}\right) - \frac{14 \, a^{2} x^{2} - 3}{x^{4}}\right)} a - \frac{{\left(15 \, a^{4} x^{4} - 10 \, a^{2} x^{2} + 3\right)} \operatorname{artanh}\left(a x\right)}{15 \, x^{5}}"," ",0,"-1/60*(16*a^4*log(a^2*x^2 - 1) - 16*a^4*log(x^2) - (14*a^2*x^2 - 3)/x^4)*a - 1/15*(15*a^4*x^4 - 10*a^2*x^2 + 3)*arctanh(a*x)/x^5","A",0
203,1,214,0,0.330223," ","integrate(x^4*(-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{1}{22680} \, a^{2} {\left(\frac{90 \, a^{7} x^{7} - 138 \, a^{5} x^{5} - 134 \, a^{3} x^{3} + 174 \, a x - 144 \, \log\left(a x + 1\right)^{2} + 288 \, \log\left(a x + 1\right) \log\left(a x - 1\right) + 144 \, \log\left(a x - 1\right)^{2} + 87 \, \log\left(a x - 1\right)}{a^{7}} - \frac{576 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a^{7}} - \frac{87 \, \log\left(a x + 1\right)}{a^{7}}\right)} + \frac{1}{3780} \, a {\left(\frac{105 \, a^{6} x^{8} - 220 \, a^{4} x^{6} + 48 \, a^{2} x^{4} + 96 \, x^{2}}{a^{4}} + \frac{96 \, \log\left(a x + 1\right)}{a^{6}} + \frac{96 \, \log\left(a x - 1\right)}{a^{6}}\right)} \operatorname{artanh}\left(a x\right) + \frac{1}{315} \, {\left(35 \, a^{4} x^{9} - 90 \, a^{2} x^{7} + 63 \, x^{5}\right)} \operatorname{artanh}\left(a x\right)^{2}"," ",0,"1/22680*a^2*((90*a^7*x^7 - 138*a^5*x^5 - 134*a^3*x^3 + 174*a*x - 144*log(a*x + 1)^2 + 288*log(a*x + 1)*log(a*x - 1) + 144*log(a*x - 1)^2 + 87*log(a*x - 1))/a^7 - 576*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a^7 - 87*log(a*x + 1)/a^7) + 1/3780*a*((105*a^6*x^8 - 220*a^4*x^6 + 48*a^2*x^4 + 96*x^2)/a^4 + 96*log(a*x + 1)/a^6 + 96*log(a*x - 1)/a^6)*arctanh(a*x) + 1/315*(35*a^4*x^9 - 90*a^2*x^7 + 63*x^5)*arctanh(a*x)^2","A",0
204,1,170,0,0.324507," ","integrate(x^3*(-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{1}{504} \, a {\left(\frac{2 \, {\left(9 \, a^{6} x^{7} - 21 \, a^{4} x^{5} + 7 \, a^{2} x^{3} + 21 \, x\right)}}{a^{4}} - \frac{21 \, \log\left(a x + 1\right)}{a^{5}} + \frac{21 \, \log\left(a x - 1\right)}{a^{5}}\right)} \operatorname{artanh}\left(a x\right) + \frac{1}{24} \, {\left(3 \, a^{4} x^{8} - 8 \, a^{2} x^{6} + 6 \, x^{4}\right)} \operatorname{artanh}\left(a x\right)^{2} + \frac{12 \, a^{6} x^{6} - 24 \, a^{4} x^{4} - 20 \, a^{2} x^{2} - 2 \, {\left(21 \, \log\left(a x - 1\right) - 32\right)} \log\left(a x + 1\right) + 21 \, \log\left(a x + 1\right)^{2} + 21 \, \log\left(a x - 1\right)^{2} + 64 \, \log\left(a x - 1\right)}{2016 \, a^{4}}"," ",0,"1/504*a*(2*(9*a^6*x^7 - 21*a^4*x^5 + 7*a^2*x^3 + 21*x)/a^4 - 21*log(a*x + 1)/a^5 + 21*log(a*x - 1)/a^5)*arctanh(a*x) + 1/24*(3*a^4*x^8 - 8*a^2*x^6 + 6*x^4)*arctanh(a*x)^2 + 1/2016*(12*a^6*x^6 - 24*a^4*x^4 - 20*a^2*x^2 - 2*(21*log(a*x - 1) - 32)*log(a*x + 1) + 21*log(a*x + 1)^2 + 21*log(a*x - 1)^2 + 64*log(a*x - 1))/a^4","A",0
205,1,198,0,0.327204," ","integrate(x^2*(-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{1}{1260} \, a^{2} {\left(\frac{12 \, a^{5} x^{5} - 34 \, a^{3} x^{3} - 6 \, a x - 24 \, \log\left(a x + 1\right)^{2} + 48 \, \log\left(a x + 1\right) \log\left(a x - 1\right) + 24 \, \log\left(a x - 1\right)^{2} - 3 \, \log\left(a x - 1\right)}{a^{5}} - \frac{96 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a^{5}} + \frac{3 \, \log\left(a x + 1\right)}{a^{5}}\right)} + \frac{1}{210} \, a {\left(\frac{10 \, a^{4} x^{6} - 27 \, a^{2} x^{4} + 16 \, x^{2}}{a^{2}} + \frac{16 \, \log\left(a x + 1\right)}{a^{4}} + \frac{16 \, \log\left(a x - 1\right)}{a^{4}}\right)} \operatorname{artanh}\left(a x\right) + \frac{1}{105} \, {\left(15 \, a^{4} x^{7} - 42 \, a^{2} x^{5} + 35 \, x^{3}\right)} \operatorname{artanh}\left(a x\right)^{2}"," ",0,"1/1260*a^2*((12*a^5*x^5 - 34*a^3*x^3 - 6*a*x - 24*log(a*x + 1)^2 + 48*log(a*x + 1)*log(a*x - 1) + 24*log(a*x - 1)^2 - 3*log(a*x - 1))/a^5 - 96*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a^5 + 3*log(a*x + 1)/a^5) + 1/210*a*((10*a^4*x^6 - 27*a^2*x^4 + 16*x^2)/a^2 + 16*log(a*x + 1)/a^4 + 16*log(a*x - 1)/a^4)*arctanh(a*x) + 1/105*(15*a^4*x^7 - 42*a^2*x^5 + 35*x^3)*arctanh(a*x)^2","A",0
206,1,93,0,0.310653," ","integrate(x*(-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{2}}{6 \, a^{2}} + \frac{{\left(3 \, a^{2} x^{4} - 14 \, x^{2} + \frac{16 \, \log\left(a x + 1\right)}{a^{2}} + \frac{16 \, \log\left(a x - 1\right)}{a^{2}}\right)} a + 4 \, {\left(3 \, a^{4} x^{5} - 10 \, a^{2} x^{3} + 15 \, x\right)} \operatorname{artanh}\left(a x\right)}{180 \, a}"," ",0,"1/6*(a^2*x^2 - 1)^3*arctanh(a*x)^2/a^2 + 1/180*((3*a^2*x^4 - 14*x^2 + 16*log(a*x + 1)/a^2 + 16*log(a*x - 1)/a^2)*a + 4*(3*a^4*x^5 - 10*a^2*x^3 + 15*x)*arctanh(a*x))/a","A",0
207,1,175,0,0.325747," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{1}{60} \, a^{2} {\left(\frac{2 \, a^{3} x^{3} - 22 \, a x - 8 \, \log\left(a x + 1\right)^{2} + 16 \, \log\left(a x + 1\right) \log\left(a x - 1\right) + 8 \, \log\left(a x - 1\right)^{2} - 11 \, \log\left(a x - 1\right)}{a^{3}} - \frac{32 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a^{3}} + \frac{11 \, \log\left(a x + 1\right)}{a^{3}}\right)} + \frac{1}{30} \, {\left(3 \, a^{2} x^{4} - 14 \, x^{2} + \frac{16 \, \log\left(a x + 1\right)}{a^{2}} + \frac{16 \, \log\left(a x - 1\right)}{a^{2}}\right)} a \operatorname{artanh}\left(a x\right) + \frac{1}{15} \, {\left(3 \, a^{4} x^{5} - 10 \, a^{2} x^{3} + 15 \, x\right)} \operatorname{artanh}\left(a x\right)^{2}"," ",0,"1/60*a^2*((2*a^3*x^3 - 22*a*x - 8*log(a*x + 1)^2 + 16*log(a*x + 1)*log(a*x - 1) + 8*log(a*x - 1)^2 - 11*log(a*x - 1))/a^3 - 32*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a^3 + 11*log(a*x + 1)/a^3) + 1/30*(3*a^2*x^4 - 14*x^2 + 16*log(a*x + 1)/a^2 + 16*log(a*x - 1)/a^2)*a*arctanh(a*x) + 1/15*(3*a^4*x^5 - 10*a^2*x^3 + 15*x)*arctanh(a*x)^2","A",0
208,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(a^{4} x^{4} - 4 \, a^{2} x^{2}\right)} \log\left(-a x + 1\right)^{2} - \frac{1}{4} \, \int -\frac{2 \, {\left(a^{5} x^{5} - a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a^{2} x^{2} + a x - 1\right)} \log\left(a x + 1\right)^{2} - {\left(a^{5} x^{5} - 4 \, a^{3} x^{3} + 4 \, {\left(a^{5} x^{5} - a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a^{2} x^{2} + a x - 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)}{2 \, {\left(a x^{2} - x\right)}}\,{d x}"," ",0,"1/16*(a^4*x^4 - 4*a^2*x^2)*log(-a*x + 1)^2 - 1/4*integrate(-1/2*(2*(a^5*x^5 - a^4*x^4 - 2*a^3*x^3 + 2*a^2*x^2 + a*x - 1)*log(a*x + 1)^2 - (a^5*x^5 - 4*a^3*x^3 + 4*(a^5*x^5 - a^4*x^4 - 2*a^3*x^3 + 2*a^2*x^2 + a*x - 1)*log(a*x + 1))*log(-a*x + 1))/(a*x^2 - x), x)","F",0
209,1,200,0,0.328354," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^2,x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} {\left(\frac{2 \, {\left(a x + 2 \, \log\left(a x + 1\right)^{2} - 4 \, \log\left(a x + 1\right) \log\left(a x - 1\right) - 2 \, \log\left(a x - 1\right)^{2}\right)}}{a} + \frac{16 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a} - \frac{6 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)}}{a} + \frac{6 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)}}{a} - \frac{\log\left(a x + 1\right)}{a} + \frac{\log\left(a x - 1\right)}{a}\right)} + \frac{1}{3} \, {\left(a^{2} x^{2} - 8 \, \log\left(a x + 1\right) - 8 \, \log\left(a x - 1\right) + 6 \, \log\left(x\right)\right)} a \operatorname{artanh}\left(a x\right) + \frac{1}{3} \, {\left(a^{4} x^{3} - 6 \, a^{2} x - \frac{3}{x}\right)} \operatorname{artanh}\left(a x\right)^{2}"," ",0,"1/6*a^2*(2*(a*x + 2*log(a*x + 1)^2 - 4*log(a*x + 1)*log(a*x - 1) - 2*log(a*x - 1)^2)/a + 16*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a - 6*(log(a*x + 1)*log(x) + dilog(-a*x))/a + 6*(log(-a*x + 1)*log(x) + dilog(a*x))/a - log(a*x + 1)/a + log(a*x - 1)/a) + 1/3*(a^2*x^2 - 8*log(a*x + 1) - 8*log(a*x - 1) + 6*log(x))*a*arctanh(a*x) + 1/3*(a^4*x^3 - 6*a^2*x - 3/x)*arctanh(a*x)^2","A",0
210,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^3,x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(2 \, x^{2} \log\left(-a x + 1\right) - a {\left(\frac{a x^{2} + 2 \, x}{a^{2}} + \frac{2 \, \log\left(a x - 1\right)}{a^{3}}\right)}\right)} a^{4} - \frac{1}{2} \, a^{4} \int x \log\left(a x + 1\right) \log\left(-a x + 1\right)\,{d x} + \frac{1}{4} \, a^{3} \int a x \log\left(a x + 1\right)^{2}\,{d x} + \frac{1}{4} \, a^{3} \int \frac{\log\left(a x + 1\right)^{2}}{a^{3} x^{3}}\,{d x} + \frac{1}{4} \, {\left(a x - {\left(a x - 1\right)} \log\left(-a x + 1\right) - 1\right)} a^{2} - \frac{1}{2} \, a^{2} \int \frac{\log\left(a x + 1\right)^{2}}{x}\,{d x} + a^{2} \int \frac{\log\left(a x + 1\right) \log\left(-a x + 1\right)}{x}\,{d x} - \frac{1}{4} \, a^{2} \int \frac{\log\left(-a x + 1\right)}{x}\,{d x} - \frac{1}{4} \, {\left(a {\left(\log\left(a x - 1\right) - \log\left(x\right)\right)} - \frac{\log\left(-a x + 1\right)}{x}\right)} a + \frac{{\left(a^{4} x^{4} - 1\right)} \log\left(-a x + 1\right)^{2}}{8 \, x^{2}} - \frac{1}{2} \, \int \frac{\log\left(a x + 1\right) \log\left(-a x + 1\right)}{x^{3}}\,{d x}"," ",0,"-1/16*(2*x^2*log(-a*x + 1) - a*((a*x^2 + 2*x)/a^2 + 2*log(a*x - 1)/a^3))*a^4 - 1/2*a^4*integrate(x*log(a*x + 1)*log(-a*x + 1), x) + 1/4*a^3*integrate(a*x*log(a*x + 1)^2, x) + 1/4*a^3*integrate(log(a*x + 1)^2/(a^3*x^3), x) + 1/4*(a*x - (a*x - 1)*log(-a*x + 1) - 1)*a^2 - 1/2*a^2*integrate(log(a*x + 1)^2/x, x) + a^2*integrate(log(a*x + 1)*log(-a*x + 1)/x, x) - 1/4*a^2*integrate(log(-a*x + 1)/x, x) - 1/4*(a*(log(a*x - 1) - log(x)) - log(-a*x + 1)/x)*a + 1/8*(a^4*x^4 - 1)*log(-a*x + 1)^2/x^2 - 1/2*integrate(log(a*x + 1)*log(-a*x + 1)/x^3, x)","F",0
211,1,203,0,0.328971," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(16 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)} a - 10 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)} a + 10 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)} a - a \log\left(a x + 1\right) + a \log\left(a x - 1\right) + \frac{2 \, {\left(2 \, a x \log\left(a x + 1\right)^{2} - 4 \, a x \log\left(a x + 1\right) \log\left(a x - 1\right) - 2 \, a x \log\left(a x - 1\right)^{2} + 1\right)}}{x}\right)} a^{2} + \frac{1}{3} \, {\left(8 \, a^{2} \log\left(a x + 1\right) + 8 \, a^{2} \log\left(a x - 1\right) - 10 \, a^{2} \log\left(x\right) - \frac{1}{x^{2}}\right)} a \operatorname{artanh}\left(a x\right) + \frac{1}{3} \, {\left(3 \, a^{4} x + \frac{6 \, a^{2} x^{2} - 1}{x^{3}}\right)} \operatorname{artanh}\left(a x\right)^{2}"," ",0,"-1/6*(16*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))*a - 10*(log(a*x + 1)*log(x) + dilog(-a*x))*a + 10*(log(-a*x + 1)*log(x) + dilog(a*x))*a - a*log(a*x + 1) + a*log(a*x - 1) + 2*(2*a*x*log(a*x + 1)^2 - 4*a*x*log(a*x + 1)*log(a*x - 1) - 2*a*x*log(a*x - 1)^2 + 1)/x)*a^2 + 1/3*(8*a^2*log(a*x + 1) + 8*a^2*log(a*x - 1) - 10*a^2*log(x) - 1/x^2)*a*arctanh(a*x) + 1/3*(3*a^4*x + (6*a^2*x^2 - 1)/x^3)*arctanh(a*x)^2","A",0
212,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^5,x, algorithm=""maxima"")","\frac{{\left(4 \, a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)^{2}}{16 \, x^{4}} - \frac{1}{4} \, \int -\frac{2 \, {\left(a^{5} x^{5} - a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a^{2} x^{2} + a x - 1\right)} \log\left(a x + 1\right)^{2} - {\left(4 \, a^{3} x^{3} - a x + 4 \, {\left(a^{5} x^{5} - a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a^{2} x^{2} + a x - 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)}{2 \, {\left(a x^{6} - x^{5}\right)}}\,{d x}"," ",0,"1/16*(4*a^2*x^2 - 1)*log(-a*x + 1)^2/x^4 - 1/4*integrate(-1/2*(2*(a^5*x^5 - a^4*x^4 - 2*a^3*x^3 + 2*a^2*x^2 + a*x - 1)*log(a*x + 1)^2 - (4*a^3*x^3 - a*x + 4*(a^5*x^5 - a^4*x^4 - 2*a^3*x^3 + 2*a^2*x^2 + a*x - 1)*log(a*x + 1))*log(-a*x + 1))/(a*x^6 - x^5), x)","F",0
213,1,239,0,0.333425," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^6,x, algorithm=""maxima"")","\frac{1}{60} \, {\left(32 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)} a^{3} - 32 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)} a^{3} + 32 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)} a^{3} - 11 \, a^{3} \log\left(a x + 1\right) + 11 \, a^{3} \log\left(a x - 1\right) + \frac{2 \, {\left(4 \, a^{3} x^{3} \log\left(a x + 1\right)^{2} - 8 \, a^{3} x^{3} \log\left(a x + 1\right) \log\left(a x - 1\right) - 4 \, a^{3} x^{3} \log\left(a x - 1\right)^{2} + 11 \, a^{2} x^{2} - 1\right)}}{x^{3}}\right)} a^{2} - \frac{1}{30} \, {\left(16 \, a^{4} \log\left(a^{2} x^{2} - 1\right) - 16 \, a^{4} \log\left(x^{2}\right) - \frac{14 \, a^{2} x^{2} - 3}{x^{4}}\right)} a \operatorname{artanh}\left(a x\right) - \frac{{\left(15 \, a^{4} x^{4} - 10 \, a^{2} x^{2} + 3\right)} \operatorname{artanh}\left(a x\right)^{2}}{15 \, x^{5}}"," ",0,"1/60*(32*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))*a^3 - 32*(log(a*x + 1)*log(x) + dilog(-a*x))*a^3 + 32*(log(-a*x + 1)*log(x) + dilog(a*x))*a^3 - 11*a^3*log(a*x + 1) + 11*a^3*log(a*x - 1) + 2*(4*a^3*x^3*log(a*x + 1)^2 - 8*a^3*x^3*log(a*x + 1)*log(a*x - 1) - 4*a^3*x^3*log(a*x - 1)^2 + 11*a^2*x^2 - 1)/x^3)*a^2 - 1/30*(16*a^4*log(a^2*x^2 - 1) - 16*a^4*log(x^2) - (14*a^2*x^2 - 3)/x^4)*a*arctanh(a*x) - 1/15*(15*a^4*x^4 - 10*a^2*x^2 + 3)*arctanh(a*x)^2/x^5","A",0
214,1,188,0,0.331768," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^7,x, algorithm=""maxima"")","\frac{1}{360} \, {\left(64 \, a^{4} \log\left(x\right) - \frac{15 \, a^{4} x^{4} \log\left(a x + 1\right)^{2} + 15 \, a^{4} x^{4} \log\left(a x - 1\right)^{2} + 32 \, a^{4} x^{4} \log\left(a x - 1\right) - 28 \, a^{2} x^{2} - 2 \, {\left(15 \, a^{4} x^{4} \log\left(a x - 1\right) - 16 \, a^{4} x^{4}\right)} \log\left(a x + 1\right) + 6}{x^{4}}\right)} a^{2} + \frac{1}{90} \, {\left(15 \, a^{5} \log\left(a x + 1\right) - 15 \, a^{5} \log\left(a x - 1\right) - \frac{2 \, {\left(15 \, a^{4} x^{4} - 10 \, a^{2} x^{2} + 3\right)}}{x^{5}}\right)} a \operatorname{artanh}\left(a x\right) - \frac{{\left(3 \, a^{4} x^{4} - 3 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{6 \, x^{6}}"," ",0,"1/360*(64*a^4*log(x) - (15*a^4*x^4*log(a*x + 1)^2 + 15*a^4*x^4*log(a*x - 1)^2 + 32*a^4*x^4*log(a*x - 1) - 28*a^2*x^2 - 2*(15*a^4*x^4*log(a*x - 1) - 16*a^4*x^4)*log(a*x + 1) + 6)/x^4)*a^2 + 1/90*(15*a^5*log(a*x + 1) - 15*a^5*log(a*x - 1) - 2*(15*a^4*x^4 - 10*a^2*x^2 + 3)/x^5)*a*arctanh(a*x) - 1/6*(3*a^4*x^4 - 3*a^2*x^2 + 1)*arctanh(a*x)^2/x^6","A",0
215,1,254,0,0.332667," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^8,x, algorithm=""maxima"")","\frac{1}{1260} \, {\left(96 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)} a^{5} - 96 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)} a^{5} + 96 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)} a^{5} - 3 \, a^{5} \log\left(a x + 1\right) + 3 \, a^{5} \log\left(a x - 1\right) + \frac{2 \, {\left(12 \, a^{5} x^{5} \log\left(a x + 1\right)^{2} - 24 \, a^{5} x^{5} \log\left(a x + 1\right) \log\left(a x - 1\right) - 12 \, a^{5} x^{5} \log\left(a x - 1\right)^{2} + 3 \, a^{4} x^{4} + 17 \, a^{2} x^{2} - 6\right)}}{x^{5}}\right)} a^{2} - \frac{1}{210} \, {\left(16 \, a^{6} \log\left(a^{2} x^{2} - 1\right) - 16 \, a^{6} \log\left(x^{2}\right) + \frac{16 \, a^{4} x^{4} - 27 \, a^{2} x^{2} + 10}{x^{6}}\right)} a \operatorname{artanh}\left(a x\right) - \frac{{\left(35 \, a^{4} x^{4} - 42 \, a^{2} x^{2} + 15\right)} \operatorname{artanh}\left(a x\right)^{2}}{105 \, x^{7}}"," ",0,"1/1260*(96*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))*a^5 - 96*(log(a*x + 1)*log(x) + dilog(-a*x))*a^5 + 96*(log(-a*x + 1)*log(x) + dilog(a*x))*a^5 - 3*a^5*log(a*x + 1) + 3*a^5*log(a*x - 1) + 2*(12*a^5*x^5*log(a*x + 1)^2 - 24*a^5*x^5*log(a*x + 1)*log(a*x - 1) - 12*a^5*x^5*log(a*x - 1)^2 + 3*a^4*x^4 + 17*a^2*x^2 - 6)/x^5)*a^2 - 1/210*(16*a^6*log(a^2*x^2 - 1) - 16*a^6*log(x^2) + (16*a^4*x^4 - 27*a^2*x^2 + 10)/x^6)*a*arctanh(a*x) - 1/105*(35*a^4*x^4 - 42*a^2*x^2 + 15)*arctanh(a*x)^2/x^7","A",0
216,1,204,0,0.321021," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^9,x, algorithm=""maxima"")","\frac{1}{2016} \, {\left(128 \, a^{6} \log\left(x\right) - \frac{21 \, a^{6} x^{6} \log\left(a x + 1\right)^{2} + 21 \, a^{6} x^{6} \log\left(a x - 1\right)^{2} + 64 \, a^{6} x^{6} \log\left(a x - 1\right) - 20 \, a^{4} x^{4} - 24 \, a^{2} x^{2} - 2 \, {\left(21 \, a^{6} x^{6} \log\left(a x - 1\right) - 32 \, a^{6} x^{6}\right)} \log\left(a x + 1\right) + 12}{x^{6}}\right)} a^{2} + \frac{1}{504} \, {\left(21 \, a^{7} \log\left(a x + 1\right) - 21 \, a^{7} \log\left(a x - 1\right) - \frac{2 \, {\left(21 \, a^{6} x^{6} + 7 \, a^{4} x^{4} - 21 \, a^{2} x^{2} + 9\right)}}{x^{7}}\right)} a \operatorname{artanh}\left(a x\right) - \frac{{\left(6 \, a^{4} x^{4} - 8 \, a^{2} x^{2} + 3\right)} \operatorname{artanh}\left(a x\right)^{2}}{24 \, x^{8}}"," ",0,"1/2016*(128*a^6*log(x) - (21*a^6*x^6*log(a*x + 1)^2 + 21*a^6*x^6*log(a*x - 1)^2 + 64*a^6*x^6*log(a*x - 1) - 20*a^4*x^4 - 24*a^2*x^2 - 2*(21*a^6*x^6*log(a*x - 1) - 32*a^6*x^6)*log(a*x + 1) + 12)/x^6)*a^2 + 1/504*(21*a^7*log(a*x + 1) - 21*a^7*log(a*x - 1) - 2*(21*a^6*x^6 + 7*a^4*x^4 - 21*a^2*x^2 + 9)/x^7)*a*arctanh(a*x) - 1/24*(6*a^4*x^4 - 8*a^2*x^2 + 3)*arctanh(a*x)^2/x^8","A",0
217,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^3,x, algorithm=""maxima"")","-\frac{{\left(36 \, a^{5} x^{5} - 45 \, a^{4} x^{4} - 140 \, a^{3} x^{3} + 210 \, a^{2} x^{2} + 480 \, a x - 60 \, {\left(3 \, a^{5} x^{5} - 10 \, a^{3} x^{3} + 15 \, a x + 8\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{2}}{2400 \, a} - \frac{{\left(\log\left(-a x + 1\right)^{3} - 3 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 6\right)} {\left(a x - 1\right)}}{8 \, a} - \frac{288 \, {\left(125 \, \log\left(-a x + 1\right)^{3} - 75 \, \log\left(-a x + 1\right)^{2} + 30 \, \log\left(-a x + 1\right) - 6\right)} {\left(a x - 1\right)}^{5} + 5625 \, {\left(32 \, \log\left(-a x + 1\right)^{3} - 24 \, \log\left(-a x + 1\right)^{2} + 12 \, \log\left(-a x + 1\right) - 3\right)} {\left(a x - 1\right)}^{4} + 40000 \, {\left(9 \, \log\left(-a x + 1\right)^{3} - 9 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 2\right)} {\left(a x - 1\right)}^{3} + 90000 \, {\left(4 \, \log\left(-a x + 1\right)^{3} - 6 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 3\right)} {\left(a x - 1\right)}^{2} + 180000 \, {\left(\log\left(-a x + 1\right)^{3} - 3 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 6\right)} {\left(a x - 1\right)}}{1440000 \, a} + \frac{4 \, {\left(9 \, \log\left(-a x + 1\right)^{3} - 9 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 2\right)} {\left(a x - 1\right)}^{3} + 27 \, {\left(4 \, \log\left(-a x + 1\right)^{3} - 6 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 3\right)} {\left(a x - 1\right)}^{2} + 108 \, {\left(\log\left(-a x + 1\right)^{3} - 3 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 6\right)} {\left(a x - 1\right)}}{432 \, a} - \frac{1}{8} \, \int -\frac{150 \, {\left(a^{5} x^{5} - a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a^{2} x^{2} + a x - 1\right)} \log\left(a x + 1\right)^{3} + {\left(36 \, a^{5} x^{5} - 45 \, a^{4} x^{4} - 140 \, a^{3} x^{3} + 210 \, a^{2} x^{2} - 450 \, {\left(a^{5} x^{5} - a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a^{2} x^{2} + a x - 1\right)} \log\left(a x + 1\right)^{2} + 480 \, a x - 60 \, {\left(3 \, a^{5} x^{5} - 10 \, a^{3} x^{3} + 15 \, a x + 8\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)}{150 \, {\left(a x - 1\right)}}\,{d x}"," ",0,"-1/2400*(36*a^5*x^5 - 45*a^4*x^4 - 140*a^3*x^3 + 210*a^2*x^2 + 480*a*x - 60*(3*a^5*x^5 - 10*a^3*x^3 + 15*a*x + 8)*log(a*x + 1))*log(-a*x + 1)^2/a - 1/8*(log(-a*x + 1)^3 - 3*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 6)*(a*x - 1)/a - 1/1440000*(288*(125*log(-a*x + 1)^3 - 75*log(-a*x + 1)^2 + 30*log(-a*x + 1) - 6)*(a*x - 1)^5 + 5625*(32*log(-a*x + 1)^3 - 24*log(-a*x + 1)^2 + 12*log(-a*x + 1) - 3)*(a*x - 1)^4 + 40000*(9*log(-a*x + 1)^3 - 9*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 2)*(a*x - 1)^3 + 90000*(4*log(-a*x + 1)^3 - 6*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 3)*(a*x - 1)^2 + 180000*(log(-a*x + 1)^3 - 3*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 6)*(a*x - 1))/a + 1/432*(4*(9*log(-a*x + 1)^3 - 9*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 2)*(a*x - 1)^3 + 27*(4*log(-a*x + 1)^3 - 6*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 3)*(a*x - 1)^2 + 108*(log(-a*x + 1)^3 - 3*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 6)*(a*x - 1))/a - 1/8*integrate(-1/150*(150*(a^5*x^5 - a^4*x^4 - 2*a^3*x^3 + 2*a^2*x^2 + a*x - 1)*log(a*x + 1)^3 + (36*a^5*x^5 - 45*a^4*x^4 - 140*a^3*x^3 + 210*a^2*x^2 - 450*(a^5*x^5 - a^4*x^4 - 2*a^3*x^3 + 2*a^2*x^2 + a*x - 1)*log(a*x + 1)^2 + 480*a*x - 60*(3*a^5*x^5 - 10*a^3*x^3 + 15*a*x + 8)*log(a*x + 1))*log(-a*x + 1))/(a*x - 1), x)","F",0
218,0,0,0,0.000000," ","integrate(x*(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2} x}{\operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*x/arctanh(a*x), x)","F",0
219,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2}}{\operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2/arctanh(a*x), x)","F",0
220,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2/x/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2}}{x \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2/(x*arctanh(a*x)), x)","F",0
221,0,0,0,0.000000," ","integrate(x*(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)}}{a \log\left(a x + 1\right) - a \log\left(-a x + 1\right)} + \int -\frac{2 \, {\left(7 \, a^{6} x^{6} - 15 \, a^{4} x^{4} + 9 \, a^{2} x^{2} - 1\right)}}{a \log\left(a x + 1\right) - a \log\left(-a x + 1\right)}\,{d x}"," ",0,"2*(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x)/(a*log(a*x + 1) - a*log(-a*x + 1)) + integrate(-2*(7*a^6*x^6 - 15*a^4*x^4 + 9*a^2*x^2 - 1)/(a*log(a*x + 1) - a*log(-a*x + 1)), x)","F",0
222,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)}}{a \log\left(a x + 1\right) - a \log\left(-a x + 1\right)} + \int -\frac{12 \, {\left(a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right)}}{\log\left(a x + 1\right) - \log\left(-a x + 1\right)}\,{d x}"," ",0,"2*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)/(a*log(a*x + 1) - a*log(-a*x + 1)) + integrate(-12*(a^5*x^5 - 2*a^3*x^3 + a*x)/(log(a*x + 1) - log(-a*x + 1)), x)","F",0
223,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2/x/arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)}}{a x \log\left(a x + 1\right) - a x \log\left(-a x + 1\right)} + \int -\frac{2 \, {\left(5 \, a^{6} x^{6} - 9 \, a^{4} x^{4} + 3 \, a^{2} x^{2} + 1\right)}}{a x^{2} \log\left(a x + 1\right) - a x^{2} \log\left(-a x + 1\right)}\,{d x}"," ",0,"2*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)/(a*x*log(a*x + 1) - a*x*log(-a*x + 1)) + integrate(-2*(5*a^6*x^6 - 9*a^4*x^4 + 3*a^2*x^2 + 1)/(a*x^2*log(a*x + 1) - a*x^2*log(-a*x + 1)), x)","F",0
224,1,82,0,0.314379," ","integrate((-a^2*x^2+1)^3*arctanh(a*x),x, algorithm=""maxima"")","-\frac{1}{210} \, {\left(5 \, a^{4} x^{6} - 24 \, a^{2} x^{4} + 57 \, x^{2} - \frac{48 \, \log\left(a x + 1\right)}{a^{2}} - \frac{48 \, \log\left(a x - 1\right)}{a^{2}}\right)} a - \frac{1}{35} \, {\left(5 \, a^{6} x^{7} - 21 \, a^{4} x^{5} + 35 \, a^{2} x^{3} - 35 \, x\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/210*(5*a^4*x^6 - 24*a^2*x^4 + 57*x^2 - 48*log(a*x + 1)/a^2 - 48*log(a*x - 1)/a^2)*a - 1/35*(5*a^6*x^7 - 21*a^4*x^5 + 35*a^2*x^3 - 35*x)*arctanh(a*x)","A",0
225,1,199,0,0.327656," ","integrate((-a^2*x^2+1)^3*arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{1}{315} \, a^{2} {\left(\frac{3 \, a^{5} x^{5} - 19 \, a^{3} x^{3} + 114 \, a x + 36 \, \log\left(a x + 1\right)^{2} - 72 \, \log\left(a x + 1\right) \log\left(a x - 1\right) - 36 \, \log\left(a x - 1\right)^{2} + 57 \, \log\left(a x - 1\right)}{a^{3}} + \frac{144 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a^{3}} - \frac{57 \, \log\left(a x + 1\right)}{a^{3}}\right)} - \frac{1}{105} \, {\left(5 \, a^{4} x^{6} - 24 \, a^{2} x^{4} + 57 \, x^{2} - \frac{48 \, \log\left(a x + 1\right)}{a^{2}} - \frac{48 \, \log\left(a x - 1\right)}{a^{2}}\right)} a \operatorname{artanh}\left(a x\right) - \frac{1}{35} \, {\left(5 \, a^{6} x^{7} - 21 \, a^{4} x^{5} + 35 \, a^{2} x^{3} - 35 \, x\right)} \operatorname{artanh}\left(a x\right)^{2}"," ",0,"-1/315*a^2*((3*a^5*x^5 - 19*a^3*x^3 + 114*a*x + 36*log(a*x + 1)^2 - 72*log(a*x + 1)*log(a*x - 1) - 36*log(a*x - 1)^2 + 57*log(a*x - 1))/a^3 + 144*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a^3 - 57*log(a*x + 1)/a^3) - 1/105*(5*a^4*x^6 - 24*a^2*x^4 + 57*x^2 - 48*log(a*x + 1)/a^2 - 48*log(a*x - 1)/a^2)*a*arctanh(a*x) - 1/35*(5*a^6*x^7 - 21*a^4*x^5 + 35*a^2*x^3 - 35*x)*arctanh(a*x)^2","A",0
226,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^3*arctanh(a*x)^3,x, algorithm=""maxima"")","\frac{{\left(150 \, a^{7} x^{7} - 175 \, a^{6} x^{6} - 672 \, a^{5} x^{5} + 840 \, a^{4} x^{4} + 1330 \, a^{3} x^{3} - 1995 \, a^{2} x^{2} - 3360 \, a x - 210 \, {\left(5 \, a^{7} x^{7} - 21 \, a^{5} x^{5} + 35 \, a^{3} x^{3} - 35 \, a x - 16\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{2}}{19600 \, a} - \frac{{\left(\log\left(-a x + 1\right)^{3} - 3 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 6\right)} {\left(a x - 1\right)}}{8 \, a} + \frac{36000 \, {\left(343 \, \log\left(-a x + 1\right)^{3} - 147 \, \log\left(-a x + 1\right)^{2} + 42 \, \log\left(-a x + 1\right) - 6\right)} {\left(a x - 1\right)}^{7} + 2401000 \, {\left(36 \, \log\left(-a x + 1\right)^{3} - 18 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 1\right)} {\left(a x - 1\right)}^{6} + 2074464 \, {\left(125 \, \log\left(-a x + 1\right)^{3} - 75 \, \log\left(-a x + 1\right)^{2} + 30 \, \log\left(-a x + 1\right) - 6\right)} {\left(a x - 1\right)}^{5} + 13505625 \, {\left(32 \, \log\left(-a x + 1\right)^{3} - 24 \, \log\left(-a x + 1\right)^{2} + 12 \, \log\left(-a x + 1\right) - 3\right)} {\left(a x - 1\right)}^{4} + 48020000 \, {\left(9 \, \log\left(-a x + 1\right)^{3} - 9 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 2\right)} {\left(a x - 1\right)}^{3} + 64827000 \, {\left(4 \, \log\left(-a x + 1\right)^{3} - 6 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 3\right)} {\left(a x - 1\right)}^{2} + 86436000 \, {\left(\log\left(-a x + 1\right)^{3} - 3 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 6\right)} {\left(a x - 1\right)}}{691488000 \, a} - \frac{288 \, {\left(125 \, \log\left(-a x + 1\right)^{3} - 75 \, \log\left(-a x + 1\right)^{2} + 30 \, \log\left(-a x + 1\right) - 6\right)} {\left(a x - 1\right)}^{5} + 5625 \, {\left(32 \, \log\left(-a x + 1\right)^{3} - 24 \, \log\left(-a x + 1\right)^{2} + 12 \, \log\left(-a x + 1\right) - 3\right)} {\left(a x - 1\right)}^{4} + 40000 \, {\left(9 \, \log\left(-a x + 1\right)^{3} - 9 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 2\right)} {\left(a x - 1\right)}^{3} + 90000 \, {\left(4 \, \log\left(-a x + 1\right)^{3} - 6 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 3\right)} {\left(a x - 1\right)}^{2} + 180000 \, {\left(\log\left(-a x + 1\right)^{3} - 3 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 6\right)} {\left(a x - 1\right)}}{480000 \, a} + \frac{4 \, {\left(9 \, \log\left(-a x + 1\right)^{3} - 9 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 2\right)} {\left(a x - 1\right)}^{3} + 27 \, {\left(4 \, \log\left(-a x + 1\right)^{3} - 6 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 3\right)} {\left(a x - 1\right)}^{2} + 108 \, {\left(\log\left(-a x + 1\right)^{3} - 3 \, \log\left(-a x + 1\right)^{2} + 6 \, \log\left(-a x + 1\right) - 6\right)} {\left(a x - 1\right)}}{288 \, a} + \frac{1}{8} \, \int -\frac{1225 \, {\left(a^{7} x^{7} - a^{6} x^{6} - 3 \, a^{5} x^{5} + 3 \, a^{4} x^{4} + 3 \, a^{3} x^{3} - 3 \, a^{2} x^{2} - a x + 1\right)} \log\left(a x + 1\right)^{3} + {\left(150 \, a^{7} x^{7} - 175 \, a^{6} x^{6} - 672 \, a^{5} x^{5} + 840 \, a^{4} x^{4} + 1330 \, a^{3} x^{3} - 1995 \, a^{2} x^{2} - 3675 \, {\left(a^{7} x^{7} - a^{6} x^{6} - 3 \, a^{5} x^{5} + 3 \, a^{4} x^{4} + 3 \, a^{3} x^{3} - 3 \, a^{2} x^{2} - a x + 1\right)} \log\left(a x + 1\right)^{2} - 3360 \, a x - 210 \, {\left(5 \, a^{7} x^{7} - 21 \, a^{5} x^{5} + 35 \, a^{3} x^{3} - 35 \, a x - 16\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)}{1225 \, {\left(a x - 1\right)}}\,{d x}"," ",0,"1/19600*(150*a^7*x^7 - 175*a^6*x^6 - 672*a^5*x^5 + 840*a^4*x^4 + 1330*a^3*x^3 - 1995*a^2*x^2 - 3360*a*x - 210*(5*a^7*x^7 - 21*a^5*x^5 + 35*a^3*x^3 - 35*a*x - 16)*log(a*x + 1))*log(-a*x + 1)^2/a - 1/8*(log(-a*x + 1)^3 - 3*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 6)*(a*x - 1)/a + 1/691488000*(36000*(343*log(-a*x + 1)^3 - 147*log(-a*x + 1)^2 + 42*log(-a*x + 1) - 6)*(a*x - 1)^7 + 2401000*(36*log(-a*x + 1)^3 - 18*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 1)*(a*x - 1)^6 + 2074464*(125*log(-a*x + 1)^3 - 75*log(-a*x + 1)^2 + 30*log(-a*x + 1) - 6)*(a*x - 1)^5 + 13505625*(32*log(-a*x + 1)^3 - 24*log(-a*x + 1)^2 + 12*log(-a*x + 1) - 3)*(a*x - 1)^4 + 48020000*(9*log(-a*x + 1)^3 - 9*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 2)*(a*x - 1)^3 + 64827000*(4*log(-a*x + 1)^3 - 6*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 3)*(a*x - 1)^2 + 86436000*(log(-a*x + 1)^3 - 3*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 6)*(a*x - 1))/a - 1/480000*(288*(125*log(-a*x + 1)^3 - 75*log(-a*x + 1)^2 + 30*log(-a*x + 1) - 6)*(a*x - 1)^5 + 5625*(32*log(-a*x + 1)^3 - 24*log(-a*x + 1)^2 + 12*log(-a*x + 1) - 3)*(a*x - 1)^4 + 40000*(9*log(-a*x + 1)^3 - 9*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 2)*(a*x - 1)^3 + 90000*(4*log(-a*x + 1)^3 - 6*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 3)*(a*x - 1)^2 + 180000*(log(-a*x + 1)^3 - 3*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 6)*(a*x - 1))/a + 1/288*(4*(9*log(-a*x + 1)^3 - 9*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 2)*(a*x - 1)^3 + 27*(4*log(-a*x + 1)^3 - 6*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 3)*(a*x - 1)^2 + 108*(log(-a*x + 1)^3 - 3*log(-a*x + 1)^2 + 6*log(-a*x + 1) - 6)*(a*x - 1))/a + 1/8*integrate(-1/1225*(1225*(a^7*x^7 - a^6*x^6 - 3*a^5*x^5 + 3*a^4*x^4 + 3*a^3*x^3 - 3*a^2*x^2 - a*x + 1)*log(a*x + 1)^3 + (150*a^7*x^7 - 175*a^6*x^6 - 672*a^5*x^5 + 840*a^4*x^4 + 1330*a^3*x^3 - 1995*a^2*x^2 - 3675*(a^7*x^7 - a^6*x^6 - 3*a^5*x^5 + 3*a^4*x^4 + 3*a^3*x^3 - 3*a^2*x^2 - a*x + 1)*log(a*x + 1)^2 - 3360*a*x - 210*(5*a^7*x^7 - 21*a^5*x^5 + 35*a^3*x^3 - 35*a*x - 16)*log(a*x + 1))*log(-a*x + 1))/(a*x - 1), x)","F",0
227,1,120,0,0.318135," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{4 \, a x - \log\left(a x + 1\right)^{2} + 2 \, \log\left(a x + 1\right) \log\left(a x - 1\right) + \log\left(a x - 1\right)^{2} + 2 \, \log\left(a x - 1\right)}{a^{5}} - \frac{4 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a^{5}} - \frac{2 \, \log\left(a x + 1\right)}{a^{5}}\right)} - \frac{1}{2} \, {\left(\frac{x^{2}}{a^{2}} + \frac{\log\left(a^{2} x^{2} - 1\right)}{a^{4}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/8*a*((4*a*x - log(a*x + 1)^2 + 2*log(a*x + 1)*log(a*x - 1) + log(a*x - 1)^2 + 2*log(a*x - 1))/a^5 - 4*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a^5 - 2*log(a*x + 1)/a^5) - 1/2*(x^2/a^2 + log(a^2*x^2 - 1)/a^4)*arctanh(a*x)","A",0
