1,1,491,0,0.246454," ","integrate(x^3*(c*d*x+d)*(a+b*arctanh(c*x)),x, algorithm=""giac"")","\frac{1}{15} \, c {\left(\frac{3 \, {\left(\frac{10 \, {\left(c x + 1\right)}^{4} b d}{{\left(c x - 1\right)}^{4}} - \frac{5 \, {\left(c x + 1\right)}^{3} b d}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} b d}{{\left(c x - 1\right)}^{2}} - \frac{5 \, {\left(c x + 1\right)} b d}{c x - 1} + b d\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{5} c^{5}}{{\left(c x - 1\right)}^{5}} - \frac{5 \, {\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} - \frac{10 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} c^{5}}{c x - 1} - c^{5}} + \frac{\frac{60 \, {\left(c x + 1\right)}^{4} a d}{{\left(c x - 1\right)}^{4}} - \frac{30 \, {\left(c x + 1\right)}^{3} a d}{{\left(c x - 1\right)}^{3}} + \frac{90 \, {\left(c x + 1\right)}^{2} a d}{{\left(c x - 1\right)}^{2}} - \frac{30 \, {\left(c x + 1\right)} a d}{c x - 1} + 6 \, a d + \frac{27 \, {\left(c x + 1\right)}^{4} b d}{{\left(c x - 1\right)}^{4}} - \frac{69 \, {\left(c x + 1\right)}^{3} b d}{{\left(c x - 1\right)}^{3}} + \frac{79 \, {\left(c x + 1\right)}^{2} b d}{{\left(c x - 1\right)}^{2}} - \frac{47 \, {\left(c x + 1\right)} b d}{c x - 1} + 10 \, b d}{\frac{{\left(c x + 1\right)}^{5} c^{5}}{{\left(c x - 1\right)}^{5}} - \frac{5 \, {\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} - \frac{10 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} c^{5}}{c x - 1} - c^{5}} - \frac{3 \, b d \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{5}} + \frac{3 \, b d \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{5}}\right)}"," ",0,"1/15*c*(3*(10*(c*x + 1)^4*b*d/(c*x - 1)^4 - 5*(c*x + 1)^3*b*d/(c*x - 1)^3 + 15*(c*x + 1)^2*b*d/(c*x - 1)^2 - 5*(c*x + 1)*b*d/(c*x - 1) + b*d)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^5*c^5/(c*x - 1)^5 - 5*(c*x + 1)^4*c^5/(c*x - 1)^4 + 10*(c*x + 1)^3*c^5/(c*x - 1)^3 - 10*(c*x + 1)^2*c^5/(c*x - 1)^2 + 5*(c*x + 1)*c^5/(c*x - 1) - c^5) + (60*(c*x + 1)^4*a*d/(c*x - 1)^4 - 30*(c*x + 1)^3*a*d/(c*x - 1)^3 + 90*(c*x + 1)^2*a*d/(c*x - 1)^2 - 30*(c*x + 1)*a*d/(c*x - 1) + 6*a*d + 27*(c*x + 1)^4*b*d/(c*x - 1)^4 - 69*(c*x + 1)^3*b*d/(c*x - 1)^3 + 79*(c*x + 1)^2*b*d/(c*x - 1)^2 - 47*(c*x + 1)*b*d/(c*x - 1) + 10*b*d)/((c*x + 1)^5*c^5/(c*x - 1)^5 - 5*(c*x + 1)^4*c^5/(c*x - 1)^4 + 10*(c*x + 1)^3*c^5/(c*x - 1)^3 - 10*(c*x + 1)^2*c^5/(c*x - 1)^2 + 5*(c*x + 1)*c^5/(c*x - 1) - c^5) - 3*b*d*log(-(c*x + 1)/(c*x - 1) + 1)/c^5 + 3*b*d*log(-(c*x + 1)/(c*x - 1))/c^5)","B",0
2,1,394,0,0.199135," ","integrate(x^2*(c*d*x+d)*(a+b*arctanh(c*x)),x, algorithm=""giac"")","\frac{1}{3} \, c {\left(\frac{{\left(\frac{6 \, {\left(c x + 1\right)}^{3} b d}{{\left(c x - 1\right)}^{3}} - \frac{3 \, {\left(c x + 1\right)}^{2} b d}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)} b d}{c x - 1} - b d\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{4} c^{4}}{{\left(c x - 1\right)}^{4}} - \frac{4 \, {\left(c x + 1\right)}^{3} c^{4}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} c^{4}}{{\left(c x - 1\right)}^{2}} - \frac{4 \, {\left(c x + 1\right)} c^{4}}{c x - 1} + c^{4}} + \frac{\frac{12 \, {\left(c x + 1\right)}^{3} a d}{{\left(c x - 1\right)}^{3}} - \frac{6 \, {\left(c x + 1\right)}^{2} a d}{{\left(c x - 1\right)}^{2}} + \frac{8 \, {\left(c x + 1\right)} a d}{c x - 1} - 2 \, a d + \frac{5 \, {\left(c x + 1\right)}^{3} b d}{{\left(c x - 1\right)}^{3}} - \frac{10 \, {\left(c x + 1\right)}^{2} b d}{{\left(c x - 1\right)}^{2}} + \frac{7 \, {\left(c x + 1\right)} b d}{c x - 1} - 2 \, b d}{\frac{{\left(c x + 1\right)}^{4} c^{4}}{{\left(c x - 1\right)}^{4}} - \frac{4 \, {\left(c x + 1\right)}^{3} c^{4}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} c^{4}}{{\left(c x - 1\right)}^{2}} - \frac{4 \, {\left(c x + 1\right)} c^{4}}{c x - 1} + c^{4}} - \frac{b d \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{4}} + \frac{b d \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{4}}\right)}"," ",0,"1/3*c*((6*(c*x + 1)^3*b*d/(c*x - 1)^3 - 3*(c*x + 1)^2*b*d/(c*x - 1)^2 + 4*(c*x + 1)*b*d/(c*x - 1) - b*d)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^4*c^4/(c*x - 1)^4 - 4*(c*x + 1)^3*c^4/(c*x - 1)^3 + 6*(c*x + 1)^2*c^4/(c*x - 1)^2 - 4*(c*x + 1)*c^4/(c*x - 1) + c^4) + (12*(c*x + 1)^3*a*d/(c*x - 1)^3 - 6*(c*x + 1)^2*a*d/(c*x - 1)^2 + 8*(c*x + 1)*a*d/(c*x - 1) - 2*a*d + 5*(c*x + 1)^3*b*d/(c*x - 1)^3 - 10*(c*x + 1)^2*b*d/(c*x - 1)^2 + 7*(c*x + 1)*b*d/(c*x - 1) - 2*b*d)/((c*x + 1)^4*c^4/(c*x - 1)^4 - 4*(c*x + 1)^3*c^4/(c*x - 1)^3 + 6*(c*x + 1)^2*c^4/(c*x - 1)^2 - 4*(c*x + 1)*c^4/(c*x - 1) + c^4) - b*d*log(-(c*x + 1)/(c*x - 1) + 1)/c^4 + b*d*log(-(c*x + 1)/(c*x - 1))/c^4)","B",0
3,1,305,0,0.161627," ","integrate(x*(c*d*x+d)*(a+b*arctanh(c*x)),x, algorithm=""giac"")","\frac{1}{3} \, c {\left(\frac{{\left(\frac{6 \, {\left(c x + 1\right)}^{2} b d}{{\left(c x - 1\right)}^{2}} - \frac{3 \, {\left(c x + 1\right)} b d}{c x - 1} + b d\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{3} c^{3}}{{\left(c x - 1\right)}^{3}} - \frac{3 \, {\left(c x + 1\right)}^{2} c^{3}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)} c^{3}}{c x - 1} - c^{3}} + \frac{\frac{12 \, {\left(c x + 1\right)}^{2} a d}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} a d}{c x - 1} + 2 \, a d + \frac{5 \, {\left(c x + 1\right)}^{2} b d}{{\left(c x - 1\right)}^{2}} - \frac{8 \, {\left(c x + 1\right)} b d}{c x - 1} + 3 \, b d}{\frac{{\left(c x + 1\right)}^{3} c^{3}}{{\left(c x - 1\right)}^{3}} - \frac{3 \, {\left(c x + 1\right)}^{2} c^{3}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)} c^{3}}{c x - 1} - c^{3}} - \frac{b d \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{3}} + \frac{b d \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{3}}\right)}"," ",0,"1/3*c*((6*(c*x + 1)^2*b*d/(c*x - 1)^2 - 3*(c*x + 1)*b*d/(c*x - 1) + b*d)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^3*c^3/(c*x - 1)^3 - 3*(c*x + 1)^2*c^3/(c*x - 1)^2 + 3*(c*x + 1)*c^3/(c*x - 1) - c^3) + (12*(c*x + 1)^2*a*d/(c*x - 1)^2 - 6*(c*x + 1)*a*d/(c*x - 1) + 2*a*d + 5*(c*x + 1)^2*b*d/(c*x - 1)^2 - 8*(c*x + 1)*b*d/(c*x - 1) + 3*b*d)/((c*x + 1)^3*c^3/(c*x - 1)^3 - 3*(c*x + 1)^2*c^3/(c*x - 1)^2 + 3*(c*x + 1)*c^3/(c*x - 1) - c^3) - b*d*log(-(c*x + 1)/(c*x - 1) + 1)/c^3 + b*d*log(-(c*x + 1)/(c*x - 1))/c^3)","B",0
4,1,211,0,0.176848," ","integrate((c*d*x+d)*(a+b*arctanh(c*x)),x, algorithm=""giac"")","-c {\left(\frac{b d \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{2}} - \frac{{\left(\frac{2 \, {\left(c x + 1\right)} b d}{c x - 1} - b d\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{2} c^{2}}{{\left(c x - 1\right)}^{2}} - \frac{2 \, {\left(c x + 1\right)} c^{2}}{c x - 1} + c^{2}} - \frac{b d \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{2}} - \frac{\frac{4 \, {\left(c x + 1\right)} a d}{c x - 1} - 2 \, a d + \frac{{\left(c x + 1\right)} b d}{c x - 1} - b d}{\frac{{\left(c x + 1\right)}^{2} c^{2}}{{\left(c x - 1\right)}^{2}} - \frac{2 \, {\left(c x + 1\right)} c^{2}}{c x - 1} + c^{2}}\right)}"," ",0,"-c*(b*d*log(-(c*x + 1)/(c*x - 1) + 1)/c^2 - (2*(c*x + 1)*b*d/(c*x - 1) - b*d)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^2*c^2/(c*x - 1)^2 - 2*(c*x + 1)*c^2/(c*x - 1) + c^2) - b*d*log(-(c*x + 1)/(c*x - 1))/c^2 - (4*(c*x + 1)*a*d/(c*x - 1) - 2*a*d + (c*x + 1)*b*d/(c*x - 1) - b*d)/((c*x + 1)^2*c^2/(c*x - 1)^2 - 2*(c*x + 1)*c^2/(c*x - 1) + c^2))","B",0
5,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}}{x}\,{d x}"," ",0,"integrate((c*d*x + d)*(b*arctanh(c*x) + a)/x, x)","F",0
6,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x^2,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}}{x^{2}}\,{d x}"," ",0,"integrate((c*d*x + d)*(b*arctanh(c*x) + a)/x^2, x)","F",0
7,1,192,0,0.195687," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x^3,x, algorithm=""giac"")","{\left(b c d \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - b c d \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{{\left(\frac{2 \, {\left(c x + 1\right)} b c d}{c x - 1} + b c d\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{2 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{\frac{4 \, {\left(c x + 1\right)} a c d}{c x - 1} + 2 \, a c d + \frac{{\left(c x + 1\right)} b c d}{c x - 1} + b c d}{\frac{{\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{2 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"(b*c*d*log(-(c*x + 1)/(c*x - 1) - 1) - b*c*d*log(-(c*x + 1)/(c*x - 1)) + (2*(c*x + 1)*b*c*d/(c*x - 1) + b*c*d)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^2/(c*x - 1)^2 + 2*(c*x + 1)/(c*x - 1) + 1) + (4*(c*x + 1)*a*c*d/(c*x - 1) + 2*a*c*d + (c*x + 1)*b*c*d/(c*x - 1) + b*c*d)/((c*x + 1)^2/(c*x - 1)^2 + 2*(c*x + 1)/(c*x - 1) + 1))*c","B",0
8,1,306,0,0.285804," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x^4,x, algorithm=""giac"")","\frac{1}{3} \, {\left(b c^{2} d \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - b c^{2} d \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{{\left(\frac{6 \, {\left(c x + 1\right)}^{2} b c^{2} d}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)} b c^{2} d}{c x - 1} + b c^{2} d\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{3 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{\frac{12 \, {\left(c x + 1\right)}^{2} a c^{2} d}{{\left(c x - 1\right)}^{2}} + \frac{6 \, {\left(c x + 1\right)} a c^{2} d}{c x - 1} + 2 \, a c^{2} d + \frac{5 \, {\left(c x + 1\right)}^{2} b c^{2} d}{{\left(c x - 1\right)}^{2}} + \frac{8 \, {\left(c x + 1\right)} b c^{2} d}{c x - 1} + 3 \, b c^{2} d}{\frac{{\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{3 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"1/3*(b*c^2*d*log(-(c*x + 1)/(c*x - 1) - 1) - b*c^2*d*log(-(c*x + 1)/(c*x - 1)) + (6*(c*x + 1)^2*b*c^2*d/(c*x - 1)^2 + 3*(c*x + 1)*b*c^2*d/(c*x - 1) + b*c^2*d)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^3/(c*x - 1)^3 + 3*(c*x + 1)^2/(c*x - 1)^2 + 3*(c*x + 1)/(c*x - 1) + 1) + (12*(c*x + 1)^2*a*c^2*d/(c*x - 1)^2 + 6*(c*x + 1)*a*c^2*d/(c*x - 1) + 2*a*c^2*d + 5*(c*x + 1)^2*b*c^2*d/(c*x - 1)^2 + 8*(c*x + 1)*b*c^2*d/(c*x - 1) + 3*b*c^2*d)/((c*x + 1)^3/(c*x - 1)^3 + 3*(c*x + 1)^2/(c*x - 1)^2 + 3*(c*x + 1)/(c*x - 1) + 1))*c","B",0