228,1,85,0,0.315772," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{2 \, x}{a^{2}} - \frac{\log\left(a x + 1\right)}{a^{3}} + \frac{\log\left(a x - 1\right)}{a^{3}}\right)} \operatorname{artanh}\left(a x\right) + \frac{2 \, {\left(\log\left(a x - 1\right) - 2\right)} \log\left(a x + 1\right) - \log\left(a x + 1\right)^{2} - \log\left(a x - 1\right)^{2} - 4 \, \log\left(a x - 1\right)}{8 \, a^{3}}"," ",0,"-1/2*(2*x/a^2 - log(a*x + 1)/a^3 + log(a*x - 1)/a^3)*arctanh(a*x) + 1/8*(2*(log(a*x - 1) - 2)*log(a*x + 1) - log(a*x + 1)^2 - log(a*x - 1)^2 - 4*log(a*x - 1))/a^3","B",0
229,1,125,0,0.318120," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{\log\left(a x + 1\right)^{2} + 2 \, \log\left(a x + 1\right) \log\left(a x - 1\right) - \log\left(a x - 1\right)^{2}}{a^{3}} - \frac{4 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a^{3}}\right)} + \frac{{\left(\frac{\log\left(a x + 1\right)}{a} - \frac{\log\left(a x - 1\right)}{a}\right)} \log\left(a^{2} x^{2} - 1\right)}{4 \, a} - \frac{\operatorname{artanh}\left(a x\right) \log\left(a^{2} x^{2} - 1\right)}{2 \, a^{2}}"," ",0,"-1/8*a*((log(a*x + 1)^2 + 2*log(a*x + 1)*log(a*x - 1) - log(a*x - 1)^2)/a^3 - 4*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a^3) + 1/4*(log(a*x + 1)/a - log(a*x - 1)/a)*log(a^2*x^2 - 1)/a - 1/2*arctanh(a*x)*log(a^2*x^2 - 1)/a^2","B",0
230,1,65,0,0.315598," ","integrate(arctanh(a*x)/(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{\log\left(a x + 1\right)}{a} - \frac{\log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right) - \frac{\log\left(a x + 1\right)^{2} - 2 \, \log\left(a x + 1\right) \log\left(a x - 1\right) + \log\left(a x - 1\right)^{2}}{8 \, a}"," ",0,"1/2*(log(a*x + 1)/a - log(a*x - 1)/a)*arctanh(a*x) - 1/8*(log(a*x + 1)^2 - 2*log(a*x + 1)*log(a*x - 1) + log(a*x - 1)^2)/a","B",0
231,1,132,0,0.333882," ","integrate(arctanh(a*x)/x/(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{\log\left(a x + 1\right)^{2} - 2 \, \log\left(a x + 1\right) \log\left(a x - 1\right) - \log\left(a x - 1\right)^{2}}{a} + \frac{4 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a} - \frac{4 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)}}{a} + \frac{4 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)}}{a}\right)} - \frac{1}{2} \, {\left(\log\left(a^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/8*a*((log(a*x + 1)^2 - 2*log(a*x + 1)*log(a*x - 1) - log(a*x - 1)^2)/a + 4*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a - 4*(log(a*x + 1)*log(x) + dilog(-a*x))/a + 4*(log(-a*x + 1)*log(x) + dilog(a*x))/a) - 1/2*(log(a^2*x^2 - 1) - log(x^2))*arctanh(a*x)","B",0
232,1,82,0,0.319366," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(2 \, {\left(\log\left(a x - 1\right) - 2\right)} \log\left(a x + 1\right) - \log\left(a x + 1\right)^{2} - \log\left(a x - 1\right)^{2} - 4 \, \log\left(a x - 1\right) + 8 \, \log\left(x\right)\right)} a + \frac{1}{2} \, {\left(a \log\left(a x + 1\right) - a \log\left(a x - 1\right) - \frac{2}{x}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/8*(2*(log(a*x - 1) - 2)*log(a*x + 1) - log(a*x + 1)^2 - log(a*x - 1)^2 - 4*log(a*x - 1) + 8*log(x))*a + 1/2*(a*log(a*x + 1) - a*log(a*x - 1) - 2/x)*arctanh(a*x)","B",0
233,1,162,0,0.325538," ","integrate(arctanh(a*x)/x^3/(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(4 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)} a - 4 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)} a + 4 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)} a + 2 \, a \log\left(a x + 1\right) - 2 \, a \log\left(a x - 1\right) + \frac{a x \log\left(a x + 1\right)^{2} - 2 \, a x \log\left(a x + 1\right) \log\left(a x - 1\right) - a x \log\left(a x - 1\right)^{2} - 4}{x}\right)} a - \frac{1}{2} \, {\left(a^{2} \log\left(a^{2} x^{2} - 1\right) - a^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/8*(4*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))*a - 4*(log(a*x + 1)*log(x) + dilog(-a*x))*a + 4*(log(-a*x + 1)*log(x) + dilog(a*x))*a + 2*a*log(a*x + 1) - 2*a*log(a*x - 1) + (a*x*log(a*x + 1)^2 - 2*a*x*log(a*x + 1)*log(a*x - 1) - a*x*log(a*x - 1)^2 - 4)/x)*a - 1/2*(a^2*log(a^2*x^2 - 1) - a^2*log(x^2) + 1/x^2)*arctanh(a*x)","B",0
234,0,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{3 \, {\left(a^{2} x^{2} + \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{2} + \log\left(-a x + 1\right)^{3}}{24 \, a^{4}} + \frac{1}{4} \, \int -\frac{a^{3} x^{3} \log\left(a x + 1\right)^{2} - {\left(a^{3} x^{3} + a^{2} x^{2} + {\left(2 \, a^{3} x^{3} + a x + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)}{a^{5} x^{2} - a^{3}}\,{d x}"," ",0,"-1/24*(3*(a^2*x^2 + log(a*x + 1))*log(-a*x + 1)^2 + log(-a*x + 1)^3)/a^4 + 1/4*integrate(-(a^3*x^3*log(a*x + 1)^2 - (a^3*x^3 + a^2*x^2 + (2*a^3*x^3 + a*x + 1)*log(a*x + 1))*log(-a*x + 1))/(a^5*x^2 - a^3), x)","F",0
235,1,200,0,0.325715," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{2 \, x}{a^{2}} - \frac{\log\left(a x + 1\right)}{a^{3}} + \frac{\log\left(a x - 1\right)}{a^{3}}\right)} \operatorname{artanh}\left(a x\right)^{2} - \frac{\frac{3 \, {\left(\log\left(a x - 1\right) - 2\right)} \log\left(a x + 1\right)^{2} - \log\left(a x + 1\right)^{3} + \log\left(a x - 1\right)^{3} - 3 \, {\left(\log\left(a x - 1\right)^{2} - 4 \, \log\left(a x - 1\right)\right)} \log\left(a x + 1\right) + 6 \, \log\left(a x - 1\right)^{2}}{a} - \frac{24 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a}}{24 \, a^{2}} + \frac{{\left(2 \, {\left(\log\left(a x - 1\right) - 2\right)} \log\left(a x + 1\right) - \log\left(a x + 1\right)^{2} - \log\left(a x - 1\right)^{2} - 4 \, \log\left(a x - 1\right)\right)} \operatorname{artanh}\left(a x\right)}{4 \, a^{3}}"," ",0,"-1/2*(2*x/a^2 - log(a*x + 1)/a^3 + log(a*x - 1)/a^3)*arctanh(a*x)^2 - 1/24*((3*(log(a*x - 1) - 2)*log(a*x + 1)^2 - log(a*x + 1)^3 + log(a*x - 1)^3 - 3*(log(a*x - 1)^2 - 4*log(a*x - 1))*log(a*x + 1) + 6*log(a*x - 1)^2)/a - 24*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a)/a^2 + 1/4*(2*(log(a*x - 1) - 2)*log(a*x + 1) - log(a*x + 1)^2 - log(a*x - 1)^2 - 4*log(a*x - 1))*arctanh(a*x)/a^3","B",0
236,0,0,0,0.000000," ","integrate(x*arctanh(a*x)^2/(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{3 \, \log\left(a x + 1\right) \log\left(-a x + 1\right)^{2} + \log\left(-a x + 1\right)^{3}}{24 \, a^{2}} + \frac{1}{4} \, \int -\frac{a x \log\left(a x + 1\right)^{2} - {\left(3 \, a x + 1\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{3} x^{2} - a}\,{d x}"," ",0,"-1/24*(3*log(a*x + 1)*log(-a*x + 1)^2 + log(-a*x + 1)^3)/a^2 + 1/4*integrate(-(a*x*log(a*x + 1)^2 - (3*a*x + 1)*log(a*x + 1)*log(-a*x + 1))/(a^3*x^2 - a), x)","F",0
237,1,127,0,0.329786," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{\log\left(a x + 1\right)}{a} - \frac{\log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right)^{2} - \frac{{\left(\log\left(a x + 1\right)^{2} - 2 \, \log\left(a x + 1\right) \log\left(a x - 1\right) + \log\left(a x - 1\right)^{2}\right)} \operatorname{artanh}\left(a x\right)}{4 \, a} + \frac{\log\left(a x + 1\right)^{3} - 3 \, \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) + 3 \, \log\left(a x + 1\right) \log\left(a x - 1\right)^{2} - \log\left(a x - 1\right)^{3}}{24 \, a}"," ",0,"1/2*(log(a*x + 1)/a - log(a*x - 1)/a)*arctanh(a*x)^2 - 1/4*(log(a*x + 1)^2 - 2*log(a*x + 1)*log(a*x - 1) + log(a*x - 1)^2)*arctanh(a*x)/a + 1/24*(log(a*x + 1)^3 - 3*log(a*x + 1)^2*log(a*x - 1) + 3*log(a*x + 1)*log(a*x - 1)^2 - log(a*x - 1)^3)/a","B",0
238,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x/(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{8} \, \log\left(a x + 1\right) \log\left(-a x + 1\right)^{2} - \frac{1}{24} \, \log\left(-a x + 1\right)^{3} + \frac{1}{4} \, \int \frac{{\left(a^{2} x^{2} + a x + 2\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right) - \log\left(a x + 1\right)^{2}}{a^{2} x^{3} - x}\,{d x}"," ",0,"-1/8*log(a*x + 1)*log(-a*x + 1)^2 - 1/24*log(-a*x + 1)^3 + 1/4*integrate(((a^2*x^2 + a*x + 2)*log(a*x + 1)*log(-a*x + 1) - log(a*x + 1)^2)/(a^2*x^3 - x), x)","F",0
239,1,237,0,0.332977," ","integrate(arctanh(a*x)^2/x^2/(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{24} \, a^{2} {\left(\frac{3 \, {\left(\log\left(a x - 1\right) - 2\right)} \log\left(a x + 1\right)^{2} - \log\left(a x + 1\right)^{3} + \log\left(a x - 1\right)^{3} - 3 \, {\left(\log\left(a x - 1\right)^{2} - 4 \, \log\left(a x - 1\right)\right)} \log\left(a x + 1\right) + 6 \, \log\left(a x - 1\right)^{2}}{a} - \frac{24 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a} + \frac{24 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)}}{a} - \frac{24 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)}}{a}\right)} + \frac{1}{4} \, {\left(2 \, {\left(\log\left(a x - 1\right) - 2\right)} \log\left(a x + 1\right) - \log\left(a x + 1\right)^{2} - \log\left(a x - 1\right)^{2} - 4 \, \log\left(a x - 1\right) + 8 \, \log\left(x\right)\right)} a \operatorname{artanh}\left(a x\right) + \frac{1}{2} \, {\left(a \log\left(a x + 1\right) - a \log\left(a x - 1\right) - \frac{2}{x}\right)} \operatorname{artanh}\left(a x\right)^{2}"," ",0,"-1/24*a^2*((3*(log(a*x - 1) - 2)*log(a*x + 1)^2 - log(a*x + 1)^3 + log(a*x - 1)^3 - 3*(log(a*x - 1)^2 - 4*log(a*x - 1))*log(a*x + 1) + 6*log(a*x - 1)^2)/a - 24*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a + 24*(log(a*x + 1)*log(x) + dilog(-a*x))/a - 24*(log(-a*x + 1)*log(x) + dilog(a*x))/a) + 1/4*(2*(log(a*x - 1) - 2)*log(a*x + 1) - log(a*x + 1)^2 - log(a*x - 1)^2 - 4*log(a*x - 1) + 8*log(x))*a*arctanh(a*x) + 1/2*(a*log(a*x + 1) - a*log(a*x - 1) - 2/x)*arctanh(a*x)^2","B",0
240,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x^3/(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{a^{2} x^{2} \log\left(-a x + 1\right)^{3} + 3 \, {\left(a^{2} x^{2} \log\left(a x + 1\right) + 1\right)} \log\left(-a x + 1\right)^{2}}{24 \, x^{2}} + \frac{1}{4} \, \int -\frac{\log\left(a x + 1\right)^{2} - {\left(a^{2} x^{2} + a x + {\left(a^{4} x^{4} + a^{3} x^{3} + 2\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)}{a^{2} x^{5} - x^{3}}\,{d x}"," ",0,"-1/24*(a^2*x^2*log(-a*x + 1)^3 + 3*(a^2*x^2*log(a*x + 1) + 1)*log(-a*x + 1)^2)/x^2 + 1/4*integrate(-(log(a*x + 1)^2 - (a^2*x^2 + a*x + (a^4*x^4 + a^3*x^3 + 2)*log(a*x + 1))*log(-a*x + 1))/(a^2*x^5 - x^3), x)","F",0
241,0,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^3/(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{4 \, {\left(a^{2} x^{2} + \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{3} + \log\left(-a x + 1\right)^{4}}{64 \, a^{4}} - \frac{1}{8} \, \int \frac{2 \, a^{3} x^{3} \log\left(a x + 1\right)^{3} - 6 \, a^{3} x^{3} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) + 3 \, {\left(a^{3} x^{3} + a^{2} x^{2} + {\left(2 \, a^{3} x^{3} + a x + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{2}}{2 \, {\left(a^{5} x^{2} - a^{3}\right)}}\,{d x}"," ",0,"1/64*(4*(a^2*x^2 + log(a*x + 1))*log(-a*x + 1)^3 + log(-a*x + 1)^4)/a^4 - 1/8*integrate(1/2*(2*a^3*x^3*log(a*x + 1)^3 - 6*a^3*x^3*log(a*x + 1)^2*log(-a*x + 1) + 3*(a^3*x^3 + a^2*x^2 + (2*a^3*x^3 + a*x + 1)*log(a*x + 1))*log(-a*x + 1)^2)/(a^5*x^2 - a^3), x)","F",0
242,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{4 \, {\left(2 \, a x - \log\left(a x + 1\right) - 2\right)} \log\left(-a x + 1\right)^{3} + \log\left(-a x + 1\right)^{4} - 6 \, {\left(4 \, {\left(a x + 1\right)} \log\left(a x + 1\right) - \log\left(a x + 1\right)^{2}\right)} \log\left(-a x + 1\right)^{2}}{64 \, a^{3}} + \frac{1}{8} \, \int -\frac{2 \, a^{2} x^{2} \log\left(a x + 1\right)^{3} - 3 \, {\left({\left(2 \, a^{2} x^{2} - a x - 1\right)} \log\left(a x + 1\right)^{2} + 4 \, {\left(a^{2} x^{2} + 2 \, a x + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)}{2 \, {\left(a^{4} x^{2} - a^{2}\right)}}\,{d x}"," ",0,"1/64*(4*(2*a*x - log(a*x + 1) - 2)*log(-a*x + 1)^3 + log(-a*x + 1)^4 - 6*(4*(a*x + 1)*log(a*x + 1) - log(a*x + 1)^2)*log(-a*x + 1)^2)/a^3 + 1/8*integrate(-1/2*(2*a^2*x^2*log(a*x + 1)^3 - 3*((2*a^2*x^2 - a*x - 1)*log(a*x + 1)^2 + 4*(a^2*x^2 + 2*a*x + 1)*log(a*x + 1))*log(-a*x + 1))/(a^4*x^2 - a^2), x)","F",0
243,0,0,0,0.000000," ","integrate(x*arctanh(a*x)^3/(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{4 \, \log\left(a x + 1\right) \log\left(-a x + 1\right)^{3} + \log\left(-a x + 1\right)^{4}}{64 \, a^{2}} - \frac{1}{8} \, \int \frac{2 \, a x \log\left(a x + 1\right)^{3} - 6 \, a x \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) + 3 \, {\left(3 \, a x + 1\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right)^{2}}{2 \, {\left(a^{3} x^{2} - a\right)}}\,{d x}"," ",0,"1/64*(4*log(a*x + 1)*log(-a*x + 1)^3 + log(-a*x + 1)^4)/a^2 - 1/8*integrate(1/2*(2*a*x*log(a*x + 1)^3 - 6*a*x*log(a*x + 1)^2*log(-a*x + 1) + 3*(3*a*x + 1)*log(a*x + 1)*log(-a*x + 1)^2)/(a^3*x^2 - a), x)","F",0
244,1,209,0,0.334972," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{\log\left(a x + 1\right)}{a} - \frac{\log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right)^{3} + \frac{1}{64} \, a {\left(\frac{8 \, {\left(\log\left(a x + 1\right)^{3} - 3 \, \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) + 3 \, \log\left(a x + 1\right) \log\left(a x - 1\right)^{2} - \log\left(a x - 1\right)^{3}\right)} \operatorname{artanh}\left(a x\right)}{a^{2}} - \frac{\log\left(a x + 1\right)^{4} - 4 \, \log\left(a x + 1\right)^{3} \log\left(a x - 1\right) + 6 \, \log\left(a x + 1\right)^{2} \log\left(a x - 1\right)^{2} - 4 \, \log\left(a x + 1\right) \log\left(a x - 1\right)^{3} + \log\left(a x - 1\right)^{4}}{a^{2}}\right)} - \frac{3 \, {\left(\log\left(a x + 1\right)^{2} - 2 \, \log\left(a x + 1\right) \log\left(a x - 1\right) + \log\left(a x - 1\right)^{2}\right)} \operatorname{artanh}\left(a x\right)^{2}}{8 \, a}"," ",0,"1/2*(log(a*x + 1)/a - log(a*x - 1)/a)*arctanh(a*x)^3 + 1/64*a*(8*(log(a*x + 1)^3 - 3*log(a*x + 1)^2*log(a*x - 1) + 3*log(a*x + 1)*log(a*x - 1)^2 - log(a*x - 1)^3)*arctanh(a*x)/a^2 - (log(a*x + 1)^4 - 4*log(a*x + 1)^3*log(a*x - 1) + 6*log(a*x + 1)^2*log(a*x - 1)^2 - 4*log(a*x + 1)*log(a*x - 1)^3 + log(a*x - 1)^4)/a^2) - 3/8*(log(a*x + 1)^2 - 2*log(a*x + 1)*log(a*x - 1) + log(a*x - 1)^2)*arctanh(a*x)^2/a","B",0
245,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x/(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{16} \, \log\left(a x + 1\right) \log\left(-a x + 1\right)^{3} + \frac{1}{64} \, \log\left(-a x + 1\right)^{4} - \frac{1}{8} \, \int \frac{3 \, {\left(a^{2} x^{2} + a x + 2\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right)^{2} + 2 \, \log\left(a x + 1\right)^{3} - 6 \, \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)}{2 \, {\left(a^{2} x^{3} - x\right)}}\,{d x}"," ",0,"1/16*log(a*x + 1)*log(-a*x + 1)^3 + 1/64*log(-a*x + 1)^4 - 1/8*integrate(1/2*(3*(a^2*x^2 + a*x + 2)*log(a*x + 1)*log(-a*x + 1)^2 + 2*log(a*x + 1)^3 - 6*log(a*x + 1)^2*log(-a*x + 1))/(a^2*x^3 - x), x)","F",0
246,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^2/(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{a x \log\left(-a x + 1\right)^{4} - 4 \, {\left(a x \log\left(a x + 1\right) + 2 \, a x - 2\right)} \log\left(-a x + 1\right)^{3} + 6 \, {\left(a x \log\left(a x + 1\right)^{2} - 4 \, {\left(a x + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{2}}{64 \, x} - \frac{1}{8} \, \int \frac{2 \, \log\left(a x + 1\right)^{3} + 3 \, {\left({\left(a^{3} x^{3} + a^{2} x^{2} - 2\right)} \log\left(a x + 1\right)^{2} - 4 \, {\left(a^{3} x^{3} + 2 \, a^{2} x^{2} + a x\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)}{2 \, {\left(a^{2} x^{4} - x^{2}\right)}}\,{d x}"," ",0,"1/64*(a*x*log(-a*x + 1)^4 - 4*(a*x*log(a*x + 1) + 2*a*x - 2)*log(-a*x + 1)^3 + 6*(a*x*log(a*x + 1)^2 - 4*(a*x + 1)*log(a*x + 1))*log(-a*x + 1)^2)/x - 1/8*integrate(1/2*(2*log(a*x + 1)^3 + 3*((a^3*x^3 + a^2*x^2 - 2)*log(a*x + 1)^2 - 4*(a^3*x^3 + 2*a^2*x^2 + a*x)*log(a*x + 1))*log(-a*x + 1))/(a^2*x^4 - x^2), x)","F",0
247,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^3/(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{a^{2} x^{2} \log\left(-a x + 1\right)^{4} + 4 \, {\left(a^{2} x^{2} \log\left(a x + 1\right) + 1\right)} \log\left(-a x + 1\right)^{3}}{64 \, x^{2}} - \frac{1}{8} \, \int \frac{2 \, \log\left(a x + 1\right)^{3} - 6 \, \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) + 3 \, {\left(a^{2} x^{2} + a x + {\left(a^{4} x^{4} + a^{3} x^{3} + 2\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{2}}{2 \, {\left(a^{2} x^{5} - x^{3}\right)}}\,{d x}"," ",0,"1/64*(a^2*x^2*log(-a*x + 1)^4 + 4*(a^2*x^2*log(a*x + 1) + 1)*log(-a*x + 1)^3)/x^2 - 1/8*integrate(1/2*(2*log(a*x + 1)^3 - 6*log(a*x + 1)^2*log(-a*x + 1) + 3*(a^2*x^2 + a*x + (a^4*x^4 + a^3*x^3 + 2)*log(a*x + 1))*log(-a*x + 1)^2)/(a^2*x^5 - x^3), x)","F",0
248,0,0,0,0.000000," ","integrate(arctanh(a*x)^(1/2)/(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{\sqrt{\operatorname{artanh}\left(a x\right)}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate(sqrt(arctanh(a*x))/(a^2*x^2 - 1), x)","F",0
249,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)/arctanh(a*x),x, algorithm=""maxima"")","-\int \frac{x}{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"-integrate(x/((a^2*x^2 - 1)*arctanh(a*x)), x)","F",0
250,1,21,0,0.308418," ","integrate(1/(-a^2*x^2+1)/arctanh(a*x),x, algorithm=""maxima"")","\frac{\log\left(-\log\left(a x + 1\right) + \log\left(-a x + 1\right)\right)}{a}"," ",0,"log(-log(a*x + 1) + log(-a*x + 1))/a","B",0
251,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)/arctanh(a*x),x, algorithm=""maxima"")","-\int \frac{1}{{\left(a^{2} x^{2} - 1\right)} x \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"-integrate(1/((a^2*x^2 - 1)*x*arctanh(a*x)), x)","F",0
252,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)/arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, x}{a \log\left(a x + 1\right) - a \log\left(-a x + 1\right)} - 2 \, \int -\frac{1}{a \log\left(a x + 1\right) - a \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2*x/(a*log(a*x + 1) - a*log(-a*x + 1)) - 2*integrate(-1/(a*log(a*x + 1) - a*log(-a*x + 1)), x)","F",0
253,1,23,0,0.326113," ","integrate(1/(-a^2*x^2+1)/arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{2}{a \log\left(a x + 1\right) - a \log\left(-a x + 1\right)}"," ",0,"-2/(a*log(a*x + 1) - a*log(-a*x + 1))","B",0
254,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)/arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{2}{a x \log\left(a x + 1\right) - a x \log\left(-a x + 1\right)} + 2 \, \int -\frac{1}{a x^{2} \log\left(a x + 1\right) - a x^{2} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2/(a*x*log(a*x + 1) - a*x*log(-a*x + 1)) + 2*integrate(-1/(a*x^2*log(a*x + 1) - a*x^2*log(-a*x + 1)), x)","F",0
255,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)/arctanh(a*x)^3,x, algorithm=""maxima"")","-\frac{2 \, a x - {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)}{a^{2} \log\left(a x + 1\right)^{2} - 2 \, a^{2} \log\left(a x + 1\right) \log\left(-a x + 1\right) + a^{2} \log\left(-a x + 1\right)^{2}} + 2 \, \int -\frac{x}{\log\left(a x + 1\right) - \log\left(-a x + 1\right)}\,{d x}"," ",0,"-(2*a*x - (a^2*x^2 - 1)*log(a*x + 1) + (a^2*x^2 - 1)*log(-a*x + 1))/(a^2*log(a*x + 1)^2 - 2*a^2*log(a*x + 1)*log(-a*x + 1) + a^2*log(-a*x + 1)^2) + 2*integrate(-x/(log(a*x + 1) - log(-a*x + 1)), x)","F",0
256,1,42,0,0.332196," ","integrate(1/(-a^2*x^2+1)/arctanh(a*x)^3,x, algorithm=""maxima"")","-\frac{2}{a \log\left(a x + 1\right)^{2} - 2 \, a \log\left(a x + 1\right) \log\left(-a x + 1\right) + a \log\left(-a x + 1\right)^{2}}"," ",0,"-2/(a*log(a*x + 1)^2 - 2*a*log(a*x + 1)*log(-a*x + 1) + a*log(-a*x + 1)^2)","B",0
257,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)/arctanh(a*x)^3,x, algorithm=""maxima"")","-\frac{2 \, a x + {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) - {\left(a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)}{a^{2} x^{2} \log\left(a x + 1\right)^{2} - 2 \, a^{2} x^{2} \log\left(a x + 1\right) \log\left(-a x + 1\right) + a^{2} x^{2} \log\left(-a x + 1\right)^{2}} - 2 \, \int -\frac{1}{a^{2} x^{3} \log\left(a x + 1\right) - a^{2} x^{3} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-(2*a*x + (a^2*x^2 - 1)*log(a*x + 1) - (a^2*x^2 - 1)*log(-a*x + 1))/(a^2*x^2*log(a*x + 1)^2 - 2*a^2*x^2*log(a*x + 1)*log(-a*x + 1) + a^2*x^2*log(-a*x + 1)^2) - 2*integrate(-1/(a^2*x^3*log(a*x + 1) - a^2*x^3*log(-a*x + 1)), x)","F",0
258,0,0,0,0.000000," ","integrate(arctanh(a*x)^p/(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{\operatorname{artanh}\left(a x\right)^{p}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate(arctanh(a*x)^p/(a^2*x^2 - 1), x)","F",0
259,1,177,0,0.326018," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{{\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 2 \, a x - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)}{a^{7} x^{2} - a^{5}} + \frac{4 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a^{5}} + \frac{\log\left(a x + 1\right)}{a^{5}}\right)} - \frac{1}{2} \, {\left(\frac{1}{a^{6} x^{2} - a^{4}} - \frac{\log\left(a^{2} x^{2} - 1\right)}{a^{4}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/8*a*(((a^2*x^2 - 1)*log(a*x + 1)^2 - 2*(a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) - (a^2*x^2 - 1)*log(a*x - 1)^2 - 2*a*x - (a^2*x^2 - 1)*log(a*x - 1))/(a^7*x^2 - a^5) + 4*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a^5 + log(a*x + 1)/a^5) - 1/2*(1/(a^6*x^2 - a^4) - log(a^2*x^2 - 1)/a^4)*arctanh(a*x)","A",0
260,1,126,0,0.315795," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(\frac{2 \, x}{a^{4} x^{2} - a^{2}} + \frac{\log\left(a x + 1\right)}{a^{3}} - \frac{\log\left(a x - 1\right)}{a^{3}}\right)} \operatorname{artanh}\left(a x\right) + \frac{{\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} + 4\right)} a}{16 \, {\left(a^{6} x^{2} - a^{4}\right)}}"," ",0,"-1/4*(2*x/(a^4*x^2 - a^2) + log(a*x + 1)/a^3 - log(a*x - 1)/a^3)*arctanh(a*x) + 1/16*((a^2*x^2 - 1)*log(a*x + 1)^2 - 2*(a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) + (a^2*x^2 - 1)*log(a*x - 1)^2 + 4)*a/(a^6*x^2 - a^4)","B",0
261,1,62,0,0.311771," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","\frac{\frac{2 \, x}{a^{2} x^{2} - 1} - \frac{\log\left(a x + 1\right)}{a} + \frac{\log\left(a x - 1\right)}{a}}{8 \, a} - \frac{\operatorname{artanh}\left(a x\right)}{2 \, {\left(a^{2} x^{2} - 1\right)} a^{2}}"," ",0,"1/8*(2*x/(a^2*x^2 - 1) - log(a*x + 1)/a + log(a*x - 1)/a)/a - 1/2*arctanh(a*x)/((a^2*x^2 - 1)*a^2)","A",0
262,1,122,0,0.313687," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(\frac{2 \, x}{a^{2} x^{2} - 1} - \frac{\log\left(a x + 1\right)}{a} + \frac{\log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right) - \frac{{\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 4\right)} a}{16 \, {\left(a^{4} x^{2} - a^{2}\right)}}"," ",0,"-1/4*(2*x/(a^2*x^2 - 1) - log(a*x + 1)/a + log(a*x - 1)/a)*arctanh(a*x) - 1/16*((a^2*x^2 - 1)*log(a*x + 1)^2 - 2*(a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) + (a^2*x^2 - 1)*log(a*x - 1)^2 - 4)*a/(a^4*x^2 - a^2)","B",0
263,1,206,0,0.336877," ","integrate(arctanh(a*x)/x/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{{\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} + 2 \, a x}{a^{3} x^{2} - a} + \frac{4 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a} - \frac{4 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)}}{a} + \frac{4 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)}}{a} - \frac{\log\left(a x + 1\right)}{a} + \frac{\log\left(a x - 1\right)}{a}\right)} - \frac{1}{2} \, {\left(\frac{1}{a^{2} x^{2} - 1} + \log\left(a^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/8*a*(((a^2*x^2 - 1)*log(a*x + 1)^2 - 2*(a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) - (a^2*x^2 - 1)*log(a*x - 1)^2 + 2*a*x)/(a^3*x^2 - a) + 4*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a - 4*(log(a*x + 1)*log(x) + dilog(-a*x))/a + 4*(log(-a*x + 1)*log(x) + dilog(a*x))/a - log(a*x + 1)/a + log(a*x - 1)/a) - 1/2*(1/(a^2*x^2 - 1) + log(a^2*x^2 - 1) - log(x^2))*arctanh(a*x)","B",0
264,1,150,0,0.330153," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","-\frac{1}{16} \, a {\left(\frac{3 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} - 6 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) + 3 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 4}{a^{2} x^{2} - 1} + 8 \, \log\left(a x + 1\right) + 8 \, \log\left(a x - 1\right) - 16 \, \log\left(x\right)\right)} + \frac{1}{4} \, {\left(3 \, a \log\left(a x + 1\right) - 3 \, a \log\left(a x - 1\right) - \frac{2 \, {\left(3 \, a^{2} x^{2} - 2\right)}}{a^{2} x^{3} - x}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/16*a*((3*(a^2*x^2 - 1)*log(a*x + 1)^2 - 6*(a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) + 3*(a^2*x^2 - 1)*log(a*x - 1)^2 - 4)/(a^2*x^2 - 1) + 8*log(a*x + 1) + 8*log(a*x - 1) - 16*log(x)) + 1/4*(3*a*log(a*x + 1) - 3*a*log(a*x - 1) - 2*(3*a^2*x^2 - 2)/(a^2*x^3 - x))*arctanh(a*x)","B",0
265,1,233,0,0.334441," ","integrate(arctanh(a*x)/x^3/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(8 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)} a - 8 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)} a + 8 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)} a + a \log\left(a x + 1\right) - a \log\left(a x - 1\right) - \frac{2 \, {\left(a^{2} x^{2} - {\left(a^{3} x^{3} - a x\right)} \log\left(a x + 1\right)^{2} + 2 \, {\left(a^{3} x^{3} - a x\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) + {\left(a^{3} x^{3} - a x\right)} \log\left(a x - 1\right)^{2} - 2\right)}}{a^{2} x^{3} - x}\right)} a - \frac{1}{2} \, {\left(2 \, a^{2} \log\left(a^{2} x^{2} - 1\right) - 2 \, a^{2} \log\left(x^{2}\right) + \frac{2 \, a^{2} x^{2} - 1}{a^{2} x^{4} - x^{2}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/8*(8*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))*a - 8*(log(a*x + 1)*log(x) + dilog(-a*x))*a + 8*(log(-a*x + 1)*log(x) + dilog(a*x))*a + a*log(a*x + 1) - a*log(a*x - 1) - 2*(a^2*x^2 - (a^3*x^3 - a*x)*log(a*x + 1)^2 + 2*(a^3*x^3 - a*x)*log(a*x + 1)*log(a*x - 1) + (a^3*x^3 - a*x)*log(a*x - 1)^2 - 2)/(a^2*x^3 - x))*a - 1/2*(2*a^2*log(a^2*x^2 - 1) - 2*a^2*log(x^2) + (2*a^2*x^2 - 1)/(a^2*x^4 - x^2))*arctanh(a*x)","B",0
266,0,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","-\frac{3}{4} \, a^{3} \int \frac{x^{3} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}}\,{d x} - \frac{1}{4} \, a^{2} \int \frac{x^{2} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}}\,{d x} - \frac{1}{32} \, {\left(a {\left(\frac{2}{a^{7} x - a^{6}} - \frac{\log\left(a x + 1\right)}{a^{6}} + \frac{\log\left(a x - 1\right)}{a^{6}}\right)} + \frac{4 \, \log\left(-a x + 1\right)}{a^{7} x^{2} - a^{5}}\right)} a + \frac{1}{4} \, a \int \frac{x \log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}}\,{d x} + \frac{{\left(a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)^{3} + 3 \, {\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) - 1\right)} \log\left(-a x + 1\right)^{2}}{24 \, {\left(a^{6} x^{2} - a^{4}\right)}} + \frac{1}{4} \, \int \frac{a^{3} x^{3} \log\left(a x + 1\right)^{2}}{a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}}\,{d x} + \frac{1}{4} \, \int \frac{\log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}}\,{d x} + \frac{1}{4} \, \int \frac{\log\left(-a x + 1\right)}{a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}}\,{d x}"," ",0,"-3/4*a^3*integrate(x^3*log(a*x + 1)*log(-a*x + 1)/(a^7*x^4 - 2*a^5*x^2 + a^3), x) - 1/4*a^2*integrate(x^2*log(a*x + 1)*log(-a*x + 1)/(a^7*x^4 - 2*a^5*x^2 + a^3), x) - 1/32*(a*(2/(a^7*x - a^6) - log(a*x + 1)/a^6 + log(a*x - 1)/a^6) + 4*log(-a*x + 1)/(a^7*x^2 - a^5))*a + 1/4*a*integrate(x*log(a*x + 1)*log(-a*x + 1)/(a^7*x^4 - 2*a^5*x^2 + a^3), x) + 1/24*((a^2*x^2 - 1)*log(-a*x + 1)^3 + 3*((a^2*x^2 - 1)*log(a*x + 1) - 1)*log(-a*x + 1)^2)/(a^6*x^2 - a^4) + 1/4*integrate(a^3*x^3*log(a*x + 1)^2/(a^7*x^4 - 2*a^5*x^2 + a^3), x) + 1/4*integrate(log(a*x + 1)*log(-a*x + 1)/(a^7*x^4 - 2*a^5*x^2 + a^3), x) + 1/4*integrate(log(-a*x + 1)/(a^7*x^4 - 2*a^5*x^2 + a^3), x)","F",0
267,1,273,0,0.336238," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(\frac{2 \, x}{a^{4} x^{2} - a^{2}} + \frac{\log\left(a x + 1\right)}{a^{3}} - \frac{\log\left(a x - 1\right)}{a^{3}}\right)} \operatorname{artanh}\left(a x\right)^{2} - \frac{{\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{3} + 12 \, a x - 3 \, {\left(2 \, a^{2} x^{2} - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 2\right)} \log\left(a x + 1\right) + 6 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} a^{2}}{48 \, {\left(a^{7} x^{2} - a^{5}\right)}} + \frac{{\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} + 4\right)} a \operatorname{artanh}\left(a x\right)}{8 \, {\left(a^{6} x^{2} - a^{4}\right)}}"," ",0,"-1/4*(2*x/(a^4*x^2 - a^2) + log(a*x + 1)/a^3 - log(a*x - 1)/a^3)*arctanh(a*x)^2 - 1/48*((a^2*x^2 - 1)*log(a*x + 1)^3 - 3*(a^2*x^2 - 1)*log(a*x + 1)^2*log(a*x - 1) - (a^2*x^2 - 1)*log(a*x - 1)^3 + 12*a*x - 3*(2*a^2*x^2 - (a^2*x^2 - 1)*log(a*x - 1)^2 - 2)*log(a*x + 1) + 6*(a^2*x^2 - 1)*log(a*x - 1))*a^2/(a^7*x^2 - a^5) + 1/8*((a^2*x^2 - 1)*log(a*x + 1)^2 - 2*(a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) + (a^2*x^2 - 1)*log(a*x - 1)^2 + 4)*a*arctanh(a*x)/(a^6*x^2 - a^4)","B",0
268,1,146,0,0.333396," ","integrate(x*arctanh(a*x)^2/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, x}{a^{2} x^{2} - 1} - \frac{\log\left(a x + 1\right)}{a} + \frac{\log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right)}{4 \, a} + \frac{{\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 4}{16 \, {\left(a^{4} x^{2} - a^{2}\right)}} - \frac{\operatorname{artanh}\left(a x\right)^{2}}{2 \, {\left(a^{2} x^{2} - 1\right)} a^{2}}"," ",0,"1/4*(2*x/(a^2*x^2 - 1) - log(a*x + 1)/a + log(a*x - 1)/a)*arctanh(a*x)/a + 1/16*((a^2*x^2 - 1)*log(a*x + 1)^2 - 2*(a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) + (a^2*x^2 - 1)*log(a*x - 1)^2 - 4)/(a^4*x^2 - a^2) - 1/2*arctanh(a*x)^2/((a^2*x^2 - 1)*a^2)","B",0
269,1,268,0,0.338099," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(\frac{2 \, x}{a^{2} x^{2} - 1} - \frac{\log\left(a x + 1\right)}{a} + \frac{\log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right)^{2} + \frac{{\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{3} - 12 \, a x + 3 \, {\left(2 \, a^{2} x^{2} + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 2\right)} \log\left(a x + 1\right) - 6 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} a^{2}}{48 \, {\left(a^{5} x^{2} - a^{3}\right)}} - \frac{{\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 4\right)} a \operatorname{artanh}\left(a x\right)}{8 \, {\left(a^{4} x^{2} - a^{2}\right)}}"," ",0,"-1/4*(2*x/(a^2*x^2 - 1) - log(a*x + 1)/a + log(a*x - 1)/a)*arctanh(a*x)^2 + 1/48*((a^2*x^2 - 1)*log(a*x + 1)^3 - 3*(a^2*x^2 - 1)*log(a*x + 1)^2*log(a*x - 1) - (a^2*x^2 - 1)*log(a*x - 1)^3 - 12*a*x + 3*(2*a^2*x^2 + (a^2*x^2 - 1)*log(a*x - 1)^2 - 2)*log(a*x + 1) - 6*(a^2*x^2 - 1)*log(a*x - 1))*a^2/(a^5*x^2 - a^3) - 1/8*((a^2*x^2 - 1)*log(a*x + 1)^2 - 2*(a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) + (a^2*x^2 - 1)*log(a*x - 1)^2 - 4)*a*arctanh(a*x)/(a^4*x^2 - a^2)","B",0
270,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{4} \int \frac{x^{4} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}\,{d x} + \frac{1}{4} \, a^{3} \int \frac{x^{3} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}\,{d x} - \frac{1}{32} \, {\left(a {\left(\frac{2}{a^{4} x - a^{3}} - \frac{\log\left(a x + 1\right)}{a^{3}} + \frac{\log\left(a x - 1\right)}{a^{3}}\right)} + \frac{4 \, \log\left(-a x + 1\right)}{a^{4} x^{2} - a^{2}}\right)} a^{2} - \frac{1}{4} \, a^{2} \int \frac{x^{2} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}\,{d x} - \frac{1}{4} \, a \int \frac{x \log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}\,{d x} + \frac{1}{4} \, a \int \frac{x \log\left(-a x + 1\right)}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}\,{d x} - \frac{{\left(a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)^{3} + 3 \, {\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) + 1\right)} \log\left(-a x + 1\right)^{2}}{24 \, {\left(a^{2} x^{2} - 1\right)}} + \frac{1}{4} \, \int \frac{\log\left(a x + 1\right)^{2}}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}\,{d x} - \frac{1}{2} \, \int \frac{\log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}\,{d x}"," ",0,"1/4*a^4*integrate(x^4*log(a*x + 1)*log(-a*x + 1)/(a^4*x^5 - 2*a^2*x^3 + x), x) + 1/4*a^3*integrate(x^3*log(a*x + 1)*log(-a*x + 1)/(a^4*x^5 - 2*a^2*x^3 + x), x) - 1/32*(a*(2/(a^4*x - a^3) - log(a*x + 1)/a^3 + log(a*x - 1)/a^3) + 4*log(-a*x + 1)/(a^4*x^2 - a^2))*a^2 - 1/4*a^2*integrate(x^2*log(a*x + 1)*log(-a*x + 1)/(a^4*x^5 - 2*a^2*x^3 + x), x) - 1/4*a*integrate(x*log(a*x + 1)*log(-a*x + 1)/(a^4*x^5 - 2*a^2*x^3 + x), x) + 1/4*a*integrate(x*log(-a*x + 1)/(a^4*x^5 - 2*a^2*x^3 + x), x) - 1/24*((a^2*x^2 - 1)*log(-a*x + 1)^3 + 3*((a^2*x^2 - 1)*log(a*x + 1) + 1)*log(-a*x + 1)^2)/(a^2*x^2 - 1) + 1/4*integrate(log(a*x + 1)^2/(a^4*x^5 - 2*a^2*x^3 + x), x) - 1/2*integrate(log(a*x + 1)*log(-a*x + 1)/(a^4*x^5 - 2*a^2*x^3 + x), x)","F",0
271,1,406,0,0.346064," ","integrate(arctanh(a*x)^2/x^2/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","\frac{1}{16} \, a^{2} {\left(\frac{{\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{3} - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{3} + {\left(4 \, a^{2} x^{2} - 3 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right) - 4\right)} \log\left(a x + 1\right)^{2} - 4 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 4 \, a x + {\left(3 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 8 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + 1\right)}{a^{3} x^{2} - a} + \frac{16 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a} - \frac{16 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)}}{a} + \frac{16 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)}}{a} + \frac{2 \, \log\left(a x + 1\right)}{a} - \frac{2 \, \log\left(a x - 1\right)}{a}\right)} - \frac{1}{8} \, a {\left(\frac{3 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} - 6 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) + 3 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 4}{a^{2} x^{2} - 1} + 8 \, \log\left(a x + 1\right) + 8 \, \log\left(a x - 1\right) - 16 \, \log\left(x\right)\right)} \operatorname{artanh}\left(a x\right) + \frac{1}{4} \, {\left(3 \, a \log\left(a x + 1\right) - 3 \, a \log\left(a x - 1\right) - \frac{2 \, {\left(3 \, a^{2} x^{2} - 2\right)}}{a^{2} x^{3} - x}\right)} \operatorname{artanh}\left(a x\right)^{2}"," ",0,"1/16*a^2*(((a^2*x^2 - 1)*log(a*x + 1)^3 - (a^2*x^2 - 1)*log(a*x - 1)^3 + (4*a^2*x^2 - 3*(a^2*x^2 - 1)*log(a*x - 1) - 4)*log(a*x + 1)^2 - 4*(a^2*x^2 - 1)*log(a*x - 1)^2 - 4*a*x + (3*(a^2*x^2 - 1)*log(a*x - 1)^2 - 8*(a^2*x^2 - 1)*log(a*x - 1))*log(a*x + 1))/(a^3*x^2 - a) + 16*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a - 16*(log(a*x + 1)*log(x) + dilog(-a*x))/a + 16*(log(-a*x + 1)*log(x) + dilog(a*x))/a + 2*log(a*x + 1)/a - 2*log(a*x - 1)/a) - 1/8*a*((3*(a^2*x^2 - 1)*log(a*x + 1)^2 - 6*(a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) + 3*(a^2*x^2 - 1)*log(a*x - 1)^2 - 4)/(a^2*x^2 - 1) + 8*log(a*x + 1) + 8*log(a*x - 1) - 16*log(x))*arctanh(a*x) + 1/4*(3*a*log(a*x + 1) - 3*a*log(a*x - 1) - 2*(3*a^2*x^2 - 2)/(a^2*x^3 - x))*arctanh(a*x)^2","B",0
272,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x^3/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{6} \int \frac{x^{6} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}\,{d x} + \frac{1}{2} \, a^{5} \int \frac{x^{5} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}\,{d x} - \frac{1}{16} \, {\left(a {\left(\frac{2}{a^{4} x - a^{3}} - \frac{\log\left(a x + 1\right)}{a^{3}} + \frac{\log\left(a x - 1\right)}{a^{3}}\right)} + \frac{4 \, \log\left(-a x + 1\right)}{a^{4} x^{2} - a^{2}}\right)} a^{4} - \frac{1}{2} \, a^{4} \int \frac{x^{4} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}\,{d x} - \frac{1}{2} \, a^{3} \int \frac{x^{3} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}\,{d x} + \frac{1}{2} \, a^{3} \int \frac{x^{3} \log\left(-a x + 1\right)}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}\,{d x} - \frac{1}{4} \, a^{2} \int \frac{x^{2} \log\left(-a x + 1\right)}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}\,{d x} - \frac{1}{4} \, a \int \frac{x \log\left(-a x + 1\right)}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}\,{d x} - \frac{2 \, {\left(a^{4} x^{4} - a^{2} x^{2}\right)} \log\left(-a x + 1\right)^{3} + 3 \, {\left(2 \, a^{2} x^{2} + 2 \, {\left(a^{4} x^{4} - a^{2} x^{2}\right)} \log\left(a x + 1\right) - 1\right)} \log\left(-a x + 1\right)^{2}}{24 \, {\left(a^{2} x^{4} - x^{2}\right)}} + \frac{1}{4} \, \int \frac{\log\left(a x + 1\right)^{2}}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}\,{d x} - \frac{1}{2} \, \int \frac{\log\left(a x + 1\right) \log\left(-a x + 1\right)}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}\,{d x}"," ",0,"1/2*a^6*integrate(x^6*log(a*x + 1)*log(-a*x + 1)/(a^4*x^7 - 2*a^2*x^5 + x^3), x) + 1/2*a^5*integrate(x^5*log(a*x + 1)*log(-a*x + 1)/(a^4*x^7 - 2*a^2*x^5 + x^3), x) - 1/16*(a*(2/(a^4*x - a^3) - log(a*x + 1)/a^3 + log(a*x - 1)/a^3) + 4*log(-a*x + 1)/(a^4*x^2 - a^2))*a^4 - 1/2*a^4*integrate(x^4*log(a*x + 1)*log(-a*x + 1)/(a^4*x^7 - 2*a^2*x^5 + x^3), x) - 1/2*a^3*integrate(x^3*log(a*x + 1)*log(-a*x + 1)/(a^4*x^7 - 2*a^2*x^5 + x^3), x) + 1/2*a^3*integrate(x^3*log(-a*x + 1)/(a^4*x^7 - 2*a^2*x^5 + x^3), x) - 1/4*a^2*integrate(x^2*log(-a*x + 1)/(a^4*x^7 - 2*a^2*x^5 + x^3), x) - 1/4*a*integrate(x*log(-a*x + 1)/(a^4*x^7 - 2*a^2*x^5 + x^3), x) - 1/24*(2*(a^4*x^4 - a^2*x^2)*log(-a*x + 1)^3 + 3*(2*a^2*x^2 + 2*(a^4*x^4 - a^2*x^2)*log(a*x + 1) - 1)*log(-a*x + 1)^2)/(a^2*x^4 - x^2) + 1/4*integrate(log(a*x + 1)^2/(a^4*x^7 - 2*a^2*x^5 + x^3), x) - 1/2*integrate(log(a*x + 1)*log(-a*x + 1)/(a^4*x^7 - 2*a^2*x^5 + x^3), x)","F",0
273,0,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)^{4} + 4 \, {\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) - 1\right)} \log\left(-a x + 1\right)^{3}}{64 \, {\left(a^{6} x^{2} - a^{4}\right)}} + \frac{1}{8} \, \int \frac{2 \, a^{3} x^{3} \log\left(a x + 1\right)^{3} - 6 \, a^{3} x^{3} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) - 3 \, {\left(a x - {\left(3 \, a^{3} x^{3} + a^{2} x^{2} - a x - 1\right)} \log\left(a x + 1\right) + 1\right)} \log\left(-a x + 1\right)^{2}}{2 \, {\left(a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}\right)}}\,{d x}"," ",0,"-1/64*((a^2*x^2 - 1)*log(-a*x + 1)^4 + 4*((a^2*x^2 - 1)*log(a*x + 1) - 1)*log(-a*x + 1)^3)/(a^6*x^2 - a^4) + 1/8*integrate(1/2*(2*a^3*x^3*log(a*x + 1)^3 - 6*a^3*x^3*log(a*x + 1)^2*log(-a*x + 1) - 3*(a*x - (3*a^3*x^3 + a^2*x^2 - a*x - 1)*log(a*x + 1) + 1)*log(-a*x + 1)^2)/(a^7*x^4 - 2*a^5*x^2 + a^3), x)","F",0
274,1,465,0,0.345564," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(\frac{2 \, x}{a^{4} x^{2} - a^{2}} + \frac{\log\left(a x + 1\right)}{a^{3}} - \frac{\log\left(a x - 1\right)}{a^{3}}\right)} \operatorname{artanh}\left(a x\right)^{3} + \frac{3 \, {\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} + 4\right)} a \operatorname{artanh}\left(a x\right)^{2}}{16 \, {\left(a^{6} x^{2} - a^{4}\right)}} + \frac{1}{128} \, {\left(\frac{{\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{4} - 4 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{3} \log\left(a x - 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{4} - 6 \, {\left(2 \, a^{2} x^{2} - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 2\right)} \log\left(a x + 1\right)^{2} - 12 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 4 \, {\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{3} - 6 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + 1\right) + 48\right)} a^{2}}{a^{8} x^{2} - a^{6}} - \frac{8 \, {\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{3} + 12 \, a x - 3 \, {\left(2 \, a^{2} x^{2} - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 2\right)} \log\left(a x + 1\right) + 6 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} a \operatorname{artanh}\left(a x\right)}{a^{7} x^{2} - a^{5}}\right)} a"," ",0,"-1/4*(2*x/(a^4*x^2 - a^2) + log(a*x + 1)/a^3 - log(a*x - 1)/a^3)*arctanh(a*x)^3 + 3/16*((a^2*x^2 - 1)*log(a*x + 1)^2 - 2*(a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) + (a^2*x^2 - 1)*log(a*x - 1)^2 + 4)*a*arctanh(a*x)^2/(a^6*x^2 - a^4) + 1/128*(((a^2*x^2 - 1)*log(a*x + 1)^4 - 4*(a^2*x^2 - 1)*log(a*x + 1)^3*log(a*x - 1) + (a^2*x^2 - 1)*log(a*x - 1)^4 - 6*(2*a^2*x^2 - (a^2*x^2 - 1)*log(a*x - 1)^2 - 2)*log(a*x + 1)^2 - 12*(a^2*x^2 - 1)*log(a*x - 1)^2 - 4*((a^2*x^2 - 1)*log(a*x - 1)^3 - 6*(a^2*x^2 - 1)*log(a*x - 1))*log(a*x + 1) + 48)*a^2/(a^8*x^2 - a^6) - 8*((a^2*x^2 - 1)*log(a*x + 1)^3 - 3*(a^2*x^2 - 1)*log(a*x + 1)^2*log(a*x - 1) - (a^2*x^2 - 1)*log(a*x - 1)^3 + 12*a*x - 3*(2*a^2*x^2 - (a^2*x^2 - 1)*log(a*x - 1)^2 - 2)*log(a*x + 1) + 6*(a^2*x^2 - 1)*log(a*x - 1))*a*arctanh(a*x)/(a^7*x^2 - a^5))*a","B",0
275,1,298,0,0.336402," ","integrate(x*arctanh(a*x)^3/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(\frac{2 \, x}{a^{2} x^{2} - 1} - \frac{\log\left(a x + 1\right)}{a} + \frac{\log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right)^{2}}{8 \, a} - \frac{\frac{{\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{3} - 12 \, a x + 3 \, {\left(2 \, a^{2} x^{2} + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 2\right)} \log\left(a x + 1\right) - 6 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} a^{2}}{a^{5} x^{2} - a^{3}} - \frac{6 \, {\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 4\right)} a \operatorname{artanh}\left(a x\right)}{a^{4} x^{2} - a^{2}}}{32 \, a} - \frac{\operatorname{artanh}\left(a x\right)^{3}}{2 \, {\left(a^{2} x^{2} - 1\right)} a^{2}}"," ",0,"3/8*(2*x/(a^2*x^2 - 1) - log(a*x + 1)/a + log(a*x - 1)/a)*arctanh(a*x)^2/a - 1/32*(((a^2*x^2 - 1)*log(a*x + 1)^3 - 3*(a^2*x^2 - 1)*log(a*x + 1)^2*log(a*x - 1) - (a^2*x^2 - 1)*log(a*x - 1)^3 - 12*a*x + 3*(2*a^2*x^2 + (a^2*x^2 - 1)*log(a*x - 1)^2 - 2)*log(a*x + 1) - 6*(a^2*x^2 - 1)*log(a*x - 1))*a^2/(a^5*x^2 - a^3) - 6*((a^2*x^2 - 1)*log(a*x + 1)^2 - 2*(a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) + (a^2*x^2 - 1)*log(a*x - 1)^2 - 4)*a*arctanh(a*x)/(a^4*x^2 - a^2))/a - 1/2*arctanh(a*x)^3/((a^2*x^2 - 1)*a^2)","B",0
276,1,459,0,0.348330," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(\frac{2 \, x}{a^{2} x^{2} - 1} - \frac{\log\left(a x + 1\right)}{a} + \frac{\log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right)^{3} - \frac{3 \, {\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 4\right)} a \operatorname{artanh}\left(a x\right)^{2}}{16 \, {\left(a^{4} x^{2} - a^{2}\right)}} - \frac{1}{128} \, {\left(\frac{{\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{4} - 4 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{3} \log\left(a x - 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{4} + 6 \, {\left(2 \, a^{2} x^{2} + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 2\right)} \log\left(a x + 1\right)^{2} + 12 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 4 \, {\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{3} + 6 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + 1\right) - 48\right)} a^{2}}{a^{6} x^{2} - a^{4}} - \frac{8 \, {\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{3} - 12 \, a x + 3 \, {\left(2 \, a^{2} x^{2} + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 2\right)} \log\left(a x + 1\right) - 6 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} a \operatorname{artanh}\left(a x\right)}{a^{5} x^{2} - a^{3}}\right)} a"," ",0,"-1/4*(2*x/(a^2*x^2 - 1) - log(a*x + 1)/a + log(a*x - 1)/a)*arctanh(a*x)^3 - 3/16*((a^2*x^2 - 1)*log(a*x + 1)^2 - 2*(a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) + (a^2*x^2 - 1)*log(a*x - 1)^2 - 4)*a*arctanh(a*x)^2/(a^4*x^2 - a^2) - 1/128*(((a^2*x^2 - 1)*log(a*x + 1)^4 - 4*(a^2*x^2 - 1)*log(a*x + 1)^3*log(a*x - 1) + (a^2*x^2 - 1)*log(a*x - 1)^4 + 6*(2*a^2*x^2 + (a^2*x^2 - 1)*log(a*x - 1)^2 - 2)*log(a*x + 1)^2 + 12*(a^2*x^2 - 1)*log(a*x - 1)^2 - 4*((a^2*x^2 - 1)*log(a*x - 1)^3 + 6*(a^2*x^2 - 1)*log(a*x - 1))*log(a*x + 1) - 48)*a^2/(a^6*x^2 - a^4) - 8*((a^2*x^2 - 1)*log(a*x + 1)^3 - 3*(a^2*x^2 - 1)*log(a*x + 1)^2*log(a*x - 1) - (a^2*x^2 - 1)*log(a*x - 1)^3 - 12*a*x + 3*(2*a^2*x^2 + (a^2*x^2 - 1)*log(a*x - 1)^2 - 2)*log(a*x + 1) - 6*(a^2*x^2 - 1)*log(a*x - 1))*a*arctanh(a*x)/(a^5*x^2 - a^3))*a","B",0
277,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","\frac{{\left(a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)^{4} + 4 \, {\left({\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) + 1\right)} \log\left(-a x + 1\right)^{3}}{64 \, {\left(a^{2} x^{2} - 1\right)}} - \frac{1}{8} \, \int -\frac{2 \, \log\left(a x + 1\right)^{3} - 6 \, \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) - 3 \, {\left(a^{2} x^{2} + a x + {\left(a^{4} x^{4} + a^{3} x^{3} - a^{2} x^{2} - a x - 2\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{2}}{2 \, {\left(a^{4} x^{5} - 2 \, a^{2} x^{3} + x\right)}}\,{d x}"," ",0,"1/64*((a^2*x^2 - 1)*log(-a*x + 1)^4 + 4*((a^2*x^2 - 1)*log(a*x + 1) + 1)*log(-a*x + 1)^3)/(a^2*x^2 - 1) - 1/8*integrate(-1/2*(2*log(a*x + 1)^3 - 6*log(a*x + 1)^2*log(-a*x + 1) - 3*(a^2*x^2 + a*x + (a^4*x^4 + a^3*x^3 - a^2*x^2 - a*x - 2)*log(a*x + 1))*log(-a*x + 1)^2)/(a^4*x^5 - 2*a^2*x^3 + x), x)","F",0
278,-2,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^2/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
279,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^3/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","\frac{{\left(a^{4} x^{4} - a^{2} x^{2}\right)} \log\left(-a x + 1\right)^{4} + 2 \, {\left(2 \, a^{2} x^{2} + 2 \, {\left(a^{4} x^{4} - a^{2} x^{2}\right)} \log\left(a x + 1\right) - 1\right)} \log\left(-a x + 1\right)^{3}}{32 \, {\left(a^{2} x^{4} - x^{2}\right)}} - \frac{1}{8} \, \int -\frac{2 \, \log\left(a x + 1\right)^{3} - 6 \, \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) - 3 \, {\left(2 \, a^{4} x^{4} + 2 \, a^{3} x^{3} - a^{2} x^{2} - a x + 2 \, {\left(a^{6} x^{6} + a^{5} x^{5} - a^{4} x^{4} - a^{3} x^{3} - 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{2}}{2 \, {\left(a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}\right)}}\,{d x}"," ",0,"1/32*((a^4*x^4 - a^2*x^2)*log(-a*x + 1)^4 + 2*(2*a^2*x^2 + 2*(a^4*x^4 - a^2*x^2)*log(a*x + 1) - 1)*log(-a*x + 1)^3)/(a^2*x^4 - x^2) - 1/8*integrate(-1/2*(2*log(a*x + 1)^3 - 6*log(a*x + 1)^2*log(-a*x + 1) - 3*(2*a^4*x^4 + 2*a^3*x^3 - a^2*x^2 - a*x + 2*(a^6*x^6 + a^5*x^5 - a^4*x^4 - a^3*x^3 - 1)*log(a*x + 1))*log(-a*x + 1)^2)/(a^4*x^7 - 2*a^2*x^5 + x^3), x)","F",0
280,0,0,0,0.000000," ","integrate(arctanh(a*x)^(1/2)/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{artanh}\left(a x\right)}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(arctanh(a*x))/(a^2*x^2 - 1)^2, x)","F",0
281,0,0,0,0.000000," ","integrate(x^4/(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^4/((a^2*x^2 - 1)^2*arctanh(a*x)), x)","F",0
282,0,0,0,0.000000," ","integrate(x^3/(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x^{3}}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^3/((a^2*x^2 - 1)^2*arctanh(a*x)), x)","F",0
283,0,0,0,0.000000," ","integrate(x^2/(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^2/((a^2*x^2 - 1)^2*arctanh(a*x)), x)","F",0
284,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x/((a^2*x^2 - 1)^2*arctanh(a*x)), x)","F",0
285,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^2*arctanh(a*x)), x)","F",0
286,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{2} x \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^2*x*arctanh(a*x)), x)","F",0
287,0,0,0,0.000000," ","integrate(x^3/(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{2 \, x^{3}}{{\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right) - {\left(a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)} + \int -\frac{2 \, {\left(a^{2} x^{4} - 3 \, x^{2}\right)}}{{\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right) - {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"2*x^3/((a^3*x^2 - a)*log(a*x + 1) - (a^3*x^2 - a)*log(-a*x + 1)) + integrate(-2*(a^2*x^4 - 3*x^2)/((a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1) - (a^5*x^4 - 2*a^3*x^2 + a)*log(-a*x + 1)), x)","F",0
288,0,0,0,0.000000," ","integrate(x^2/(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{2 \, x^{2}}{{\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right) - {\left(a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)} - 4 \, \int -\frac{x}{{\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right) - {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"2*x^2/((a^3*x^2 - a)*log(a*x + 1) - (a^3*x^2 - a)*log(-a*x + 1)) - 4*integrate(-x/((a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1) - (a^5*x^4 - 2*a^3*x^2 + a)*log(-a*x + 1)), x)","F",0
289,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{2 \, x}{{\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right) - {\left(a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)} - \int -\frac{2 \, {\left(a^{2} x^{2} + 1\right)}}{{\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right) - {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"2*x/((a^3*x^2 - a)*log(a*x + 1) - (a^3*x^2 - a)*log(-a*x + 1)) - integrate(-2*(a^2*x^2 + 1)/((a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1) - (a^5*x^4 - 2*a^3*x^2 + a)*log(-a*x + 1)), x)","F",0
290,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""maxima"")","-4 \, a \int -\frac{x}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)}\,{d x} + \frac{2}{{\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right) - {\left(a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)}"," ",0,"-4*a*integrate(-x/((a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) - (a^4*x^4 - 2*a^2*x^2 + 1)*log(-a*x + 1)), x) + 2/((a^3*x^2 - a)*log(a*x + 1) - (a^3*x^2 - a)*log(-a*x + 1))","F",0
291,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{2}{{\left(a^{3} x^{3} - a x\right)} \log\left(a x + 1\right) - {\left(a^{3} x^{3} - a x\right)} \log\left(-a x + 1\right)} - \int -\frac{2 \, {\left(3 \, a^{2} x^{2} - 1\right)}}{{\left(a^{5} x^{6} - 2 \, a^{3} x^{4} + a x^{2}\right)} \log\left(a x + 1\right) - {\left(a^{5} x^{6} - 2 \, a^{3} x^{4} + a x^{2}\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"2/((a^3*x^3 - a*x)*log(a*x + 1) - (a^3*x^3 - a*x)*log(-a*x + 1)) - integrate(-2*(3*a^2*x^2 - 1)/((a^5*x^6 - 2*a^3*x^4 + a*x^2)*log(a*x + 1) - (a^5*x^6 - 2*a^3*x^4 + a*x^2)*log(-a*x + 1)), x)","F",0
292,0,0,0,0.000000," ","integrate(x^3/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, a x^{3} - {\left(a^{2} x^{4} - 3 \, x^{2}\right)} \log\left(a x + 1\right) + {\left(a^{2} x^{4} - 3 \, x^{2}\right)} \log\left(-a x + 1\right)}{{\left(a^{4} x^{2} - a^{2}\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{4} x^{2} - a^{2}\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right) + {\left(a^{4} x^{2} - a^{2}\right)} \log\left(-a x + 1\right)^{2}} - \int -\frac{2 \, {\left(a^{4} x^{5} - 2 \, a^{2} x^{3} + 3 \, x\right)}}{{\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(a x + 1\right) - {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"(2*a*x^3 - (a^2*x^4 - 3*x^2)*log(a*x + 1) + (a^2*x^4 - 3*x^2)*log(-a*x + 1))/((a^4*x^2 - a^2)*log(a*x + 1)^2 - 2*(a^4*x^2 - a^2)*log(a*x + 1)*log(-a*x + 1) + (a^4*x^2 - a^2)*log(-a*x + 1)^2) - integrate(-2*(a^4*x^5 - 2*a^2*x^3 + 3*x)/((a^6*x^4 - 2*a^4*x^2 + a^2)*log(a*x + 1) - (a^6*x^4 - 2*a^4*x^2 + a^2)*log(-a*x + 1)), x)","F",0
293,0,0,0,0.000000," ","integrate(x^2/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(a x^{2} + x \log\left(a x + 1\right) - x \log\left(-a x + 1\right)\right)}}{{\left(a^{4} x^{2} - a^{2}\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{4} x^{2} - a^{2}\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right) + {\left(a^{4} x^{2} - a^{2}\right)} \log\left(-a x + 1\right)^{2}} - \int -\frac{2 \, {\left(a^{2} x^{2} + 1\right)}}{{\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(a x + 1\right) - {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"2*(a*x^2 + x*log(a*x + 1) - x*log(-a*x + 1))/((a^4*x^2 - a^2)*log(a*x + 1)^2 - 2*(a^4*x^2 - a^2)*log(a*x + 1)*log(-a*x + 1) + (a^4*x^2 - a^2)*log(-a*x + 1)^2) - integrate(-2*(a^2*x^2 + 1)/((a^6*x^4 - 2*a^4*x^2 + a^2)*log(a*x + 1) - (a^6*x^4 - 2*a^4*x^2 + a^2)*log(-a*x + 1)), x)","F",0
294,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, a x + {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - {\left(a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)}{{\left(a^{4} x^{2} - a^{2}\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{4} x^{2} - a^{2}\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right) + {\left(a^{4} x^{2} - a^{2}\right)} \log\left(-a x + 1\right)^{2}} - 4 \, \int -\frac{x}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"(2*a*x + (a^2*x^2 + 1)*log(a*x + 1) - (a^2*x^2 + 1)*log(-a*x + 1))/((a^4*x^2 - a^2)*log(a*x + 1)^2 - 2*(a^4*x^2 - a^2)*log(a*x + 1)*log(-a*x + 1) + (a^4*x^2 - a^2)*log(-a*x + 1)^2) - 4*integrate(-x/((a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) - (a^4*x^4 - 2*a^2*x^2 + 1)*log(-a*x + 1)), x)","F",0
295,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(a x \log\left(a x + 1\right) - a x \log\left(-a x + 1\right) + 1\right)}}{{\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right) + {\left(a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)^{2}} - \int -\frac{2 \, {\left(a^{2} x^{2} + 1\right)}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"2*(a*x*log(a*x + 1) - a*x*log(-a*x + 1) + 1)/((a^3*x^2 - a)*log(a*x + 1)^2 - 2*(a^3*x^2 - a)*log(a*x + 1)*log(-a*x + 1) + (a^3*x^2 - a)*log(-a*x + 1)^2) - integrate(-2*(a^2*x^2 + 1)/((a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) - (a^4*x^4 - 2*a^2*x^2 + 1)*log(-a*x + 1)), x)","F",0
296,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, a x + {\left(3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) - {\left(3 \, a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)}{{\left(a^{4} x^{4} - a^{2} x^{2}\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{4} x^{4} - a^{2} x^{2}\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right) + {\left(a^{4} x^{4} - a^{2} x^{2}\right)} \log\left(-a x + 1\right)^{2}} - \int -\frac{2 \, {\left(3 \, a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)}}{{\left(a^{6} x^{7} - 2 \, a^{4} x^{5} + a^{2} x^{3}\right)} \log\left(a x + 1\right) - {\left(a^{6} x^{7} - 2 \, a^{4} x^{5} + a^{2} x^{3}\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"(2*a*x + (3*a^2*x^2 - 1)*log(a*x + 1) - (3*a^2*x^2 - 1)*log(-a*x + 1))/((a^4*x^4 - a^2*x^2)*log(a*x + 1)^2 - 2*(a^4*x^4 - a^2*x^2)*log(a*x + 1)*log(-a*x + 1) + (a^4*x^4 - a^2*x^2)*log(-a*x + 1)^2) - integrate(-2*(3*a^4*x^4 - 2*a^2*x^2 + 1)/((a^6*x^7 - 2*a^4*x^5 + a^2*x^3)*log(a*x + 1) - (a^6*x^7 - 2*a^4*x^5 + a^2*x^3)*log(-a*x + 1)), x)","F",0
297,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^4,x, algorithm=""maxima"")","-8 \, a \int -\frac{x}{3 \, {\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)\right)}}\,{d x} + \frac{2 \, {\left(2 \, a x \log\left(a x + 1\right) + {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + {\left(a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)^{2} - 2 \, {\left(a x + {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right) + 4\right)}}{3 \, {\left({\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) + 3 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right)^{2} - {\left(a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)^{3}\right)}}"," ",0,"-8*a*integrate(-1/3*x/((a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) - (a^4*x^4 - 2*a^2*x^2 + 1)*log(-a*x + 1)), x) + 2/3*(2*a*x*log(a*x + 1) + (a^2*x^2 + 1)*log(a*x + 1)^2 + (a^2*x^2 + 1)*log(-a*x + 1)^2 - 2*(a*x + (a^2*x^2 + 1)*log(a*x + 1))*log(-a*x + 1) + 4)/((a^3*x^2 - a)*log(a*x + 1)^3 - 3*(a^3*x^2 - a)*log(a*x + 1)^2*log(-a*x + 1) + 3*(a^3*x^2 - a)*log(a*x + 1)*log(-a*x + 1)^2 - (a^3*x^2 - a)*log(-a*x + 1)^3)","F",0
298,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^5,x, algorithm=""maxima"")","\frac{2 \, a x \log\left(a x + 1\right)^{3} - 2 \, a x \log\left(-a x + 1\right)^{3} + 4 \, a x \log\left(a x + 1\right) + {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + {\left(a^{2} x^{2} + 6 \, a x \log\left(a x + 1\right) + 1\right)} \log\left(-a x + 1\right)^{2} - 2 \, {\left(3 \, a x \log\left(a x + 1\right)^{2} + 2 \, a x + {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right) + 12}{3 \, {\left({\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{4} - 4 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{3} \log\left(-a x + 1\right) + 6 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)^{2} - 4 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right)^{3} + {\left(a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)^{4}\right)}} - \int -\frac{2 \, {\left(a^{2} x^{2} + 1\right)}}{3 \, {\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)\right)}}\,{d x}"," ",0,"1/3*(2*a*x*log(a*x + 1)^3 - 2*a*x*log(-a*x + 1)^3 + 4*a*x*log(a*x + 1) + (a^2*x^2 + 1)*log(a*x + 1)^2 + (a^2*x^2 + 6*a*x*log(a*x + 1) + 1)*log(-a*x + 1)^2 - 2*(3*a*x*log(a*x + 1)^2 + 2*a*x + (a^2*x^2 + 1)*log(a*x + 1))*log(-a*x + 1) + 12)/((a^3*x^2 - a)*log(a*x + 1)^4 - 4*(a^3*x^2 - a)*log(a*x + 1)^3*log(-a*x + 1) + 6*(a^3*x^2 - a)*log(a*x + 1)^2*log(-a*x + 1)^2 - 4*(a^3*x^2 - a)*log(a*x + 1)*log(-a*x + 1)^3 + (a^3*x^2 - a)*log(-a*x + 1)^4) - integrate(-2/3*(a^2*x^2 + 1)/((a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) - (a^4*x^4 - 2*a^2*x^2 + 1)*log(-a*x + 1)), x)","F",0
299,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^6,x, algorithm=""maxima"")","-8 \, a \int -\frac{x}{15 \, {\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)\right)}}\,{d x} + \frac{2 \, {\left(2 \, a x \log\left(a x + 1\right)^{3} + {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{4} + {\left(a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)^{4} - 2 \, {\left(a x + 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{3} + 12 \, a x \log\left(a x + 1\right) + 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 2 \, {\left(a^{2} x^{2} + 3 \, a x \log\left(a x + 1\right) + 3 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 1\right)} \log\left(-a x + 1\right)^{2} - 2 \, {\left(3 \, a x \log\left(a x + 1\right)^{2} + 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{3} + 6 \, a x + 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right) + 48\right)}}{15 \, {\left({\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{5} - 5 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{4} \log\left(-a x + 1\right) + 10 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{3} \log\left(-a x + 1\right)^{2} - 10 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)^{3} + 5 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right)^{4} - {\left(a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)^{5}\right)}}"," ",0,"-8*a*integrate(-1/15*x/((a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) - (a^4*x^4 - 2*a^2*x^2 + 1)*log(-a*x + 1)), x) + 2/15*(2*a*x*log(a*x + 1)^3 + (a^2*x^2 + 1)*log(a*x + 1)^4 + (a^2*x^2 + 1)*log(-a*x + 1)^4 - 2*(a*x + 2*(a^2*x^2 + 1)*log(a*x + 1))*log(-a*x + 1)^3 + 12*a*x*log(a*x + 1) + 2*(a^2*x^2 + 1)*log(a*x + 1)^2 + 2*(a^2*x^2 + 3*a*x*log(a*x + 1) + 3*(a^2*x^2 + 1)*log(a*x + 1)^2 + 1)*log(-a*x + 1)^2 - 2*(3*a*x*log(a*x + 1)^2 + 2*(a^2*x^2 + 1)*log(a*x + 1)^3 + 6*a*x + 2*(a^2*x^2 + 1)*log(a*x + 1))*log(-a*x + 1) + 48)/((a^3*x^2 - a)*log(a*x + 1)^5 - 5*(a^3*x^2 - a)*log(a*x + 1)^4*log(-a*x + 1) + 10*(a^3*x^2 - a)*log(a*x + 1)^3*log(-a*x + 1)^2 - 10*(a^3*x^2 - a)*log(a*x + 1)^2*log(-a*x + 1)^3 + 5*(a^3*x^2 - a)*log(a*x + 1)*log(-a*x + 1)^4 - (a^3*x^2 - a)*log(-a*x + 1)^5)","F",0
300,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^7,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, a x \log\left(a x + 1\right)^{5} - 2 \, a x \log\left(-a x + 1\right)^{5} + 4 \, a x \log\left(a x + 1\right)^{3} + {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{4} + {\left(a^{2} x^{2} + 10 \, a x \log\left(a x + 1\right) + 1\right)} \log\left(-a x + 1\right)^{4} - 4 \, {\left(5 \, a x \log\left(a x + 1\right)^{2} + a x + {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{3} + 48 \, a x \log\left(a x + 1\right) + 6 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 2 \, {\left(10 \, a x \log\left(a x + 1\right)^{3} + 3 \, a^{2} x^{2} + 6 \, a x \log\left(a x + 1\right) + 3 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 3\right)} \log\left(-a x + 1\right)^{2} - 2 \, {\left(5 \, a x \log\left(a x + 1\right)^{4} + 6 \, a x \log\left(a x + 1\right)^{2} + 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{3} + 24 \, a x + 6 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right) + 240\right)}}{45 \, {\left({\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{6} - 6 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{5} \log\left(-a x + 1\right) + 15 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{4} \log\left(-a x + 1\right)^{2} - 20 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{3} \log\left(-a x + 1\right)^{3} + 15 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)^{4} - 6 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right)^{5} + {\left(a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)^{6}\right)}} - \int -\frac{4 \, {\left(a^{2} x^{2} + 1\right)}}{45 \, {\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)\right)}}\,{d x}"," ",0,"2/45*(2*a*x*log(a*x + 1)^5 - 2*a*x*log(-a*x + 1)^5 + 4*a*x*log(a*x + 1)^3 + (a^2*x^2 + 1)*log(a*x + 1)^4 + (a^2*x^2 + 10*a*x*log(a*x + 1) + 1)*log(-a*x + 1)^4 - 4*(5*a*x*log(a*x + 1)^2 + a*x + (a^2*x^2 + 1)*log(a*x + 1))*log(-a*x + 1)^3 + 48*a*x*log(a*x + 1) + 6*(a^2*x^2 + 1)*log(a*x + 1)^2 + 2*(10*a*x*log(a*x + 1)^3 + 3*a^2*x^2 + 6*a*x*log(a*x + 1) + 3*(a^2*x^2 + 1)*log(a*x + 1)^2 + 3)*log(-a*x + 1)^2 - 2*(5*a*x*log(a*x + 1)^4 + 6*a*x*log(a*x + 1)^2 + 2*(a^2*x^2 + 1)*log(a*x + 1)^3 + 24*a*x + 6*(a^2*x^2 + 1)*log(a*x + 1))*log(-a*x + 1) + 240)/((a^3*x^2 - a)*log(a*x + 1)^6 - 6*(a^3*x^2 - a)*log(a*x + 1)^5*log(-a*x + 1) + 15*(a^3*x^2 - a)*log(a*x + 1)^4*log(-a*x + 1)^2 - 20*(a^3*x^2 - a)*log(a*x + 1)^3*log(-a*x + 1)^3 + 15*(a^3*x^2 - a)*log(a*x + 1)^2*log(-a*x + 1)^4 - 6*(a^3*x^2 - a)*log(a*x + 1)*log(-a*x + 1)^5 + (a^3*x^2 - a)*log(-a*x + 1)^6) - integrate(-4/45*(a^2*x^2 + 1)/((a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) - (a^4*x^4 - 2*a^2*x^2 + 1)*log(-a*x + 1)), x)","F",0