9,1,401,0,0.166605," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x^5,x, algorithm=""giac"")","\frac{1}{3} \, {\left(b c^{3} d \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - b c^{3} d \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{{\left(\frac{6 \, {\left(c x + 1\right)}^{3} b c^{3} d}{{\left(c x - 1\right)}^{3}} + \frac{3 \, {\left(c x + 1\right)}^{2} b c^{3} d}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)} b c^{3} d}{c x - 1} + b c^{3} d\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{4 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{\frac{12 \, {\left(c x + 1\right)}^{3} a c^{3} d}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} a c^{3} d}{{\left(c x - 1\right)}^{2}} + \frac{8 \, {\left(c x + 1\right)} a c^{3} d}{c x - 1} + 2 \, a c^{3} d + \frac{5 \, {\left(c x + 1\right)}^{3} b c^{3} d}{{\left(c x - 1\right)}^{3}} + \frac{10 \, {\left(c x + 1\right)}^{2} b c^{3} d}{{\left(c x - 1\right)}^{2}} + \frac{7 \, {\left(c x + 1\right)} b c^{3} d}{c x - 1} + 2 \, b c^{3} d}{\frac{{\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{4 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"1/3*(b*c^3*d*log(-(c*x + 1)/(c*x - 1) - 1) - b*c^3*d*log(-(c*x + 1)/(c*x - 1)) + (6*(c*x + 1)^3*b*c^3*d/(c*x - 1)^3 + 3*(c*x + 1)^2*b*c^3*d/(c*x - 1)^2 + 4*(c*x + 1)*b*c^3*d/(c*x - 1) + b*c^3*d)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^4/(c*x - 1)^4 + 4*(c*x + 1)^3/(c*x - 1)^3 + 6*(c*x + 1)^2/(c*x - 1)^2 + 4*(c*x + 1)/(c*x - 1) + 1) + (12*(c*x + 1)^3*a*c^3*d/(c*x - 1)^3 + 6*(c*x + 1)^2*a*c^3*d/(c*x - 1)^2 + 8*(c*x + 1)*a*c^3*d/(c*x - 1) + 2*a*c^3*d + 5*(c*x + 1)^3*b*c^3*d/(c*x - 1)^3 + 10*(c*x + 1)^2*b*c^3*d/(c*x - 1)^2 + 7*(c*x + 1)*b*c^3*d/(c*x - 1) + 2*b*c^3*d)/((c*x + 1)^4/(c*x - 1)^4 + 4*(c*x + 1)^3/(c*x - 1)^3 + 6*(c*x + 1)^2/(c*x - 1)^2 + 4*(c*x + 1)/(c*x - 1) + 1))*c","B",0
10,1,620,0,0.276403," ","integrate(x^3*(c*d*x+d)^2*(a+b*arctanh(c*x)),x, algorithm=""giac"")","\frac{1}{45} \, c {\left(\frac{6 \, {\left(\frac{30 \, {\left(c x + 1\right)}^{5} b d^{2}}{{\left(c x - 1\right)}^{5}} - \frac{30 \, {\left(c x + 1\right)}^{4} b d^{2}}{{\left(c x - 1\right)}^{4}} + \frac{70 \, {\left(c x + 1\right)}^{3} b d^{2}}{{\left(c x - 1\right)}^{3}} - \frac{45 \, {\left(c x + 1\right)}^{2} b d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{18 \, {\left(c x + 1\right)} b d^{2}}{c x - 1} - 3 \, b d^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{6} c^{5}}{{\left(c x - 1\right)}^{6}} - \frac{6 \, {\left(c x + 1\right)}^{5} c^{5}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} - \frac{20 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} c^{5}}{c x - 1} + c^{5}} + \frac{\frac{360 \, {\left(c x + 1\right)}^{5} a d^{2}}{{\left(c x - 1\right)}^{5}} - \frac{360 \, {\left(c x + 1\right)}^{4} a d^{2}}{{\left(c x - 1\right)}^{4}} + \frac{840 \, {\left(c x + 1\right)}^{3} a d^{2}}{{\left(c x - 1\right)}^{3}} - \frac{540 \, {\left(c x + 1\right)}^{2} a d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{216 \, {\left(c x + 1\right)} a d^{2}}{c x - 1} - 36 \, a d^{2} + \frac{162 \, {\left(c x + 1\right)}^{5} b d^{2}}{{\left(c x - 1\right)}^{5}} - \frac{531 \, {\left(c x + 1\right)}^{4} b d^{2}}{{\left(c x - 1\right)}^{4}} + \frac{818 \, {\left(c x + 1\right)}^{3} b d^{2}}{{\left(c x - 1\right)}^{3}} - \frac{696 \, {\left(c x + 1\right)}^{2} b d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{300 \, {\left(c x + 1\right)} b d^{2}}{c x - 1} - 53 \, b d^{2}}{\frac{{\left(c x + 1\right)}^{6} c^{5}}{{\left(c x - 1\right)}^{6}} - \frac{6 \, {\left(c x + 1\right)}^{5} c^{5}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} - \frac{20 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} c^{5}}{c x - 1} + c^{5}} - \frac{18 \, b d^{2} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{5}} + \frac{18 \, b d^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{5}}\right)}"," ",0,"1/45*c*(6*(30*(c*x + 1)^5*b*d^2/(c*x - 1)^5 - 30*(c*x + 1)^4*b*d^2/(c*x - 1)^4 + 70*(c*x + 1)^3*b*d^2/(c*x - 1)^3 - 45*(c*x + 1)^2*b*d^2/(c*x - 1)^2 + 18*(c*x + 1)*b*d^2/(c*x - 1) - 3*b*d^2)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^6*c^5/(c*x - 1)^6 - 6*(c*x + 1)^5*c^5/(c*x - 1)^5 + 15*(c*x + 1)^4*c^5/(c*x - 1)^4 - 20*(c*x + 1)^3*c^5/(c*x - 1)^3 + 15*(c*x + 1)^2*c^5/(c*x - 1)^2 - 6*(c*x + 1)*c^5/(c*x - 1) + c^5) + (360*(c*x + 1)^5*a*d^2/(c*x - 1)^5 - 360*(c*x + 1)^4*a*d^2/(c*x - 1)^4 + 840*(c*x + 1)^3*a*d^2/(c*x - 1)^3 - 540*(c*x + 1)^2*a*d^2/(c*x - 1)^2 + 216*(c*x + 1)*a*d^2/(c*x - 1) - 36*a*d^2 + 162*(c*x + 1)^5*b*d^2/(c*x - 1)^5 - 531*(c*x + 1)^4*b*d^2/(c*x - 1)^4 + 818*(c*x + 1)^3*b*d^2/(c*x - 1)^3 - 696*(c*x + 1)^2*b*d^2/(c*x - 1)^2 + 300*(c*x + 1)*b*d^2/(c*x - 1) - 53*b*d^2)/((c*x + 1)^6*c^5/(c*x - 1)^6 - 6*(c*x + 1)^5*c^5/(c*x - 1)^5 + 15*(c*x + 1)^4*c^5/(c*x - 1)^4 - 20*(c*x + 1)^3*c^5/(c*x - 1)^3 + 15*(c*x + 1)^2*c^5/(c*x - 1)^2 - 6*(c*x + 1)*c^5/(c*x - 1) + c^5) - 18*b*d^2*log(-(c*x + 1)/(c*x - 1) + 1)/c^5 + 18*b*d^2*log(-(c*x + 1)/(c*x - 1))/c^5)","B",0
11,1,525,0,0.233405," ","integrate(x^2*(c*d*x+d)^2*(a+b*arctanh(c*x)),x, algorithm=""giac"")","\frac{4}{15} \, c {\left(\frac{{\left(\frac{15 \, {\left(c x + 1\right)}^{4} b d^{2}}{{\left(c x - 1\right)}^{4}} - \frac{15 \, {\left(c x + 1\right)}^{3} b d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{20 \, {\left(c x + 1\right)}^{2} b d^{2}}{{\left(c x - 1\right)}^{2}} - \frac{10 \, {\left(c x + 1\right)} b d^{2}}{c x - 1} + 2 \, b d^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{5} c^{4}}{{\left(c x - 1\right)}^{5}} - \frac{5 \, {\left(c x + 1\right)}^{4} c^{4}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3} c^{4}}{{\left(c x - 1\right)}^{3}} - \frac{10 \, {\left(c x + 1\right)}^{2} c^{4}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} c^{4}}{c x - 1} - c^{4}} + \frac{\frac{30 \, {\left(c x + 1\right)}^{4} a d^{2}}{{\left(c x - 1\right)}^{4}} - \frac{30 \, {\left(c x + 1\right)}^{3} a d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{40 \, {\left(c x + 1\right)}^{2} a d^{2}}{{\left(c x - 1\right)}^{2}} - \frac{20 \, {\left(c x + 1\right)} a d^{2}}{c x - 1} + 4 \, a d^{2} + \frac{13 \, {\left(c x + 1\right)}^{4} b d^{2}}{{\left(c x - 1\right)}^{4}} - \frac{36 \, {\left(c x + 1\right)}^{3} b d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{41 \, {\left(c x + 1\right)}^{2} b d^{2}}{{\left(c x - 1\right)}^{2}} - \frac{23 \, {\left(c x + 1\right)} b d^{2}}{c x - 1} + 5 \, b d^{2}}{\frac{{\left(c x + 1\right)}^{5} c^{4}}{{\left(c x - 1\right)}^{5}} - \frac{5 \, {\left(c x + 1\right)}^{4} c^{4}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3} c^{4}}{{\left(c x - 1\right)}^{3}} - \frac{10 \, {\left(c x + 1\right)}^{2} c^{4}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} c^{4}}{c x - 1} - c^{4}} - \frac{2 \, b d^{2} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{4}} + \frac{2 \, b d^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{4}}\right)}"," ",0,"4/15*c*((15*(c*x + 1)^4*b*d^2/(c*x - 1)^4 - 15*(c*x + 1)^3*b*d^2/(c*x - 1)^3 + 20*(c*x + 1)^2*b*d^2/(c*x - 1)^2 - 10*(c*x + 1)*b*d^2/(c*x - 1) + 2*b*d^2)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^5*c^4/(c*x - 1)^5 - 5*(c*x + 1)^4*c^4/(c*x - 1)^4 + 10*(c*x + 1)^3*c^4/(c*x - 1)^3 - 10*(c*x + 1)^2*c^4/(c*x - 1)^2 + 5*(c*x + 1)*c^4/(c*x - 1) - c^4) + (30*(c*x + 1)^4*a*d^2/(c*x - 1)^4 - 30*(c*x + 1)^3*a*d^2/(c*x - 1)^3 + 40*(c*x + 1)^2*a*d^2/(c*x - 1)^2 - 20*(c*x + 1)*a*d^2/(c*x - 1) + 4*a*d^2 + 13*(c*x + 1)^4*b*d^2/(c*x - 1)^4 - 36*(c*x + 1)^3*b*d^2/(c*x - 1)^3 + 41*(c*x + 1)^2*b*d^2/(c*x - 1)^2 - 23*(c*x + 1)*b*d^2/(c*x - 1) + 5*b*d^2)/((c*x + 1)^5*c^4/(c*x - 1)^5 - 5*(c*x + 1)^4*c^4/(c*x - 1)^4 + 10*(c*x + 1)^3*c^4/(c*x - 1)^3 - 10*(c*x + 1)^2*c^4/(c*x - 1)^2 + 5*(c*x + 1)*c^4/(c*x - 1) - c^4) - 2*b*d^2*log(-(c*x + 1)/(c*x - 1) + 1)/c^4 + 2*b*d^2*log(-(c*x + 1)/(c*x - 1))/c^4)","B",0
12,1,425,0,0.407944," ","integrate(x*(c*d*x+d)^2*(a+b*arctanh(c*x)),x, algorithm=""giac"")","-\frac{1}{3} \, c {\left(\frac{2 \, b d^{2} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{3}} - \frac{2 \, {\left(\frac{6 \, {\left(c x + 1\right)}^{3} b d^{2}}{{\left(c x - 1\right)}^{3}} - \frac{6 \, {\left(c x + 1\right)}^{2} b d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)} b d^{2}}{c x - 1} - b d^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{4} c^{3}}{{\left(c x - 1\right)}^{4}} - \frac{4 \, {\left(c x + 1\right)}^{3} c^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} c^{3}}{{\left(c x - 1\right)}^{2}} - \frac{4 \, {\left(c x + 1\right)} c^{3}}{c x - 1} + c^{3}} - \frac{2 \, b d^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{3}} - \frac{\frac{24 \, {\left(c x + 1\right)}^{3} a d^{2}}{{\left(c x - 1\right)}^{3}} - \frac{24 \, {\left(c x + 1\right)}^{2} a d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{16 \, {\left(c x + 1\right)} a d^{2}}{c x - 1} - 4 \, a d^{2} + \frac{10 \, {\left(c x + 1\right)}^{3} b d^{2}}{{\left(c x - 1\right)}^{3}} - \frac{23 \, {\left(c x + 1\right)}^{2} b d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{18 \, {\left(c x + 1\right)} b d^{2}}{c x - 1} - 5 \, b d^{2}}{\frac{{\left(c x + 1\right)}^{4} c^{3}}{{\left(c x - 1\right)}^{4}} - \frac{4 \, {\left(c x + 1\right)}^{3} c^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} c^{3}}{{\left(c x - 1\right)}^{2}} - \frac{4 \, {\left(c x + 1\right)} c^{3}}{c x - 1} + c^{3}}\right)}"," ",0,"-1/3*c*(2*b*d^2*log(-(c*x + 1)/(c*x - 1) + 1)/c^3 - 2*(6*(c*x + 1)^3*b*d^2/(c*x - 1)^3 - 6*(c*x + 1)^2*b*d^2/(c*x - 1)^2 + 4*(c*x + 1)*b*d^2/(c*x - 1) - b*d^2)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^4*c^3/(c*x - 1)^4 - 4*(c*x + 1)^3*c^3/(c*x - 1)^3 + 6*(c*x + 1)^2*c^3/(c*x - 1)^2 - 4*(c*x + 1)*c^3/(c*x - 1) + c^3) - 2*b*d^2*log(-(c*x + 1)/(c*x - 1))/c^3 - (24*(c*x + 1)^3*a*d^2/(c*x - 1)^3 - 24*(c*x + 1)^2*a*d^2/(c*x - 1)^2 + 16*(c*x + 1)*a*d^2/(c*x - 1) - 4*a*d^2 + 10*(c*x + 1)^3*b*d^2/(c*x - 1)^3 - 23*(c*x + 1)^2*b*d^2/(c*x - 1)^2 + 18*(c*x + 1)*b*d^2/(c*x - 1) - 5*b*d^2)/((c*x + 1)^4*c^3/(c*x - 1)^4 - 4*(c*x + 1)^3*c^3/(c*x - 1)^3 + 6*(c*x + 1)^2*c^3/(c*x - 1)^2 - 4*(c*x + 1)*c^3/(c*x - 1) + c^3))","B",0
13,1,330,0,0.202763," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x)),x, algorithm=""giac"")","-\frac{2}{3} \, {\left(\frac{2 \, b d^{2} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{2}} - \frac{2 \, b d^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{2}} - \frac{2 \, {\left(\frac{3 \, {\left(c x + 1\right)}^{2} b d^{2}}{{\left(c x - 1\right)}^{2}} - \frac{3 \, {\left(c x + 1\right)} b d^{2}}{c x - 1} + b d^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{3} c^{2}}{{\left(c x - 1\right)}^{3}} - \frac{3 \, {\left(c x + 1\right)}^{2} c^{2}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)} c^{2}}{c x - 1} - c^{2}} - \frac{\frac{12 \, {\left(c x + 1\right)}^{2} a d^{2}}{{\left(c x - 1\right)}^{2}} - \frac{12 \, {\left(c x + 1\right)} a d^{2}}{c x - 1} + 4 \, a d^{2} + \frac{4 \, {\left(c x + 1\right)}^{2} b d^{2}}{{\left(c x - 1\right)}^{2}} - \frac{7 \, {\left(c x + 1\right)} b d^{2}}{c x - 1} + 3 \, b d^{2}}{\frac{{\left(c x + 1\right)}^{3} c^{2}}{{\left(c x - 1\right)}^{3}} - \frac{3 \, {\left(c x + 1\right)}^{2} c^{2}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)} c^{2}}{c x - 1} - c^{2}}\right)} c"," ",0,"-2/3*(2*b*d^2*log(-(c*x + 1)/(c*x - 1) + 1)/c^2 - 2*b*d^2*log(-(c*x + 1)/(c*x - 1))/c^2 - 2*(3*(c*x + 1)^2*b*d^2/(c*x - 1)^2 - 3*(c*x + 1)*b*d^2/(c*x - 1) + b*d^2)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^3*c^2/(c*x - 1)^3 - 3*(c*x + 1)^2*c^2/(c*x - 1)^2 + 3*(c*x + 1)*c^2/(c*x - 1) - c^2) - (12*(c*x + 1)^2*a*d^2/(c*x - 1)^2 - 12*(c*x + 1)*a*d^2/(c*x - 1) + 4*a*d^2 + 4*(c*x + 1)^2*b*d^2/(c*x - 1)^2 - 7*(c*x + 1)*b*d^2/(c*x - 1) + 3*b*d^2)/((c*x + 1)^3*c^2/(c*x - 1)^3 - 3*(c*x + 1)^2*c^2/(c*x - 1)^2 + 3*(c*x + 1)*c^2/(c*x - 1) - c^2))*c","B",0