301,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^8,x, algorithm=""maxima"")","-16 \, a \int -\frac{x}{315 \, {\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)\right)}}\,{d x} + \frac{4 \, {\left(2 \, a x \log\left(a x + 1\right)^{5} + {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{6} + {\left(a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)^{6} - 2 \, {\left(a x + 3 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{5} + 12 \, a x \log\left(a x + 1\right)^{3} + 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{4} + {\left(2 \, a^{2} x^{2} + 10 \, a x \log\left(a x + 1\right) + 15 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 2\right)} \log\left(-a x + 1\right)^{4} - 4 \, {\left(5 \, a x \log\left(a x + 1\right)^{2} + 5 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{3} + 3 \, a x + 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{3} + 240 \, a x \log\left(a x + 1\right) + 24 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + {\left(20 \, a x \log\left(a x + 1\right)^{3} + 15 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{4} + 24 \, a^{2} x^{2} + 36 \, a x \log\left(a x + 1\right) + 12 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 24\right)} \log\left(-a x + 1\right)^{2} - 2 \, {\left(5 \, a x \log\left(a x + 1\right)^{4} + 3 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{5} + 18 \, a x \log\left(a x + 1\right)^{2} + 4 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{3} + 120 \, a x + 24 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right) + 1440\right)}}{315 \, {\left({\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{7} - 7 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{6} \log\left(-a x + 1\right) + 21 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{5} \log\left(-a x + 1\right)^{2} - 35 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{4} \log\left(-a x + 1\right)^{3} + 35 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{3} \log\left(-a x + 1\right)^{4} - 21 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)^{5} + 7 \, {\left(a^{3} x^{2} - a\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right)^{6} - {\left(a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)^{7}\right)}}"," ",0,"-16*a*integrate(-1/315*x/((a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) - (a^4*x^4 - 2*a^2*x^2 + 1)*log(-a*x + 1)), x) + 4/315*(2*a*x*log(a*x + 1)^5 + (a^2*x^2 + 1)*log(a*x + 1)^6 + (a^2*x^2 + 1)*log(-a*x + 1)^6 - 2*(a*x + 3*(a^2*x^2 + 1)*log(a*x + 1))*log(-a*x + 1)^5 + 12*a*x*log(a*x + 1)^3 + 2*(a^2*x^2 + 1)*log(a*x + 1)^4 + (2*a^2*x^2 + 10*a*x*log(a*x + 1) + 15*(a^2*x^2 + 1)*log(a*x + 1)^2 + 2)*log(-a*x + 1)^4 - 4*(5*a*x*log(a*x + 1)^2 + 5*(a^2*x^2 + 1)*log(a*x + 1)^3 + 3*a*x + 2*(a^2*x^2 + 1)*log(a*x + 1))*log(-a*x + 1)^3 + 240*a*x*log(a*x + 1) + 24*(a^2*x^2 + 1)*log(a*x + 1)^2 + (20*a*x*log(a*x + 1)^3 + 15*(a^2*x^2 + 1)*log(a*x + 1)^4 + 24*a^2*x^2 + 36*a*x*log(a*x + 1) + 12*(a^2*x^2 + 1)*log(a*x + 1)^2 + 24)*log(-a*x + 1)^2 - 2*(5*a*x*log(a*x + 1)^4 + 3*(a^2*x^2 + 1)*log(a*x + 1)^5 + 18*a*x*log(a*x + 1)^2 + 4*(a^2*x^2 + 1)*log(a*x + 1)^3 + 120*a*x + 24*(a^2*x^2 + 1)*log(a*x + 1))*log(-a*x + 1) + 1440)/((a^3*x^2 - a)*log(a*x + 1)^7 - 7*(a^3*x^2 - a)*log(a*x + 1)^6*log(-a*x + 1) + 21*(a^3*x^2 - a)*log(a*x + 1)^5*log(-a*x + 1)^2 - 35*(a^3*x^2 - a)*log(a*x + 1)^4*log(-a*x + 1)^3 + 35*(a^3*x^2 - a)*log(a*x + 1)^3*log(-a*x + 1)^4 - 21*(a^3*x^2 - a)*log(a*x + 1)^2*log(-a*x + 1)^5 + 7*(a^3*x^2 - a)*log(a*x + 1)*log(-a*x + 1)^6 - (a^3*x^2 - a)*log(-a*x + 1)^7)","F",0
302,1,99,0,0.312138," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","-\frac{1}{64} \, a {\left(\frac{2 \, {\left(5 \, a^{2} x^{3} - 3 \, x\right)}}{a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}} - \frac{5 \, \log\left(a x + 1\right)}{a^{5}} + \frac{5 \, \log\left(a x - 1\right)}{a^{5}}\right)} + \frac{{\left(2 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)}{4 \, {\left(a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}\right)}}"," ",0,"-1/64*a*(2*(5*a^2*x^3 - 3*x)/(a^8*x^4 - 2*a^6*x^2 + a^4) - 5*log(a*x + 1)/a^5 + 5*log(a*x - 1)/a^5) + 1/4*(2*a^2*x^2 - 1)*arctanh(a*x)/(a^8*x^4 - 2*a^6*x^2 + a^4)","A",0
303,1,179,0,0.323784," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(\frac{2 \, {\left(a^{2} x^{3} + x\right)}}{a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}} - \frac{\log\left(a x + 1\right)}{a^{3}} + \frac{\log\left(a x - 1\right)}{a^{3}}\right)} \operatorname{artanh}\left(a x\right) - \frac{{\left(4 \, a^{2} x^{2} - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2}\right)} a}{64 \, {\left(a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}\right)}}"," ",0,"1/16*(2*(a^2*x^3 + x)/(a^6*x^4 - 2*a^4*x^2 + a^2) - log(a*x + 1)/a^3 + log(a*x - 1)/a^3)*arctanh(a*x) - 1/64*(4*a^2*x^2 - (a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2 + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)*log(a*x - 1) - (a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2)*a/(a^8*x^4 - 2*a^6*x^2 + a^4)","B",0
304,1,82,0,0.308289," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(3 \, a^{2} x^{3} - 5 \, x\right)}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1} - \frac{3 \, \log\left(a x + 1\right)}{a} + \frac{3 \, \log\left(a x - 1\right)}{a}}{64 \, a} + \frac{\operatorname{artanh}\left(a x\right)}{4 \, {\left(a^{2} x^{2} - 1\right)}^{2} a^{2}}"," ",0,"1/64*(2*(3*a^2*x^3 - 5*x)/(a^4*x^4 - 2*a^2*x^2 + 1) - 3*log(a*x + 1)/a + 3*log(a*x - 1)/a)/a + 1/4*arctanh(a*x)/((a^2*x^2 - 1)^2*a^2)","A",0
305,1,182,0,0.323526," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(\frac{2 \, {\left(3 \, a^{2} x^{3} - 5 \, x\right)}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1} - \frac{3 \, \log\left(a x + 1\right)}{a} + \frac{3 \, \log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right) + \frac{{\left(12 \, a^{2} x^{2} - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 6 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 16\right)} a}{64 \, {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)}}"," ",0,"-1/16*(2*(3*a^2*x^3 - 5*x)/(a^4*x^4 - 2*a^2*x^2 + 1) - 3*log(a*x + 1)/a + 3*log(a*x - 1)/a)*arctanh(a*x) + 1/64*(12*a^2*x^2 - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2 + 6*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)*log(a*x - 1) - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 16)*a/(a^6*x^4 - 2*a^4*x^2 + a^2)","B",0
306,1,268,0,0.329834," ","integrate(arctanh(a*x)/x/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","\frac{1}{64} \, a {\left(\frac{2 \, {\left(11 \, a^{3} x^{3} + 4 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} - 8 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - 4 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 13 \, a x\right)}}{a^{5} x^{4} - 2 \, a^{3} x^{2} + a} + \frac{32 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a} - \frac{32 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)}}{a} + \frac{32 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)}}{a} - \frac{11 \, \log\left(a x + 1\right)}{a} + \frac{11 \, \log\left(a x - 1\right)}{a}\right)} - \frac{1}{4} \, {\left(\frac{2 \, a^{2} x^{2} - 3}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1} + 2 \, \log\left(a^{2} x^{2} - 1\right) - 2 \, \log\left(x^{2}\right)\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/64*a*(2*(11*a^3*x^3 + 4*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2 - 8*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)*log(a*x - 1) - 4*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 13*a*x)/(a^5*x^4 - 2*a^3*x^2 + a) + 32*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a - 32*(log(a*x + 1)*log(x) + dilog(-a*x))/a + 32*(log(-a*x + 1)*log(x) + dilog(a*x))/a - 11*log(a*x + 1)/a + 11*log(a*x - 1)/a) - 1/4*((2*a^2*x^2 - 3)/(a^4*x^4 - 2*a^2*x^2 + 1) + 2*log(a^2*x^2 - 1) - 2*log(x^2))*arctanh(a*x)","B",0
307,1,204,0,0.333307," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","\frac{1}{64} \, a {\left(\frac{28 \, a^{2} x^{2} - 15 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 30 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - 15 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 32}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1} - 32 \, \log\left(a x + 1\right) - 32 \, \log\left(a x - 1\right) + 64 \, \log\left(x\right)\right)} + \frac{1}{16} \, {\left(15 \, a \log\left(a x + 1\right) - 15 \, a \log\left(a x - 1\right) - \frac{2 \, {\left(15 \, a^{4} x^{4} - 25 \, a^{2} x^{2} + 8\right)}}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/64*a*((28*a^2*x^2 - 15*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2 + 30*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)*log(a*x - 1) - 15*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 32)/(a^4*x^4 - 2*a^2*x^2 + 1) - 32*log(a*x + 1) - 32*log(a*x - 1) + 64*log(x)) + 1/16*(15*a*log(a*x + 1) - 15*a*log(a*x - 1) - 2*(15*a^4*x^4 - 25*a^2*x^2 + 8)/(a^4*x^5 - 2*a^2*x^3 + x))*arctanh(a*x)","A",0
308,1,226,0,0.327530," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","-\frac{1}{32} \, a {\left(\frac{2 \, {\left(5 \, a^{2} x^{3} - 3 \, x\right)}}{a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}} - \frac{5 \, \log\left(a x + 1\right)}{a^{5}} + \frac{5 \, \log\left(a x - 1\right)}{a^{5}}\right)} \operatorname{artanh}\left(a x\right) + \frac{{\left(20 \, a^{2} x^{2} - 5 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 10 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - 5 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 16\right)} a^{2}}{128 \, {\left(a^{10} x^{4} - 2 \, a^{8} x^{2} + a^{6}\right)}} + \frac{{\left(2 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{4 \, {\left(a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}\right)}}"," ",0,"-1/32*a*(2*(5*a^2*x^3 - 3*x)/(a^8*x^4 - 2*a^6*x^2 + a^4) - 5*log(a*x + 1)/a^5 + 5*log(a*x - 1)/a^5)*arctanh(a*x) + 1/128*(20*a^2*x^2 - 5*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2 + 10*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)*log(a*x - 1) - 5*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 16)*a^2/(a^10*x^4 - 2*a^8*x^2 + a^6) + 1/4*(2*a^2*x^2 - 1)*arctanh(a*x)^2/(a^8*x^4 - 2*a^6*x^2 + a^4)","B",0
309,1,388,0,0.329445," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(\frac{2 \, {\left(a^{2} x^{3} + x\right)}}{a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}} - \frac{\log\left(a x + 1\right)}{a^{3}} + \frac{\log\left(a x - 1\right)}{a^{3}}\right)} \operatorname{artanh}\left(a x\right)^{2} + \frac{{\left(6 \, a^{3} x^{3} - 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{3} + 6 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{3} + 6 \, a x - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} + 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)\right)} a^{2}}{384 \, {\left(a^{9} x^{4} - 2 \, a^{7} x^{2} + a^{5}\right)}} - \frac{{\left(4 \, a^{2} x^{2} - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2}\right)} a \operatorname{artanh}\left(a x\right)}{32 \, {\left(a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}\right)}}"," ",0,"1/16*(2*(a^2*x^3 + x)/(a^6*x^4 - 2*a^4*x^2 + a^2) - log(a*x + 1)/a^3 + log(a*x - 1)/a^3)*arctanh(a*x)^2 + 1/384*(6*a^3*x^3 - 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^3 + 6*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2*log(a*x - 1) + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^3 + 6*a*x - 3*(a^4*x^4 - 2*a^2*x^2 + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 + 1)*log(a*x + 1) + 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))*a^2/(a^9*x^4 - 2*a^7*x^2 + a^5) - 1/32*(4*a^2*x^2 - (a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2 + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)*log(a*x - 1) - (a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2)*a*arctanh(a*x)/(a^8*x^4 - 2*a^6*x^2 + a^4)","B",0
310,1,206,0,0.325580," ","integrate(x*arctanh(a*x)^2/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, {\left(3 \, a^{2} x^{3} - 5 \, x\right)}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1} - \frac{3 \, \log\left(a x + 1\right)}{a} + \frac{3 \, \log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right)}{32 \, a} - \frac{12 \, a^{2} x^{2} - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 6 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 16}{128 \, {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)}} + \frac{\operatorname{artanh}\left(a x\right)^{2}}{4 \, {\left(a^{2} x^{2} - 1\right)}^{2} a^{2}}"," ",0,"1/32*(2*(3*a^2*x^3 - 5*x)/(a^4*x^4 - 2*a^2*x^2 + 1) - 3*log(a*x + 1)/a + 3*log(a*x - 1)/a)*arctanh(a*x)/a - 1/128*(12*a^2*x^2 - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2 + 6*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)*log(a*x - 1) - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 16)/(a^6*x^4 - 2*a^4*x^2 + a^2) + 1/4*arctanh(a*x)^2/((a^2*x^2 - 1)^2*a^2)","A",0
311,1,392,0,0.337956," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(\frac{2 \, {\left(3 \, a^{2} x^{3} - 5 \, x\right)}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1} - \frac{3 \, \log\left(a x + 1\right)}{a} + \frac{3 \, \log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right)^{2} - \frac{{\left(30 \, a^{3} x^{3} - 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{3} + 6 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{3} - 34 \, a x - 3 \, {\left(5 \, a^{4} x^{4} - 10 \, a^{2} x^{2} + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} + 5\right)} \log\left(a x + 1\right) + 15 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)\right)} a^{2}}{128 \, {\left(a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}\right)}} + \frac{{\left(12 \, a^{2} x^{2} - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 6 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 16\right)} a \operatorname{artanh}\left(a x\right)}{32 \, {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)}}"," ",0,"-1/16*(2*(3*a^2*x^3 - 5*x)/(a^4*x^4 - 2*a^2*x^2 + 1) - 3*log(a*x + 1)/a + 3*log(a*x - 1)/a)*arctanh(a*x)^2 - 1/128*(30*a^3*x^3 - 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^3 + 6*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2*log(a*x - 1) + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^3 - 34*a*x - 3*(5*a^4*x^4 - 10*a^2*x^2 + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 + 5)*log(a*x + 1) + 15*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))*a^2/(a^7*x^4 - 2*a^5*x^2 + a^3) + 1/32*(12*a^2*x^2 - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2 + 6*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)*log(a*x - 1) - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 16)*a*arctanh(a*x)/(a^6*x^4 - 2*a^4*x^2 + a^2)","B",0
312,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{6} \int \frac{x^{6} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{2 \, {\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)}}\,{d x} + \frac{1}{2} \, a^{5} \int \frac{x^{5} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{2 \, {\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)}}\,{d x} - \frac{1}{256} \, {\left(a {\left(\frac{2 \, {\left(5 \, a^{2} x^{2} + 3 \, a x - 6\right)}}{a^{8} x^{3} - a^{7} x^{2} - a^{6} x + a^{5}} - \frac{5 \, \log\left(a x + 1\right)}{a^{5}} + \frac{5 \, \log\left(a x - 1\right)}{a^{5}}\right)} + \frac{16 \, {\left(2 \, a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)}{a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}}\right)} a^{4} - a^{4} \int \frac{x^{4} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{2 \, {\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)}}\,{d x} - a^{3} \int \frac{x^{3} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{2 \, {\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)}}\,{d x} + \frac{1}{2} \, a^{3} \int \frac{x^{3} \log\left(-a x + 1\right)}{2 \, {\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)}}\,{d x} - \frac{3}{512} \, {\left(a {\left(\frac{2 \, {\left(3 \, a^{2} x^{2} - 3 \, a x - 2\right)}}{a^{6} x^{3} - a^{5} x^{2} - a^{4} x + a^{3}} - \frac{3 \, \log\left(a x + 1\right)}{a^{3}} + \frac{3 \, \log\left(a x - 1\right)}{a^{3}}\right)} - \frac{16 \, \log\left(-a x + 1\right)}{a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}}\right)} a^{2} + \frac{1}{2} \, a^{2} \int \frac{x^{2} \log\left(a x + 1\right) \log\left(-a x + 1\right)}{2 \, {\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)}}\,{d x} + \frac{1}{2} \, a \int \frac{x \log\left(a x + 1\right) \log\left(-a x + 1\right)}{2 \, {\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)}}\,{d x} - \frac{3}{4} \, a \int \frac{x \log\left(-a x + 1\right)}{2 \, {\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)}}\,{d x} - \frac{2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)^{3} + 3 \, {\left(2 \, a^{2} x^{2} + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - 3\right)} \log\left(-a x + 1\right)^{2}}{48 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)}} - \frac{1}{2} \, \int \frac{\log\left(a x + 1\right)^{2}}{2 \, {\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)}}\,{d x} + \int \frac{\log\left(a x + 1\right) \log\left(-a x + 1\right)}{2 \, {\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)}}\,{d x}"," ",0,"1/2*a^6*integrate(1/2*x^6*log(a*x + 1)*log(-a*x + 1)/(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x), x) + 1/2*a^5*integrate(1/2*x^5*log(a*x + 1)*log(-a*x + 1)/(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x), x) - 1/256*(a*(2*(5*a^2*x^2 + 3*a*x - 6)/(a^8*x^3 - a^7*x^2 - a^6*x + a^5) - 5*log(a*x + 1)/a^5 + 5*log(a*x - 1)/a^5) + 16*(2*a^2*x^2 - 1)*log(-a*x + 1)/(a^8*x^4 - 2*a^6*x^2 + a^4))*a^4 - a^4*integrate(1/2*x^4*log(a*x + 1)*log(-a*x + 1)/(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x), x) - a^3*integrate(1/2*x^3*log(a*x + 1)*log(-a*x + 1)/(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x), x) + 1/2*a^3*integrate(1/2*x^3*log(-a*x + 1)/(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x), x) - 3/512*(a*(2*(3*a^2*x^2 - 3*a*x - 2)/(a^6*x^3 - a^5*x^2 - a^4*x + a^3) - 3*log(a*x + 1)/a^3 + 3*log(a*x - 1)/a^3) - 16*log(-a*x + 1)/(a^6*x^4 - 2*a^4*x^2 + a^2))*a^2 + 1/2*a^2*integrate(1/2*x^2*log(a*x + 1)*log(-a*x + 1)/(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x), x) + 1/2*a*integrate(1/2*x*log(a*x + 1)*log(-a*x + 1)/(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x), x) - 3/4*a*integrate(1/2*x*log(-a*x + 1)/(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x), x) - 1/48*(2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(-a*x + 1)^3 + 3*(2*a^2*x^2 + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) - 3)*log(-a*x + 1)^2)/(a^4*x^4 - 2*a^2*x^2 + 1) - 1/2*integrate(1/2*log(a*x + 1)^2/(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x), x) + integrate(1/2*log(a*x + 1)*log(-a*x + 1)/(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x), x)","F",0
313,1,534,0,0.346159," ","integrate(arctanh(a*x)^2/x^2/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","-\frac{1}{128} \, a^{2} {\left(\frac{2 \, {\left(31 \, a^{3} x^{3} - 5 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{3} + 5 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{3} - {\left(16 \, a^{4} x^{4} - 32 \, a^{2} x^{2} - 15 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right) + 16\right)} \log\left(a x + 1\right)^{2} + 16 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 33 \, a x - {\left(15 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 32 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + 1\right)\right)}}{a^{5} x^{4} - 2 \, a^{3} x^{2} + a} - \frac{128 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a} + \frac{128 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)}}{a} - \frac{128 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)}}{a} - \frac{31 \, \log\left(a x + 1\right)}{a} + \frac{31 \, \log\left(a x - 1\right)}{a}\right)} + \frac{1}{32} \, a {\left(\frac{28 \, a^{2} x^{2} - 15 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 30 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - 15 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 32}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1} - 32 \, \log\left(a x + 1\right) - 32 \, \log\left(a x - 1\right) + 64 \, \log\left(x\right)\right)} \operatorname{artanh}\left(a x\right) + \frac{1}{16} \, {\left(15 \, a \log\left(a x + 1\right) - 15 \, a \log\left(a x - 1\right) - \frac{2 \, {\left(15 \, a^{4} x^{4} - 25 \, a^{2} x^{2} + 8\right)}}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}\right)} \operatorname{artanh}\left(a x\right)^{2}"," ",0,"-1/128*a^2*(2*(31*a^3*x^3 - 5*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^3 + 5*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^3 - (16*a^4*x^4 - 32*a^2*x^2 - 15*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1) + 16)*log(a*x + 1)^2 + 16*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 33*a*x - (15*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 32*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))*log(a*x + 1))/(a^5*x^4 - 2*a^3*x^2 + a) - 128*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a + 128*(log(a*x + 1)*log(x) + dilog(-a*x))/a - 128*(log(-a*x + 1)*log(x) + dilog(a*x))/a - 31*log(a*x + 1)/a + 31*log(a*x - 1)/a) + 1/32*a*((28*a^2*x^2 - 15*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2 + 30*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)*log(a*x - 1) - 15*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 32)/(a^4*x^4 - 2*a^2*x^2 + 1) - 32*log(a*x + 1) - 32*log(a*x - 1) + 64*log(x))*arctanh(a*x) + 1/16*(15*a*log(a*x + 1) - 15*a*log(a*x - 1) - 2*(15*a^4*x^4 - 25*a^2*x^2 + 8)/(a^4*x^5 - 2*a^2*x^3 + x))*arctanh(a*x)^2","B",0
314,1,437,0,0.341542," ","integrate(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","-\frac{3}{64} \, a {\left(\frac{2 \, {\left(5 \, a^{2} x^{3} - 3 \, x\right)}}{a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}} - \frac{5 \, \log\left(a x + 1\right)}{a^{5}} + \frac{5 \, \log\left(a x - 1\right)}{a^{5}}\right)} \operatorname{artanh}\left(a x\right)^{2} + \frac{{\left(2 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{3}}{4 \, {\left(a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}\right)}} - \frac{1}{512} \, {\left(\frac{{\left(102 \, a^{3} x^{3} - 10 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{3} + 30 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) + 10 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{3} - 90 \, a x - 3 \, {\left(17 \, a^{4} x^{4} - 34 \, a^{2} x^{2} + 10 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} + 17\right)} \log\left(a x + 1\right) + 51 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)\right)} a^{2}}{a^{11} x^{4} - 2 \, a^{9} x^{2} + a^{7}} - \frac{12 \, {\left(20 \, a^{2} x^{2} - 5 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 10 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - 5 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 16\right)} a \operatorname{artanh}\left(a x\right)}{a^{10} x^{4} - 2 \, a^{8} x^{2} + a^{6}}\right)} a"," ",0,"-3/64*a*(2*(5*a^2*x^3 - 3*x)/(a^8*x^4 - 2*a^6*x^2 + a^4) - 5*log(a*x + 1)/a^5 + 5*log(a*x - 1)/a^5)*arctanh(a*x)^2 + 1/4*(2*a^2*x^2 - 1)*arctanh(a*x)^3/(a^8*x^4 - 2*a^6*x^2 + a^4) - 1/512*((102*a^3*x^3 - 10*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^3 + 30*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2*log(a*x - 1) + 10*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^3 - 90*a*x - 3*(17*a^4*x^4 - 34*a^2*x^2 + 10*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 + 17)*log(a*x + 1) + 51*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))*a^2/(a^11*x^4 - 2*a^9*x^2 + a^7) - 12*(20*a^2*x^2 - 5*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2 + 10*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)*log(a*x - 1) - 5*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 16)*a*arctanh(a*x)/(a^10*x^4 - 2*a^8*x^2 + a^6))*a","B",0
315,1,657,0,0.347047," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(\frac{2 \, {\left(a^{2} x^{3} + x\right)}}{a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}} - \frac{\log\left(a x + 1\right)}{a^{3}} + \frac{\log\left(a x - 1\right)}{a^{3}}\right)} \operatorname{artanh}\left(a x\right)^{3} - \frac{3 \, {\left(4 \, a^{2} x^{2} - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2}\right)} a \operatorname{artanh}\left(a x\right)^{2}}{64 \, {\left(a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}\right)}} + \frac{1}{512} \, {\left(\frac{{\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{4} - 4 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{3} \log\left(a x - 1\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{4} - 12 \, a^{2} x^{2} + 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 2 \, {\left(2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{3} + 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + 1\right)\right)} a^{2}}{a^{10} x^{4} - 2 \, a^{8} x^{2} + a^{6}} + \frac{4 \, {\left(6 \, a^{3} x^{3} - 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{3} + 6 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{3} + 6 \, a x - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} + 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)\right)} a \operatorname{artanh}\left(a x\right)}{a^{9} x^{4} - 2 \, a^{7} x^{2} + a^{5}}\right)} a"," ",0,"1/16*(2*(a^2*x^3 + x)/(a^6*x^4 - 2*a^4*x^2 + a^2) - log(a*x + 1)/a^3 + log(a*x - 1)/a^3)*arctanh(a*x)^3 - 3/64*(4*a^2*x^2 - (a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2 + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)*log(a*x - 1) - (a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2)*a*arctanh(a*x)^2/(a^8*x^4 - 2*a^6*x^2 + a^4) + 1/512*(((a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^4 - 4*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^3*log(a*x - 1) + (a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^4 - 12*a^2*x^2 + 3*(a^4*x^4 - 2*a^2*x^2 + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 + 1)*log(a*x + 1)^2 + 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 2*(2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^3 + 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))*log(a*x + 1))*a^2/(a^10*x^4 - 2*a^8*x^2 + a^6) + 4*(6*a^3*x^3 - 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^3 + 6*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2*log(a*x - 1) + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^3 + 6*a*x - 3*(a^4*x^4 - 2*a^2*x^2 + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 + 1)*log(a*x + 1) + 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))*a*arctanh(a*x)/(a^9*x^4 - 2*a^7*x^2 + a^5))*a","B",0
316,1,422,0,0.337780," ","integrate(x*arctanh(a*x)^3/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(\frac{2 \, {\left(3 \, a^{2} x^{3} - 5 \, x\right)}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1} - \frac{3 \, \log\left(a x + 1\right)}{a} + \frac{3 \, \log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right)^{2}}{64 \, a} + \frac{3 \, {\left(\frac{{\left(30 \, a^{3} x^{3} - 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{3} + 6 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{3} - 34 \, a x - 3 \, {\left(5 \, a^{4} x^{4} - 10 \, a^{2} x^{2} + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} + 5\right)} \log\left(a x + 1\right) + 15 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)\right)} a^{2}}{a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}} - \frac{4 \, {\left(12 \, a^{2} x^{2} - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 6 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 16\right)} a \operatorname{artanh}\left(a x\right)}{a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}}\right)}}{512 \, a} + \frac{\operatorname{artanh}\left(a x\right)^{3}}{4 \, {\left(a^{2} x^{2} - 1\right)}^{2} a^{2}}"," ",0,"3/64*(2*(3*a^2*x^3 - 5*x)/(a^4*x^4 - 2*a^2*x^2 + 1) - 3*log(a*x + 1)/a + 3*log(a*x - 1)/a)*arctanh(a*x)^2/a + 3/512*((30*a^3*x^3 - 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^3 + 6*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2*log(a*x - 1) + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^3 - 34*a*x - 3*(5*a^4*x^4 - 10*a^2*x^2 + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 + 5)*log(a*x + 1) + 15*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))*a^2/(a^7*x^4 - 2*a^5*x^2 + a^3) - 4*(12*a^2*x^2 - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2 + 6*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)*log(a*x - 1) - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 16)*a*arctanh(a*x)/(a^6*x^4 - 2*a^4*x^2 + a^2))/a + 1/4*arctanh(a*x)^3/((a^2*x^2 - 1)^2*a^2)","B",0