14,0,0,0,0.000000," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{2} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}}{x}\,{d x}"," ",0,"integrate((c*d*x + d)^2*(b*arctanh(c*x) + a)/x, x)","F",0
15,1,410,0,1.802173," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^2,x, algorithm=""giac"")","\frac{1}{6} \, {\left(\frac{6 \, a d^{2}}{\frac{{\left(c x + 1\right)} c^{2}}{c x - 1} + c^{2}} + \frac{5 \, b d^{2} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{2}} + \frac{3 \, b d^{2} \log\left(-\frac{c x + 1}{c x - 1} - 1\right)}{c^{2}} + {\left(\frac{3 \, b d^{2}}{\frac{{\left(c x + 1\right)} c^{2}}{c x - 1} + c^{2}} - \frac{\frac{3 \, {\left(c x + 1\right)}^{2} b d^{2}}{{\left(c x - 1\right)}^{2}} - \frac{12 \, {\left(c x + 1\right)} b d^{2}}{c x - 1} + 5 \, b d^{2}}{\frac{{\left(c x + 1\right)}^{3} c^{2}}{{\left(c x - 1\right)}^{3}} - \frac{3 \, {\left(c x + 1\right)}^{2} c^{2}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)} c^{2}}{c x - 1} - c^{2}}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right) - \frac{8 \, b d^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{2}} - \frac{2 \, {\left(\frac{3 \, {\left(c x + 1\right)}^{2} a d^{2}}{{\left(c x - 1\right)}^{2}} - \frac{12 \, {\left(c x + 1\right)} a d^{2}}{c x - 1} + 5 \, a d^{2} - \frac{{\left(c x + 1\right)}^{2} b d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{{\left(c x + 1\right)} b d^{2}}{c x - 1}\right)}}{\frac{{\left(c x + 1\right)}^{3} c^{2}}{{\left(c x - 1\right)}^{3}} - \frac{3 \, {\left(c x + 1\right)}^{2} c^{2}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)} c^{2}}{c x - 1} - c^{2}}\right)} c^{2}"," ",0,"1/6*(6*a*d^2/((c*x + 1)*c^2/(c*x - 1) + c^2) + 5*b*d^2*log(-(c*x + 1)/(c*x - 1) + 1)/c^2 + 3*b*d^2*log(-(c*x + 1)/(c*x - 1) - 1)/c^2 + (3*b*d^2/((c*x + 1)*c^2/(c*x - 1) + c^2) - (3*(c*x + 1)^2*b*d^2/(c*x - 1)^2 - 12*(c*x + 1)*b*d^2/(c*x - 1) + 5*b*d^2)/((c*x + 1)^3*c^2/(c*x - 1)^3 - 3*(c*x + 1)^2*c^2/(c*x - 1)^2 + 3*(c*x + 1)*c^2/(c*x - 1) - c^2))*log(-(c*x + 1)/(c*x - 1)) - 8*b*d^2*log(-(c*x + 1)/(c*x - 1))/c^2 - 2*(3*(c*x + 1)^2*a*d^2/(c*x - 1)^2 - 12*(c*x + 1)*a*d^2/(c*x - 1) + 5*a*d^2 - (c*x + 1)^2*b*d^2/(c*x - 1)^2 + (c*x + 1)*b*d^2/(c*x - 1))/((c*x + 1)^3*c^2/(c*x - 1)^3 - 3*(c*x + 1)^2*c^2/(c*x - 1)^2 + 3*(c*x + 1)*c^2/(c*x - 1) - c^2))*c^2","B",0
16,0,0,0,0.000000," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^3,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{2} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}}{x^{3}}\,{d x}"," ",0,"integrate((c*d*x + d)^2*(b*arctanh(c*x) + a)/x^3, x)","F",0
17,1,330,0,0.153331," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^4,x, algorithm=""giac"")","\frac{2}{3} \, {\left(2 \, b c^{2} d^{2} \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - 2 \, b c^{2} d^{2} \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{2 \, {\left(\frac{3 \, {\left(c x + 1\right)}^{2} b c^{2} d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)} b c^{2} d^{2}}{c x - 1} + b c^{2} d^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{3 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{\frac{12 \, {\left(c x + 1\right)}^{2} a c^{2} d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{12 \, {\left(c x + 1\right)} a c^{2} d^{2}}{c x - 1} + 4 \, a c^{2} d^{2} + \frac{4 \, {\left(c x + 1\right)}^{2} b c^{2} d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{7 \, {\left(c x + 1\right)} b c^{2} d^{2}}{c x - 1} + 3 \, b c^{2} d^{2}}{\frac{{\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{3 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"2/3*(2*b*c^2*d^2*log(-(c*x + 1)/(c*x - 1) - 1) - 2*b*c^2*d^2*log(-(c*x + 1)/(c*x - 1)) + 2*(3*(c*x + 1)^2*b*c^2*d^2/(c*x - 1)^2 + 3*(c*x + 1)*b*c^2*d^2/(c*x - 1) + b*c^2*d^2)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^3/(c*x - 1)^3 + 3*(c*x + 1)^2/(c*x - 1)^2 + 3*(c*x + 1)/(c*x - 1) + 1) + (12*(c*x + 1)^2*a*c^2*d^2/(c*x - 1)^2 + 12*(c*x + 1)*a*c^2*d^2/(c*x - 1) + 4*a*c^2*d^2 + 4*(c*x + 1)^2*b*c^2*d^2/(c*x - 1)^2 + 7*(c*x + 1)*b*c^2*d^2/(c*x - 1) + 3*b*c^2*d^2)/((c*x + 1)^3/(c*x - 1)^3 + 3*(c*x + 1)^2/(c*x - 1)^2 + 3*(c*x + 1)/(c*x - 1) + 1))*c","B",0
18,1,431,0,0.282193," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^5,x, algorithm=""giac"")","\frac{1}{3} \, {\left(2 \, b c^{3} d^{2} \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - 2 \, b c^{3} d^{2} \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{2 \, {\left(\frac{6 \, {\left(c x + 1\right)}^{3} b c^{3} d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} b c^{3} d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)} b c^{3} d^{2}}{c x - 1} + b c^{3} d^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{4 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{\frac{24 \, {\left(c x + 1\right)}^{3} a c^{3} d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{24 \, {\left(c x + 1\right)}^{2} a c^{3} d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{16 \, {\left(c x + 1\right)} a c^{3} d^{2}}{c x - 1} + 4 \, a c^{3} d^{2} + \frac{10 \, {\left(c x + 1\right)}^{3} b c^{3} d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{23 \, {\left(c x + 1\right)}^{2} b c^{3} d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{18 \, {\left(c x + 1\right)} b c^{3} d^{2}}{c x - 1} + 5 \, b c^{3} d^{2}}{\frac{{\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{4 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"1/3*(2*b*c^3*d^2*log(-(c*x + 1)/(c*x - 1) - 1) - 2*b*c^3*d^2*log(-(c*x + 1)/(c*x - 1)) + 2*(6*(c*x + 1)^3*b*c^3*d^2/(c*x - 1)^3 + 6*(c*x + 1)^2*b*c^3*d^2/(c*x - 1)^2 + 4*(c*x + 1)*b*c^3*d^2/(c*x - 1) + b*c^3*d^2)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^4/(c*x - 1)^4 + 4*(c*x + 1)^3/(c*x - 1)^3 + 6*(c*x + 1)^2/(c*x - 1)^2 + 4*(c*x + 1)/(c*x - 1) + 1) + (24*(c*x + 1)^3*a*c^3*d^2/(c*x - 1)^3 + 24*(c*x + 1)^2*a*c^3*d^2/(c*x - 1)^2 + 16*(c*x + 1)*a*c^3*d^2/(c*x - 1) + 4*a*c^3*d^2 + 10*(c*x + 1)^3*b*c^3*d^2/(c*x - 1)^3 + 23*(c*x + 1)^2*b*c^3*d^2/(c*x - 1)^2 + 18*(c*x + 1)*b*c^3*d^2/(c*x - 1) + 5*b*c^3*d^2)/((c*x + 1)^4/(c*x - 1)^4 + 4*(c*x + 1)^3/(c*x - 1)^3 + 6*(c*x + 1)^2/(c*x - 1)^2 + 4*(c*x + 1)/(c*x - 1) + 1))*c","B",0
19,1,532,0,0.270756," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^6,x, algorithm=""giac"")","\frac{4}{15} \, {\left(2 \, b c^{4} d^{2} \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - 2 \, b c^{4} d^{2} \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{{\left(\frac{15 \, {\left(c x + 1\right)}^{4} b c^{4} d^{2}}{{\left(c x - 1\right)}^{4}} + \frac{15 \, {\left(c x + 1\right)}^{3} b c^{4} d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{20 \, {\left(c x + 1\right)}^{2} b c^{4} d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{10 \, {\left(c x + 1\right)} b c^{4} d^{2}}{c x - 1} + 2 \, b c^{4} d^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{5}}{{\left(c x - 1\right)}^{5}} + \frac{5 \, {\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{10 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{\frac{30 \, {\left(c x + 1\right)}^{4} a c^{4} d^{2}}{{\left(c x - 1\right)}^{4}} + \frac{30 \, {\left(c x + 1\right)}^{3} a c^{4} d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{40 \, {\left(c x + 1\right)}^{2} a c^{4} d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{20 \, {\left(c x + 1\right)} a c^{4} d^{2}}{c x - 1} + 4 \, a c^{4} d^{2} + \frac{13 \, {\left(c x + 1\right)}^{4} b c^{4} d^{2}}{{\left(c x - 1\right)}^{4}} + \frac{36 \, {\left(c x + 1\right)}^{3} b c^{4} d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{41 \, {\left(c x + 1\right)}^{2} b c^{4} d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{23 \, {\left(c x + 1\right)} b c^{4} d^{2}}{c x - 1} + 5 \, b c^{4} d^{2}}{\frac{{\left(c x + 1\right)}^{5}}{{\left(c x - 1\right)}^{5}} + \frac{5 \, {\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{10 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"4/15*(2*b*c^4*d^2*log(-(c*x + 1)/(c*x - 1) - 1) - 2*b*c^4*d^2*log(-(c*x + 1)/(c*x - 1)) + (15*(c*x + 1)^4*b*c^4*d^2/(c*x - 1)^4 + 15*(c*x + 1)^3*b*c^4*d^2/(c*x - 1)^3 + 20*(c*x + 1)^2*b*c^4*d^2/(c*x - 1)^2 + 10*(c*x + 1)*b*c^4*d^2/(c*x - 1) + 2*b*c^4*d^2)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^5/(c*x - 1)^5 + 5*(c*x + 1)^4/(c*x - 1)^4 + 10*(c*x + 1)^3/(c*x - 1)^3 + 10*(c*x + 1)^2/(c*x - 1)^2 + 5*(c*x + 1)/(c*x - 1) + 1) + (30*(c*x + 1)^4*a*c^4*d^2/(c*x - 1)^4 + 30*(c*x + 1)^3*a*c^4*d^2/(c*x - 1)^3 + 40*(c*x + 1)^2*a*c^4*d^2/(c*x - 1)^2 + 20*(c*x + 1)*a*c^4*d^2/(c*x - 1) + 4*a*c^4*d^2 + 13*(c*x + 1)^4*b*c^4*d^2/(c*x - 1)^4 + 36*(c*x + 1)^3*b*c^4*d^2/(c*x - 1)^3 + 41*(c*x + 1)^2*b*c^4*d^2/(c*x - 1)^2 + 23*(c*x + 1)*b*c^4*d^2/(c*x - 1) + 5*b*c^4*d^2)/((c*x + 1)^5/(c*x - 1)^5 + 5*(c*x + 1)^4/(c*x - 1)^4 + 10*(c*x + 1)^3/(c*x - 1)^3 + 10*(c*x + 1)^2/(c*x - 1)^2 + 5*(c*x + 1)/(c*x - 1) + 1))*c","B",0
20,1,722,0,0.273850," ","integrate(x^3*(c*d*x+d)^3*(a+b*arctanh(c*x)),x, algorithm=""giac"")","\frac{1}{105} \, c {\left(\frac{6 \, {\left(\frac{140 \, {\left(c x + 1\right)}^{6} b d^{3}}{{\left(c x - 1\right)}^{6}} - \frac{210 \, {\left(c x + 1\right)}^{5} b d^{3}}{{\left(c x - 1\right)}^{5}} + \frac{490 \, {\left(c x + 1\right)}^{4} b d^{3}}{{\left(c x - 1\right)}^{4}} - \frac{455 \, {\left(c x + 1\right)}^{3} b d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{273 \, {\left(c x + 1\right)}^{2} b d^{3}}{{\left(c x - 1\right)}^{2}} - \frac{91 \, {\left(c x + 1\right)} b d^{3}}{c x - 1} + 13 \, b d^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{7} c^{5}}{{\left(c x - 1\right)}^{7}} - \frac{7 \, {\left(c x + 1\right)}^{6} c^{5}}{{\left(c x - 1\right)}^{6}} + \frac{21 \, {\left(c x + 1\right)}^{5} c^{5}}{{\left(c x - 1\right)}^{5}} - \frac{35 \, {\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} + \frac{35 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} - \frac{21 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} + \frac{7 \, {\left(c x + 1\right)} c^{5}}{c x - 1} - c^{5}} + \frac{\frac{1680 \, {\left(c x + 1\right)}^{6} a d^{3}}{{\left(c x - 1\right)}^{6}} - \frac{2520 \, {\left(c x + 1\right)}^{5} a d^{3}}{{\left(c x - 1\right)}^{5}} + \frac{5880 \, {\left(c x + 1\right)}^{4} a d^{3}}{{\left(c x - 1\right)}^{4}} - \frac{5460 \, {\left(c x + 1\right)}^{3} a d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{3276 \, {\left(c x + 1\right)}^{2} a d^{3}}{{\left(c x - 1\right)}^{2}} - \frac{1092 \, {\left(c x + 1\right)} a d^{3}}{c x - 1} + 156 \, a d^{3} + \frac{762 \, {\left(c x + 1\right)}^{6} b d^{3}}{{\left(c x - 1\right)}^{6}} - \frac{3063 \, {\left(c x + 1\right)}^{5} b d^{3}}{{\left(c x - 1\right)}^{5}} + \frac{5959 \, {\left(c x + 1\right)}^{4} b d^{3}}{{\left(c x - 1\right)}^{4}} - \frac{6694 \, {\left(c x + 1\right)}^{3} b d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{4344 \, {\left(c x + 1\right)}^{2} b d^{3}}{{\left(c x - 1\right)}^{2}} - \frac{1539 \, {\left(c x + 1\right)} b d^{3}}{c x - 1} + 231 \, b d^{3}}{\frac{{\left(c x + 1\right)}^{7} c^{5}}{{\left(c x - 1\right)}^{7}} - \frac{7 \, {\left(c x + 1\right)}^{6} c^{5}}{{\left(c x - 1\right)}^{6}} + \frac{21 \, {\left(c x + 1\right)}^{5} c^{5}}{{\left(c x - 1\right)}^{5}} - \frac{35 \, {\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} + \frac{35 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} - \frac{21 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} + \frac{7 \, {\left(c x + 1\right)} c^{5}}{c x - 1} - c^{5}} - \frac{78 \, b d^{3} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{5}} + \frac{78 \, b d^{3} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{5}}\right)}"," ",0,"1/105*c*(6*(140*(c*x + 1)^6*b*d^3/(c*x - 1)^6 - 210*(c*x + 1)^5*b*d^3/(c*x - 1)^5 + 490*(c*x + 1)^4*b*d^3/(c*x - 1)^4 - 455*(c*x + 1)^3*b*d^3/(c*x - 1)^3 + 273*(c*x + 1)^2*b*d^3/(c*x - 1)^2 - 91*(c*x + 1)*b*d^3/(c*x - 1) + 13*b*d^3)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^7*c^5/(c*x - 1)^7 - 7*(c*x + 1)^6*c^5/(c*x - 1)^6 + 21*(c*x + 1)^5*c^5/(c*x - 1)^5 - 35*(c*x + 1)^4*c^5/(c*x - 1)^4 + 35*(c*x + 1)^3*c^5/(c*x - 1)^3 - 21*(c*x + 1)^2*c^5/(c*x - 1)^2 + 7*(c*x + 1)*c^5/(c*x - 1) - c^5) + (1680*(c*x + 1)^6*a*d^3/(c*x - 1)^6 - 2520*(c*x + 1)^5*a*d^3/(c*x - 1)^5 + 5880*(c*x + 1)^4*a*d^3/(c*x - 1)^4 - 5460*(c*x + 1)^3*a*d^3/(c*x - 1)^3 + 3276*(c*x + 1)^2*a*d^3/(c*x - 1)^2 - 1092*(c*x + 1)*a*d^3/(c*x - 1) + 156*a*d^3 + 762*(c*x + 1)^6*b*d^3/(c*x - 1)^6 - 3063*(c*x + 1)^5*b*d^3/(c*x - 1)^5 + 5959*(c*x + 1)^4*b*d^3/(c*x - 1)^4 - 6694*(c*x + 1)^3*b*d^3/(c*x - 1)^3 + 4344*(c*x + 1)^2*b*d^3/(c*x - 1)^2 - 1539*(c*x + 1)*b*d^3/(c*x - 1) + 231*b*d^3)/((c*x + 1)^7*c^5/(c*x - 1)^7 - 7*(c*x + 1)^6*c^5/(c*x - 1)^6 + 21*(c*x + 1)^5*c^5/(c*x - 1)^5 - 35*(c*x + 1)^4*c^5/(c*x - 1)^4 + 35*(c*x + 1)^3*c^5/(c*x - 1)^3 - 21*(c*x + 1)^2*c^5/(c*x - 1)^2 + 7*(c*x + 1)*c^5/(c*x - 1) - c^5) - 78*b*d^3*log(-(c*x + 1)/(c*x - 1) + 1)/c^5 + 78*b*d^3*log(-(c*x + 1)/(c*x - 1))/c^5)","B",0
21,1,621,0,0.231038," ","integrate(x^2*(c*d*x+d)^3*(a+b*arctanh(c*x)),x, algorithm=""giac"")","-\frac{1}{45} \, c {\left(\frac{42 \, b d^{3} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{4}} - \frac{6 \, {\left(\frac{60 \, {\left(c x + 1\right)}^{5} b d^{3}}{{\left(c x - 1\right)}^{5}} - \frac{90 \, {\left(c x + 1\right)}^{4} b d^{3}}{{\left(c x - 1\right)}^{4}} + \frac{140 \, {\left(c x + 1\right)}^{3} b d^{3}}{{\left(c x - 1\right)}^{3}} - \frac{105 \, {\left(c x + 1\right)}^{2} b d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{42 \, {\left(c x + 1\right)} b d^{3}}{c x - 1} - 7 \, b d^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{6} c^{4}}{{\left(c x - 1\right)}^{6}} - \frac{6 \, {\left(c x + 1\right)}^{5} c^{4}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4} c^{4}}{{\left(c x - 1\right)}^{4}} - \frac{20 \, {\left(c x + 1\right)}^{3} c^{4}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} c^{4}}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} c^{4}}{c x - 1} + c^{4}} - \frac{42 \, b d^{3} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{4}} - \frac{\frac{720 \, {\left(c x + 1\right)}^{5} a d^{3}}{{\left(c x - 1\right)}^{5}} - \frac{1080 \, {\left(c x + 1\right)}^{4} a d^{3}}{{\left(c x - 1\right)}^{4}} + \frac{1680 \, {\left(c x + 1\right)}^{3} a d^{3}}{{\left(c x - 1\right)}^{3}} - \frac{1260 \, {\left(c x + 1\right)}^{2} a d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{504 \, {\left(c x + 1\right)} a d^{3}}{c x - 1} - 84 \, a d^{3} + \frac{318 \, {\left(c x + 1\right)}^{5} b d^{3}}{{\left(c x - 1\right)}^{5}} - \frac{1119 \, {\left(c x + 1\right)}^{4} b d^{3}}{{\left(c x - 1\right)}^{4}} + \frac{1742 \, {\left(c x + 1\right)}^{3} b d^{3}}{{\left(c x - 1\right)}^{3}} - \frac{1464 \, {\left(c x + 1\right)}^{2} b d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{636 \, {\left(c x + 1\right)} b d^{3}}{c x - 1} - 113 \, b d^{3}}{\frac{{\left(c x + 1\right)}^{6} c^{4}}{{\left(c x - 1\right)}^{6}} - \frac{6 \, {\left(c x + 1\right)}^{5} c^{4}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4} c^{4}}{{\left(c x - 1\right)}^{4}} - \frac{20 \, {\left(c x + 1\right)}^{3} c^{4}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} c^{4}}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} c^{4}}{c x - 1} + c^{4}}\right)}"," ",0,"-1/45*c*(42*b*d^3*log(-(c*x + 1)/(c*x - 1) + 1)/c^4 - 6*(60*(c*x + 1)^5*b*d^3/(c*x - 1)^5 - 90*(c*x + 1)^4*b*d^3/(c*x - 1)^4 + 140*(c*x + 1)^3*b*d^3/(c*x - 1)^3 - 105*(c*x + 1)^2*b*d^3/(c*x - 1)^2 + 42*(c*x + 1)*b*d^3/(c*x - 1) - 7*b*d^3)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^6*c^4/(c*x - 1)^6 - 6*(c*x + 1)^5*c^4/(c*x - 1)^5 + 15*(c*x + 1)^4*c^4/(c*x - 1)^4 - 20*(c*x + 1)^3*c^4/(c*x - 1)^3 + 15*(c*x + 1)^2*c^4/(c*x - 1)^2 - 6*(c*x + 1)*c^4/(c*x - 1) + c^4) - 42*b*d^3*log(-(c*x + 1)/(c*x - 1))/c^4 - (720*(c*x + 1)^5*a*d^3/(c*x - 1)^5 - 1080*(c*x + 1)^4*a*d^3/(c*x - 1)^4 + 1680*(c*x + 1)^3*a*d^3/(c*x - 1)^3 - 1260*(c*x + 1)^2*a*d^3/(c*x - 1)^2 + 504*(c*x + 1)*a*d^3/(c*x - 1) - 84*a*d^3 + 318*(c*x + 1)^5*b*d^3/(c*x - 1)^5 - 1119*(c*x + 1)^4*b*d^3/(c*x - 1)^4 + 1742*(c*x + 1)^3*b*d^3/(c*x - 1)^3 - 1464*(c*x + 1)^2*b*d^3/(c*x - 1)^2 + 636*(c*x + 1)*b*d^3/(c*x - 1) - 113*b*d^3)/((c*x + 1)^6*c^4/(c*x - 1)^6 - 6*(c*x + 1)^5*c^4/(c*x - 1)^5 + 15*(c*x + 1)^4*c^4/(c*x - 1)^4 - 20*(c*x + 1)^3*c^4/(c*x - 1)^3 + 15*(c*x + 1)^2*c^4/(c*x - 1)^2 - 6*(c*x + 1)*c^4/(c*x - 1) + c^4))","B",0
22,1,527,0,0.518415," ","integrate(x*(c*d*x+d)^3*(a+b*arctanh(c*x)),x, algorithm=""giac"")","-\frac{1}{5} \, {\left(\frac{6 \, b d^{3} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{3}} - \frac{6 \, b d^{3} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{3}} - \frac{2 \, {\left(\frac{20 \, {\left(c x + 1\right)}^{4} b d^{3}}{{\left(c x - 1\right)}^{4}} - \frac{30 \, {\left(c x + 1\right)}^{3} b d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{30 \, {\left(c x + 1\right)}^{2} b d^{3}}{{\left(c x - 1\right)}^{2}} - \frac{15 \, {\left(c x + 1\right)} b d^{3}}{c x - 1} + 3 \, b d^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{5} c^{3}}{{\left(c x - 1\right)}^{5}} - \frac{5 \, {\left(c x + 1\right)}^{4} c^{3}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3} c^{3}}{{\left(c x - 1\right)}^{3}} - \frac{10 \, {\left(c x + 1\right)}^{2} c^{3}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} c^{3}}{c x - 1} - c^{3}} - \frac{\frac{80 \, {\left(c x + 1\right)}^{4} a d^{3}}{{\left(c x - 1\right)}^{4}} - \frac{120 \, {\left(c x + 1\right)}^{3} a d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{120 \, {\left(c x + 1\right)}^{2} a d^{3}}{{\left(c x - 1\right)}^{2}} - \frac{60 \, {\left(c x + 1\right)} a d^{3}}{c x - 1} + 12 \, a d^{3} + \frac{34 \, {\left(c x + 1\right)}^{4} b d^{3}}{{\left(c x - 1\right)}^{4}} - \frac{103 \, {\left(c x + 1\right)}^{3} b d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{123 \, {\left(c x + 1\right)}^{2} b d^{3}}{{\left(c x - 1\right)}^{2}} - \frac{69 \, {\left(c x + 1\right)} b d^{3}}{c x - 1} + 15 \, b d^{3}}{\frac{{\left(c x + 1\right)}^{5} c^{3}}{{\left(c x - 1\right)}^{5}} - \frac{5 \, {\left(c x + 1\right)}^{4} c^{3}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3} c^{3}}{{\left(c x - 1\right)}^{3}} - \frac{10 \, {\left(c x + 1\right)}^{2} c^{3}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} c^{3}}{c x - 1} - c^{3}}\right)} c"," ",0,"-1/5*(6*b*d^3*log(-(c*x + 1)/(c*x - 1) + 1)/c^3 - 6*b*d^3*log(-(c*x + 1)/(c*x - 1))/c^3 - 2*(20*(c*x + 1)^4*b*d^3/(c*x - 1)^4 - 30*(c*x + 1)^3*b*d^3/(c*x - 1)^3 + 30*(c*x + 1)^2*b*d^3/(c*x - 1)^2 - 15*(c*x + 1)*b*d^3/(c*x - 1) + 3*b*d^3)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^5*c^3/(c*x - 1)^5 - 5*(c*x + 1)^4*c^3/(c*x - 1)^4 + 10*(c*x + 1)^3*c^3/(c*x - 1)^3 - 10*(c*x + 1)^2*c^3/(c*x - 1)^2 + 5*(c*x + 1)*c^3/(c*x - 1) - c^3) - (80*(c*x + 1)^4*a*d^3/(c*x - 1)^4 - 120*(c*x + 1)^3*a*d^3/(c*x - 1)^3 + 120*(c*x + 1)^2*a*d^3/(c*x - 1)^2 - 60*(c*x + 1)*a*d^3/(c*x - 1) + 12*a*d^3 + 34*(c*x + 1)^4*b*d^3/(c*x - 1)^4 - 103*(c*x + 1)^3*b*d^3/(c*x - 1)^3 + 123*(c*x + 1)^2*b*d^3/(c*x - 1)^2 - 69*(c*x + 1)*b*d^3/(c*x - 1) + 15*b*d^3)/((c*x + 1)^5*c^3/(c*x - 1)^5 - 5*(c*x + 1)^4*c^3/(c*x - 1)^4 + 10*(c*x + 1)^3*c^3/(c*x - 1)^3 - 10*(c*x + 1)^2*c^3/(c*x - 1)^2 + 5*(c*x + 1)*c^3/(c*x - 1) - c^3))*c","B",0
23,1,425,0,0.216650," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x)),x, algorithm=""giac"")","-\frac{1}{3} \, {\left(\frac{6 \, b d^{3} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{2}} - \frac{6 \, b d^{3} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{2}} - \frac{6 \, {\left(\frac{4 \, {\left(c x + 1\right)}^{3} b d^{3}}{{\left(c x - 1\right)}^{3}} - \frac{6 \, {\left(c x + 1\right)}^{2} b d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)} b d^{3}}{c x - 1} - b d^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{4} c^{2}}{{\left(c x - 1\right)}^{4}} - \frac{4 \, {\left(c x + 1\right)}^{3} c^{2}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} c^{2}}{{\left(c x - 1\right)}^{2}} - \frac{4 \, {\left(c x + 1\right)} c^{2}}{c x - 1} + c^{2}} - \frac{\frac{48 \, {\left(c x + 1\right)}^{3} a d^{3}}{{\left(c x - 1\right)}^{3}} - \frac{72 \, {\left(c x + 1\right)}^{2} a d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{48 \, {\left(c x + 1\right)} a d^{3}}{c x - 1} - 12 \, a d^{3} + \frac{18 \, {\left(c x + 1\right)}^{3} b d^{3}}{{\left(c x - 1\right)}^{3}} - \frac{45 \, {\left(c x + 1\right)}^{2} b d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{38 \, {\left(c x + 1\right)} b d^{3}}{c x - 1} - 11 \, b d^{3}}{\frac{{\left(c x + 1\right)}^{4} c^{2}}{{\left(c x - 1\right)}^{4}} - \frac{4 \, {\left(c x + 1\right)}^{3} c^{2}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} c^{2}}{{\left(c x - 1\right)}^{2}} - \frac{4 \, {\left(c x + 1\right)} c^{2}}{c x - 1} + c^{2}}\right)} c"," ",0,"-1/3*(6*b*d^3*log(-(c*x + 1)/(c*x - 1) + 1)/c^2 - 6*b*d^3*log(-(c*x + 1)/(c*x - 1))/c^2 - 6*(4*(c*x + 1)^3*b*d^3/(c*x - 1)^3 - 6*(c*x + 1)^2*b*d^3/(c*x - 1)^2 + 4*(c*x + 1)*b*d^3/(c*x - 1) - b*d^3)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^4*c^2/(c*x - 1)^4 - 4*(c*x + 1)^3*c^2/(c*x - 1)^3 + 6*(c*x + 1)^2*c^2/(c*x - 1)^2 - 4*(c*x + 1)*c^2/(c*x - 1) + c^2) - (48*(c*x + 1)^3*a*d^3/(c*x - 1)^3 - 72*(c*x + 1)^2*a*d^3/(c*x - 1)^2 + 48*(c*x + 1)*a*d^3/(c*x - 1) - 12*a*d^3 + 18*(c*x + 1)^3*b*d^3/(c*x - 1)^3 - 45*(c*x + 1)^2*b*d^3/(c*x - 1)^2 + 38*(c*x + 1)*b*d^3/(c*x - 1) - 11*b*d^3)/((c*x + 1)^4*c^2/(c*x - 1)^4 - 4*(c*x + 1)^3*c^2/(c*x - 1)^3 + 6*(c*x + 1)^2*c^2/(c*x - 1)^2 - 4*(c*x + 1)*c^2/(c*x - 1) + c^2))*c","B",0