317,1,663,0,0.347700," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(\frac{2 \, {\left(3 \, a^{2} x^{3} - 5 \, x\right)}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1} - \frac{3 \, \log\left(a x + 1\right)}{a} + \frac{3 \, \log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right)^{3} + \frac{3 \, {\left(12 \, a^{2} x^{2} - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 6 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 16\right)} a \operatorname{artanh}\left(a x\right)^{2}}{64 \, {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)}} - \frac{3}{512} \, {\left(\frac{{\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{4} - 4 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{3} \log\left(a x - 1\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{4} - 60 \, a^{2} x^{2} + 3 \, {\left(5 \, a^{4} x^{4} - 10 \, a^{2} x^{2} + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} + 5\right)} \log\left(a x + 1\right)^{2} + 15 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 2 \, {\left(2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{3} + 15 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + 1\right) + 64\right)} a^{2}}{a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}} + \frac{4 \, {\left(30 \, a^{3} x^{3} - 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{3} + 6 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{3} - 34 \, a x - 3 \, {\left(5 \, a^{4} x^{4} - 10 \, a^{2} x^{2} + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} + 5\right)} \log\left(a x + 1\right) + 15 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)\right)} a \operatorname{artanh}\left(a x\right)}{a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}}\right)} a"," ",0,"-1/16*(2*(3*a^2*x^3 - 5*x)/(a^4*x^4 - 2*a^2*x^2 + 1) - 3*log(a*x + 1)/a + 3*log(a*x - 1)/a)*arctanh(a*x)^3 + 3/64*(12*a^2*x^2 - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2 + 6*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)*log(a*x - 1) - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 16)*a*arctanh(a*x)^2/(a^6*x^4 - 2*a^4*x^2 + a^2) - 3/512*(((a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^4 - 4*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^3*log(a*x - 1) + (a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^4 - 60*a^2*x^2 + 3*(5*a^4*x^4 - 10*a^2*x^2 + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 + 5)*log(a*x + 1)^2 + 15*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 2*(2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^3 + 15*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))*log(a*x + 1) + 64)*a^2/(a^8*x^4 - 2*a^6*x^2 + a^4) + 4*(30*a^3*x^3 - 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^3 + 6*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2*log(a*x - 1) + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^3 - 34*a*x - 3*(5*a^4*x^4 - 10*a^2*x^2 + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 + 5)*log(a*x + 1) + 15*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))*a*arctanh(a*x)/(a^7*x^4 - 2*a^5*x^2 + a^3))*a","B",0
318,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","\frac{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)^{4} + 2 \, {\left(2 \, a^{2} x^{2} + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - 3\right)} \log\left(-a x + 1\right)^{3}}{64 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)}} - \frac{1}{8} \, \int \frac{4 \, \log\left(a x + 1\right)^{3} - 12 \, \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) + 3 \, {\left(2 \, a^{4} x^{4} + 2 \, a^{3} x^{3} - 3 \, a^{2} x^{2} - 3 \, a x + 2 \, {\left(a^{6} x^{6} + a^{5} x^{5} - 2 \, a^{4} x^{4} - 2 \, a^{3} x^{3} + a^{2} x^{2} + a x + 2\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{2}}{4 \, {\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)}}\,{d x}"," ",0,"1/64*((a^4*x^4 - 2*a^2*x^2 + 1)*log(-a*x + 1)^4 + 2*(2*a^2*x^2 + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) - 3)*log(-a*x + 1)^3)/(a^4*x^4 - 2*a^2*x^2 + 1) - 1/8*integrate(1/4*(4*log(a*x + 1)^3 - 12*log(a*x + 1)^2*log(-a*x + 1) + 3*(2*a^4*x^4 + 2*a^3*x^3 - 3*a^2*x^2 - 3*a*x + 2*(a^6*x^6 + a^5*x^5 - 2*a^4*x^4 - 2*a^3*x^3 + a^2*x^2 + a*x + 2)*log(a*x + 1))*log(-a*x + 1)^2)/(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x), x)","F",0
319,-2,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^2/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
320,0,0,0,0.000000," ","integrate(arctanh(a*x)^(1/2)/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","-\int \frac{\sqrt{\operatorname{artanh}\left(a x\right)}}{{\left(a^{2} x^{2} - 1\right)}^{3}}\,{d x}"," ",0,"-integrate(sqrt(arctanh(a*x))/(a^2*x^2 - 1)^3, x)","F",0
321,0,0,0,0.000000," ","integrate(x^6/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""maxima"")","-\int \frac{x^{6}}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"-integrate(x^6/((a^2*x^2 - 1)^3*arctanh(a*x)), x)","F",0
322,0,0,0,0.000000," ","integrate(x^5/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""maxima"")","-\int \frac{x^{5}}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"-integrate(x^5/((a^2*x^2 - 1)^3*arctanh(a*x)), x)","F",0
323,0,0,0,0.000000," ","integrate(x^4/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""maxima"")","-\int \frac{x^{4}}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"-integrate(x^4/((a^2*x^2 - 1)^3*arctanh(a*x)), x)","F",0
324,0,0,0,0.000000," ","integrate(x^3/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""maxima"")","-\int \frac{x^{3}}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"-integrate(x^3/((a^2*x^2 - 1)^3*arctanh(a*x)), x)","F",0
325,0,0,0,0.000000," ","integrate(x^2/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""maxima"")","-\int \frac{x^{2}}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"-integrate(x^2/((a^2*x^2 - 1)^3*arctanh(a*x)), x)","F",0
326,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""maxima"")","-\int \frac{x}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"-integrate(x/((a^2*x^2 - 1)^3*arctanh(a*x)), x)","F",0
327,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""maxima"")","-\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"-integrate(1/((a^2*x^2 - 1)^3*arctanh(a*x)), x)","F",0
328,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""maxima"")","-\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{3} x \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"-integrate(1/((a^2*x^2 - 1)^3*x*arctanh(a*x)), x)","F",0
329,0,0,0,0.000000," ","integrate(x^5/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, x^{5}}{{\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right) - {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-a x + 1\right)} - \int -\frac{2 \, {\left(a^{2} x^{6} - 5 \, x^{4}\right)}}{{\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(a x + 1\right) - {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2*x^5/((a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1) - (a^5*x^4 - 2*a^3*x^2 + a)*log(-a*x + 1)) - integrate(-2*(a^2*x^6 - 5*x^4)/((a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(a*x + 1) - (a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(-a*x + 1)), x)","F",0
330,0,0,0,0.000000," ","integrate(x^4/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, x^{4}}{{\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right) - {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-a x + 1\right)} + 8 \, \int -\frac{x^{3}}{{\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(a x + 1\right) - {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2*x^4/((a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1) - (a^5*x^4 - 2*a^3*x^2 + a)*log(-a*x + 1)) + 8*integrate(-x^3/((a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(a*x + 1) - (a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(-a*x + 1)), x)","F",0
331,0,0,0,0.000000," ","integrate(x^3/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, x^{3}}{{\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right) - {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-a x + 1\right)} + \int -\frac{2 \, {\left(a^{2} x^{4} + 3 \, x^{2}\right)}}{{\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(a x + 1\right) - {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2*x^3/((a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1) - (a^5*x^4 - 2*a^3*x^2 + a)*log(-a*x + 1)) + integrate(-2*(a^2*x^4 + 3*x^2)/((a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(a*x + 1) - (a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(-a*x + 1)), x)","F",0
332,0,0,0,0.000000," ","integrate(x^2/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, x^{2}}{{\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right) - {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-a x + 1\right)} + \int -\frac{4 \, {\left(a^{2} x^{3} + x\right)}}{{\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(a x + 1\right) - {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2*x^2/((a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1) - (a^5*x^4 - 2*a^3*x^2 + a)*log(-a*x + 1)) + integrate(-4*(a^2*x^3 + x)/((a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(a*x + 1) - (a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(-a*x + 1)), x)","F",0
333,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, x}{{\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right) - {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-a x + 1\right)} + \int -\frac{2 \, {\left(3 \, a^{2} x^{2} + 1\right)}}{{\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(a x + 1\right) - {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2*x/((a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1) - (a^5*x^4 - 2*a^3*x^2 + a)*log(-a*x + 1)) + integrate(-2*(3*a^2*x^2 + 1)/((a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(a*x + 1) - (a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(-a*x + 1)), x)","F",0
334,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""maxima"")","8 \, a \int -\frac{x}{{\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) - {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)}\,{d x} - \frac{2}{{\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right) - {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-a x + 1\right)}"," ",0,"8*a*integrate(-x/((a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1) - (a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(-a*x + 1)), x) - 2/((a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1) - (a^5*x^4 - 2*a^3*x^2 + a)*log(-a*x + 1))","F",0
335,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""maxima"")","-\frac{2}{{\left(a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right)} \log\left(a x + 1\right) - {\left(a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right)} \log\left(-a x + 1\right)} + \int -\frac{2 \, {\left(5 \, a^{2} x^{2} - 1\right)}}{{\left(a^{7} x^{8} - 3 \, a^{5} x^{6} + 3 \, a^{3} x^{4} - a x^{2}\right)} \log\left(a x + 1\right) - {\left(a^{7} x^{8} - 3 \, a^{5} x^{6} + 3 \, a^{3} x^{4} - a x^{2}\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2/((a^5*x^5 - 2*a^3*x^3 + a*x)*log(a*x + 1) - (a^5*x^5 - 2*a^3*x^3 + a*x)*log(-a*x + 1)) + integrate(-2*(5*a^2*x^2 - 1)/((a^7*x^8 - 3*a^5*x^6 + 3*a^3*x^4 - a*x^2)*log(a*x + 1) - (a^7*x^8 - 3*a^5*x^6 + 3*a^3*x^4 - a*x^2)*log(-a*x + 1)), x)","F",0
336,0,0,0,0.000000," ","integrate(x^4/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(a x^{4} + 2 \, x^{3} \log\left(a x + 1\right) - 2 \, x^{3} \log\left(-a x + 1\right)\right)}}{{\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right) + {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(-a x + 1\right)^{2}} + \int -\frac{4 \, {\left(a^{2} x^{4} + 3 \, x^{2}\right)}}{{\left(a^{8} x^{6} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} - a^{2}\right)} \log\left(a x + 1\right) - {\left(a^{8} x^{6} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} - a^{2}\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2*(a*x^4 + 2*x^3*log(a*x + 1) - 2*x^3*log(-a*x + 1))/((a^6*x^4 - 2*a^4*x^2 + a^2)*log(a*x + 1)^2 - 2*(a^6*x^4 - 2*a^4*x^2 + a^2)*log(a*x + 1)*log(-a*x + 1) + (a^6*x^4 - 2*a^4*x^2 + a^2)*log(-a*x + 1)^2) + integrate(-4*(a^2*x^4 + 3*x^2)/((a^8*x^6 - 3*a^6*x^4 + 3*a^4*x^2 - a^2)*log(a*x + 1) - (a^8*x^6 - 3*a^6*x^4 + 3*a^4*x^2 - a^2)*log(-a*x + 1)), x)","F",0
337,0,0,0,0.000000," ","integrate(x^3/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""maxima"")","-\frac{2 \, a x^{3} + {\left(a^{2} x^{4} + 3 \, x^{2}\right)} \log\left(a x + 1\right) - {\left(a^{2} x^{4} + 3 \, x^{2}\right)} \log\left(-a x + 1\right)}{{\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right) + {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(-a x + 1\right)^{2}} + \int -\frac{2 \, {\left(5 \, a^{2} x^{3} + 3 \, x\right)}}{{\left(a^{8} x^{6} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} - a^{2}\right)} \log\left(a x + 1\right) - {\left(a^{8} x^{6} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} - a^{2}\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-(2*a*x^3 + (a^2*x^4 + 3*x^2)*log(a*x + 1) - (a^2*x^4 + 3*x^2)*log(-a*x + 1))/((a^6*x^4 - 2*a^4*x^2 + a^2)*log(a*x + 1)^2 - 2*(a^6*x^4 - 2*a^4*x^2 + a^2)*log(a*x + 1)*log(-a*x + 1) + (a^6*x^4 - 2*a^4*x^2 + a^2)*log(-a*x + 1)^2) + integrate(-2*(5*a^2*x^3 + 3*x)/((a^8*x^6 - 3*a^6*x^4 + 3*a^4*x^2 - a^2)*log(a*x + 1) - (a^8*x^6 - 3*a^6*x^4 + 3*a^4*x^2 - a^2)*log(-a*x + 1)), x)","F",0
338,0,0,0,0.000000," ","integrate(x^2/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(a x^{2} + {\left(a^{2} x^{3} + x\right)} \log\left(a x + 1\right) - {\left(a^{2} x^{3} + x\right)} \log\left(-a x + 1\right)\right)}}{{\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right) + {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(-a x + 1\right)^{2}} + \int -\frac{2 \, {\left(a^{4} x^{4} + 6 \, a^{2} x^{2} + 1\right)}}{{\left(a^{8} x^{6} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} - a^{2}\right)} \log\left(a x + 1\right) - {\left(a^{8} x^{6} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} - a^{2}\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2*(a*x^2 + (a^2*x^3 + x)*log(a*x + 1) - (a^2*x^3 + x)*log(-a*x + 1))/((a^6*x^4 - 2*a^4*x^2 + a^2)*log(a*x + 1)^2 - 2*(a^6*x^4 - 2*a^4*x^2 + a^2)*log(a*x + 1)*log(-a*x + 1) + (a^6*x^4 - 2*a^4*x^2 + a^2)*log(-a*x + 1)^2) + integrate(-2*(a^4*x^4 + 6*a^2*x^2 + 1)/((a^8*x^6 - 3*a^6*x^4 + 3*a^4*x^2 - a^2)*log(a*x + 1) - (a^8*x^6 - 3*a^6*x^4 + 3*a^4*x^2 - a^2)*log(-a*x + 1)), x)","F",0
339,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""maxima"")","-\frac{2 \, a x + {\left(3 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - {\left(3 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)}{{\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right) + {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(-a x + 1\right)^{2}} + \int -\frac{2 \, {\left(3 \, a^{2} x^{3} + 5 \, x\right)}}{{\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) - {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-(2*a*x + (3*a^2*x^2 + 1)*log(a*x + 1) - (3*a^2*x^2 + 1)*log(-a*x + 1))/((a^6*x^4 - 2*a^4*x^2 + a^2)*log(a*x + 1)^2 - 2*(a^6*x^4 - 2*a^4*x^2 + a^2)*log(a*x + 1)*log(-a*x + 1) + (a^6*x^4 - 2*a^4*x^2 + a^2)*log(-a*x + 1)^2) + integrate(-2*(3*a^2*x^3 + 5*x)/((a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1) - (a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(-a*x + 1)), x)","F",0
340,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(2 \, a x \log\left(a x + 1\right) - 2 \, a x \log\left(-a x + 1\right) + 1\right)}}{{\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right) + {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-a x + 1\right)^{2}} + \int -\frac{4 \, {\left(3 \, a^{2} x^{2} + 1\right)}}{{\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) - {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-2*(2*a*x*log(a*x + 1) - 2*a*x*log(-a*x + 1) + 1)/((a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1)^2 - 2*(a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1)*log(-a*x + 1) + (a^5*x^4 - 2*a^3*x^2 + a)*log(-a*x + 1)^2) + integrate(-4*(3*a^2*x^2 + 1)/((a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1) - (a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(-a*x + 1)), x)","F",0
341,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""maxima"")","-\frac{2 \, a x + {\left(5 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) - {\left(5 \, a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)}{{\left(a^{6} x^{6} - 2 \, a^{4} x^{4} + a^{2} x^{2}\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{6} x^{6} - 2 \, a^{4} x^{4} + a^{2} x^{2}\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right) + {\left(a^{6} x^{6} - 2 \, a^{4} x^{4} + a^{2} x^{2}\right)} \log\left(-a x + 1\right)^{2}} + \int -\frac{2 \, {\left(10 \, a^{4} x^{4} - 3 \, a^{2} x^{2} + 1\right)}}{{\left(a^{8} x^{9} - 3 \, a^{6} x^{7} + 3 \, a^{4} x^{5} - a^{2} x^{3}\right)} \log\left(a x + 1\right) - {\left(a^{8} x^{9} - 3 \, a^{6} x^{7} + 3 \, a^{4} x^{5} - a^{2} x^{3}\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"-(2*a*x + (5*a^2*x^2 - 1)*log(a*x + 1) - (5*a^2*x^2 - 1)*log(-a*x + 1))/((a^6*x^6 - 2*a^4*x^4 + a^2*x^2)*log(a*x + 1)^2 - 2*(a^6*x^6 - 2*a^4*x^4 + a^2*x^2)*log(a*x + 1)*log(-a*x + 1) + (a^6*x^6 - 2*a^4*x^4 + a^2*x^2)*log(-a*x + 1)^2) + integrate(-2*(10*a^4*x^4 - 3*a^2*x^2 + 1)/((a^8*x^9 - 3*a^6*x^7 + 3*a^4*x^5 - a^2*x^3)*log(a*x + 1) - (a^8*x^9 - 3*a^6*x^7 + 3*a^4*x^5 - a^2*x^3)*log(-a*x + 1)), x)","F",0
342,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^4,x, algorithm=""maxima"")","-\frac{4 \, {\left(2 \, a x \log\left(a x + 1\right) + {\left(3 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + {\left(3 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)^{2} - 2 \, {\left(a x + {\left(3 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right) + 2\right)}}{3 \, {\left({\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right) + 3 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right)^{2} - {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-a x + 1\right)^{3}\right)}} + \int -\frac{8 \, {\left(3 \, a^{3} x^{3} + 5 \, a x\right)}}{3 \, {\left({\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) - {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)\right)}}\,{d x}"," ",0,"-4/3*(2*a*x*log(a*x + 1) + (3*a^2*x^2 + 1)*log(a*x + 1)^2 + (3*a^2*x^2 + 1)*log(-a*x + 1)^2 - 2*(a*x + (3*a^2*x^2 + 1)*log(a*x + 1))*log(-a*x + 1) + 2)/((a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1)^3 - 3*(a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1)^2*log(-a*x + 1) + 3*(a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1)*log(-a*x + 1)^2 - (a^5*x^4 - 2*a^3*x^2 + a)*log(-a*x + 1)^3) + integrate(-8/3*(3*a^3*x^3 + 5*a*x)/((a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1) - (a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(-a*x + 1)), x)","F",0
343,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^5,x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(3 \, a^{3} x^{3} + 5 \, a x\right)} \log\left(a x + 1\right)^{3} - {\left(3 \, a^{3} x^{3} + 5 \, a x\right)} \log\left(-a x + 1\right)^{3} + 4 \, a x \log\left(a x + 1\right) + {\left(3 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + {\left(3 \, a^{2} x^{2} + 3 \, {\left(3 \, a^{3} x^{3} + 5 \, a x\right)} \log\left(a x + 1\right) + 1\right)} \log\left(-a x + 1\right)^{2} - {\left(3 \, {\left(3 \, a^{3} x^{3} + 5 \, a x\right)} \log\left(a x + 1\right)^{2} + 4 \, a x + 2 \, {\left(3 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right) + 6\right)}}{3 \, {\left({\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right)^{4} - 4 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right)^{3} \log\left(-a x + 1\right) + 6 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)^{2} - 4 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right)^{3} + {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-a x + 1\right)^{4}\right)}} + \int -\frac{2 \, {\left(3 \, a^{4} x^{4} + 24 \, a^{2} x^{2} + 5\right)}}{3 \, {\left({\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) - {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)\right)}}\,{d x}"," ",0,"-2/3*((3*a^3*x^3 + 5*a*x)*log(a*x + 1)^3 - (3*a^3*x^3 + 5*a*x)*log(-a*x + 1)^3 + 4*a*x*log(a*x + 1) + (3*a^2*x^2 + 1)*log(a*x + 1)^2 + (3*a^2*x^2 + 3*(3*a^3*x^3 + 5*a*x)*log(a*x + 1) + 1)*log(-a*x + 1)^2 - (3*(3*a^3*x^3 + 5*a*x)*log(a*x + 1)^2 + 4*a*x + 2*(3*a^2*x^2 + 1)*log(a*x + 1))*log(-a*x + 1) + 6)/((a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1)^4 - 4*(a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1)^3*log(-a*x + 1) + 6*(a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1)^2*log(-a*x + 1)^2 - 4*(a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1)*log(-a*x + 1)^3 + (a^5*x^4 - 2*a^3*x^2 + a)*log(-a*x + 1)^4) + integrate(-2/3*(3*a^4*x^4 + 24*a^2*x^2 + 5)/((a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1) - (a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(-a*x + 1)), x)","F",0
344,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^6,x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(3 \, a^{4} x^{4} + 24 \, a^{2} x^{2} + 5\right)} \log\left(a x + 1\right)^{4} + {\left(3 \, a^{4} x^{4} + 24 \, a^{2} x^{2} + 5\right)} \log\left(-a x + 1\right)^{4} + 2 \, {\left(3 \, a^{3} x^{3} + 5 \, a x\right)} \log\left(a x + 1\right)^{3} - 2 \, {\left(3 \, a^{3} x^{3} + 5 \, a x + 2 \, {\left(3 \, a^{4} x^{4} + 24 \, a^{2} x^{2} + 5\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right)^{3} + 24 \, a x \log\left(a x + 1\right) + 4 \, {\left(3 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 2 \, {\left(6 \, a^{2} x^{2} + 3 \, {\left(3 \, a^{4} x^{4} + 24 \, a^{2} x^{2} + 5\right)} \log\left(a x + 1\right)^{2} + 3 \, {\left(3 \, a^{3} x^{3} + 5 \, a x\right)} \log\left(a x + 1\right) + 2\right)} \log\left(-a x + 1\right)^{2} - 2 \, {\left(2 \, {\left(3 \, a^{4} x^{4} + 24 \, a^{2} x^{2} + 5\right)} \log\left(a x + 1\right)^{3} + 3 \, {\left(3 \, a^{3} x^{3} + 5 \, a x\right)} \log\left(a x + 1\right)^{2} + 12 \, a x + 4 \, {\left(3 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)\right)} \log\left(-a x + 1\right) + 48\right)}}{15 \, {\left({\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right)^{5} - 5 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right)^{4} \log\left(-a x + 1\right) + 10 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right)^{3} \log\left(-a x + 1\right)^{2} - 10 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right)^{2} \log\left(-a x + 1\right)^{3} + 5 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right)^{4} - {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-a x + 1\right)^{5}\right)}} + \int -\frac{8 \, {\left(15 \, a^{3} x^{3} + 17 \, a x\right)}}{15 \, {\left({\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) - {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(-a x + 1\right)\right)}}\,{d x}"," ",0,"-2/15*((3*a^4*x^4 + 24*a^2*x^2 + 5)*log(a*x + 1)^4 + (3*a^4*x^4 + 24*a^2*x^2 + 5)*log(-a*x + 1)^4 + 2*(3*a^3*x^3 + 5*a*x)*log(a*x + 1)^3 - 2*(3*a^3*x^3 + 5*a*x + 2*(3*a^4*x^4 + 24*a^2*x^2 + 5)*log(a*x + 1))*log(-a*x + 1)^3 + 24*a*x*log(a*x + 1) + 4*(3*a^2*x^2 + 1)*log(a*x + 1)^2 + 2*(6*a^2*x^2 + 3*(3*a^4*x^4 + 24*a^2*x^2 + 5)*log(a*x + 1)^2 + 3*(3*a^3*x^3 + 5*a*x)*log(a*x + 1) + 2)*log(-a*x + 1)^2 - 2*(2*(3*a^4*x^4 + 24*a^2*x^2 + 5)*log(a*x + 1)^3 + 3*(3*a^3*x^3 + 5*a*x)*log(a*x + 1)^2 + 12*a*x + 4*(3*a^2*x^2 + 1)*log(a*x + 1))*log(-a*x + 1) + 48)/((a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1)^5 - 5*(a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1)^4*log(-a*x + 1) + 10*(a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1)^3*log(-a*x + 1)^2 - 10*(a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1)^2*log(-a*x + 1)^3 + 5*(a^5*x^4 - 2*a^3*x^2 + a)*log(a*x + 1)*log(-a*x + 1)^4 - (a^5*x^4 - 2*a^3*x^2 + a)*log(-a*x + 1)^5) + integrate(-8/15*(15*a^3*x^3 + 17*a*x)/((a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1) - (a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(-a*x + 1)), x)","F",0
345,1,240,0,0.323367," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^4,x, algorithm=""maxima"")","-\frac{1}{96} \, {\left(\frac{2 \, {\left(15 \, a^{4} x^{5} - 40 \, a^{2} x^{3} + 33 \, x\right)}}{a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1} - \frac{15 \, \log\left(a x + 1\right)}{a} + \frac{15 \, \log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right) + \frac{{\left(180 \, a^{4} x^{4} - 420 \, a^{2} x^{2} - 45 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} + 90 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - 45 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} + 272\right)} a}{1152 \, {\left(a^{8} x^{6} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} - a^{2}\right)}}"," ",0,"-1/96*(2*(15*a^4*x^5 - 40*a^2*x^3 + 33*x)/(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1) - 15*log(a*x + 1)/a + 15*log(a*x - 1)/a)*arctanh(a*x) + 1/1152*(180*a^4*x^4 - 420*a^2*x^2 - 45*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1)^2 + 90*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) - 45*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1)^2 + 272)*a/(a^8*x^6 - 3*a^6*x^4 + 3*a^4*x^2 - a^2)","B",0
346,1,516,0,0.338395," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^4,x, algorithm=""maxima"")","-\frac{1}{96} \, {\left(\frac{2 \, {\left(15 \, a^{4} x^{5} - 40 \, a^{2} x^{3} + 33 \, x\right)}}{a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1} - \frac{15 \, \log\left(a x + 1\right)}{a} + \frac{15 \, \log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right)^{2} - \frac{{\left(1470 \, a^{5} x^{5} - 3200 \, a^{3} x^{3} - 90 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{3} + 270 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) + 90 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{3} + 1794 \, a x - 15 \, {\left(49 \, a^{6} x^{6} - 147 \, a^{4} x^{4} + 147 \, a^{2} x^{2} + 18 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 49\right)} \log\left(a x + 1\right) + 735 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} a^{2}}{6912 \, {\left(a^{9} x^{6} - 3 \, a^{7} x^{4} + 3 \, a^{5} x^{2} - a^{3}\right)}} + \frac{{\left(180 \, a^{4} x^{4} - 420 \, a^{2} x^{2} - 45 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} + 90 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - 45 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} + 272\right)} a \operatorname{artanh}\left(a x\right)}{576 \, {\left(a^{8} x^{6} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} - a^{2}\right)}}"," ",0,"-1/96*(2*(15*a^4*x^5 - 40*a^2*x^3 + 33*x)/(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1) - 15*log(a*x + 1)/a + 15*log(a*x - 1)/a)*arctanh(a*x)^2 - 1/6912*(1470*a^5*x^5 - 3200*a^3*x^3 - 90*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1)^3 + 270*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1)^2*log(a*x - 1) + 90*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1)^3 + 1794*a*x - 15*(49*a^6*x^6 - 147*a^4*x^4 + 147*a^2*x^2 + 18*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1)^2 - 49)*log(a*x + 1) + 735*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1))*a^2/(a^9*x^6 - 3*a^7*x^4 + 3*a^5*x^2 - a^3) + 1/576*(180*a^4*x^4 - 420*a^2*x^2 - 45*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1)^2 + 90*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) - 45*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1)^2 + 272)*a*arctanh(a*x)/(a^8*x^6 - 3*a^6*x^4 + 3*a^4*x^2 - a^2)","B",0
347,1,871,0,0.372833," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^4,x, algorithm=""maxima"")","-\frac{1}{96} \, {\left(\frac{2 \, {\left(15 \, a^{4} x^{5} - 40 \, a^{2} x^{3} + 33 \, x\right)}}{a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1} - \frac{15 \, \log\left(a x + 1\right)}{a} + \frac{15 \, \log\left(a x - 1\right)}{a}\right)} \operatorname{artanh}\left(a x\right)^{3} + \frac{{\left(180 \, a^{4} x^{4} - 420 \, a^{2} x^{2} - 45 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} + 90 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - 45 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} + 272\right)} a \operatorname{artanh}\left(a x\right)^{2}}{384 \, {\left(a^{8} x^{6} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} - a^{2}\right)}} + \frac{1}{27648} \, {\left(\frac{{\left(8820 \, a^{4} x^{4} - 135 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{4} + 540 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{3} \log\left(a x - 1\right) - 135 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{4} - 18420 \, a^{2} x^{2} - 45 \, {\left(49 \, a^{6} x^{6} - 147 \, a^{4} x^{4} + 147 \, a^{2} x^{2} + 18 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 49\right)} \log\left(a x + 1\right)^{2} - 2205 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} + 90 \, {\left(6 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{3} + 49 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + 1\right) + 9728\right)} a^{2}}{a^{10} x^{6} - 3 \, a^{8} x^{4} + 3 \, a^{6} x^{2} - a^{4}} - \frac{12 \, {\left(1470 \, a^{5} x^{5} - 3200 \, a^{3} x^{3} - 90 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{3} + 270 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} \log\left(a x - 1\right) + 90 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{3} + 1794 \, a x - 15 \, {\left(49 \, a^{6} x^{6} - 147 \, a^{4} x^{4} + 147 \, a^{2} x^{2} + 18 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} - 49\right)} \log\left(a x + 1\right) + 735 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} a \operatorname{artanh}\left(a x\right)}{a^{9} x^{6} - 3 \, a^{7} x^{4} + 3 \, a^{5} x^{2} - a^{3}}\right)} a"," ",0,"-1/96*(2*(15*a^4*x^5 - 40*a^2*x^3 + 33*x)/(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1) - 15*log(a*x + 1)/a + 15*log(a*x - 1)/a)*arctanh(a*x)^3 + 1/384*(180*a^4*x^4 - 420*a^2*x^2 - 45*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1)^2 + 90*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) - 45*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1)^2 + 272)*a*arctanh(a*x)^2/(a^8*x^6 - 3*a^6*x^4 + 3*a^4*x^2 - a^2) + 1/27648*((8820*a^4*x^4 - 135*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1)^4 + 540*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1)^3*log(a*x - 1) - 135*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1)^4 - 18420*a^2*x^2 - 45*(49*a^6*x^6 - 147*a^4*x^4 + 147*a^2*x^2 + 18*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1)^2 - 49)*log(a*x + 1)^2 - 2205*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1)^2 + 90*(6*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1)^3 + 49*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1))*log(a*x + 1) + 9728)*a^2/(a^10*x^6 - 3*a^8*x^4 + 3*a^6*x^2 - a^4) - 12*(1470*a^5*x^5 - 3200*a^3*x^3 - 90*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1)^3 + 270*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1)^2*log(a*x - 1) + 90*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1)^3 + 1794*a*x - 15*(49*a^6*x^6 - 147*a^4*x^4 + 147*a^2*x^2 + 18*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1)^2 - 49)*log(a*x + 1) + 735*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1))*a*arctanh(a*x)/(a^9*x^6 - 3*a^7*x^4 + 3*a^5*x^2 - a^3))*a","B",0
348,0,0,0,0.000000," ","integrate(arctanh(a*x)^(1/2)/(-a^2*x^2+1)^4,x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{artanh}\left(a x\right)}}{{\left(a^{2} x^{2} - 1\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt(arctanh(a*x))/(a^2*x^2 - 1)^4, x)","F",0
349,0,0,0,0.000000," ","integrate(x^8/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x^{8}}{{\left(a^{2} x^{2} - 1\right)}^{4} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^8/((a^2*x^2 - 1)^4*arctanh(a*x)), x)","F",0
350,0,0,0,0.000000," ","integrate(x^7/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x^{7}}{{\left(a^{2} x^{2} - 1\right)}^{4} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^7/((a^2*x^2 - 1)^4*arctanh(a*x)), x)","F",0
351,0,0,0,0.000000," ","integrate(x^6/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x^{6}}{{\left(a^{2} x^{2} - 1\right)}^{4} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^6/((a^2*x^2 - 1)^4*arctanh(a*x)), x)","F",0