24,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}}{x}\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)/x, x)","F",0
25,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^2,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}}{x^{2}}\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)/x^2, x)","F",0
26,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^3,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}}{x^{3}}\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)/x^3, x)","F",0
27,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^4,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}}{x^{4}}\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)/x^4, x)","F",0
28,1,431,0,0.243922," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^5,x, algorithm=""giac"")","\frac{1}{3} \, {\left(6 \, b c^{3} d^{3} \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - 6 \, b c^{3} d^{3} \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{6 \, {\left(\frac{4 \, {\left(c x + 1\right)}^{3} b c^{3} d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} b c^{3} d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)} b c^{3} d^{3}}{c x - 1} + b c^{3} d^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{4 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{\frac{48 \, {\left(c x + 1\right)}^{3} a c^{3} d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{72 \, {\left(c x + 1\right)}^{2} a c^{3} d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{48 \, {\left(c x + 1\right)} a c^{3} d^{3}}{c x - 1} + 12 \, a c^{3} d^{3} + \frac{18 \, {\left(c x + 1\right)}^{3} b c^{3} d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{45 \, {\left(c x + 1\right)}^{2} b c^{3} d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{38 \, {\left(c x + 1\right)} b c^{3} d^{3}}{c x - 1} + 11 \, b c^{3} d^{3}}{\frac{{\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{4 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"1/3*(6*b*c^3*d^3*log(-(c*x + 1)/(c*x - 1) - 1) - 6*b*c^3*d^3*log(-(c*x + 1)/(c*x - 1)) + 6*(4*(c*x + 1)^3*b*c^3*d^3/(c*x - 1)^3 + 6*(c*x + 1)^2*b*c^3*d^3/(c*x - 1)^2 + 4*(c*x + 1)*b*c^3*d^3/(c*x - 1) + b*c^3*d^3)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^4/(c*x - 1)^4 + 4*(c*x + 1)^3/(c*x - 1)^3 + 6*(c*x + 1)^2/(c*x - 1)^2 + 4*(c*x + 1)/(c*x - 1) + 1) + (48*(c*x + 1)^3*a*c^3*d^3/(c*x - 1)^3 + 72*(c*x + 1)^2*a*c^3*d^3/(c*x - 1)^2 + 48*(c*x + 1)*a*c^3*d^3/(c*x - 1) + 12*a*c^3*d^3 + 18*(c*x + 1)^3*b*c^3*d^3/(c*x - 1)^3 + 45*(c*x + 1)^2*b*c^3*d^3/(c*x - 1)^2 + 38*(c*x + 1)*b*c^3*d^3/(c*x - 1) + 11*b*c^3*d^3)/((c*x + 1)^4/(c*x - 1)^4 + 4*(c*x + 1)^3/(c*x - 1)^3 + 6*(c*x + 1)^2/(c*x - 1)^2 + 4*(c*x + 1)/(c*x - 1) + 1))*c","B",0
29,1,533,0,0.200430," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^6,x, algorithm=""giac"")","\frac{1}{5} \, {\left(6 \, b c^{4} d^{3} \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - 6 \, b c^{4} d^{3} \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{2 \, {\left(\frac{20 \, {\left(c x + 1\right)}^{4} b c^{4} d^{3}}{{\left(c x - 1\right)}^{4}} + \frac{30 \, {\left(c x + 1\right)}^{3} b c^{4} d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{30 \, {\left(c x + 1\right)}^{2} b c^{4} d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{15 \, {\left(c x + 1\right)} b c^{4} d^{3}}{c x - 1} + 3 \, b c^{4} d^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{5}}{{\left(c x - 1\right)}^{5}} + \frac{5 \, {\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{10 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{\frac{80 \, {\left(c x + 1\right)}^{4} a c^{4} d^{3}}{{\left(c x - 1\right)}^{4}} + \frac{120 \, {\left(c x + 1\right)}^{3} a c^{4} d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{120 \, {\left(c x + 1\right)}^{2} a c^{4} d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{60 \, {\left(c x + 1\right)} a c^{4} d^{3}}{c x - 1} + 12 \, a c^{4} d^{3} + \frac{34 \, {\left(c x + 1\right)}^{4} b c^{4} d^{3}}{{\left(c x - 1\right)}^{4}} + \frac{103 \, {\left(c x + 1\right)}^{3} b c^{4} d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{123 \, {\left(c x + 1\right)}^{2} b c^{4} d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{69 \, {\left(c x + 1\right)} b c^{4} d^{3}}{c x - 1} + 15 \, b c^{4} d^{3}}{\frac{{\left(c x + 1\right)}^{5}}{{\left(c x - 1\right)}^{5}} + \frac{5 \, {\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{10 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"1/5*(6*b*c^4*d^3*log(-(c*x + 1)/(c*x - 1) - 1) - 6*b*c^4*d^3*log(-(c*x + 1)/(c*x - 1)) + 2*(20*(c*x + 1)^4*b*c^4*d^3/(c*x - 1)^4 + 30*(c*x + 1)^3*b*c^4*d^3/(c*x - 1)^3 + 30*(c*x + 1)^2*b*c^4*d^3/(c*x - 1)^2 + 15*(c*x + 1)*b*c^4*d^3/(c*x - 1) + 3*b*c^4*d^3)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^5/(c*x - 1)^5 + 5*(c*x + 1)^4/(c*x - 1)^4 + 10*(c*x + 1)^3/(c*x - 1)^3 + 10*(c*x + 1)^2/(c*x - 1)^2 + 5*(c*x + 1)/(c*x - 1) + 1) + (80*(c*x + 1)^4*a*c^4*d^3/(c*x - 1)^4 + 120*(c*x + 1)^3*a*c^4*d^3/(c*x - 1)^3 + 120*(c*x + 1)^2*a*c^4*d^3/(c*x - 1)^2 + 60*(c*x + 1)*a*c^4*d^3/(c*x - 1) + 12*a*c^4*d^3 + 34*(c*x + 1)^4*b*c^4*d^3/(c*x - 1)^4 + 103*(c*x + 1)^3*b*c^4*d^3/(c*x - 1)^3 + 123*(c*x + 1)^2*b*c^4*d^3/(c*x - 1)^2 + 69*(c*x + 1)*b*c^4*d^3/(c*x - 1) + 15*b*c^4*d^3)/((c*x + 1)^5/(c*x - 1)^5 + 5*(c*x + 1)^4/(c*x - 1)^4 + 10*(c*x + 1)^3/(c*x - 1)^3 + 10*(c*x + 1)^2/(c*x - 1)^2 + 5*(c*x + 1)/(c*x - 1) + 1))*c","B",0
30,1,634,0,0.164415," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^7,x, algorithm=""giac"")","\frac{1}{45} \, {\left(42 \, b c^{5} d^{3} \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - 42 \, b c^{5} d^{3} \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{6 \, {\left(\frac{60 \, {\left(c x + 1\right)}^{5} b c^{5} d^{3}}{{\left(c x - 1\right)}^{5}} + \frac{90 \, {\left(c x + 1\right)}^{4} b c^{5} d^{3}}{{\left(c x - 1\right)}^{4}} + \frac{140 \, {\left(c x + 1\right)}^{3} b c^{5} d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{105 \, {\left(c x + 1\right)}^{2} b c^{5} d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{42 \, {\left(c x + 1\right)} b c^{5} d^{3}}{c x - 1} + 7 \, b c^{5} d^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{6}}{{\left(c x - 1\right)}^{6}} + \frac{6 \, {\left(c x + 1\right)}^{5}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{20 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{6 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{\frac{720 \, {\left(c x + 1\right)}^{5} a c^{5} d^{3}}{{\left(c x - 1\right)}^{5}} + \frac{1080 \, {\left(c x + 1\right)}^{4} a c^{5} d^{3}}{{\left(c x - 1\right)}^{4}} + \frac{1680 \, {\left(c x + 1\right)}^{3} a c^{5} d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{1260 \, {\left(c x + 1\right)}^{2} a c^{5} d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{504 \, {\left(c x + 1\right)} a c^{5} d^{3}}{c x - 1} + 84 \, a c^{5} d^{3} + \frac{318 \, {\left(c x + 1\right)}^{5} b c^{5} d^{3}}{{\left(c x - 1\right)}^{5}} + \frac{1119 \, {\left(c x + 1\right)}^{4} b c^{5} d^{3}}{{\left(c x - 1\right)}^{4}} + \frac{1742 \, {\left(c x + 1\right)}^{3} b c^{5} d^{3}}{{\left(c x - 1\right)}^{3}} + \frac{1464 \, {\left(c x + 1\right)}^{2} b c^{5} d^{3}}{{\left(c x - 1\right)}^{2}} + \frac{636 \, {\left(c x + 1\right)} b c^{5} d^{3}}{c x - 1} + 113 \, b c^{5} d^{3}}{\frac{{\left(c x + 1\right)}^{6}}{{\left(c x - 1\right)}^{6}} + \frac{6 \, {\left(c x + 1\right)}^{5}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{20 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{6 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"1/45*(42*b*c^5*d^3*log(-(c*x + 1)/(c*x - 1) - 1) - 42*b*c^5*d^3*log(-(c*x + 1)/(c*x - 1)) + 6*(60*(c*x + 1)^5*b*c^5*d^3/(c*x - 1)^5 + 90*(c*x + 1)^4*b*c^5*d^3/(c*x - 1)^4 + 140*(c*x + 1)^3*b*c^5*d^3/(c*x - 1)^3 + 105*(c*x + 1)^2*b*c^5*d^3/(c*x - 1)^2 + 42*(c*x + 1)*b*c^5*d^3/(c*x - 1) + 7*b*c^5*d^3)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^6/(c*x - 1)^6 + 6*(c*x + 1)^5/(c*x - 1)^5 + 15*(c*x + 1)^4/(c*x - 1)^4 + 20*(c*x + 1)^3/(c*x - 1)^3 + 15*(c*x + 1)^2/(c*x - 1)^2 + 6*(c*x + 1)/(c*x - 1) + 1) + (720*(c*x + 1)^5*a*c^5*d^3/(c*x - 1)^5 + 1080*(c*x + 1)^4*a*c^5*d^3/(c*x - 1)^4 + 1680*(c*x + 1)^3*a*c^5*d^3/(c*x - 1)^3 + 1260*(c*x + 1)^2*a*c^5*d^3/(c*x - 1)^2 + 504*(c*x + 1)*a*c^5*d^3/(c*x - 1) + 84*a*c^5*d^3 + 318*(c*x + 1)^5*b*c^5*d^3/(c*x - 1)^5 + 1119*(c*x + 1)^4*b*c^5*d^3/(c*x - 1)^4 + 1742*(c*x + 1)^3*b*c^5*d^3/(c*x - 1)^3 + 1464*(c*x + 1)^2*b*c^5*d^3/(c*x - 1)^2 + 636*(c*x + 1)*b*c^5*d^3/(c*x - 1) + 113*b*c^5*d^3)/((c*x + 1)^6/(c*x - 1)^6 + 6*(c*x + 1)^5/(c*x - 1)^5 + 15*(c*x + 1)^4/(c*x - 1)^4 + 20*(c*x + 1)^3/(c*x - 1)^3 + 15*(c*x + 1)^2/(c*x - 1)^2 + 6*(c*x + 1)/(c*x - 1) + 1))*c","B",0
31,1,817,0,0.343121," ","integrate(x^3*(c*d*x+d)^4*(a+b*arctanh(c*x)),x, algorithm=""giac"")","-\frac{4}{105} \, c {\left(\frac{36 \, b d^{4} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{5}} - \frac{12 \, {\left(\frac{35 \, {\left(c x + 1\right)}^{7} b d^{4}}{{\left(c x - 1\right)}^{7}} - \frac{70 \, {\left(c x + 1\right)}^{6} b d^{4}}{{\left(c x - 1\right)}^{6}} + \frac{175 \, {\left(c x + 1\right)}^{5} b d^{4}}{{\left(c x - 1\right)}^{5}} - \frac{210 \, {\left(c x + 1\right)}^{4} b d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{168 \, {\left(c x + 1\right)}^{3} b d^{4}}{{\left(c x - 1\right)}^{3}} - \frac{84 \, {\left(c x + 1\right)}^{2} b d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{24 \, {\left(c x + 1\right)} b d^{4}}{c x - 1} - 3 \, b d^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{8} c^{5}}{{\left(c x - 1\right)}^{8}} - \frac{8 \, {\left(c x + 1\right)}^{7} c^{5}}{{\left(c x - 1\right)}^{7}} + \frac{28 \, {\left(c x + 1\right)}^{6} c^{5}}{{\left(c x - 1\right)}^{6}} - \frac{56 \, {\left(c x + 1\right)}^{5} c^{5}}{{\left(c x - 1\right)}^{5}} + \frac{70 \, {\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} - \frac{56 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} + \frac{28 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} - \frac{8 \, {\left(c x + 1\right)} c^{5}}{c x - 1} + c^{5}} - \frac{36 \, b d^{4} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{5}} - \frac{\frac{840 \, {\left(c x + 1\right)}^{7} a d^{4}}{{\left(c x - 1\right)}^{7}} - \frac{1680 \, {\left(c x + 1\right)}^{6} a d^{4}}{{\left(c x - 1\right)}^{6}} + \frac{4200 \, {\left(c x + 1\right)}^{5} a d^{4}}{{\left(c x - 1\right)}^{5}} - \frac{5040 \, {\left(c x + 1\right)}^{4} a d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{4032 \, {\left(c x + 1\right)}^{3} a d^{4}}{{\left(c x - 1\right)}^{3}} - \frac{2016 \, {\left(c x + 1\right)}^{2} a d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{576 \, {\left(c x + 1\right)} a d^{4}}{c x - 1} - 72 \, a d^{4} + \frac{384 \, {\left(c x + 1\right)}^{7} b d^{4}}{{\left(c x - 1\right)}^{7}} - \frac{1830 \, {\left(c x + 1\right)}^{6} b d^{4}}{{\left(c x - 1\right)}^{6}} + \frac{4304 \, {\left(c x + 1\right)}^{5} b d^{4}}{{\left(c x - 1\right)}^{5}} - \frac{6031 \, {\left(c x + 1\right)}^{4} b d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{5228 \, {\left(c x + 1\right)}^{3} b d^{4}}{{\left(c x - 1\right)}^{3}} - \frac{2782 \, {\left(c x + 1\right)}^{2} b d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{836 \, {\left(c x + 1\right)} b d^{4}}{c x - 1} - 109 \, b d^{4}}{\frac{{\left(c x + 1\right)}^{8} c^{5}}{{\left(c x - 1\right)}^{8}} - \frac{8 \, {\left(c x + 1\right)}^{7} c^{5}}{{\left(c x - 1\right)}^{7}} + \frac{28 \, {\left(c x + 1\right)}^{6} c^{5}}{{\left(c x - 1\right)}^{6}} - \frac{56 \, {\left(c x + 1\right)}^{5} c^{5}}{{\left(c x - 1\right)}^{5}} + \frac{70 \, {\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} - \frac{56 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} + \frac{28 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} - \frac{8 \, {\left(c x + 1\right)} c^{5}}{c x - 1} + c^{5}}\right)}"," ",0,"-4/105*c*(36*b*d^4*log(-(c*x + 1)/(c*x - 1) + 1)/c^5 - 12*(35*(c*x + 1)^7*b*d^4/(c*x - 1)^7 - 70*(c*x + 1)^6*b*d^4/(c*x - 1)^6 + 175*(c*x + 1)^5*b*d^4/(c*x - 1)^5 - 210*(c*x + 1)^4*b*d^4/(c*x - 1)^4 + 168*(c*x + 1)^3*b*d^4/(c*x - 1)^3 - 84*(c*x + 1)^2*b*d^4/(c*x - 1)^2 + 24*(c*x + 1)*b*d^4/(c*x - 1) - 3*b*d^4)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^8*c^5/(c*x - 1)^8 - 8*(c*x + 1)^7*c^5/(c*x - 1)^7 + 28*(c*x + 1)^6*c^5/(c*x - 1)^6 - 56*(c*x + 1)^5*c^5/(c*x - 1)^5 + 70*(c*x + 1)^4*c^5/(c*x - 1)^4 - 56*(c*x + 1)^3*c^5/(c*x - 1)^3 + 28*(c*x + 1)^2*c^5/(c*x - 1)^2 - 8*(c*x + 1)*c^5/(c*x - 1) + c^5) - 36*b*d^4*log(-(c*x + 1)/(c*x - 1))/c^5 - (840*(c*x + 1)^7*a*d^4/(c*x - 1)^7 - 1680*(c*x + 1)^6*a*d^4/(c*x - 1)^6 + 4200*(c*x + 1)^5*a*d^4/(c*x - 1)^5 - 5040*(c*x + 1)^4*a*d^4/(c*x - 1)^4 + 4032*(c*x + 1)^3*a*d^4/(c*x - 1)^3 - 2016*(c*x + 1)^2*a*d^4/(c*x - 1)^2 + 576*(c*x + 1)*a*d^4/(c*x - 1) - 72*a*d^4 + 384*(c*x + 1)^7*b*d^4/(c*x - 1)^7 - 1830*(c*x + 1)^6*b*d^4/(c*x - 1)^6 + 4304*(c*x + 1)^5*b*d^4/(c*x - 1)^5 - 6031*(c*x + 1)^4*b*d^4/(c*x - 1)^4 + 5228*(c*x + 1)^3*b*d^4/(c*x - 1)^3 - 2782*(c*x + 1)^2*b*d^4/(c*x - 1)^2 + 836*(c*x + 1)*b*d^4/(c*x - 1) - 109*b*d^4)/((c*x + 1)^8*c^5/(c*x - 1)^8 - 8*(c*x + 1)^7*c^5/(c*x - 1)^7 + 28*(c*x + 1)^6*c^5/(c*x - 1)^6 - 56*(c*x + 1)^5*c^5/(c*x - 1)^5 + 70*(c*x + 1)^4*c^5/(c*x - 1)^4 - 56*(c*x + 1)^3*c^5/(c*x - 1)^3 + 28*(c*x + 1)^2*c^5/(c*x - 1)^2 - 8*(c*x + 1)*c^5/(c*x - 1) + c^5))","B",0
32,1,723,0,0.188044," ","integrate(x^2*(c*d*x+d)^4*(a+b*arctanh(c*x)),x, algorithm=""giac"")","-\frac{4}{315} \, {\left(\frac{132 \, b d^{4} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{4}} - \frac{132 \, b d^{4} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{4}} - \frac{12 \, {\left(\frac{105 \, {\left(c x + 1\right)}^{6} b d^{4}}{{\left(c x - 1\right)}^{6}} - \frac{210 \, {\left(c x + 1\right)}^{5} b d^{4}}{{\left(c x - 1\right)}^{5}} + \frac{385 \, {\left(c x + 1\right)}^{4} b d^{4}}{{\left(c x - 1\right)}^{4}} - \frac{385 \, {\left(c x + 1\right)}^{3} b d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{231 \, {\left(c x + 1\right)}^{2} b d^{4}}{{\left(c x - 1\right)}^{2}} - \frac{77 \, {\left(c x + 1\right)} b d^{4}}{c x - 1} + 11 \, b d^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{7} c^{4}}{{\left(c x - 1\right)}^{7}} - \frac{7 \, {\left(c x + 1\right)}^{6} c^{4}}{{\left(c x - 1\right)}^{6}} + \frac{21 \, {\left(c x + 1\right)}^{5} c^{4}}{{\left(c x - 1\right)}^{5}} - \frac{35 \, {\left(c x + 1\right)}^{4} c^{4}}{{\left(c x - 1\right)}^{4}} + \frac{35 \, {\left(c x + 1\right)}^{3} c^{4}}{{\left(c x - 1\right)}^{3}} - \frac{21 \, {\left(c x + 1\right)}^{2} c^{4}}{{\left(c x - 1\right)}^{2}} + \frac{7 \, {\left(c x + 1\right)} c^{4}}{c x - 1} - c^{4}} - \frac{\frac{2520 \, {\left(c x + 1\right)}^{6} a d^{4}}{{\left(c x - 1\right)}^{6}} - \frac{5040 \, {\left(c x + 1\right)}^{5} a d^{4}}{{\left(c x - 1\right)}^{5}} + \frac{9240 \, {\left(c x + 1\right)}^{4} a d^{4}}{{\left(c x - 1\right)}^{4}} - \frac{9240 \, {\left(c x + 1\right)}^{3} a d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{5544 \, {\left(c x + 1\right)}^{2} a d^{4}}{{\left(c x - 1\right)}^{2}} - \frac{1848 \, {\left(c x + 1\right)} a d^{4}}{c x - 1} + 264 \, a d^{4} + \frac{1128 \, {\left(c x + 1\right)}^{6} b d^{4}}{{\left(c x - 1\right)}^{6}} - \frac{4812 \, {\left(c x + 1\right)}^{5} b d^{4}}{{\left(c x - 1\right)}^{5}} + \frac{9476 \, {\left(c x + 1\right)}^{4} b d^{4}}{{\left(c x - 1\right)}^{4}} - \frac{10631 \, {\left(c x + 1\right)}^{3} b d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{6933 \, {\left(c x + 1\right)}^{2} b d^{4}}{{\left(c x - 1\right)}^{2}} - \frac{2465 \, {\left(c x + 1\right)} b d^{4}}{c x - 1} + 371 \, b d^{4}}{\frac{{\left(c x + 1\right)}^{7} c^{4}}{{\left(c x - 1\right)}^{7}} - \frac{7 \, {\left(c x + 1\right)}^{6} c^{4}}{{\left(c x - 1\right)}^{6}} + \frac{21 \, {\left(c x + 1\right)}^{5} c^{4}}{{\left(c x - 1\right)}^{5}} - \frac{35 \, {\left(c x + 1\right)}^{4} c^{4}}{{\left(c x - 1\right)}^{4}} + \frac{35 \, {\left(c x + 1\right)}^{3} c^{4}}{{\left(c x - 1\right)}^{3}} - \frac{21 \, {\left(c x + 1\right)}^{2} c^{4}}{{\left(c x - 1\right)}^{2}} + \frac{7 \, {\left(c x + 1\right)} c^{4}}{c x - 1} - c^{4}}\right)} c"," ",0,"-4/315*(132*b*d^4*log(-(c*x + 1)/(c*x - 1) + 1)/c^4 - 132*b*d^4*log(-(c*x + 1)/(c*x - 1))/c^4 - 12*(105*(c*x + 1)^6*b*d^4/(c*x - 1)^6 - 210*(c*x + 1)^5*b*d^4/(c*x - 1)^5 + 385*(c*x + 1)^4*b*d^4/(c*x - 1)^4 - 385*(c*x + 1)^3*b*d^4/(c*x - 1)^3 + 231*(c*x + 1)^2*b*d^4/(c*x - 1)^2 - 77*(c*x + 1)*b*d^4/(c*x - 1) + 11*b*d^4)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^7*c^4/(c*x - 1)^7 - 7*(c*x + 1)^6*c^4/(c*x - 1)^6 + 21*(c*x + 1)^5*c^4/(c*x - 1)^5 - 35*(c*x + 1)^4*c^4/(c*x - 1)^4 + 35*(c*x + 1)^3*c^4/(c*x - 1)^3 - 21*(c*x + 1)^2*c^4/(c*x - 1)^2 + 7*(c*x + 1)*c^4/(c*x - 1) - c^4) - (2520*(c*x + 1)^6*a*d^4/(c*x - 1)^6 - 5040*(c*x + 1)^5*a*d^4/(c*x - 1)^5 + 9240*(c*x + 1)^4*a*d^4/(c*x - 1)^4 - 9240*(c*x + 1)^3*a*d^4/(c*x - 1)^3 + 5544*(c*x + 1)^2*a*d^4/(c*x - 1)^2 - 1848*(c*x + 1)*a*d^4/(c*x - 1) + 264*a*d^4 + 1128*(c*x + 1)^6*b*d^4/(c*x - 1)^6 - 4812*(c*x + 1)^5*b*d^4/(c*x - 1)^5 + 9476*(c*x + 1)^4*b*d^4/(c*x - 1)^4 - 10631*(c*x + 1)^3*b*d^4/(c*x - 1)^3 + 6933*(c*x + 1)^2*b*d^4/(c*x - 1)^2 - 2465*(c*x + 1)*b*d^4/(c*x - 1) + 371*b*d^4)/((c*x + 1)^7*c^4/(c*x - 1)^7 - 7*(c*x + 1)^6*c^4/(c*x - 1)^6 + 21*(c*x + 1)^5*c^4/(c*x - 1)^5 - 35*(c*x + 1)^4*c^4/(c*x - 1)^4 + 35*(c*x + 1)^3*c^4/(c*x - 1)^3 - 21*(c*x + 1)^2*c^4/(c*x - 1)^2 + 7*(c*x + 1)*c^4/(c*x - 1) - c^4))*c","B",0
33,1,621,0,0.275527," ","integrate(x*(c*d*x+d)^4*(a+b*arctanh(c*x)),x, algorithm=""giac"")","-\frac{8}{45} \, {\left(\frac{12 \, b d^{4} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{3}} - \frac{12 \, b d^{4} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{3}} - \frac{6 \, {\left(\frac{15 \, {\left(c x + 1\right)}^{5} b d^{4}}{{\left(c x - 1\right)}^{5}} - \frac{30 \, {\left(c x + 1\right)}^{4} b d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{40 \, {\left(c x + 1\right)}^{3} b d^{4}}{{\left(c x - 1\right)}^{3}} - \frac{30 \, {\left(c x + 1\right)}^{2} b d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{12 \, {\left(c x + 1\right)} b d^{4}}{c x - 1} - 2 \, b d^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{6} c^{3}}{{\left(c x - 1\right)}^{6}} - \frac{6 \, {\left(c x + 1\right)}^{5} c^{3}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4} c^{3}}{{\left(c x - 1\right)}^{4}} - \frac{20 \, {\left(c x + 1\right)}^{3} c^{3}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} c^{3}}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} c^{3}}{c x - 1} + c^{3}} - \frac{\frac{180 \, {\left(c x + 1\right)}^{5} a d^{4}}{{\left(c x - 1\right)}^{5}} - \frac{360 \, {\left(c x + 1\right)}^{4} a d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{480 \, {\left(c x + 1\right)}^{3} a d^{4}}{{\left(c x - 1\right)}^{3}} - \frac{360 \, {\left(c x + 1\right)}^{2} a d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{144 \, {\left(c x + 1\right)} a d^{4}}{c x - 1} - 24 \, a d^{4} + \frac{78 \, {\left(c x + 1\right)}^{5} b d^{4}}{{\left(c x - 1\right)}^{5}} - \frac{294 \, {\left(c x + 1\right)}^{4} b d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{472 \, {\left(c x + 1\right)}^{3} b d^{4}}{{\left(c x - 1\right)}^{3}} - \frac{399 \, {\left(c x + 1\right)}^{2} b d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{174 \, {\left(c x + 1\right)} b d^{4}}{c x - 1} - 31 \, b d^{4}}{\frac{{\left(c x + 1\right)}^{6} c^{3}}{{\left(c x - 1\right)}^{6}} - \frac{6 \, {\left(c x + 1\right)}^{5} c^{3}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4} c^{3}}{{\left(c x - 1\right)}^{4}} - \frac{20 \, {\left(c x + 1\right)}^{3} c^{3}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} c^{3}}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} c^{3}}{c x - 1} + c^{3}}\right)} c"," ",0,"-8/45*(12*b*d^4*log(-(c*x + 1)/(c*x - 1) + 1)/c^3 - 12*b*d^4*log(-(c*x + 1)/(c*x - 1))/c^3 - 6*(15*(c*x + 1)^5*b*d^4/(c*x - 1)^5 - 30*(c*x + 1)^4*b*d^4/(c*x - 1)^4 + 40*(c*x + 1)^3*b*d^4/(c*x - 1)^3 - 30*(c*x + 1)^2*b*d^4/(c*x - 1)^2 + 12*(c*x + 1)*b*d^4/(c*x - 1) - 2*b*d^4)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^6*c^3/(c*x - 1)^6 - 6*(c*x + 1)^5*c^3/(c*x - 1)^5 + 15*(c*x + 1)^4*c^3/(c*x - 1)^4 - 20*(c*x + 1)^3*c^3/(c*x - 1)^3 + 15*(c*x + 1)^2*c^3/(c*x - 1)^2 - 6*(c*x + 1)*c^3/(c*x - 1) + c^3) - (180*(c*x + 1)^5*a*d^4/(c*x - 1)^5 - 360*(c*x + 1)^4*a*d^4/(c*x - 1)^4 + 480*(c*x + 1)^3*a*d^4/(c*x - 1)^3 - 360*(c*x + 1)^2*a*d^4/(c*x - 1)^2 + 144*(c*x + 1)*a*d^4/(c*x - 1) - 24*a*d^4 + 78*(c*x + 1)^5*b*d^4/(c*x - 1)^5 - 294*(c*x + 1)^4*b*d^4/(c*x - 1)^4 + 472*(c*x + 1)^3*b*d^4/(c*x - 1)^3 - 399*(c*x + 1)^2*b*d^4/(c*x - 1)^2 + 174*(c*x + 1)*b*d^4/(c*x - 1) - 31*b*d^4)/((c*x + 1)^6*c^3/(c*x - 1)^6 - 6*(c*x + 1)^5*c^3/(c*x - 1)^5 + 15*(c*x + 1)^4*c^3/(c*x - 1)^4 - 20*(c*x + 1)^3*c^3/(c*x - 1)^3 + 15*(c*x + 1)^2*c^3/(c*x - 1)^2 - 6*(c*x + 1)*c^3/(c*x - 1) + c^3))*c","B",0