352,0,0,0,0.000000," ","integrate(x^5/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x^{5}}{{\left(a^{2} x^{2} - 1\right)}^{4} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^5/((a^2*x^2 - 1)^4*arctanh(a*x)), x)","F",0
353,0,0,0,0.000000," ","integrate(x^4/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(a^{2} x^{2} - 1\right)}^{4} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^4/((a^2*x^2 - 1)^4*arctanh(a*x)), x)","F",0
354,0,0,0,0.000000," ","integrate(x^3/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x^{3}}{{\left(a^{2} x^{2} - 1\right)}^{4} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^3/((a^2*x^2 - 1)^4*arctanh(a*x)), x)","F",0
355,0,0,0,0.000000," ","integrate(x^2/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(a^{2} x^{2} - 1\right)}^{4} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^2/((a^2*x^2 - 1)^4*arctanh(a*x)), x)","F",0
356,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x}{{\left(a^{2} x^{2} - 1\right)}^{4} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x/((a^2*x^2 - 1)^4*arctanh(a*x)), x)","F",0
357,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{4} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^4*arctanh(a*x)), x)","F",0
358,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{4} x \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^4*x*arctanh(a*x)), x)","F",0
359,0,0,0,0.000000," ","integrate(1/x^2/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{4} x^{2} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^4*x^2*arctanh(a*x)), x)","F",0
360,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^4/arctanh(a*x)^2,x, algorithm=""maxima"")","\frac{2 \, x}{{\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(a x + 1\right) - {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)} - \int -\frac{2 \, {\left(5 \, a^{2} x^{2} + 1\right)}}{{\left(a^{9} x^{8} - 4 \, a^{7} x^{6} + 6 \, a^{5} x^{4} - 4 \, a^{3} x^{2} + a\right)} \log\left(a x + 1\right) - {\left(a^{9} x^{8} - 4 \, a^{7} x^{6} + 6 \, a^{5} x^{4} - 4 \, a^{3} x^{2} + a\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"2*x/((a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(a*x + 1) - (a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(-a*x + 1)) - integrate(-2*(5*a^2*x^2 + 1)/((a^9*x^8 - 4*a^7*x^6 + 6*a^5*x^4 - 4*a^3*x^2 + a)*log(a*x + 1) - (a^9*x^8 - 4*a^7*x^6 + 6*a^5*x^4 - 4*a^3*x^2 + a)*log(-a*x + 1)), x)","F",0
361,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^4/arctanh(a*x)^2,x, algorithm=""maxima"")","-12 \, a \int -\frac{x}{{\left(a^{8} x^{8} - 4 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - 4 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - {\left(a^{8} x^{8} - 4 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - 4 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)}\,{d x} + \frac{2}{{\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(a x + 1\right) - {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)}"," ",0,"-12*a*integrate(-x/((a^8*x^8 - 4*a^6*x^6 + 6*a^4*x^4 - 4*a^2*x^2 + 1)*log(a*x + 1) - (a^8*x^8 - 4*a^6*x^6 + 6*a^4*x^4 - 4*a^2*x^2 + 1)*log(-a*x + 1)), x) + 2/((a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(a*x + 1) - (a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(-a*x + 1))","F",0
362,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^4/arctanh(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, a x + {\left(5 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - {\left(5 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)}{{\left(a^{8} x^{6} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} - a^{2}\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{8} x^{6} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} - a^{2}\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right) + {\left(a^{8} x^{6} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} - a^{2}\right)} \log\left(-a x + 1\right)^{2}} - \int -\frac{4 \, {\left(5 \, a^{2} x^{3} + 4 \, x\right)}}{{\left(a^{8} x^{8} - 4 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - 4 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - {\left(a^{8} x^{8} - 4 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - 4 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"(2*a*x + (5*a^2*x^2 + 1)*log(a*x + 1) - (5*a^2*x^2 + 1)*log(-a*x + 1))/((a^8*x^6 - 3*a^6*x^4 + 3*a^4*x^2 - a^2)*log(a*x + 1)^2 - 2*(a^8*x^6 - 3*a^6*x^4 + 3*a^4*x^2 - a^2)*log(a*x + 1)*log(-a*x + 1) + (a^8*x^6 - 3*a^6*x^4 + 3*a^4*x^2 - a^2)*log(-a*x + 1)^2) - integrate(-4*(5*a^2*x^3 + 4*x)/((a^8*x^8 - 4*a^6*x^6 + 6*a^4*x^4 - 4*a^2*x^2 + 1)*log(a*x + 1) - (a^8*x^8 - 4*a^6*x^6 + 6*a^4*x^4 - 4*a^2*x^2 + 1)*log(-a*x + 1)), x)","F",0
363,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^4/arctanh(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, a x \log\left(a x + 1\right) - 3 \, a x \log\left(-a x + 1\right) + 1\right)}}{{\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(a x + 1\right)^{2} - 2 \, {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(a x + 1\right) \log\left(-a x + 1\right) + {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(-a x + 1\right)^{2}} - \int -\frac{6 \, {\left(5 \, a^{2} x^{2} + 1\right)}}{{\left(a^{8} x^{8} - 4 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - 4 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) - {\left(a^{8} x^{8} - 4 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - 4 \, a^{2} x^{2} + 1\right)} \log\left(-a x + 1\right)}\,{d x}"," ",0,"2*(3*a*x*log(a*x + 1) - 3*a*x*log(-a*x + 1) + 1)/((a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(a*x + 1)^2 - 2*(a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(a*x + 1)*log(-a*x + 1) + (a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(-a*x + 1)^2) - integrate(-6*(5*a^2*x^2 + 1)/((a^8*x^8 - 4*a^6*x^6 + 6*a^4*x^4 - 4*a^2*x^2 + 1)*log(a*x + 1) - (a^8*x^8 - 4*a^6*x^6 + 6*a^4*x^4 - 4*a^2*x^2 + 1)*log(-a*x + 1)), x)","F",0
364,1,163,0,0.409475," ","integrate(x^5*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{120} \, a {\left(\frac{3 \, {\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 \, \arcsin\left(a x\right)}{a^{5}}\right)}}{a^{2}} + \frac{16 \, {\left(\frac{\sqrt{-a^{2} x^{2} + 1} x}{a^{2}} - \frac{\arcsin\left(a x\right)}{a^{3}}\right)}}{a^{4}} - \frac{64 \, \arcsin\left(a x\right)}{a^{7}}\right)} - \frac{1}{15} \, {\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)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/120*a*(3*(2*sqrt(-a^2*x^2 + 1)*x^3/a^2 + 3*sqrt(-a^2*x^2 + 1)*x/a^4 - 3*arcsin(a*x)/a^5)/a^2 + 16*(sqrt(-a^2*x^2 + 1)*x/a^2 - arcsin(a*x)/a^3)/a^4 - 64*arcsin(a*x)/a^7) - 1/15*(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)*arctanh(a*x)","A",0
365,0,0,0,0.000000," ","integrate(x^4*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4} \operatorname{artanh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^4*arctanh(a*x)/sqrt(-a^2*x^2 + 1), x)","F",0
366,1,88,0,0.414815," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{\frac{\sqrt{-a^{2} x^{2} + 1} x}{a^{2}} - \frac{\arcsin\left(a x\right)}{a^{3}}}{a^{2}} - \frac{4 \, \arcsin\left(a x\right)}{a^{5}}\right)} - \frac{1}{3} \, {\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{a^{2}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{4}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/6*a*((sqrt(-a^2*x^2 + 1)*x/a^2 - arcsin(a*x)/a^3)/a^2 - 4*arcsin(a*x)/a^5) - 1/3*(sqrt(-a^2*x^2 + 1)*x^2/a^2 + 2*sqrt(-a^2*x^2 + 1)/a^4)*arctanh(a*x)","A",0
367,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} \operatorname{artanh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^2*arctanh(a*x)/sqrt(-a^2*x^2 + 1), x)","F",0
368,1,30,0,0.404904," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{a^{2}} + \frac{\arcsin\left(a x\right)}{a^{2}}"," ",0,"-sqrt(-a^2*x^2 + 1)*arctanh(a*x)/a^2 + arcsin(a*x)/a^2","A",0
369,0,0,0,0.000000," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(arctanh(a*x)/sqrt(-a^2*x^2 + 1), x)","F",0
370,0,0,0,0.000000," ","integrate(arctanh(a*x)/x/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(arctanh(a*x)/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
371,1,51,0,0.408810," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-a \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x}"," ",0,"-a*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x","A",0
372,0,0,0,0.000000," ","integrate(arctanh(a*x)/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate(arctanh(a*x)/(sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
373,0,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3} \operatorname{artanh}\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^3*arctanh(a*x)^2/sqrt(-a^2*x^2 + 1), x)","F",0
374,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} \operatorname{artanh}\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^2*arctanh(a*x)^2/sqrt(-a^2*x^2 + 1), x)","F",0
375,0,0,0,0.000000," ","integrate(x*arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x \operatorname{artanh}\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x*arctanh(a*x)^2/sqrt(-a^2*x^2 + 1), x)","F",0
376,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/sqrt(-a^2*x^2 + 1), x)","F",0
377,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
378,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/(sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
379,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/(sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
380,0,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3} \operatorname{artanh}\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^3*arctanh(a*x)^3/sqrt(-a^2*x^2 + 1), x)","F",0
381,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} \operatorname{artanh}\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^2*arctanh(a*x)^3/sqrt(-a^2*x^2 + 1), x)","F",0
382,0,0,0,0.000000," ","integrate(x*arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x \operatorname{artanh}\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x*arctanh(a*x)^3/sqrt(-a^2*x^2 + 1), x)","F",0
383,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/sqrt(-a^2*x^2 + 1), x)","F",0
384,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
385,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/(sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
386,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/(sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
387,0,0,0,0.000000," ","integrate(x^m*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{m} \operatorname{artanh}\left(a x\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m*arctanh(a*x)/(-a^2*x^2 + 1)^(3/2), x)","F",0
388,1,96,0,0.406125," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","a {\left(\frac{\frac{x}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{\arcsin\left(a x\right)}{a^{3}}}{a^{2}} - \frac{2 \, x}{\sqrt{-a^{2} x^{2} + 1} a^{4}}\right)} - {\left(\frac{x^{2}}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{2}{\sqrt{-a^{2} x^{2} + 1} a^{4}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"a*((x/(sqrt(-a^2*x^2 + 1)*a^2) - arcsin(a*x)/a^3)/a^2 - 2*x/(sqrt(-a^2*x^2 + 1)*a^4)) - (x^2/(sqrt(-a^2*x^2 + 1)*a^2) - 2/(sqrt(-a^2*x^2 + 1)*a^4))*arctanh(a*x)","A",0
389,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2} \operatorname{artanh}\left(a x\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2*arctanh(a*x)/(-a^2*x^2 + 1)^(3/2), x)","F",0
390,1,39,0,0.306064," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{x}{\sqrt{-a^{2} x^{2} + 1} a} + \frac{\operatorname{artanh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1} a^{2}}"," ",0,"-x/(sqrt(-a^2*x^2 + 1)*a) + arctanh(a*x)/(sqrt(-a^2*x^2 + 1)*a^2)","A",0
391,1,36,0,0.302634," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{x \operatorname{artanh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} a}"," ",0,"x*arctanh(a*x)/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*a)","A",0
392,0,0,0,0.000000," ","integrate(arctanh(a*x)/x/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(arctanh(a*x)/((-a^2*x^2 + 1)^(3/2)*x), x)","F",0
393,1,84,0,0.306303," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{1}{\sqrt{-a^{2} x^{2} + 1}} + \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)\right)} + {\left(\frac{2 \, a^{2} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} x}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-a*(1/sqrt(-a^2*x^2 + 1) + log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))) + (2*a^2*x/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*x))*arctanh(a*x)","A",0
394,0,0,0,0.000000," ","integrate(arctanh(a*x)/x^3/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(arctanh(a*x)/((-a^2*x^2 + 1)^(3/2)*x^3), x)","F",0
395,0,0,0,0.000000," ","integrate(x^m*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{m} \operatorname{artanh}\left(a x\right)^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m*arctanh(a*x)^2/(-a^2*x^2 + 1)^(3/2), x)","F",0
396,0,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{3} \operatorname{artanh}\left(a x\right)^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3*arctanh(a*x)^2/(-a^2*x^2 + 1)^(3/2), x)","F",0
397,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2} \operatorname{artanh}\left(a x\right)^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2*arctanh(a*x)^2/(-a^2*x^2 + 1)^(3/2), x)","F",0
398,1,62,0,0.312958," ","integrate(x*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, x \operatorname{artanh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1} a} + \frac{\operatorname{artanh}\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1} a^{2}} + \frac{2}{\sqrt{-a^{2} x^{2} + 1} a^{2}}"," ",0,"-2*x*arctanh(a*x)/(sqrt(-a^2*x^2 + 1)*a) + arctanh(a*x)^2/(sqrt(-a^2*x^2 + 1)*a^2) + 2/(sqrt(-a^2*x^2 + 1)*a^2)","A",0
399,1,57,0,0.308720," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{x \operatorname{artanh}\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1}} + \frac{2 \, x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{2 \, \operatorname{artanh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1} a}"," ",0,"x*arctanh(a*x)^2/sqrt(-a^2*x^2 + 1) + 2*x/sqrt(-a^2*x^2 + 1) - 2*arctanh(a*x)/(sqrt(-a^2*x^2 + 1)*a)","A",0
400,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/((-a^2*x^2 + 1)^(3/2)*x), x)","F",0
401,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x^2/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/((-a^2*x^2 + 1)^(3/2)*x^2), x)","F",0
402,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x^3/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/((-a^2*x^2 + 1)^(3/2)*x^3), x)","F",0
403,0,0,0,0.000000," ","integrate(x^m*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{m} \operatorname{artanh}\left(a x\right)^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m*arctanh(a*x)^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
404,0,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{3} \operatorname{artanh}\left(a x\right)^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3*arctanh(a*x)^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
405,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2} \operatorname{artanh}\left(a x\right)^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2*arctanh(a*x)^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
406,1,88,0,0.318527," ","integrate(x*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{3 \, x \operatorname{artanh}\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1} a} + \frac{\operatorname{artanh}\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{6 \, {\left(\frac{x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{\operatorname{artanh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1} a}\right)}}{a}"," ",0,"-3*x*arctanh(a*x)^2/(sqrt(-a^2*x^2 + 1)*a) + arctanh(a*x)^3/(sqrt(-a^2*x^2 + 1)*a^2) - 6*(x/sqrt(-a^2*x^2 + 1) - arctanh(a*x)/(sqrt(-a^2*x^2 + 1)*a))/a","A",0
407,1,86,0,0.321762," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{x \operatorname{artanh}\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1}} + 6 \, a {\left(\frac{x \operatorname{artanh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1} a} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} a^{2}}\right)} - \frac{3 \, \operatorname{artanh}\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1} a}"," ",0,"x*arctanh(a*x)^3/sqrt(-a^2*x^2 + 1) + 6*a*(x*arctanh(a*x)/(sqrt(-a^2*x^2 + 1)*a) - 1/(sqrt(-a^2*x^2 + 1)*a^2)) - 3*arctanh(a*x)^2/(sqrt(-a^2*x^2 + 1)*a)","A",0
408,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/((-a^2*x^2 + 1)^(3/2)*x), x)","F",0
409,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^2/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/((-a^2*x^2 + 1)^(3/2)*x^2), x)","F",0
410,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^3/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/((-a^2*x^2 + 1)^(3/2)*x^3), x)","F",0
411,0,0,0,0.000000," ","integrate(x^m/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^m/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)), x)","F",0
412,0,0,0,0.000000," ","integrate(x^2/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^2/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)), x)","F",0
413,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(x/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)), x)","F",0
414,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)), x)","F",0
415,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(3/2)*x*arctanh(a*x)), x)","F",0
416,0,0,0,0.000000," ","integrate(x^m/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x^m/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)^2), x)","F",0
417,0,0,0,0.000000," ","integrate(x^2/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x^2/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)^2), x)","F",0
418,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""maxima"")","\int \frac{x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)^2), x)","F",0
419,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)^2), x)","F",0
420,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(3/2)*x*arctanh(a*x)^2), x)","F",0
421,0,0,0,0.000000," ","integrate(x^m/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x^m/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)^3), x)","F",0
422,0,0,0,0.000000," ","integrate(x^2/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x^2/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)^3), x)","F",0
423,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""maxima"")","\int \frac{x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)^3), x)","F",0
424,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)^3), x)","F",0
425,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(3/2)*x*arctanh(a*x)^3), x)","F",0
426,0,0,0,0.000000," ","integrate(x^4*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} x^{2} + 1} x^{4} \operatorname{artanh}\left(a x\right)\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*x^4*arctanh(a*x), x)","F",0
427,1,128,0,0.416614," ","integrate(x^3*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{120} \, a {\left(\frac{3 \, {\left(\frac{2 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{a^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1} x}{a^{2}} - \frac{\arcsin\left(a x\right)}{a^{3}}\right)}}{a^{2}} - \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} x + \frac{\arcsin\left(a x\right)}{a}\right)}}{a^{4}}\right)} - \frac{1}{15} \, {\left(\frac{3 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{a^{2}} + \frac{2 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{4}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/120*a*(3*(2*(-a^2*x^2 + 1)^(3/2)*x/a^2 - sqrt(-a^2*x^2 + 1)*x/a^2 - arcsin(a*x)/a^3)/a^2 - 8*(sqrt(-a^2*x^2 + 1)*x + arcsin(a*x)/a)/a^4) - 1/15*(3*(-a^2*x^2 + 1)^(3/2)*x^2/a^2 + 2*(-a^2*x^2 + 1)^(3/2)/a^4)*arctanh(a*x)","A",0
428,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} x^{2} + 1} x^{2} \operatorname{artanh}\left(a x\right)\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*x^2*arctanh(a*x), x)","F",0
429,1,50,0,0.413506," ","integrate(x*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)}{3 \, a^{2}} + \frac{\sqrt{-a^{2} x^{2} + 1} x + \frac{\arcsin\left(a x\right)}{a}}{6 \, a}"," ",0,"-1/3*(-a^2*x^2 + 1)^(3/2)*arctanh(a*x)/a^2 + 1/6*(sqrt(-a^2*x^2 + 1)*x + arcsin(a*x)/a)/a","A",0
430,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x),x, algorithm=""maxima"")","\int \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*arctanh(a*x), x)","F",0
431,0,0,0,0.000000," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x, x)","F",0
432,0,0,0,0.000000," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x^2, x)","F",0
433,0,0,0,0.000000," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x^3, x)","F",0
434,1,90,0,0.406742," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \sqrt{-a^{2} x^{2} + 1} a^{2} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{x^{2}}\right)} a - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)}{3 \, x^{3}}"," ",0,"1/6*(a^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - sqrt(-a^2*x^2 + 1)*a^2 - (-a^2*x^2 + 1)^(3/2)/x^2)*a - 1/3*(-a^2*x^2 + 1)^(3/2)*arctanh(a*x)/x^3","A",0
435,0,0,0,0.000000," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x^{5}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x^5, x)","F",0
436,1,204,0,0.405856," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^6,x, algorithm=""maxima"")","\frac{1}{120} \, {\left(3 \, a^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - 3 \, \sqrt{-a^{2} x^{2} + 1} a^{4} + 8 \, {\left(a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \sqrt{-a^{2} x^{2} + 1} a^{2} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{x^{2}}\right)} a^{2} - \frac{3 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{x^{2}} - \frac{6 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{x^{4}}\right)} a - \frac{1}{15} \, {\left(\frac{2 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{x^{3}} + \frac{3 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{x^{5}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/120*(3*a^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 3*sqrt(-a^2*x^2 + 1)*a^4 + 8*(a^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - sqrt(-a^2*x^2 + 1)*a^2 - (-a^2*x^2 + 1)^(3/2)/x^2)*a^2 - 3*(-a^2*x^2 + 1)^(3/2)*a^2/x^2 - 6*(-a^2*x^2 + 1)^(3/2)/x^4)*a - 1/15*(2*(-a^2*x^2 + 1)^(3/2)*a^2/x^3 + 3*(-a^2*x^2 + 1)^(3/2)/x^5)*arctanh(a*x)","A",0
437,0,0,0,0.000000," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^7,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x^{7}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x^7, x)","F",0
438,0,0,0,0.000000," ","integrate(x^4*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} x^{2} + 1} x^{4} \operatorname{artanh}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*x^4*arctanh(a*x)^2, x)","F",0
439,0,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} x^{2} + 1} x^{3} \operatorname{artanh}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*x^3*arctanh(a*x)^2, x)","F",0
440,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} x^{2} + 1} x^{2} \operatorname{artanh}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*x^2*arctanh(a*x)^2, x)","F",0
441,0,0,0,0.000000," ","integrate(x*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} x^{2} + 1} x \operatorname{artanh}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*x*arctanh(a*x)^2, x)","F",0
442,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x)^2,x, algorithm=""maxima"")","\int \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2, x)","F",0
443,0,0,0,0.000000," ","integrate(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{x}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/x, x)","F",0
444,0,0,0,0.000000," ","integrate(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/x^2, x)","F",0
445,0,0,0,0.000000," ","integrate(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/x^3, x)","F",0
446,0,0,0,0.000000," ","integrate(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/x^4, x)","F",0
447,0,0,0,0.000000," ","integrate(x^4*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""maxima"")","\int {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{4} \operatorname{artanh}\left(a x\right)\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*x^4*arctanh(a*x), x)","F",0
448,1,163,0,0.411502," ","integrate(x^3*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""maxima"")","-\frac{1}{1680} \, a {\left(\frac{5 \, {\left(\frac{8 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} x}{a^{2}} - \frac{2 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{a^{2}} - \frac{3 \, \sqrt{-a^{2} x^{2} + 1} x}{a^{2}} - \frac{3 \, \arcsin\left(a x\right)}{a^{3}}\right)}}{a^{2}} - \frac{12 \, {\left(2 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x + 3 \, \sqrt{-a^{2} x^{2} + 1} x + \frac{3 \, \arcsin\left(a x\right)}{a}\right)}}{a^{4}}\right)} - \frac{1}{35} \, {\left(\frac{5 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} x^{2}}{a^{2}} + \frac{2 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{a^{4}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/1680*a*(5*(8*(-a^2*x^2 + 1)^(5/2)*x/a^2 - 2*(-a^2*x^2 + 1)^(3/2)*x/a^2 - 3*sqrt(-a^2*x^2 + 1)*x/a^2 - 3*arcsin(a*x)/a^3)/a^2 - 12*(2*(-a^2*x^2 + 1)^(3/2)*x + 3*sqrt(-a^2*x^2 + 1)*x + 3*arcsin(a*x)/a)/a^4) - 1/35*(5*(-a^2*x^2 + 1)^(5/2)*x^2/a^2 + 2*(-a^2*x^2 + 1)^(5/2)/a^4)*arctanh(a*x)","A",0
449,0,0,0,0.000000," ","integrate(x^2*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""maxima"")","\int {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2} \operatorname{artanh}\left(a x\right)\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*x^2*arctanh(a*x), x)","F",0
450,1,67,0,0.405077," ","integrate(x*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""maxima"")","-\frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} \operatorname{artanh}\left(a x\right)}{5 \, a^{2}} + \frac{2 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x + 3 \, \sqrt{-a^{2} x^{2} + 1} x + \frac{3 \, \arcsin\left(a x\right)}{a}}{40 \, a}"," ",0,"-1/5*(-a^2*x^2 + 1)^(5/2)*arctanh(a*x)/a^2 + 1/40*(2*(-a^2*x^2 + 1)^(3/2)*x + 3*sqrt(-a^2*x^2 + 1)*x + 3*arcsin(a*x)/a)/a","A",0
451,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""maxima"")","\int {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*arctanh(a*x), x)","F",0
452,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)}{x}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)/x, x)","F",0
453,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)}{x^{2}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)/x^2, x)","F",0
454,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)}{x^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)/x^3, x)","F",0
455,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)}{x^{4}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)/x^4, x)","F",0
456,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^5,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)}{x^{5}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)/x^5, x)","F",0
457,1,126,0,0.415745," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^6,x, algorithm=""maxima"")","\frac{1}{40} \, {\left({\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{4} - 3 \, a^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + 3 \, \sqrt{-a^{2} x^{2} + 1} a^{4} + \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a^{2}}{x^{2}} - \frac{2 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{x^{4}}\right)} a - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} \operatorname{artanh}\left(a x\right)}{5 \, x^{5}}"," ",0,"1/40*((-a^2*x^2 + 1)^(3/2)*a^4 - 3*a^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 3*sqrt(-a^2*x^2 + 1)*a^4 + (-a^2*x^2 + 1)^(5/2)*a^2/x^2 - 2*(-a^2*x^2 + 1)^(5/2)/x^4)*a - 1/5*(-a^2*x^2 + 1)^(5/2)*arctanh(a*x)/x^5","A",0
458,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^7,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)}{x^{7}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)/x^7, x)","F",0
459,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(5/2)*arctanh(a*x),x, algorithm=""maxima"")","\int {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} \operatorname{artanh}\left(a x\right)\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(5/2)*arctanh(a*x), x)","F",0
460,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""maxima"")","\int {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*arctanh(a*x), x)","F",0
461,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x),x, algorithm=""maxima"")","\int \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*arctanh(a*x), x)","F",0
462,1,74,0,0.308678," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(5/2),x, algorithm=""maxima"")","-\frac{1}{9} \, a {\left(\frac{6}{\sqrt{-a^{2} x^{2} + 1} a^{2}} + \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}}\right)} + \frac{1}{3} \, {\left(\frac{2 \, x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/9*a*(6/(sqrt(-a^2*x^2 + 1)*a^2) + 1/((-a^2*x^2 + 1)^(3/2)*a^2)) + 1/3*(2*x/sqrt(-a^2*x^2 + 1) + x/(-a^2*x^2 + 1)^(3/2))*arctanh(a*x)","A",0
463,1,108,0,0.306896," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(7/2),x, algorithm=""maxima"")","-\frac{1}{225} \, a {\left(\frac{120}{\sqrt{-a^{2} x^{2} + 1} a^{2}} + \frac{20}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}} + \frac{9}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a^{2}}\right)} + \frac{1}{15} \, {\left(\frac{8 \, x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{4 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}} + \frac{3 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/225*a*(120/(sqrt(-a^2*x^2 + 1)*a^2) + 20/((-a^2*x^2 + 1)^(3/2)*a^2) + 9/((-a^2*x^2 + 1)^(5/2)*a^2)) + 1/15*(8*x/sqrt(-a^2*x^2 + 1) + 4*x/(-a^2*x^2 + 1)^(3/2) + 3*x/(-a^2*x^2 + 1)^(5/2))*arctanh(a*x)","A",0
464,1,140,0,0.329100," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(9/2),x, algorithm=""maxima"")","-\frac{1}{3675} \, a {\left(\frac{1680}{\sqrt{-a^{2} x^{2} + 1} a^{2}} + \frac{280}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}} + \frac{126}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a^{2}} + \frac{75}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{7}{2}} a^{2}}\right)} + \frac{1}{35} \, {\left(\frac{16 \, x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{8 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}} + \frac{6 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}} + \frac{5 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{7}{2}}}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/3675*a*(1680/(sqrt(-a^2*x^2 + 1)*a^2) + 280/((-a^2*x^2 + 1)^(3/2)*a^2) + 126/((-a^2*x^2 + 1)^(5/2)*a^2) + 75/((-a^2*x^2 + 1)^(7/2)*a^2)) + 1/35*(16*x/sqrt(-a^2*x^2 + 1) + 8*x/(-a^2*x^2 + 1)^(3/2) + 6*x/(-a^2*x^2 + 1)^(5/2) + 5*x/(-a^2*x^2 + 1)^(7/2))*arctanh(a*x)","A",0