34,1,526,0,0.239367," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x)),x, algorithm=""giac"")","-\frac{4}{15} \, {\left(\frac{12 \, b d^{4} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{2}} - \frac{12 \, b d^{4} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{2}} - \frac{12 \, {\left(\frac{5 \, {\left(c x + 1\right)}^{4} b d^{4}}{{\left(c x - 1\right)}^{4}} - \frac{10 \, {\left(c x + 1\right)}^{3} b d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{10 \, {\left(c x + 1\right)}^{2} b d^{4}}{{\left(c x - 1\right)}^{2}} - \frac{5 \, {\left(c x + 1\right)} b d^{4}}{c x - 1} + b d^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{5} c^{2}}{{\left(c x - 1\right)}^{5}} - \frac{5 \, {\left(c x + 1\right)}^{4} c^{2}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3} c^{2}}{{\left(c x - 1\right)}^{3}} - \frac{10 \, {\left(c x + 1\right)}^{2} c^{2}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} c^{2}}{c x - 1} - c^{2}} - \frac{\frac{120 \, {\left(c x + 1\right)}^{4} a d^{4}}{{\left(c x - 1\right)}^{4}} - \frac{240 \, {\left(c x + 1\right)}^{3} a d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{240 \, {\left(c x + 1\right)}^{2} a d^{4}}{{\left(c x - 1\right)}^{2}} - \frac{120 \, {\left(c x + 1\right)} a d^{4}}{c x - 1} + 24 \, a d^{4} + \frac{48 \, {\left(c x + 1\right)}^{4} b d^{4}}{{\left(c x - 1\right)}^{4}} - \frac{156 \, {\left(c x + 1\right)}^{3} b d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{196 \, {\left(c x + 1\right)}^{2} b d^{4}}{{\left(c x - 1\right)}^{2}} - \frac{113 \, {\left(c x + 1\right)} b d^{4}}{c x - 1} + 25 \, b d^{4}}{\frac{{\left(c x + 1\right)}^{5} c^{2}}{{\left(c x - 1\right)}^{5}} - \frac{5 \, {\left(c x + 1\right)}^{4} c^{2}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3} c^{2}}{{\left(c x - 1\right)}^{3}} - \frac{10 \, {\left(c x + 1\right)}^{2} c^{2}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} c^{2}}{c x - 1} - c^{2}}\right)} c"," ",0,"-4/15*(12*b*d^4*log(-(c*x + 1)/(c*x - 1) + 1)/c^2 - 12*b*d^4*log(-(c*x + 1)/(c*x - 1))/c^2 - 12*(5*(c*x + 1)^4*b*d^4/(c*x - 1)^4 - 10*(c*x + 1)^3*b*d^4/(c*x - 1)^3 + 10*(c*x + 1)^2*b*d^4/(c*x - 1)^2 - 5*(c*x + 1)*b*d^4/(c*x - 1) + b*d^4)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^5*c^2/(c*x - 1)^5 - 5*(c*x + 1)^4*c^2/(c*x - 1)^4 + 10*(c*x + 1)^3*c^2/(c*x - 1)^3 - 10*(c*x + 1)^2*c^2/(c*x - 1)^2 + 5*(c*x + 1)*c^2/(c*x - 1) - c^2) - (120*(c*x + 1)^4*a*d^4/(c*x - 1)^4 - 240*(c*x + 1)^3*a*d^4/(c*x - 1)^3 + 240*(c*x + 1)^2*a*d^4/(c*x - 1)^2 - 120*(c*x + 1)*a*d^4/(c*x - 1) + 24*a*d^4 + 48*(c*x + 1)^4*b*d^4/(c*x - 1)^4 - 156*(c*x + 1)^3*b*d^4/(c*x - 1)^3 + 196*(c*x + 1)^2*b*d^4/(c*x - 1)^2 - 113*(c*x + 1)*b*d^4/(c*x - 1) + 25*b*d^4)/((c*x + 1)^5*c^2/(c*x - 1)^5 - 5*(c*x + 1)^4*c^2/(c*x - 1)^4 + 10*(c*x + 1)^3*c^2/(c*x - 1)^3 - 10*(c*x + 1)^2*c^2/(c*x - 1)^2 + 5*(c*x + 1)*c^2/(c*x - 1) - c^2))*c","B",0
35,0,0,0,0.000000," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{4} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}}{x}\,{d x}"," ",0,"integrate((c*d*x + d)^4*(b*arctanh(c*x) + a)/x, x)","F",0
36,0,0,0,0.000000," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^2,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{4} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}}{x^{2}}\,{d x}"," ",0,"integrate((c*d*x + d)^4*(b*arctanh(c*x) + a)/x^2, x)","F",0
37,0,0,0,0.000000," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^3,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{4} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}}{x^{3}}\,{d x}"," ",0,"integrate((c*d*x + d)^4*(b*arctanh(c*x) + a)/x^3, x)","F",0
38,0,0,0,0.000000," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^4,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{4} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}}{x^{4}}\,{d x}"," ",0,"integrate((c*d*x + d)^4*(b*arctanh(c*x) + a)/x^4, x)","F",0
39,0,0,0,0.000000," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^5,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{4} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}}{x^{5}}\,{d x}"," ",0,"integrate((c*d*x + d)^4*(b*arctanh(c*x) + a)/x^5, x)","F",0
40,1,532,0,0.232638," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^6,x, algorithm=""giac"")","\frac{4}{15} \, {\left(12 \, b c^{4} d^{4} \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - 12 \, b c^{4} d^{4} \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{12 \, {\left(\frac{5 \, {\left(c x + 1\right)}^{4} b c^{4} d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3} b c^{4} d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{10 \, {\left(c x + 1\right)}^{2} b c^{4} d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} b c^{4} d^{4}}{c x - 1} + b c^{4} d^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{5}}{{\left(c x - 1\right)}^{5}} + \frac{5 \, {\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{10 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{\frac{120 \, {\left(c x + 1\right)}^{4} a c^{4} d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{240 \, {\left(c x + 1\right)}^{3} a c^{4} d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{240 \, {\left(c x + 1\right)}^{2} a c^{4} d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{120 \, {\left(c x + 1\right)} a c^{4} d^{4}}{c x - 1} + 24 \, a c^{4} d^{4} + \frac{48 \, {\left(c x + 1\right)}^{4} b c^{4} d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{156 \, {\left(c x + 1\right)}^{3} b c^{4} d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{196 \, {\left(c x + 1\right)}^{2} b c^{4} d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{113 \, {\left(c x + 1\right)} b c^{4} d^{4}}{c x - 1} + 25 \, b c^{4} d^{4}}{\frac{{\left(c x + 1\right)}^{5}}{{\left(c x - 1\right)}^{5}} + \frac{5 \, {\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{10 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"4/15*(12*b*c^4*d^4*log(-(c*x + 1)/(c*x - 1) - 1) - 12*b*c^4*d^4*log(-(c*x + 1)/(c*x - 1)) + 12*(5*(c*x + 1)^4*b*c^4*d^4/(c*x - 1)^4 + 10*(c*x + 1)^3*b*c^4*d^4/(c*x - 1)^3 + 10*(c*x + 1)^2*b*c^4*d^4/(c*x - 1)^2 + 5*(c*x + 1)*b*c^4*d^4/(c*x - 1) + b*c^4*d^4)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^5/(c*x - 1)^5 + 5*(c*x + 1)^4/(c*x - 1)^4 + 10*(c*x + 1)^3/(c*x - 1)^3 + 10*(c*x + 1)^2/(c*x - 1)^2 + 5*(c*x + 1)/(c*x - 1) + 1) + (120*(c*x + 1)^4*a*c^4*d^4/(c*x - 1)^4 + 240*(c*x + 1)^3*a*c^4*d^4/(c*x - 1)^3 + 240*(c*x + 1)^2*a*c^4*d^4/(c*x - 1)^2 + 120*(c*x + 1)*a*c^4*d^4/(c*x - 1) + 24*a*c^4*d^4 + 48*(c*x + 1)^4*b*c^4*d^4/(c*x - 1)^4 + 156*(c*x + 1)^3*b*c^4*d^4/(c*x - 1)^3 + 196*(c*x + 1)^2*b*c^4*d^4/(c*x - 1)^2 + 113*(c*x + 1)*b*c^4*d^4/(c*x - 1) + 25*b*c^4*d^4)/((c*x + 1)^5/(c*x - 1)^5 + 5*(c*x + 1)^4/(c*x - 1)^4 + 10*(c*x + 1)^3/(c*x - 1)^3 + 10*(c*x + 1)^2/(c*x - 1)^2 + 5*(c*x + 1)/(c*x - 1) + 1))*c","B",0
41,1,634,0,0.557446," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^7,x, algorithm=""giac"")","\frac{8}{45} \, {\left(12 \, b c^{5} d^{4} \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - 12 \, b c^{5} d^{4} \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{6 \, {\left(\frac{15 \, {\left(c x + 1\right)}^{5} b c^{5} d^{4}}{{\left(c x - 1\right)}^{5}} + \frac{30 \, {\left(c x + 1\right)}^{4} b c^{5} d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{40 \, {\left(c x + 1\right)}^{3} b c^{5} d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{30 \, {\left(c x + 1\right)}^{2} b c^{5} d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{12 \, {\left(c x + 1\right)} b c^{5} d^{4}}{c x - 1} + 2 \, b c^{5} d^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{6}}{{\left(c x - 1\right)}^{6}} + \frac{6 \, {\left(c x + 1\right)}^{5}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{20 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{6 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{\frac{180 \, {\left(c x + 1\right)}^{5} a c^{5} d^{4}}{{\left(c x - 1\right)}^{5}} + \frac{360 \, {\left(c x + 1\right)}^{4} a c^{5} d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{480 \, {\left(c x + 1\right)}^{3} a c^{5} d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{360 \, {\left(c x + 1\right)}^{2} a c^{5} d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{144 \, {\left(c x + 1\right)} a c^{5} d^{4}}{c x - 1} + 24 \, a c^{5} d^{4} + \frac{78 \, {\left(c x + 1\right)}^{5} b c^{5} d^{4}}{{\left(c x - 1\right)}^{5}} + \frac{294 \, {\left(c x + 1\right)}^{4} b c^{5} d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{472 \, {\left(c x + 1\right)}^{3} b c^{5} d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{399 \, {\left(c x + 1\right)}^{2} b c^{5} d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{174 \, {\left(c x + 1\right)} b c^{5} d^{4}}{c x - 1} + 31 \, b c^{5} d^{4}}{\frac{{\left(c x + 1\right)}^{6}}{{\left(c x - 1\right)}^{6}} + \frac{6 \, {\left(c x + 1\right)}^{5}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{20 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{6 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"8/45*(12*b*c^5*d^4*log(-(c*x + 1)/(c*x - 1) - 1) - 12*b*c^5*d^4*log(-(c*x + 1)/(c*x - 1)) + 6*(15*(c*x + 1)^5*b*c^5*d^4/(c*x - 1)^5 + 30*(c*x + 1)^4*b*c^5*d^4/(c*x - 1)^4 + 40*(c*x + 1)^3*b*c^5*d^4/(c*x - 1)^3 + 30*(c*x + 1)^2*b*c^5*d^4/(c*x - 1)^2 + 12*(c*x + 1)*b*c^5*d^4/(c*x - 1) + 2*b*c^5*d^4)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^6/(c*x - 1)^6 + 6*(c*x + 1)^5/(c*x - 1)^5 + 15*(c*x + 1)^4/(c*x - 1)^4 + 20*(c*x + 1)^3/(c*x - 1)^3 + 15*(c*x + 1)^2/(c*x - 1)^2 + 6*(c*x + 1)/(c*x - 1) + 1) + (180*(c*x + 1)^5*a*c^5*d^4/(c*x - 1)^5 + 360*(c*x + 1)^4*a*c^5*d^4/(c*x - 1)^4 + 480*(c*x + 1)^3*a*c^5*d^4/(c*x - 1)^3 + 360*(c*x + 1)^2*a*c^5*d^4/(c*x - 1)^2 + 144*(c*x + 1)*a*c^5*d^4/(c*x - 1) + 24*a*c^5*d^4 + 78*(c*x + 1)^5*b*c^5*d^4/(c*x - 1)^5 + 294*(c*x + 1)^4*b*c^5*d^4/(c*x - 1)^4 + 472*(c*x + 1)^3*b*c^5*d^4/(c*x - 1)^3 + 399*(c*x + 1)^2*b*c^5*d^4/(c*x - 1)^2 + 174*(c*x + 1)*b*c^5*d^4/(c*x - 1) + 31*b*c^5*d^4)/((c*x + 1)^6/(c*x - 1)^6 + 6*(c*x + 1)^5/(c*x - 1)^5 + 15*(c*x + 1)^4/(c*x - 1)^4 + 20*(c*x + 1)^3/(c*x - 1)^3 + 15*(c*x + 1)^2/(c*x - 1)^2 + 6*(c*x + 1)/(c*x - 1) + 1))*c","B",0