465,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)*arctanh(a*x),x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*arctanh(a*x), x)","F",0
466,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*arctanh(a*x),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} \operatorname{artanh}\left(a x\right)\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*arctanh(a*x), x)","F",0
467,0,0,0,0.000000," ","integrate(arctanh(a*x)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(arctanh(a*x)/sqrt(-a^2*c*x^2 + c), x)","F",0
468,1,90,0,0.432234," ","integrate(arctanh(a*x)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{\sqrt{-a^{2} c x^{2} + c}}{a^{4} c x + a^{3} c} - \frac{\sqrt{-a^{2} c x^{2} + c}}{a^{4} c x - a^{3} c}\right)}}{2 \, c} + \frac{x \operatorname{artanh}\left(a x\right)}{\sqrt{-a^{2} c x^{2} + c} c}"," ",0,"-1/2*a^2*(sqrt(-a^2*c*x^2 + c)/(a^4*c*x + a^3*c) - sqrt(-a^2*c*x^2 + c)/(a^4*c*x - a^3*c))/c + x*arctanh(a*x)/(sqrt(-a^2*c*x^2 + c)*c)","B",0
469,1,90,0,0.342894," ","integrate(arctanh(a*x)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","-\frac{1}{9} \, a {\left(\frac{6}{\sqrt{-a^{2} c x^{2} + c} a^{2} c^{2}} + \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{2} c}\right)} + \frac{1}{3} \, {\left(\frac{2 \, x}{\sqrt{-a^{2} c x^{2} + c} c^{2}} + \frac{x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/9*a*(6/(sqrt(-a^2*c*x^2 + c)*a^2*c^2) + 1/((-a^2*c*x^2 + c)^(3/2)*a^2*c)) + 1/3*(2*x/(sqrt(-a^2*c*x^2 + c)*c^2) + x/((-a^2*c*x^2 + c)^(3/2)*c))*arctanh(a*x)","A",0
470,1,132,0,0.345142," ","integrate(arctanh(a*x)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","-\frac{1}{225} \, a {\left(\frac{120}{\sqrt{-a^{2} c x^{2} + c} a^{2} c^{3}} + \frac{20}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{2} c^{2}} + \frac{9}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} a^{2} c}\right)} + \frac{1}{15} \, {\left(\frac{8 \, x}{\sqrt{-a^{2} c x^{2} + c} c^{3}} + \frac{4 \, x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c^{2}} + \frac{3 \, x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} c}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"-1/225*a*(120/(sqrt(-a^2*c*x^2 + c)*a^2*c^3) + 20/((-a^2*c*x^2 + c)^(3/2)*a^2*c^2) + 9/((-a^2*c*x^2 + c)^(5/2)*a^2*c)) + 1/15*(8*x/(sqrt(-a^2*c*x^2 + c)*c^3) + 4*x/((-a^2*c*x^2 + c)^(3/2)*c^2) + 3*x/((-a^2*c*x^2 + c)^(5/2)*c))*arctanh(a*x)","A",0
471,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x)^2,x, algorithm=""maxima"")","\int \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2, x)","F",0
472,1,304,0,0.495729," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{2 \, x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\right)} \operatorname{artanh}\left(a x\right)^{2} + \frac{1}{27} \, a {\left(\frac{\frac{2 \, x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} a^{2} x + \sqrt{-a^{2} x^{2} + 1} a}}{a} + \frac{\frac{2 \, x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} a^{2} x - \sqrt{-a^{2} x^{2} + 1} a}}{a} - \frac{18 \, \sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} x + a\right)} a} - \frac{18 \, \sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} x - a\right)} a} - \frac{18 \, \log\left(a x + 1\right)}{\sqrt{-a^{2} x^{2} + 1} a^{2}} + \frac{18 \, \log\left(-a x + 1\right)}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{3 \, \log\left(a x + 1\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}} + \frac{3 \, \log\left(-a x + 1\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}}\right)}"," ",0,"1/3*(2*x/sqrt(-a^2*x^2 + 1) + x/(-a^2*x^2 + 1)^(3/2))*arctanh(a*x)^2 + 1/27*a*((2*x/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*a^2*x + sqrt(-a^2*x^2 + 1)*a))/a + (2*x/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*a^2*x - sqrt(-a^2*x^2 + 1)*a))/a - 18*sqrt(-a^2*x^2 + 1)/((a^2*x + a)*a) - 18*sqrt(-a^2*x^2 + 1)/((a^2*x - a)*a) - 18*log(a*x + 1)/(sqrt(-a^2*x^2 + 1)*a^2) + 18*log(-a*x + 1)/(sqrt(-a^2*x^2 + 1)*a^2) - 3*log(a*x + 1)/((-a^2*x^2 + 1)^(3/2)*a^2) + 3*log(-a*x + 1)/((-a^2*x^2 + 1)^(3/2)*a^2))","B",0
473,1,514,0,0.519356," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^(7/2),x, algorithm=""maxima"")","\frac{1}{15} \, {\left(\frac{8 \, x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{4 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}} + \frac{3 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}\right)} \operatorname{artanh}\left(a x\right)^{2} + \frac{1}{3375} \, a {\left(\frac{9 \, {\left(\frac{8 \, x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{4 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}} - \frac{3}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2} x + {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a}\right)}}{a} + \frac{9 \, {\left(\frac{8 \, x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{4 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}} - \frac{3}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2} x - {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a}\right)}}{a} + \frac{100 \, {\left(\frac{2 \, x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} a^{2} x + \sqrt{-a^{2} x^{2} + 1} a}\right)}}{a} + \frac{100 \, {\left(\frac{2 \, x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} a^{2} x - \sqrt{-a^{2} x^{2} + 1} a}\right)}}{a} - \frac{1800 \, \sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} x + a\right)} a} - \frac{1800 \, \sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} x - a\right)} a} - \frac{1800 \, \log\left(a x + 1\right)}{\sqrt{-a^{2} x^{2} + 1} a^{2}} + \frac{1800 \, \log\left(-a x + 1\right)}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{300 \, \log\left(a x + 1\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}} + \frac{300 \, \log\left(-a x + 1\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}} - \frac{135 \, \log\left(a x + 1\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a^{2}} + \frac{135 \, \log\left(-a x + 1\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a^{2}}\right)}"," ",0,"1/15*(8*x/sqrt(-a^2*x^2 + 1) + 4*x/(-a^2*x^2 + 1)^(3/2) + 3*x/(-a^2*x^2 + 1)^(5/2))*arctanh(a*x)^2 + 1/3375*a*(9*(8*x/sqrt(-a^2*x^2 + 1) + 4*x/(-a^2*x^2 + 1)^(3/2) - 3/((-a^2*x^2 + 1)^(3/2)*a^2*x + (-a^2*x^2 + 1)^(3/2)*a))/a + 9*(8*x/sqrt(-a^2*x^2 + 1) + 4*x/(-a^2*x^2 + 1)^(3/2) - 3/((-a^2*x^2 + 1)^(3/2)*a^2*x - (-a^2*x^2 + 1)^(3/2)*a))/a + 100*(2*x/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*a^2*x + sqrt(-a^2*x^2 + 1)*a))/a + 100*(2*x/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*a^2*x - sqrt(-a^2*x^2 + 1)*a))/a - 1800*sqrt(-a^2*x^2 + 1)/((a^2*x + a)*a) - 1800*sqrt(-a^2*x^2 + 1)/((a^2*x - a)*a) - 1800*log(a*x + 1)/(sqrt(-a^2*x^2 + 1)*a^2) + 1800*log(-a*x + 1)/(sqrt(-a^2*x^2 + 1)*a^2) - 300*log(a*x + 1)/((-a^2*x^2 + 1)^(3/2)*a^2) + 300*log(-a*x + 1)/((-a^2*x^2 + 1)^(3/2)*a^2) - 135*log(a*x + 1)/((-a^2*x^2 + 1)^(5/2)*a^2) + 135*log(-a*x + 1)/((-a^2*x^2 + 1)^(5/2)*a^2))","B",0
474,1,751,0,0.520839," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^(9/2),x, algorithm=""maxima"")","\frac{1}{35} \, {\left(\frac{16 \, x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{8 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}} + \frac{6 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}} + \frac{5 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{7}{2}}}\right)} \operatorname{artanh}\left(a x\right)^{2} + \frac{1}{385875} \, a {\left(\frac{225 \, {\left(\frac{16 \, x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{8 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}} - \frac{5}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a^{2} x + {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a} + \frac{6 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}\right)}}{a} + \frac{225 \, {\left(\frac{16 \, x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{8 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}} - \frac{5}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a^{2} x - {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a} + \frac{6 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}\right)}}{a} + \frac{882 \, {\left(\frac{8 \, x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{4 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}} - \frac{3}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2} x + {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a}\right)}}{a} + \frac{882 \, {\left(\frac{8 \, x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{4 \, x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}} - \frac{3}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2} x - {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a}\right)}}{a} + \frac{9800 \, {\left(\frac{2 \, x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} a^{2} x + \sqrt{-a^{2} x^{2} + 1} a}\right)}}{a} + \frac{9800 \, {\left(\frac{2 \, x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} a^{2} x - \sqrt{-a^{2} x^{2} + 1} a}\right)}}{a} - \frac{176400 \, \sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} x + a\right)} a} - \frac{176400 \, \sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} x - a\right)} a} - \frac{176400 \, \log\left(a x + 1\right)}{\sqrt{-a^{2} x^{2} + 1} a^{2}} + \frac{176400 \, \log\left(-a x + 1\right)}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{29400 \, \log\left(a x + 1\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}} + \frac{29400 \, \log\left(-a x + 1\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}} - \frac{13230 \, \log\left(a x + 1\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a^{2}} + \frac{13230 \, \log\left(-a x + 1\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a^{2}} - \frac{7875 \, \log\left(a x + 1\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{7}{2}} a^{2}} + \frac{7875 \, \log\left(-a x + 1\right)}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{7}{2}} a^{2}}\right)}"," ",0,"1/35*(16*x/sqrt(-a^2*x^2 + 1) + 8*x/(-a^2*x^2 + 1)^(3/2) + 6*x/(-a^2*x^2 + 1)^(5/2) + 5*x/(-a^2*x^2 + 1)^(7/2))*arctanh(a*x)^2 + 1/385875*a*(225*(16*x/sqrt(-a^2*x^2 + 1) + 8*x/(-a^2*x^2 + 1)^(3/2) - 5/((-a^2*x^2 + 1)^(5/2)*a^2*x + (-a^2*x^2 + 1)^(5/2)*a) + 6*x/(-a^2*x^2 + 1)^(5/2))/a + 225*(16*x/sqrt(-a^2*x^2 + 1) + 8*x/(-a^2*x^2 + 1)^(3/2) - 5/((-a^2*x^2 + 1)^(5/2)*a^2*x - (-a^2*x^2 + 1)^(5/2)*a) + 6*x/(-a^2*x^2 + 1)^(5/2))/a + 882*(8*x/sqrt(-a^2*x^2 + 1) + 4*x/(-a^2*x^2 + 1)^(3/2) - 3/((-a^2*x^2 + 1)^(3/2)*a^2*x + (-a^2*x^2 + 1)^(3/2)*a))/a + 882*(8*x/sqrt(-a^2*x^2 + 1) + 4*x/(-a^2*x^2 + 1)^(3/2) - 3/((-a^2*x^2 + 1)^(3/2)*a^2*x - (-a^2*x^2 + 1)^(3/2)*a))/a + 9800*(2*x/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*a^2*x + sqrt(-a^2*x^2 + 1)*a))/a + 9800*(2*x/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*a^2*x - sqrt(-a^2*x^2 + 1)*a))/a - 176400*sqrt(-a^2*x^2 + 1)/((a^2*x + a)*a) - 176400*sqrt(-a^2*x^2 + 1)/((a^2*x - a)*a) - 176400*log(a*x + 1)/(sqrt(-a^2*x^2 + 1)*a^2) + 176400*log(-a*x + 1)/(sqrt(-a^2*x^2 + 1)*a^2) - 29400*log(a*x + 1)/((-a^2*x^2 + 1)^(3/2)*a^2) + 29400*log(-a*x + 1)/((-a^2*x^2 + 1)^(3/2)*a^2) - 13230*log(a*x + 1)/((-a^2*x^2 + 1)^(5/2)*a^2) + 13230*log(-a*x + 1)/((-a^2*x^2 + 1)^(5/2)*a^2) - 7875*log(a*x + 1)/((-a^2*x^2 + 1)^(7/2)*a^2) + 7875*log(-a*x + 1)/((-a^2*x^2 + 1)^(7/2)*a^2))","B",0
475,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x)^3,x, algorithm=""maxima"")","\int \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{3}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^3, x)","F",0
476,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^(5/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/(-a^2*x^2 + 1)^(5/2), x)","F",0
477,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^(7/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/(-a^2*x^2 + 1)^(7/2), x)","F",0
478,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^(9/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/(-a^2*x^2 + 1)^(9/2), x)","F",0
479,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(1/2)/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{\operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/arctanh(a*x), x)","F",0
480,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(1/2)/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*x^2 + 1)*arctanh(a*x)), x)","F",0
481,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)), x)","F",0
482,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(5/2)/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(5/2)*arctanh(a*x)), x)","F",0
483,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(7/2)/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{7}{2}} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(7/2)*arctanh(a*x)), x)","F",0
484,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(9/2)/arctanh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{9}{2}} \operatorname{artanh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(9/2)*arctanh(a*x)), x)","F",0
485,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(1/2)/arctanh(a*x)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{\operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/arctanh(a*x)^2, x)","F",0
486,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(1/2)/arctanh(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2), x)","F",0
487,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)^2), x)","F",0
488,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(5/2)/arctanh(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(5/2)*arctanh(a*x)^2), x)","F",0
489,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(7/2)/arctanh(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{7}{2}} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(7/2)*arctanh(a*x)^2), x)","F",0
490,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(9/2)/arctanh(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{9}{2}} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(9/2)*arctanh(a*x)^2), x)","F",0
491,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^(1/2)/arctanh(a*x)^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{\operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/arctanh(a*x)^3, x)","F",0
492,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(1/2)/arctanh(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^3), x)","F",0
493,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(3/2)*arctanh(a*x)^3), x)","F",0
494,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(5/2)/arctanh(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(5/2)*arctanh(a*x)^3), x)","F",0
495,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(7/2)/arctanh(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{7}{2}} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(7/2)*arctanh(a*x)^3), x)","F",0
496,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(9/2)/arctanh(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{9}{2}} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((-a^2*x^2 + 1)^(9/2)*arctanh(a*x)^3), x)","F",0
497,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*arctanh(c*x))^2/(-c^2*x^2+1),x, algorithm=""maxima"")","a b d {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} \operatorname{artanh}\left(c x\right) + \frac{1}{2} \, a^{2} d {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} - \frac{{\left(\log\left(c x + 1\right)^{2} - 2 \, \log\left(c x + 1\right) \log\left(c x - 1\right) + \log\left(c x - 1\right)^{2}\right)} a b d}{4 \, c} - \frac{a^{2} e \log\left(c^{2} x^{2} - 1\right)}{2 \, c^{2}} + \frac{3 \, {\left(c d - e\right)} b^{2} \log\left(c x + 1\right) \log\left(-c x + 1\right)^{2} - {\left(c d + e\right)} b^{2} \log\left(-c x + 1\right)^{3}}{24 \, c^{2}} - \int \frac{4 \, a b c e x \log\left(c x + 1\right) + {\left(b^{2} c e x + b^{2} c d\right)} \log\left(c x + 1\right)^{2} - {\left(4 \, a b c e x - {\left({\left(c^{2} d - 3 \, c e\right)} b^{2} x - {\left(c d + e\right)} b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{4 \, {\left(c^{3} x^{2} - c\right)}}\,{d x}"," ",0,"a*b*d*(log(c*x + 1)/c - log(c*x - 1)/c)*arctanh(c*x) + 1/2*a^2*d*(log(c*x + 1)/c - log(c*x - 1)/c) - 1/4*(log(c*x + 1)^2 - 2*log(c*x + 1)*log(c*x - 1) + log(c*x - 1)^2)*a*b*d/c - 1/2*a^2*e*log(c^2*x^2 - 1)/c^2 + 1/24*(3*(c*d - e)*b^2*log(c*x + 1)*log(-c*x + 1)^2 - (c*d + e)*b^2*log(-c*x + 1)^3)/c^2 - integrate(1/4*(4*a*b*c*e*x*log(c*x + 1) + (b^2*c*e*x + b^2*c*d)*log(c*x + 1)^2 - (4*a*b*c*e*x - ((c^2*d - 3*c*e)*b^2*x - (c*d + e)*b^2)*log(c*x + 1))*log(-c*x + 1))/(c^3*x^2 - c), x)","F",0
498,1,276,0,0.308542," ","integrate((d*x^2+c)^4*arctanh(a*x),x, algorithm=""maxima"")","\frac{1}{7560} \, a {\left(\frac{105 \, a^{6} d^{4} x^{8} + 20 \, {\left(36 \, a^{6} c d^{3} + 7 \, a^{4} d^{4}\right)} x^{6} + 6 \, {\left(378 \, a^{6} c^{2} d^{2} + 180 \, a^{4} c d^{3} + 35 \, a^{2} d^{4}\right)} x^{4} + 12 \, {\left(420 \, a^{6} c^{3} d + 378 \, a^{4} c^{2} d^{2} + 180 \, a^{2} c d^{3} + 35 \, d^{4}\right)} x^{2}}{a^{8}} + \frac{12 \, {\left(315 \, a^{8} c^{4} + 420 \, a^{6} c^{3} d + 378 \, a^{4} c^{2} d^{2} + 180 \, a^{2} c d^{3} + 35 \, d^{4}\right)} \log\left(a x + 1\right)}{a^{10}} + \frac{12 \, {\left(315 \, a^{8} c^{4} + 420 \, a^{6} c^{3} d + 378 \, a^{4} c^{2} d^{2} + 180 \, a^{2} c d^{3} + 35 \, d^{4}\right)} \log\left(a x - 1\right)}{a^{10}}\right)} + \frac{1}{315} \, {\left(35 \, d^{4} x^{9} + 180 \, c d^{3} x^{7} + 378 \, c^{2} d^{2} x^{5} + 420 \, c^{3} d x^{3} + 315 \, c^{4} x\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/7560*a*((105*a^6*d^4*x^8 + 20*(36*a^6*c*d^3 + 7*a^4*d^4)*x^6 + 6*(378*a^6*c^2*d^2 + 180*a^4*c*d^3 + 35*a^2*d^4)*x^4 + 12*(420*a^6*c^3*d + 378*a^4*c^2*d^2 + 180*a^2*c*d^3 + 35*d^4)*x^2)/a^8 + 12*(315*a^8*c^4 + 420*a^6*c^3*d + 378*a^4*c^2*d^2 + 180*a^2*c*d^3 + 35*d^4)*log(a*x + 1)/a^10 + 12*(315*a^8*c^4 + 420*a^6*c^3*d + 378*a^4*c^2*d^2 + 180*a^2*c*d^3 + 35*d^4)*log(a*x - 1)/a^10) + 1/315*(35*d^4*x^9 + 180*c*d^3*x^7 + 378*c^2*d^2*x^5 + 420*c^3*d*x^3 + 315*c^4*x)*arctanh(a*x)","A",0
499,1,198,0,0.305797," ","integrate((d*x^2+c)^3*arctanh(a*x),x, algorithm=""maxima"")","\frac{1}{420} \, a {\left(\frac{10 \, a^{4} d^{3} x^{6} + 3 \, {\left(21 \, a^{4} c d^{2} + 5 \, a^{2} d^{3}\right)} x^{4} + 6 \, {\left(35 \, a^{4} c^{2} d + 21 \, a^{2} c d^{2} + 5 \, d^{3}\right)} x^{2}}{a^{6}} + \frac{6 \, {\left(35 \, a^{6} c^{3} + 35 \, a^{4} c^{2} d + 21 \, a^{2} c d^{2} + 5 \, d^{3}\right)} \log\left(a x + 1\right)}{a^{8}} + \frac{6 \, {\left(35 \, a^{6} c^{3} + 35 \, a^{4} c^{2} d + 21 \, a^{2} c d^{2} + 5 \, d^{3}\right)} \log\left(a x - 1\right)}{a^{8}}\right)} + \frac{1}{35} \, {\left(5 \, d^{3} x^{7} + 21 \, c d^{2} x^{5} + 35 \, c^{2} d x^{3} + 35 \, c^{3} x\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/420*a*((10*a^4*d^3*x^6 + 3*(21*a^4*c*d^2 + 5*a^2*d^3)*x^4 + 6*(35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*x^2)/a^6 + 6*(35*a^6*c^3 + 35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*log(a*x + 1)/a^8 + 6*(35*a^6*c^3 + 35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*log(a*x - 1)/a^8) + 1/35*(5*d^3*x^7 + 21*c*d^2*x^5 + 35*c^2*d*x^3 + 35*c^3*x)*arctanh(a*x)","A",0
500,1,131,0,0.304165," ","integrate((d*x^2+c)^2*arctanh(a*x),x, algorithm=""maxima"")","\frac{1}{60} \, a {\left(\frac{3 \, a^{2} d^{2} x^{4} + 2 \, {\left(10 \, a^{2} c d + 3 \, d^{2}\right)} x^{2}}{a^{4}} + \frac{2 \, {\left(15 \, a^{4} c^{2} + 10 \, a^{2} c d + 3 \, d^{2}\right)} \log\left(a x + 1\right)}{a^{6}} + \frac{2 \, {\left(15 \, a^{4} c^{2} + 10 \, a^{2} c d + 3 \, d^{2}\right)} \log\left(a x - 1\right)}{a^{6}}\right)} + \frac{1}{15} \, {\left(3 \, d^{2} x^{5} + 10 \, c d x^{3} + 15 \, c^{2} x\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/60*a*((3*a^2*d^2*x^4 + 2*(10*a^2*c*d + 3*d^2)*x^2)/a^4 + 2*(15*a^4*c^2 + 10*a^2*c*d + 3*d^2)*log(a*x + 1)/a^6 + 2*(15*a^4*c^2 + 10*a^2*c*d + 3*d^2)*log(a*x - 1)/a^6) + 1/15*(3*d^2*x^5 + 10*c*d*x^3 + 15*c^2*x)*arctanh(a*x)","A",0
501,1,65,0,0.317129," ","integrate((d*x^2+c)*arctanh(a*x),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{d x^{2}}{a^{2}} + \frac{{\left(3 \, a^{2} c + d\right)} \log\left(a x + 1\right)}{a^{4}} + \frac{{\left(3 \, a^{2} c + d\right)} \log\left(a x - 1\right)}{a^{4}}\right)} + \frac{1}{3} \, {\left(d x^{3} + 3 \, c x\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/6*a*(d*x^2/a^2 + (3*a^2*c + d)*log(a*x + 1)/a^4 + (3*a^2*c + d)*log(a*x - 1)/a^4) + 1/3*(d*x^3 + 3*c*x)*arctanh(a*x)","A",0
502,1,406,0,0.573799," ","integrate(arctanh(a*x)/(d*x^2+c),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{d x}{\sqrt{c d}}\right) \operatorname{artanh}\left(a x\right)}{\sqrt{c d}} + \frac{{\left(\arctan\left(\frac{{\left(a^{2} x + a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + d}, \frac{a d x + d}{a^{2} c + d}\right) - \arctan\left(\frac{{\left(a^{2} x - a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + d}, -\frac{a d x - d}{a^{2} c + d}\right)\right)} \log\left(d x^{2} + c\right) - \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{a^{2} d x^{2} + 2 \, a d x + d}{a^{2} c + d}\right) + \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{a^{2} d x^{2} - 2 \, a d x + d}{a^{2} c + d}\right) - i \, {\rm Li}_2\left(\frac{a^{2} c + a d x - {\left(i \, a^{2} x - i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 i \, a \sqrt{c} \sqrt{d} - d}\right) - i \, {\rm Li}_2\left(\frac{a^{2} c - a d x + {\left(i \, a^{2} x + i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + i \, {\rm Li}_2\left(\frac{a^{2} c + a d x + {\left(i \, a^{2} x - i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + i \, {\rm Li}_2\left(\frac{a^{2} c - a d x - {\left(i \, a^{2} x + i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 i \, a \sqrt{c} \sqrt{d} - d}\right)}{4 \, \sqrt{c d}}"," ",0,"arctan(d*x/sqrt(c*d))*arctanh(a*x)/sqrt(c*d) + 1/4*((arctan2((a^2*x + a)*sqrt(c)*sqrt(d)/(a^2*c + d), (a*d*x + d)/(a^2*c + d)) - arctan2((a^2*x - a)*sqrt(c)*sqrt(d)/(a^2*c + d), -(a*d*x - d)/(a^2*c + d)))*log(d*x^2 + c) - arctan(sqrt(d)*x/sqrt(c))*log((a^2*d*x^2 + 2*a*d*x + d)/(a^2*c + d)) + arctan(sqrt(d)*x/sqrt(c))*log((a^2*d*x^2 - 2*a*d*x + d)/(a^2*c + d)) - I*dilog((a^2*c + a*d*x - (I*a^2*x - I*a)*sqrt(c)*sqrt(d))/(a^2*c + 2*I*a*sqrt(c)*sqrt(d) - d)) - I*dilog((a^2*c - a*d*x + (I*a^2*x + I*a)*sqrt(c)*sqrt(d))/(a^2*c + 2*I*a*sqrt(c)*sqrt(d) - d)) + I*dilog((a^2*c + a*d*x + (I*a^2*x - I*a)*sqrt(c)*sqrt(d))/(a^2*c - 2*I*a*sqrt(c)*sqrt(d) - d)) + I*dilog((a^2*c - a*d*x - (I*a^2*x + I*a)*sqrt(c)*sqrt(d))/(a^2*c - 2*I*a*sqrt(c)*sqrt(d) - d)))/sqrt(c*d)","C",0
503,1,550,0,0.534692," ","integrate(arctanh(a*x)/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{x}{c d x^{2} + c^{2}} + \frac{\arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} c}\right)} \operatorname{artanh}\left(a x\right) - \frac{{\left(2 \, a c d \log\left(d x^{2} + c\right) - 2 \, a c d \log\left(a x + 1\right) - 2 \, a c d \log\left(a x - 1\right) + {\left({\left(a^{2} c + d\right)} \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{a^{2} d x^{2} + 2 \, a d x + d}{a^{2} c + d}\right) - {\left(a^{2} c + d\right)} \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{a^{2} d x^{2} - 2 \, a d x + d}{a^{2} c + d}\right) + {\left(i \, a^{2} c + i \, d\right)} {\rm Li}_2\left(\frac{a^{2} c + a d x - {\left(i \, a^{2} x - i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + {\left(i \, a^{2} c + i \, d\right)} {\rm Li}_2\left(\frac{a^{2} c - a d x + {\left(i \, a^{2} x + i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + {\left(-i \, a^{2} c - i \, d\right)} {\rm Li}_2\left(\frac{a^{2} c + a d x + {\left(i \, a^{2} x - i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + {\left(-i \, a^{2} c - i \, d\right)} {\rm Li}_2\left(\frac{a^{2} c - a d x - {\left(i \, a^{2} x + i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 i \, a \sqrt{c} \sqrt{d} - d}\right) - {\left({\left(a^{2} c + d\right)} \arctan\left(\frac{{\left(a^{2} x + a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + d}, \frac{a d x + d}{a^{2} c + d}\right) - {\left(a^{2} c + d\right)} \arctan\left(\frac{{\left(a^{2} x - a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + d}, -\frac{a d x - d}{a^{2} c + d}\right)\right)} \log\left(d x^{2} + c\right)\right)} \sqrt{c} \sqrt{d}\right)} a}{8 \, {\left(a^{3} c^{3} d + a c^{2} d^{2}\right)}}"," ",0,"1/2*(x/(c*d*x^2 + c^2) + arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c))*arctanh(a*x) - 1/8*(2*a*c*d*log(d*x^2 + c) - 2*a*c*d*log(a*x + 1) - 2*a*c*d*log(a*x - 1) + ((a^2*c + d)*arctan(sqrt(d)*x/sqrt(c))*log((a^2*d*x^2 + 2*a*d*x + d)/(a^2*c + d)) - (a^2*c + d)*arctan(sqrt(d)*x/sqrt(c))*log((a^2*d*x^2 - 2*a*d*x + d)/(a^2*c + d)) + (I*a^2*c + I*d)*dilog((a^2*c + a*d*x - (I*a^2*x - I*a)*sqrt(c)*sqrt(d))/(a^2*c + 2*I*a*sqrt(c)*sqrt(d) - d)) + (I*a^2*c + I*d)*dilog((a^2*c - a*d*x + (I*a^2*x + I*a)*sqrt(c)*sqrt(d))/(a^2*c + 2*I*a*sqrt(c)*sqrt(d) - d)) + (-I*a^2*c - I*d)*dilog((a^2*c + a*d*x + (I*a^2*x - I*a)*sqrt(c)*sqrt(d))/(a^2*c - 2*I*a*sqrt(c)*sqrt(d) - d)) + (-I*a^2*c - I*d)*dilog((a^2*c - a*d*x - (I*a^2*x + I*a)*sqrt(c)*sqrt(d))/(a^2*c - 2*I*a*sqrt(c)*sqrt(d) - d)) - ((a^2*c + d)*arctan2((a^2*x + a)*sqrt(c)*sqrt(d)/(a^2*c + d), (a*d*x + d)/(a^2*c + d)) - (a^2*c + d)*arctan2((a^2*x - a)*sqrt(c)*sqrt(d)/(a^2*c + d), -(a*d*x - d)/(a^2*c + d)))*log(d*x^2 + c))*sqrt(c)*sqrt(d))*a/(a^3*c^3*d + a*c^2*d^2)","A",0
504,1,1084,0,0.602980," ","integrate(arctanh(a*x)/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{3 \, d x^{3} + 5 \, c x}{c^{2} d^{2} x^{4} + 2 \, c^{3} d x^{2} + c^{4}} + \frac{3 \, \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} c^{2}}\right)} \operatorname{artanh}\left(a x\right) + \frac{{\left(4 \, a^{3} c^{3} d + 4 \, a c^{2} d^{2} - {\left(3 \, {\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2} + {\left(a^{4} c^{2} d + 2 \, a^{2} c d^{2} + d^{3}\right)} x^{2}\right)} \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{a^{2} d x^{2} + 2 \, a d x + d}{a^{2} c + d}\right) - 3 \, {\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2} + {\left(a^{4} c^{2} d + 2 \, a^{2} c d^{2} + d^{3}\right)} x^{2}\right)} \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{a^{2} d x^{2} - 2 \, a d x + d}{a^{2} c + d}\right) + {\left(3 i \, a^{4} c^{3} + 6 i \, a^{2} c^{2} d + 3 i \, c d^{2} + {\left(3 i \, a^{4} c^{2} d + 6 i \, a^{2} c d^{2} + 3 i \, d^{3}\right)} x^{2}\right)} {\rm Li}_2\left(\frac{a^{2} c + a d x - {\left(i \, a^{2} x - i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + {\left(3 i \, a^{4} c^{3} + 6 i \, a^{2} c^{2} d + 3 i \, c d^{2} + {\left(3 i \, a^{4} c^{2} d + 6 i \, a^{2} c d^{2} + 3 i \, d^{3}\right)} x^{2}\right)} {\rm Li}_2\left(\frac{a^{2} c - a d x + {\left(i \, a^{2} x + i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + {\left(-3 i \, a^{4} c^{3} - 6 i \, a^{2} c^{2} d - 3 i \, c d^{2} + {\left(-3 i \, a^{4} c^{2} d - 6 i \, a^{2} c d^{2} - 3 i \, d^{3}\right)} x^{2}\right)} {\rm Li}_2\left(\frac{a^{2} c + a d x + {\left(i \, a^{2} x - i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + {\left(-3 i \, a^{4} c^{3} - 6 i \, a^{2} c^{2} d - 3 i \, c d^{2} + {\left(-3 i \, a^{4} c^{2} d - 6 i \, a^{2} c d^{2} - 3 i \, d^{3}\right)} x^{2}\right)} {\rm Li}_2\left(\frac{a^{2} c - a d x - {\left(i \, a^{2} x + i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 i \, a \sqrt{c} \sqrt{d} - d}\right) - 3 \, {\left({\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2} + {\left(a^{4} c^{2} d + 2 \, a^{2} c d^{2} + d^{3}\right)} x^{2}\right)} \arctan\left(\frac{{\left(a^{2} x + a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + d}, \frac{a d x + d}{a^{2} c + d}\right) - {\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2} + {\left(a^{4} c^{2} d + 2 \, a^{2} c d^{2} + d^{3}\right)} x^{2}\right)} \arctan\left(\frac{{\left(a^{2} x - a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + d}, -\frac{a d x - d}{a^{2} c + d}\right)\right)} \log\left(d x^{2} + c\right)\right)} \sqrt{c} \sqrt{d} - 2 \, {\left(5 \, a^{3} c^{3} d + 3 \, a c^{2} d^{2} + {\left(5 \, a^{3} c^{2} d^{2} + 3 \, a c d^{3}\right)} x^{2}\right)} \log\left(d x^{2} + c\right) + 2 \, {\left(5 \, a^{3} c^{3} d + 3 \, a c^{2} d^{2} + {\left(5 \, a^{3} c^{2} d^{2} + 3 \, a c d^{3}\right)} x^{2}\right)} \log\left(a x + 1\right) + 2 \, {\left(5 \, a^{3} c^{3} d + 3 \, a c^{2} d^{2} + {\left(5 \, a^{3} c^{2} d^{2} + 3 \, a c d^{3}\right)} x^{2}\right)} \log\left(a x - 1\right)\right)} a}{32 \, {\left(a^{5} c^{6} d + 2 \, a^{3} c^{5} d^{2} + a c^{4} d^{3} + {\left(a^{5} c^{5} d^{2} + 2 \, a^{3} c^{4} d^{3} + a c^{3} d^{4}\right)} x^{2}\right)}}"," ",0,"1/8*((3*d*x^3 + 5*c*x)/(c^2*d^2*x^4 + 2*c^3*d*x^2 + c^4) + 3*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^2))*arctanh(a*x) + 1/32*(4*a^3*c^3*d + 4*a*c^2*d^2 - (3*(a^4*c^3 + 2*a^2*c^2*d + c*d^2 + (a^4*c^2*d + 2*a^2*c*d^2 + d^3)*x^2)*arctan(sqrt(d)*x/sqrt(c))*log((a^2*d*x^2 + 2*a*d*x + d)/(a^2*c + d)) - 3*(a^4*c^3 + 2*a^2*c^2*d + c*d^2 + (a^4*c^2*d + 2*a^2*c*d^2 + d^3)*x^2)*arctan(sqrt(d)*x/sqrt(c))*log((a^2*d*x^2 - 2*a*d*x + d)/(a^2*c + d)) + (3*I*a^4*c^3 + 6*I*a^2*c^2*d + 3*I*c*d^2 + (3*I*a^4*c^2*d + 6*I*a^2*c*d^2 + 3*I*d^3)*x^2)*dilog((a^2*c + a*d*x - (I*a^2*x - I*a)*sqrt(c)*sqrt(d))/(a^2*c + 2*I*a*sqrt(c)*sqrt(d) - d)) + (3*I*a^4*c^3 + 6*I*a^2*c^2*d + 3*I*c*d^2 + (3*I*a^4*c^2*d + 6*I*a^2*c*d^2 + 3*I*d^3)*x^2)*dilog((a^2*c - a*d*x + (I*a^2*x + I*a)*sqrt(c)*sqrt(d))/(a^2*c + 2*I*a*sqrt(c)*sqrt(d) - d)) + (-3*I*a^4*c^3 - 6*I*a^2*c^2*d - 3*I*c*d^2 + (-3*I*a^4*c^2*d - 6*I*a^2*c*d^2 - 3*I*d^3)*x^2)*dilog((a^2*c + a*d*x + (I*a^2*x - I*a)*sqrt(c)*sqrt(d))/(a^2*c - 2*I*a*sqrt(c)*sqrt(d) - d)) + (-3*I*a^4*c^3 - 6*I*a^2*c^2*d - 3*I*c*d^2 + (-3*I*a^4*c^2*d - 6*I*a^2*c*d^2 - 3*I*d^3)*x^2)*dilog((a^2*c - a*d*x - (I*a^2*x + I*a)*sqrt(c)*sqrt(d))/(a^2*c - 2*I*a*sqrt(c)*sqrt(d) - d)) - 3*((a^4*c^3 + 2*a^2*c^2*d + c*d^2 + (a^4*c^2*d + 2*a^2*c*d^2 + d^3)*x^2)*arctan2((a^2*x + a)*sqrt(c)*sqrt(d)/(a^2*c + d), (a*d*x + d)/(a^2*c + d)) - (a^4*c^3 + 2*a^2*c^2*d + c*d^2 + (a^4*c^2*d + 2*a^2*c*d^2 + d^3)*x^2)*arctan2((a^2*x - a)*sqrt(c)*sqrt(d)/(a^2*c + d), -(a*d*x - d)/(a^2*c + d)))*log(d*x^2 + c))*sqrt(c)*sqrt(d) - 2*(5*a^3*c^3*d + 3*a*c^2*d^2 + (5*a^3*c^2*d^2 + 3*a*c*d^3)*x^2)*log(d*x^2 + c) + 2*(5*a^3*c^3*d + 3*a*c^2*d^2 + (5*a^3*c^2*d^2 + 3*a*c*d^3)*x^2)*log(a*x + 1) + 2*(5*a^3*c^3*d + 3*a*c^2*d^2 + (5*a^3*c^2*d^2 + 3*a*c*d^3)*x^2)*log(a*x - 1))*a/(a^5*c^6*d + 2*a^3*c^5*d^2 + a*c^4*d^3 + (a^5*c^5*d^2 + 2*a^3*c^4*d^3 + a*c^3*d^4)*x^2)","B",0
505,1,23,0,0.350732," ","integrate(1/(-a*x^2+a)/(b-2*b*arctanh(x)),x, algorithm=""maxima"")","-\frac{\log\left(-\log\left(x + 1\right) + \log\left(-x + 1\right) + 1\right)}{2 \, a b}"," ",0,"-1/2*log(-log(x + 1) + log(-x + 1) + 1)/(a*b)","A",0
506,1,180,0,0.311084," ","integrate(arctanh(b*x)/(-x^2+1),x, algorithm=""maxima"")","\frac{1}{4} \, b {\left(\frac{\log\left(x + 1\right) \log\left(-\frac{b x + b}{b + 1} + 1\right) + {\rm Li}_2\left(\frac{b x + b}{b + 1}\right)}{b} + \frac{\log\left(x - 1\right) \log\left(\frac{b x - b}{b + 1} + 1\right) + {\rm Li}_2\left(-\frac{b x - b}{b + 1}\right)}{b} - \frac{\log\left(x + 1\right) \log\left(-\frac{b x + b}{b - 1} + 1\right) + {\rm Li}_2\left(\frac{b x + b}{b - 1}\right)}{b} - \frac{\log\left(x - 1\right) \log\left(\frac{b x - b}{b - 1} + 1\right) + {\rm Li}_2\left(-\frac{b x - b}{b - 1}\right)}{b}\right)} + \frac{1}{2} \, {\left(\log\left(x + 1\right) - \log\left(x - 1\right)\right)} \operatorname{artanh}\left(b x\right)"," ",0,"1/4*b*((log(x + 1)*log(-(b*x + b)/(b + 1) + 1) + dilog((b*x + b)/(b + 1)))/b + (log(x - 1)*log((b*x - b)/(b + 1) + 1) + dilog(-(b*x - b)/(b + 1)))/b - (log(x + 1)*log(-(b*x + b)/(b - 1) + 1) + dilog((b*x + b)/(b - 1)))/b - (log(x - 1)*log((b*x - b)/(b - 1) + 1) + dilog(-(b*x - b)/(b - 1)))/b) + 1/2*(log(x + 1) - log(x - 1))*arctanh(b*x)","A",0
507,1,198,0,0.319367," ","integrate(arctanh(b*x+a)/(-x^2+1),x, algorithm=""maxima"")","\frac{1}{4} \, b {\left(\frac{\log\left(x - 1\right) \log\left(\frac{b x - b}{a + b + 1} + 1\right) + {\rm Li}_2\left(-\frac{b x - b}{a + b + 1}\right)}{b} - \frac{\log\left(x - 1\right) \log\left(\frac{b x - b}{a + b - 1} + 1\right) + {\rm Li}_2\left(-\frac{b x - b}{a + b - 1}\right)}{b} - \frac{\log\left(x + 1\right) \log\left(\frac{b x + b}{a - b + 1} + 1\right) + {\rm Li}_2\left(-\frac{b x + b}{a - b + 1}\right)}{b} + \frac{\log\left(x + 1\right) \log\left(\frac{b x + b}{a - b - 1} + 1\right) + {\rm Li}_2\left(-\frac{b x + b}{a - b - 1}\right)}{b}\right)} + \frac{1}{2} \, {\left(\log\left(x + 1\right) - \log\left(x - 1\right)\right)} \operatorname{artanh}\left(b x + a\right)"," ",0,"1/4*b*((log(x - 1)*log((b*x - b)/(a + b + 1) + 1) + dilog(-(b*x - b)/(a + b + 1)))/b - (log(x - 1)*log((b*x - b)/(a + b - 1) + 1) + dilog(-(b*x - b)/(a + b - 1)))/b - (log(x + 1)*log((b*x + b)/(a - b + 1) + 1) + dilog(-(b*x + b)/(a - b + 1)))/b + (log(x + 1)*log((b*x + b)/(a - b - 1) + 1) + dilog(-(b*x + b)/(a - b - 1)))/b) + 1/2*(log(x + 1) - log(x - 1))*arctanh(b*x + a)","A",0
508,1,119,0,0.304781," ","integrate(arctanh(x)/(b*x+a),x, algorithm=""maxima"")","-\frac{{\left(\log\left(x + 1\right) - \log\left(x - 1\right)\right)} \log\left(b x + a\right)}{2 \, b} + \frac{\operatorname{artanh}\left(x\right) \log\left(b x + a\right)}{b} - \frac{\log\left(x - 1\right) \log\left(\frac{b x - b}{a + b} + 1\right) + {\rm Li}_2\left(-\frac{b x - b}{a + b}\right)}{2 \, b} + \frac{\log\left(x + 1\right) \log\left(\frac{b x + b}{a - b} + 1\right) + {\rm Li}_2\left(-\frac{b x + b}{a - b}\right)}{2 \, b}"," ",0,"-1/2*(log(x + 1) - log(x - 1))*log(b*x + a)/b + arctanh(x)*log(b*x + a)/b - 1/2*(log(x - 1)*log((b*x - b)/(a + b) + 1) + dilog(-(b*x - b)/(a + b)))/b + 1/2*(log(x + 1)*log((b*x + b)/(a - b) + 1) + dilog(-(b*x + b)/(a - b)))/b","A",0
509,1,304,0,0.516740," ","integrate(arctanh(x)/(b*x^2+a),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{b x}{\sqrt{a b}}\right) \operatorname{artanh}\left(x\right)}{\sqrt{a b}} + \frac{{\left(\arctan\left(\frac{\sqrt{a} \sqrt{b} {\left(x + 1\right)}}{a + b}, \frac{b x + b}{a + b}\right) - \arctan\left(\frac{\sqrt{a} \sqrt{b} {\left(x - 1\right)}}{a + b}, -\frac{b x - b}{a + b}\right)\right)} \log\left(b x^{2} + a\right) - \arctan\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log\left(\frac{b x^{2} + 2 \, b x + b}{a + b}\right) + \arctan\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log\left(\frac{b x^{2} - 2 \, b x + b}{a + b}\right) - i \, {\rm Li}_2\left(-\frac{b x - \sqrt{a} \sqrt{b} {\left(i \, x + i\right)} - a}{a + 2 i \, \sqrt{a} \sqrt{b} - b}\right) - i \, {\rm Li}_2\left(\frac{b x - \sqrt{a} \sqrt{b} {\left(i \, x - i\right)} + a}{a + 2 i \, \sqrt{a} \sqrt{b} - b}\right) + i \, {\rm Li}_2\left(-\frac{b x + \sqrt{a} \sqrt{b} {\left(i \, x + i\right)} - a}{a - 2 i \, \sqrt{a} \sqrt{b} - b}\right) + i \, {\rm Li}_2\left(\frac{b x + \sqrt{a} \sqrt{b} {\left(i \, x - i\right)} + a}{a - 2 i \, \sqrt{a} \sqrt{b} - b}\right)}{4 \, \sqrt{a b}}"," ",0,"arctan(b*x/sqrt(a*b))*arctanh(x)/sqrt(a*b) + 1/4*((arctan2(sqrt(a)*sqrt(b)*(x + 1)/(a + b), (b*x + b)/(a + b)) - arctan2(sqrt(a)*sqrt(b)*(x - 1)/(a + b), -(b*x - b)/(a + b)))*log(b*x^2 + a) - arctan(sqrt(b)*x/sqrt(a))*log((b*x^2 + 2*b*x + b)/(a + b)) + arctan(sqrt(b)*x/sqrt(a))*log((b*x^2 - 2*b*x + b)/(a + b)) - I*dilog(-(b*x - sqrt(a)*sqrt(b)*(I*x + I) - a)/(a + 2*I*sqrt(a)*sqrt(b) - b)) - I*dilog((b*x - sqrt(a)*sqrt(b)*(I*x - I) + a)/(a + 2*I*sqrt(a)*sqrt(b) - b)) + I*dilog(-(b*x + sqrt(a)*sqrt(b)*(I*x + I) - a)/(a - 2*I*sqrt(a)*sqrt(b) - b)) + I*dilog((b*x + sqrt(a)*sqrt(b)*(I*x - I) + a)/(a - 2*I*sqrt(a)*sqrt(b) - b)))/sqrt(a*b)","C",0
510,-2,0,0,0.000000," ","integrate(arctanh(x)/(c*x^2+b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
511,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)*arctanh(a*x),x, algorithm=""maxima"")","\int \sqrt{d x^{2} + c} \operatorname{artanh}\left(a x\right)\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)*arctanh(a*x), x)","F",0
512,0,0,0,0.000000," ","integrate(arctanh(a*x)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(a x\right)}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(arctanh(a*x)/sqrt(d*x^2 + c), x)","F",0
513,1,153,0,0.352304," ","integrate(arctanh(a*x)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{\operatorname{arsinh}\left(-\frac{2 \, a^{2} c}{\sqrt{c d} {\left| 2 \, a^{2} x + 2 \, a \right|}} + \frac{2 \, a d x}{\sqrt{c d} {\left| 2 \, a^{2} x + 2 \, a \right|}}\right)}{a^{3} \sqrt{c + \frac{d}{a^{2}}}} - \frac{\operatorname{arsinh}\left(\frac{2 \, a^{2} c}{\sqrt{c d} {\left| 2 \, a^{2} x - 2 \, a \right|}} + \frac{2 \, a d x}{\sqrt{c d} {\left| 2 \, a^{2} x - 2 \, a \right|}}\right)}{a^{3} \sqrt{c + \frac{d}{a^{2}}}}\right)}}{2 \, c} + \frac{x \operatorname{artanh}\left(a x\right)}{\sqrt{d x^{2} + c} c}"," ",0,"1/2*a^2*(arcsinh(-2*a^2*c/(sqrt(c*d)*abs(2*a^2*x + 2*a)) + 2*a*d*x/(sqrt(c*d)*abs(2*a^2*x + 2*a)))/(a^3*sqrt(c + d/a^2)) - arcsinh(2*a^2*c/(sqrt(c*d)*abs(2*a^2*x - 2*a)) + 2*a*d*x/(sqrt(c*d)*abs(2*a^2*x - 2*a)))/(a^3*sqrt(c + d/a^2)))/c + x*arctanh(a*x)/(sqrt(d*x^2 + c)*c)","B",0
514,1,223,0,0.417890," ","integrate(arctanh(a*x)/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{\frac{a d \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{{\left(a^{2} c^{2} + c d\right)} \sqrt{a^{2} c + d}} + \frac{2 \, d}{{\left(a^{2} c^{2} + c d\right)} \sqrt{d x^{2} + c}}}{d} + \frac{2 \, \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{\sqrt{a^{2} c + d} a c^{2}}\right)} + \frac{1}{3} \, {\left(\frac{2 \, x}{\sqrt{d x^{2} + c} c^{2}} + \frac{x}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} c}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/6*a*((a*d*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/((a^2*c^2 + c*d)*sqrt(a^2*c + d)) + 2*d/((a^2*c^2 + c*d)*sqrt(d*x^2 + c)))/d + 2*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/(sqrt(a^2*c + d)*a*c^2)) + 1/3*(2*x/(sqrt(d*x^2 + c)*c^2) + x/((d*x^2 + c)^(3/2)*c))*arctanh(a*x)","B",0
515,1,401,0,0.432880," ","integrate(arctanh(a*x)/(d*x^2+c)^(7/2),x, algorithm=""maxima"")","\frac{1}{30} \, a {\left(\frac{\frac{3 \, a^{3} d \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{{\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2}\right)} \sqrt{a^{2} c + d}} + \frac{2 \, {\left(3 \, {\left(d x^{2} + c\right)} a^{2} d + a^{2} c d + d^{2}\right)}}{{\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2}\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}}{d} + \frac{4 \, {\left(\frac{a d \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{{\left(a^{2} c^{3} + c^{2} d\right)} \sqrt{a^{2} c + d}} + \frac{2 \, d}{{\left(a^{2} c^{3} + c^{2} d\right)} \sqrt{d x^{2} + c}}\right)}}{d} + \frac{8 \, \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{\sqrt{a^{2} c + d} a c^{3}}\right)} + \frac{1}{15} \, {\left(\frac{8 \, x}{\sqrt{d x^{2} + c} c^{3}} + \frac{4 \, x}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2}} + \frac{3 \, x}{{\left(d x^{2} + c\right)}^{\frac{5}{2}} c}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/30*a*((3*a^3*d*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/((a^4*c^3 + 2*a^2*c^2*d + c*d^2)*sqrt(a^2*c + d)) + 2*(3*(d*x^2 + c)*a^2*d + a^2*c*d + d^2)/((a^4*c^3 + 2*a^2*c^2*d + c*d^2)*(d*x^2 + c)^(3/2)))/d + 4*(a*d*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/((a^2*c^3 + c^2*d)*sqrt(a^2*c + d)) + 2*d/((a^2*c^3 + c^2*d)*sqrt(d*x^2 + c)))/d + 8*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/(sqrt(a^2*c + d)*a*c^3)) + 1/15*(8*x/(sqrt(d*x^2 + c)*c^3) + 4*x/((d*x^2 + c)^(3/2)*c^2) + 3*x/((d*x^2 + c)^(5/2)*c))*arctanh(a*x)","B",0
516,1,639,0,0.464868," ","integrate(arctanh(a*x)/(d*x^2+c)^(9/2),x, algorithm=""maxima"")","\frac{1}{210} \, a {\left(\frac{\frac{15 \, a^{5} d \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{{\left(a^{6} c^{4} + 3 \, a^{4} c^{3} d + 3 \, a^{2} c^{2} d^{2} + c d^{3}\right)} \sqrt{a^{2} c + d}} + \frac{2 \, {\left(15 \, {\left(d x^{2} + c\right)}^{2} a^{4} d + 3 \, a^{4} c^{2} d + 6 \, a^{2} c d^{2} + 3 \, d^{3} + 5 \, {\left(a^{4} c d + a^{2} d^{2}\right)} {\left(d x^{2} + c\right)}\right)}}{{\left(a^{6} c^{4} + 3 \, a^{4} c^{3} d + 3 \, a^{2} c^{2} d^{2} + c d^{3}\right)} {\left(d x^{2} + c\right)}^{\frac{5}{2}}}}{d} + \frac{6 \, {\left(\frac{3 \, a^{3} d \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{{\left(a^{4} c^{4} + 2 \, a^{2} c^{3} d + c^{2} d^{2}\right)} \sqrt{a^{2} c + d}} + \frac{2 \, {\left(3 \, {\left(d x^{2} + c\right)} a^{2} d + a^{2} c d + d^{2}\right)}}{{\left(a^{4} c^{4} + 2 \, a^{2} c^{3} d + c^{2} d^{2}\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}\right)}}{d} + \frac{24 \, {\left(\frac{a d \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{{\left(a^{2} c^{4} + c^{3} d\right)} \sqrt{a^{2} c + d}} + \frac{2 \, d}{{\left(a^{2} c^{4} + c^{3} d\right)} \sqrt{d x^{2} + c}}\right)}}{d} + \frac{48 \, \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{\sqrt{a^{2} c + d} a c^{4}}\right)} + \frac{1}{35} \, {\left(\frac{16 \, x}{\sqrt{d x^{2} + c} c^{4}} + \frac{8 \, x}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{3}} + \frac{6 \, x}{{\left(d x^{2} + c\right)}^{\frac{5}{2}} c^{2}} + \frac{5 \, x}{{\left(d x^{2} + c\right)}^{\frac{7}{2}} c}\right)} \operatorname{artanh}\left(a x\right)"," ",0,"1/210*a*((15*a^5*d*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/((a^6*c^4 + 3*a^4*c^3*d + 3*a^2*c^2*d^2 + c*d^3)*sqrt(a^2*c + d)) + 2*(15*(d*x^2 + c)^2*a^4*d + 3*a^4*c^2*d + 6*a^2*c*d^2 + 3*d^3 + 5*(a^4*c*d + a^2*d^2)*(d*x^2 + c))/((a^6*c^4 + 3*a^4*c^3*d + 3*a^2*c^2*d^2 + c*d^3)*(d*x^2 + c)^(5/2)))/d + 6*(3*a^3*d*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/((a^4*c^4 + 2*a^2*c^3*d + c^2*d^2)*sqrt(a^2*c + d)) + 2*(3*(d*x^2 + c)*a^2*d + a^2*c*d + d^2)/((a^4*c^4 + 2*a^2*c^3*d + c^2*d^2)*(d*x^2 + c)^(3/2)))/d + 24*(a*d*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/((a^2*c^4 + c^3*d)*sqrt(a^2*c + d)) + 2*d/((a^2*c^4 + c^3*d)*sqrt(d*x^2 + c)))/d + 48*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/(sqrt(a^2*c + d)*a*c^4)) + 1/35*(16*x/(sqrt(d*x^2 + c)*c^4) + 8*x/((d*x^2 + c)^(3/2)*c^3) + 6*x/((d*x^2 + c)^(5/2)*c^2) + 5*x/((d*x^2 + c)^(7/2)*c))*arctanh(a*x)","B",0
517,0,0,0,0.000000," ","integrate((-a*x^2+a)^(1/2)*arctanh(x),x, algorithm=""maxima"")","\int \sqrt{-a x^{2} + a} \operatorname{artanh}\left(x\right)\,{d x}"," ",0,"integrate(sqrt(-a*x^2 + a)*arctanh(x), x)","F",0
518,0,0,0,0.000000," ","integrate(arctanh(x)/(-a*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(x\right)}{\sqrt{-a x^{2} + a}}\,{d x}"," ",0,"integrate(arctanh(x)/sqrt(-a*x^2 + a), x)","F",0
519,1,63,0,0.420153," ","integrate(arctanh(x)/(-a*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{x \operatorname{artanh}\left(x\right)}{\sqrt{-a x^{2} + a} a} - \frac{\frac{\sqrt{-a x^{2} + a}}{a x + a} - \frac{\sqrt{-a x^{2} + a}}{a x - a}}{2 \, a}"," ",0,"x*arctanh(x)/(sqrt(-a*x^2 + a)*a) - 1/2*(sqrt(-a*x^2 + a)/(a*x + a) - sqrt(-a*x^2 + a)/(a*x - a))/a","A",0
520,1,67,0,0.325035," ","integrate(arctanh(x)/(-a*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{2 \, x}{\sqrt{-a x^{2} + a} a^{2}} + \frac{x}{{\left(-a x^{2} + a\right)}^{\frac{3}{2}} a}\right)} \operatorname{artanh}\left(x\right) - \frac{2}{3 \, \sqrt{-a x^{2} + a} a^{2}} - \frac{1}{9 \, {\left(-a x^{2} + a\right)}^{\frac{3}{2}} a}"," ",0,"1/3*(2*x/(sqrt(-a*x^2 + a)*a^2) + x/((-a*x^2 + a)^(3/2)*a))*arctanh(x) - 2/3/(sqrt(-a*x^2 + a)*a^2) - 1/9/((-a*x^2 + a)^(3/2)*a)","A",0
521,1,99,0,0.337382," ","integrate(arctanh(x)/(-a*x^2+a)^(7/2),x, algorithm=""maxima"")","\frac{1}{15} \, {\left(\frac{8 \, x}{\sqrt{-a x^{2} + a} a^{3}} + \frac{4 \, x}{{\left(-a x^{2} + a\right)}^{\frac{3}{2}} a^{2}} + \frac{3 \, x}{{\left(-a x^{2} + a\right)}^{\frac{5}{2}} a}\right)} \operatorname{artanh}\left(x\right) - \frac{8}{15 \, \sqrt{-a x^{2} + a} a^{3}} - \frac{4}{45 \, {\left(-a x^{2} + a\right)}^{\frac{3}{2}} a^{2}} - \frac{1}{25 \, {\left(-a x^{2} + a\right)}^{\frac{5}{2}} a}"," ",0,"1/15*(8*x/(sqrt(-a*x^2 + a)*a^3) + 4*x/((-a*x^2 + a)^(3/2)*a^2) + 3*x/((-a*x^2 + a)^(5/2)*a))*arctanh(x) - 8/15/(sqrt(-a*x^2 + a)*a^3) - 4/45/((-a*x^2 + a)^(3/2)*a^2) - 1/25/((-a*x^2 + a)^(5/2)*a)","A",0
522,1,314,0,0.340603," ","integrate(x^4*(a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""maxima"")","\frac{1}{5} \, a d x^{5} + \frac{1}{75} \, {\left(15 \, x^{5} \log\left(-c^{2} x^{2} + 1\right) - c^{2} {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} b e \operatorname{artanh}\left(c x\right) + \frac{1}{20} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b d + \frac{1}{75} \, {\left(15 \, x^{5} \log\left(-c^{2} x^{2} + 1\right) - c^{2} {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} a e + \frac{{\left({\left(30 i \, \pi c^{4} - 27 \, c^{4}\right)} x^{4} + {\left(60 i \, \pi c^{2} - 154 \, c^{2}\right)} x^{2} + {\left(60 i \, \pi + 30 \, c^{4} x^{4} + 60 \, c^{2} x^{2} + 120 \, \log\left(c x - 1\right) - 274\right)} \log\left(c x + 1\right) - 2 \, {\left(-30 i \, \pi - 15 \, c^{4} x^{4} - 30 \, c^{2} x^{2} + 137\right)} \log\left(c x - 1\right)\right)} b e}{600 \, c^{5}}"," ",0,"1/5*a*d*x^5 + 1/75*(15*x^5*log(-c^2*x^2 + 1) - c^2*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*b*e*arctanh(c*x) + 1/20*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*d + 1/75*(15*x^5*log(-c^2*x^2 + 1) - c^2*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*a*e + 1/600*((30*I*pi*c^4 - 27*c^4)*x^4 + (60*I*pi*c^2 - 154*c^2)*x^2 + (60*I*pi + 30*c^4*x^4 + 60*c^2*x^2 + 120*log(c*x - 1) - 274)*log(c*x + 1) - 2*(-30*I*pi - 15*c^4*x^4 - 30*c^2*x^2 + 137)*log(c*x - 1))*b*e/c^5","C",0
523,1,269,0,0.331687," ","integrate(x^3*(a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""maxima"")","\frac{1}{4} \, a d x^{4} + \frac{1}{8} \, {\left(2 \, x^{4} \log\left(-c^{2} x^{2} + 1\right) - c^{2} {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b e \operatorname{artanh}\left(c x\right) + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b d + \frac{1}{8} \, {\left(2 \, x^{4} \log\left(-c^{2} x^{2} + 1\right) - c^{2} {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} a e + \frac{{\left({\left(12 i \, \pi c^{3} - 14 \, c^{3}\right)} x^{3} + {\left(36 i \, \pi c - 150 \, c\right)} x - 3 \, {\left(6 i \, \pi - 4 \, c^{3} x^{3} - 12 \, c x - 25\right)} \log\left(c x + 1\right) - 3 \, {\left(-6 i \, \pi - 4 \, c^{3} x^{3} - 12 \, c x + 25\right)} \log\left(c x - 1\right)\right)} b e}{144 \, c^{4}}"," ",0,"1/4*a*d*x^4 + 1/8*(2*x^4*log(-c^2*x^2 + 1) - c^2*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*e*arctanh(c*x) + 1/24*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*d + 1/8*(2*x^4*log(-c^2*x^2 + 1) - c^2*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*a*e + 1/144*((12*I*pi*c^3 - 14*c^3)*x^3 + (36*I*pi*c - 150*c)*x - 3*(6*I*pi - 4*c^3*x^3 - 12*c*x - 25)*log(c*x + 1) - 3*(-6*I*pi - 4*c^3*x^3 - 12*c*x + 25)*log(c*x - 1))*b*e/c^4","C",0
524,1,252,0,0.336051," ","integrate(x^2*(a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""maxima"")","\frac{1}{3} \, a d x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \log\left(-c^{2} x^{2} + 1\right) - c^{2} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b e \operatorname{artanh}\left(c x\right) + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b d + \frac{1}{9} \, {\left(3 \, x^{3} \log\left(-c^{2} x^{2} + 1\right) - c^{2} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a e + \frac{{\left({\left(3 i \, \pi c^{2} - 5 \, c^{2}\right)} x^{2} + {\left(3 i \, \pi + 3 \, c^{2} x^{2} + 6 \, \log\left(c x - 1\right) - 11\right)} \log\left(c x + 1\right) + {\left(3 i \, \pi + 3 \, c^{2} x^{2} - 11\right)} \log\left(c x - 1\right)\right)} b e}{18 \, c^{3}}"," ",0,"1/3*a*d*x^3 + 1/9*(3*x^3*log(-c^2*x^2 + 1) - c^2*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*e*arctanh(c*x) + 1/6*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*d + 1/9*(3*x^3*log(-c^2*x^2 + 1) - c^2*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a*e + 1/18*((3*I*pi*c^2 - 5*c^2)*x^2 + (3*I*pi + 3*c^2*x^2 + 6*log(c*x - 1) - 11)*log(c*x + 1) + (3*I*pi + 3*c^2*x^2 - 11)*log(c*x - 1))*b*e/c^3","C",0
525,1,171,0,0.320198," ","integrate(x*(a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""maxima"")","\frac{1}{2} \, a d x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b d - \frac{{\left(c^{2} x^{2} - {\left(c^{2} x^{2} - 1\right)} \log\left(-c^{2} x^{2} + 1\right) - 1\right)} b e \operatorname{artanh}\left(c x\right)}{2 \, c^{2}} - \frac{{\left(c^{2} x^{2} - {\left(c^{2} x^{2} - 1\right)} \log\left(-c^{2} x^{2} + 1\right) - 1\right)} a e}{2 \, c^{2}} - \frac{{\left(3 \, c x - {\left(c x + 1\right)} \log\left(c x + 1\right) - {\left(c x - 1\right)} \log\left(-c x + 1\right)\right)} b e}{2 \, c^{2}}"," ",0,"1/2*a*d*x^2 + 1/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*d - 1/2*(c^2*x^2 - (c^2*x^2 - 1)*log(-c^2*x^2 + 1) - 1)*b*e*arctanh(c*x)/c^2 - 1/2*(c^2*x^2 - (c^2*x^2 - 1)*log(-c^2*x^2 + 1) - 1)*a*e/c^2 - 1/2*(3*c*x - (c*x + 1)*log(c*x + 1) - (c*x - 1)*log(-c*x + 1))*b*e/c^2","A",0
526,1,178,0,0.324535," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""maxima"")","-{\left(c^{2} {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} - x \log\left(-c^{2} x^{2} + 1\right)\right)} b e \operatorname{artanh}\left(c x\right) - {\left(c^{2} {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} - x \log\left(-c^{2} x^{2} + 1\right)\right)} a e + a d x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d}{2 \, c} + \frac{{\left({\left(i \, \pi + 2 \, \log\left(c x - 1\right) - 2\right)} \log\left(c x + 1\right) + {\left(i \, \pi - 2\right)} \log\left(c x - 1\right)\right)} b e}{2 \, c}"," ",0,"-(c^2*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3) - x*log(-c^2*x^2 + 1))*b*e*arctanh(c*x) - (c^2*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3) - x*log(-c^2*x^2 + 1))*a*e + a*d*x + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*d/c + 1/2*((I*pi + 2*log(c*x - 1) - 2)*log(c*x + 1) + (I*pi - 2)*log(c*x - 1))*b*e/c","C",0
527,1,152,0,0.472883," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1))/x,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\log\left(c x\right) \log\left(-c x + 1\right)^{2} + 2 \, {\rm Li}_2\left(-c x + 1\right) \log\left(-c x + 1\right) - 2 \, {\rm Li}_{3}(-c x + 1)\right)} b e + \frac{1}{2} \, {\left(\log\left(c x + 1\right)^{2} \log\left(-c x\right) + 2 \, {\rm Li}_2\left(c x + 1\right) \log\left(c x + 1\right) - 2 \, {\rm Li}_{3}(c x + 1)\right)} b e + a d \log\left(x\right) - \frac{1}{2} \, {\left(b d - 2 \, a e\right)} {\left(\log\left(c x\right) \log\left(-c x + 1\right) + {\rm Li}_2\left(-c x + 1\right)\right)} + \frac{1}{2} \, {\left(b d + 2 \, a e\right)} {\left(\log\left(c x + 1\right) \log\left(-c x\right) + {\rm Li}_2\left(c x + 1\right)\right)}"," ",0,"-1/2*(log(c*x)*log(-c*x + 1)^2 + 2*dilog(-c*x + 1)*log(-c*x + 1) - 2*polylog(3, -c*x + 1))*b*e + 1/2*(log(c*x + 1)^2*log(-c*x) + 2*dilog(c*x + 1)*log(c*x + 1) - 2*polylog(3, c*x + 1))*b*e + a*d*log(x) - 1/2*(b*d - 2*a*e)*(log(c*x)*log(-c*x + 1) + dilog(-c*x + 1)) + 1/2*(b*d + 2*a*e)*(log(c*x + 1)*log(-c*x) + dilog(c*x + 1))","A",0
528,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1))/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b d - {\left(c^{2} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} + \frac{\log\left(-c^{2} x^{2} + 1\right)}{x}\right)} a e + \frac{1}{2} \, b e {\left(\frac{\log\left(-c x + 1\right)^{2}}{x} - \int -\frac{{\left(c x - 1\right)} \log\left(c x + 1\right)^{2} - 2 \, c x \log\left(-c x + 1\right)}{c x^{3} - x^{2}}\,{d x}\right)} - \frac{a d}{x}"," ",0,"-1/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*d - (c^2*(log(c*x + 1)/c - log(c*x - 1)/c) + log(-c^2*x^2 + 1)/x)*a*e + 1/2*b*e*(log(-c*x + 1)^2/x - integrate(-((c*x - 1)*log(c*x + 1)^2 - 2*c*x*log(-c*x + 1))/(c*x^3 - x^2), x)) - a*d/x","F",0
529,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1))/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b d + \frac{1}{2} \, {\left(c^{2} {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} - \frac{\log\left(-c^{2} x^{2} + 1\right)}{x^{2}}\right)} a e + \frac{1}{4} \, b e {\left(\frac{\log\left(-c x + 1\right)^{2}}{x^{2}} - 2 \, \int -\frac{{\left(c x - 1\right)} \log\left(c x + 1\right)^{2} - c x \log\left(-c x + 1\right)}{c x^{4} - x^{3}}\,{d x}\right)} - \frac{a d}{2 \, x^{2}}"," ",0,"1/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*d + 1/2*(c^2*(log(c^2*x^2 - 1) - log(x^2)) - log(-c^2*x^2 + 1)/x^2)*a*e + 1/4*b*e*(log(-c*x + 1)^2/x^2 - 2*integrate(-((c*x - 1)*log(c*x + 1)^2 - c*x*log(-c*x + 1))/(c*x^4 - x^3), x)) - 1/2*a*d/x^2","F",0
530,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b d - \frac{1}{3} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c^{2} + \frac{\log\left(-c^{2} x^{2} + 1\right)}{x^{3}}\right)} a e + \frac{1}{6} \, b e {\left(\frac{\log\left(-c x + 1\right)^{2}}{x^{3}} - 3 \, \int -\frac{3 \, {\left(c x - 1\right)} \log\left(c x + 1\right)^{2} - 2 \, c x \log\left(-c x + 1\right)}{3 \, {\left(c x^{5} - x^{4}\right)}}\,{d x}\right)} - \frac{a d}{3 \, x^{3}}"," ",0,"-1/6*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b*d - 1/3*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c^2 + log(-c^2*x^2 + 1)/x^3)*a*e + 1/6*b*e*(log(-c*x + 1)^2/x^3 - 3*integrate(-1/3*(3*(c*x - 1)*log(c*x + 1)^2 - 2*c*x*log(-c*x + 1))/(c*x^5 - x^4), x)) - 1/3*a*d/x^3","F",0
531,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1))/x^5,x, algorithm=""maxima"")","\frac{1}{24} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} b d + \frac{1}{4} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c^{2} - \frac{\log\left(-c^{2} x^{2} + 1\right)}{x^{4}}\right)} a e + \frac{1}{8} \, b e {\left(\frac{\log\left(-c x + 1\right)^{2}}{x^{4}} - 4 \, \int -\frac{2 \, {\left(c x - 1\right)} \log\left(c x + 1\right)^{2} - c x \log\left(-c x + 1\right)}{2 \, {\left(c x^{6} - x^{5}\right)}}\,{d x}\right)} - \frac{a d}{4 \, x^{4}}"," ",0,"1/24*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*b*d + 1/4*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c^2 - log(-c^2*x^2 + 1)/x^4)*a*e + 1/8*b*e*(log(-c*x + 1)^2/x^4 - 4*integrate(-1/2*(2*(c*x - 1)*log(c*x + 1)^2 - c*x*log(-c*x + 1))/(c*x^6 - x^5), x)) - 1/4*a*d/x^4","F",0
532,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1))/x^6,x, algorithm=""maxima"")","-\frac{1}{20} \, {\left({\left(2 \, c^{4} \log\left(c^{2} x^{2} - 1\right) - 2 \, c^{4} \log\left(x^{2}\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} c + \frac{4 \, \operatorname{artanh}\left(c x\right)}{x^{5}}\right)} b d - \frac{1}{15} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c^{2} + \frac{3 \, \log\left(-c^{2} x^{2} + 1\right)}{x^{5}}\right)} a e + \frac{1}{10} \, b e {\left(\frac{\log\left(-c x + 1\right)^{2}}{x^{5}} - 5 \, \int -\frac{5 \, {\left(c x - 1\right)} \log\left(c x + 1\right)^{2} - 2 \, c x \log\left(-c x + 1\right)}{5 \, {\left(c x^{7} - x^{6}\right)}}\,{d x}\right)} - \frac{a d}{5 \, x^{5}}"," ",0,"-1/20*((2*c^4*log(c^2*x^2 - 1) - 2*c^4*log(x^2) + (2*c^2*x^2 + 1)/x^4)*c + 4*arctanh(c*x)/x^5)*b*d - 1/15*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c^2 + 3*log(-c^2*x^2 + 1)/x^5)*a*e + 1/10*b*e*(log(-c*x + 1)^2/x^5 - 5*integrate(-1/5*(5*(c*x - 1)*log(c*x + 1)^2 - 2*c*x*log(-c*x + 1))/(c*x^7 - x^6), x)) - 1/5*a*d/x^5","F",0
533,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))*(d+e*log(g*x^2+f)),x, algorithm=""maxima"")","\frac{1}{2} \, a d x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b d - \frac{1}{4} \, {\left(2 \, c^{2} g \int \frac{x^{3} \log\left(c x + 1\right)}{c^{2} g x^{2} + c^{2} f}\,{d x} - 2 \, c^{2} g \int \frac{x^{3} \log\left(-c x + 1\right)}{c^{2} g x^{2} + c^{2} f}\,{d x} - 2 \, c g {\left(-\frac{i \, f {\left(\log\left(\frac{i \, g x}{\sqrt{f g}} + 1\right) - \log\left(-\frac{i \, g x}{\sqrt{f g}} + 1\right)\right)}}{\sqrt{f g} c^{2} g} - \frac{2 \, x}{c^{2} g}\right)} - 2 \, g \int \frac{x \log\left(c x + 1\right)}{c^{2} g x^{2} + c^{2} f}\,{d x} + 2 \, g \int \frac{x \log\left(-c x + 1\right)}{c^{2} g x^{2} + c^{2} f}\,{d x} - \frac{{\left(2 \, c x + {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) - {\left(c^{2} x^{2} - 1\right)} \log\left(-c x + 1\right)\right)} \log\left(g x^{2} + f\right)}{c^{2}}\right)} b e - \frac{{\left(g x^{2} - {\left(g x^{2} + f\right)} \log\left(g x^{2} + f\right) + f\right)} a e}{2 \, g}"," ",0,"1/2*a*d*x^2 + 1/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*d - 1/4*(2*c^2*g*integrate(x^3*log(c*x + 1)/(c^2*g*x^2 + c^2*f), x) - 2*c^2*g*integrate(x^3*log(-c*x + 1)/(c^2*g*x^2 + c^2*f), x) - 2*c*g*(-I*f*(log(I*g*x/sqrt(f*g) + 1) - log(-I*g*x/sqrt(f*g) + 1))/(sqrt(f*g)*c^2*g) - 2*x/(c^2*g)) - 2*g*integrate(x*log(c*x + 1)/(c^2*g*x^2 + c^2*f), x) + 2*g*integrate(x*log(-c*x + 1)/(c^2*g*x^2 + c^2*f), x) - (2*c*x + (c^2*x^2 - 1)*log(c*x + 1) - (c^2*x^2 - 1)*log(-c*x + 1))*log(g*x^2 + f)/c^2)*b*e - 1/2*(g*x^2 - (g*x^2 + f)*log(g*x^2 + f) + f)*a*e/g","F",0
534,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))*(d+e*log(g*x^2+f)),x, algorithm=""maxima"")","{\left(2 \, g {\left(\frac{f \arctan\left(\frac{g x}{\sqrt{f g}}\right)}{\sqrt{f g} g} - \frac{x}{g}\right)} + x \log\left(g x^{2} + f\right)\right)} a e + a d x + \frac{1}{2} \, b e {\left(\frac{{\left({\left(c x + 1\right)} \log\left(c x + 1\right) - {\left(c x - 1\right)} \log\left(-c x + 1\right)\right)} \log\left(g x^{2} + f\right)}{c} + \int -\frac{2 \, {\left({\left(c g x^{2} + g x\right)} \log\left(c x + 1\right) - {\left(c g x^{2} - g x\right)} \log\left(-c x + 1\right)\right)}}{c g x^{2} + c f}\,{d x}\right)} + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d}{2 \, c}"," ",0,"(2*g*(f*arctan(g*x/sqrt(f*g))/(sqrt(f*g)*g) - x/g) + x*log(g*x^2 + f))*a*e + a*d*x + 1/2*b*e*(((c*x + 1)*log(c*x + 1) - (c*x - 1)*log(-c*x + 1))*log(g*x^2 + f)/c + integrate(-2*((c*g*x^2 + g*x)*log(c*x + 1) - (c*g*x^2 - g*x)*log(-c*x + 1))/(c*g*x^2 + c*f), x)) + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*d/c","F",0
535,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))*(d+e*log(g*x^2+f))/x,x, algorithm=""maxima"")","a d \log\left(x\right) + \int \frac{b e {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)} \log\left(g x^{2} + f\right)}{2 \, x} + \frac{b d {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{2 \, x} + \frac{a e \log\left(g x^{2} + f\right)}{x}\,{d x}"," ",0,"a*d*log(x) + integrate(1/2*b*e*(log(c*x + 1) - log(-c*x + 1))*log(g*x^2 + f)/x + 1/2*b*d*(log(c*x + 1) - log(-c*x + 1))/x + a*e*log(g*x^2 + f)/x, x)","F",0
536,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))*(d+e*log(g*x^2+f))/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b d + {\left(\frac{2 \, g \arctan\left(\frac{g x}{\sqrt{f g}}\right)}{\sqrt{f g}} - \frac{\log\left(g x^{2} + f\right)}{x}\right)} a e + \frac{1}{2} \, b e \int \frac{{\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)} \log\left(g x^{2} + f\right)}{x^{2}}\,{d x} - \frac{a d}{x}"," ",0,"-1/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b*d + (2*g*arctan(g*x/sqrt(f*g))/sqrt(f*g) - log(g*x^2 + f)/x)*a*e + 1/2*b*e*integrate((log(c*x + 1) - log(-c*x + 1))*log(g*x^2 + f)/x^2, x) - a*d/x","F",0
537,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))*(d+e*log(g*x^2+f))/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b d - \frac{1}{2} \, {\left(g {\left(\frac{\log\left(g x^{2} + f\right)}{f} - \frac{\log\left(x^{2}\right)}{f}\right)} + \frac{\log\left(g x^{2} + f\right)}{x^{2}}\right)} a e - \frac{1}{4} \, {\left(2 \, c^{2} g \int \frac{x^{2} \log\left(c x + 1\right)}{g x^{3} + f x}\,{d x} - 2 \, c^{2} g \int \frac{x^{2} \log\left(-c x + 1\right)}{g x^{3} + f x}\,{d x} + \frac{2 i \, c g {\left(\log\left(\frac{i \, g x}{\sqrt{f g}} + 1\right) - \log\left(-\frac{i \, g x}{\sqrt{f g}} + 1\right)\right)}}{\sqrt{f g}} - 2 \, g \int \frac{\log\left(c x + 1\right)}{g x^{3} + f x}\,{d x} + 2 \, g \int \frac{\log\left(-c x + 1\right)}{g x^{3} + f x}\,{d x} + \frac{{\left(2 \, c x - {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + {\left(c^{2} x^{2} - 1\right)} \log\left(-c x + 1\right)\right)} \log\left(g x^{2} + f\right)}{x^{2}}\right)} b e - \frac{a d}{2 \, x^{2}}"," ",0,"1/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b*d - 1/2*(g*(log(g*x^2 + f)/f - log(x^2)/f) + log(g*x^2 + f)/x^2)*a*e - 1/4*(2*c^2*g*integrate(x^2*log(c*x + 1)/(g*x^3 + f*x), x) - 2*c^2*g*integrate(x^2*log(-c*x + 1)/(g*x^3 + f*x), x) + 2*I*c*g*(log(I*g*x/sqrt(f*g) + 1) - log(-I*g*x/sqrt(f*g) + 1))/sqrt(f*g) - 2*g*integrate(log(c*x + 1)/(g*x^3 + f*x), x) + 2*g*integrate(log(-c*x + 1)/(g*x^3 + f*x), x) + (2*c*x - (c^2*x^2 - 1)*log(c*x + 1) + (c^2*x^2 - 1)*log(-c*x + 1))*log(g*x^2 + f)/x^2)*b*e - 1/2*a*d/x^2","F",0
538,1,226,0,0.400964," ","integrate(arctanh(c*x)*(a+b*arctanh(c*x))/(c*x+1)^2,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(b c {\left(\frac{2}{c^{4} x + c^{3}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} + 2 \, a {\left(\frac{2}{c^{3} x + c^{2}} - \frac{\log\left(c x + 1\right)}{c^{2}} + \frac{\log\left(c x - 1\right)}{c^{2}}\right)} + \frac{-2 i \, \pi b + {\left(i \, \pi b + {\left(i \, \pi b c - b c\right)} x + b\right)} \log\left(c x + 1\right) + {\left(-i \, \pi b + {\left(-i \, \pi b c + b c\right)} x - b\right)} \log\left(c x - 1\right) + 2 \, b}{c^{3} x + c^{2}}\right)} c - \frac{1}{4} \, {\left({\left(c {\left(\frac{2}{c^{3} x + c^{2}} - \frac{\log\left(c x + 1\right)}{c^{2}} + \frac{\log\left(c x - 1\right)}{c^{2}}\right)} + \frac{4 \, \operatorname{artanh}\left(c x\right)}{c^{2} x + c}\right)} b + \frac{4 \, a}{c^{2} x + c}\right)} \operatorname{artanh}\left(c x\right)"," ",0,"-1/8*(b*c*(2/(c^4*x + c^3) - log(c*x + 1)/c^3 + log(c*x - 1)/c^3) + 2*a*(2/(c^3*x + c^2) - log(c*x + 1)/c^2 + log(c*x - 1)/c^2) + (-2*I*pi*b + (I*pi*b + (I*pi*b*c - b*c)*x + b)*log(c*x + 1) + (-I*pi*b + (-I*pi*b*c + b*c)*x - b)*log(c*x - 1) + 2*b)/(c^3*x + c^2))*c - 1/4*((c*(2/(c^3*x + c^2) - log(c*x + 1)/c^2 + log(c*x - 1)/c^2) + 4*arctanh(c*x)/(c^2*x + c))*b + 4*a/(c^2*x + c))*arctanh(c*x)","C",0