42,1,735,0,0.328308," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^8,x, algorithm=""giac"")","\frac{4}{315} \, {\left(132 \, b c^{6} d^{4} \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - 132 \, b c^{6} d^{4} \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{12 \, {\left(\frac{105 \, {\left(c x + 1\right)}^{6} b c^{6} d^{4}}{{\left(c x - 1\right)}^{6}} + \frac{210 \, {\left(c x + 1\right)}^{5} b c^{6} d^{4}}{{\left(c x - 1\right)}^{5}} + \frac{385 \, {\left(c x + 1\right)}^{4} b c^{6} d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{385 \, {\left(c x + 1\right)}^{3} b c^{6} d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{231 \, {\left(c x + 1\right)}^{2} b c^{6} d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{77 \, {\left(c x + 1\right)} b c^{6} d^{4}}{c x - 1} + 11 \, b c^{6} d^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{7}}{{\left(c x - 1\right)}^{7}} + \frac{7 \, {\left(c x + 1\right)}^{6}}{{\left(c x - 1\right)}^{6}} + \frac{21 \, {\left(c x + 1\right)}^{5}}{{\left(c x - 1\right)}^{5}} + \frac{35 \, {\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{35 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{21 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{7 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{\frac{2520 \, {\left(c x + 1\right)}^{6} a c^{6} d^{4}}{{\left(c x - 1\right)}^{6}} + \frac{5040 \, {\left(c x + 1\right)}^{5} a c^{6} d^{4}}{{\left(c x - 1\right)}^{5}} + \frac{9240 \, {\left(c x + 1\right)}^{4} a c^{6} d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{9240 \, {\left(c x + 1\right)}^{3} a c^{6} d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{5544 \, {\left(c x + 1\right)}^{2} a c^{6} d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{1848 \, {\left(c x + 1\right)} a c^{6} d^{4}}{c x - 1} + 264 \, a c^{6} d^{4} + \frac{1128 \, {\left(c x + 1\right)}^{6} b c^{6} d^{4}}{{\left(c x - 1\right)}^{6}} + \frac{4812 \, {\left(c x + 1\right)}^{5} b c^{6} d^{4}}{{\left(c x - 1\right)}^{5}} + \frac{9476 \, {\left(c x + 1\right)}^{4} b c^{6} d^{4}}{{\left(c x - 1\right)}^{4}} + \frac{10631 \, {\left(c x + 1\right)}^{3} b c^{6} d^{4}}{{\left(c x - 1\right)}^{3}} + \frac{6933 \, {\left(c x + 1\right)}^{2} b c^{6} d^{4}}{{\left(c x - 1\right)}^{2}} + \frac{2465 \, {\left(c x + 1\right)} b c^{6} d^{4}}{c x - 1} + 371 \, b c^{6} d^{4}}{\frac{{\left(c x + 1\right)}^{7}}{{\left(c x - 1\right)}^{7}} + \frac{7 \, {\left(c x + 1\right)}^{6}}{{\left(c x - 1\right)}^{6}} + \frac{21 \, {\left(c x + 1\right)}^{5}}{{\left(c x - 1\right)}^{5}} + \frac{35 \, {\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{35 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{21 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{7 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"4/315*(132*b*c^6*d^4*log(-(c*x + 1)/(c*x - 1) - 1) - 132*b*c^6*d^4*log(-(c*x + 1)/(c*x - 1)) + 12*(105*(c*x + 1)^6*b*c^6*d^4/(c*x - 1)^6 + 210*(c*x + 1)^5*b*c^6*d^4/(c*x - 1)^5 + 385*(c*x + 1)^4*b*c^6*d^4/(c*x - 1)^4 + 385*(c*x + 1)^3*b*c^6*d^4/(c*x - 1)^3 + 231*(c*x + 1)^2*b*c^6*d^4/(c*x - 1)^2 + 77*(c*x + 1)*b*c^6*d^4/(c*x - 1) + 11*b*c^6*d^4)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^7/(c*x - 1)^7 + 7*(c*x + 1)^6/(c*x - 1)^6 + 21*(c*x + 1)^5/(c*x - 1)^5 + 35*(c*x + 1)^4/(c*x - 1)^4 + 35*(c*x + 1)^3/(c*x - 1)^3 + 21*(c*x + 1)^2/(c*x - 1)^2 + 7*(c*x + 1)/(c*x - 1) + 1) + (2520*(c*x + 1)^6*a*c^6*d^4/(c*x - 1)^6 + 5040*(c*x + 1)^5*a*c^6*d^4/(c*x - 1)^5 + 9240*(c*x + 1)^4*a*c^6*d^4/(c*x - 1)^4 + 9240*(c*x + 1)^3*a*c^6*d^4/(c*x - 1)^3 + 5544*(c*x + 1)^2*a*c^6*d^4/(c*x - 1)^2 + 1848*(c*x + 1)*a*c^6*d^4/(c*x - 1) + 264*a*c^6*d^4 + 1128*(c*x + 1)^6*b*c^6*d^4/(c*x - 1)^6 + 4812*(c*x + 1)^5*b*c^6*d^4/(c*x - 1)^5 + 9476*(c*x + 1)^4*b*c^6*d^4/(c*x - 1)^4 + 10631*(c*x + 1)^3*b*c^6*d^4/(c*x - 1)^3 + 6933*(c*x + 1)^2*b*c^6*d^4/(c*x - 1)^2 + 2465*(c*x + 1)*b*c^6*d^4/(c*x - 1) + 371*b*c^6*d^4)/((c*x + 1)^7/(c*x - 1)^7 + 7*(c*x + 1)^6/(c*x - 1)^6 + 21*(c*x + 1)^5/(c*x - 1)^5 + 35*(c*x + 1)^4/(c*x - 1)^4 + 35*(c*x + 1)^3/(c*x - 1)^3 + 21*(c*x + 1)^2/(c*x - 1)^2 + 7*(c*x + 1)/(c*x - 1) + 1))*c","B",0
43,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x))/(c*d*x+d),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} x^{3}}{c d x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*x^3/(c*d*x + d), x)","F",0
44,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))/(c*d*x+d),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} x^{2}}{c d x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*x^2/(c*d*x + d), x)","F",0
45,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))/(c*d*x+d),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} x}{c d x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*x/(c*d*x + d), x)","F",0
46,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/(c*d*x+d),x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{c d x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/(c*d*x + d), x)","F",0
47,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x/(c*d*x+d),x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{{\left(c d x + d\right)} x}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/((c*d*x + 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=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{{\left(c d x + d\right)} x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/((c*d*x + 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=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{{\left(c d x + d\right)} x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/((c*d*x + 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=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{{\left(c d x + d\right)} x^{4}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/((c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} x^{3}}{{\left(c d x + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*x^3/(c*d*x + d)^2, x)","F",0
52,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))/(c*d*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} x^{2}}{{\left(c d x + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*x^2/(c*d*x + d)^2, x)","F",0
53,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))/(c*d*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} x}{{\left(c d x + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*x/(c*d*x + d)^2, x)","F",0
54,1,63,0,0.242879," ","integrate((a+b*arctanh(c*x))/(c*d*x+d)^2,x, algorithm=""giac"")","\frac{1}{4} \, c {\left(\frac{{\left(c x - 1\right)} b \log\left(-\frac{c x + 1}{c x - 1}\right)}{{\left(c x + 1\right)} c^{2} d^{2}} + \frac{{\left(c x - 1\right)} {\left(2 \, a + b\right)}}{{\left(c x + 1\right)} c^{2} d^{2}}\right)}"," ",0,"1/4*c*((c*x - 1)*b*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)*c^2*d^2) + (c*x - 1)*(2*a + b)/((c*x + 1)*c^2*d^2))","A",0
55,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x/(c*d*x+d)^2,x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{{\left(c d x + d\right)}^{2} x}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/((c*d*x + 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=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{{\left(c d x + d\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/((c*d*x + 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=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{{\left(c d x + d\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/((c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} x^{4}}{{\left(c d x + d\right)}^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*x^4/(c*d*x + d)^3, x)","F",0
59,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x))/(c*d*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} x^{3}}{{\left(c d x + d\right)}^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*x^3/(c*d*x + d)^3, x)","F",0
60,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))/(c*d*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} x^{2}}{{\left(c d x + d\right)}^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*x^2/(c*d*x + d)^3, x)","F",0
61,1,114,0,0.201129," ","integrate(x*(a+b*arctanh(c*x))/(c*d*x+d)^3,x, algorithm=""giac"")","\frac{1}{32} \, c {\left(\frac{2 \, {\left(c x - 1\right)}^{2} {\left(\frac{2 \, {\left(c x + 1\right)} b}{c x - 1} + b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{{\left(c x + 1\right)}^{2} c^{3} d^{3}} + \frac{{\left(c x - 1\right)}^{2} {\left(\frac{8 \, {\left(c x + 1\right)} a}{c x - 1} + 4 \, a + \frac{4 \, {\left(c x + 1\right)} b}{c x - 1} + b\right)}}{{\left(c x + 1\right)}^{2} c^{3} d^{3}}\right)}"," ",0,"1/32*c*(2*(c*x - 1)^2*(2*(c*x + 1)*b/(c*x - 1) + b)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^2*c^3*d^3) + (c*x - 1)^2*(8*(c*x + 1)*a/(c*x - 1) + 4*a + 4*(c*x + 1)*b/(c*x - 1) + b)/((c*x + 1)^2*c^3*d^3))","A",0
62,1,118,0,0.218307," ","integrate((a+b*arctanh(c*x))/(c*d*x+d)^3,x, algorithm=""giac"")","\frac{1}{32} \, c {\left(\frac{2 \, {\left(c x - 1\right)}^{2} {\left(\frac{2 \, {\left(c x + 1\right)} b}{c x - 1} - b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{{\left(c x + 1\right)}^{2} c^{2} d^{3}} + \frac{{\left(c x - 1\right)}^{2} {\left(\frac{8 \, {\left(c x + 1\right)} a}{c x - 1} - 4 \, a + \frac{4 \, {\left(c x + 1\right)} b}{c x - 1} - b\right)}}{{\left(c x + 1\right)}^{2} c^{2} d^{3}}\right)}"," ",0,"1/32*c*(2*(c*x - 1)^2*(2*(c*x + 1)*b/(c*x - 1) - b)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^2*c^2*d^3) + (c*x - 1)^2*(8*(c*x + 1)*a/(c*x - 1) - 4*a + 4*(c*x + 1)*b/(c*x - 1) - b)/((c*x + 1)^2*c^2*d^3))","A",0
63,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x/(c*d*x+d)^3,x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{{\left(c d x + d\right)}^{3} x}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/((c*d*x + 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=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{{\left(c d x + d\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/((c*d*x + 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=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{{\left(c d x + d\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/((c*d*x + d)^3*x^3), x)","F",0
66,1,161,0,0.198805," ","integrate((a+b*arctanh(c*x))/(c*x+1)^4,x, algorithm=""giac"")","\frac{1}{288} \, c {\left(\frac{6 \, {\left(c x - 1\right)}^{3} {\left(\frac{3 \, {\left(c x + 1\right)}^{2} b}{{\left(c x - 1\right)}^{2}} - \frac{3 \, {\left(c x + 1\right)} b}{c x - 1} + b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{{\left(c x + 1\right)}^{3} c^{2}} + \frac{{\left(c x - 1\right)}^{3} {\left(\frac{36 \, {\left(c x + 1\right)}^{2} a}{{\left(c x - 1\right)}^{2}} - \frac{36 \, {\left(c x + 1\right)} a}{c x - 1} + 12 \, a + \frac{18 \, {\left(c x + 1\right)}^{2} b}{{\left(c x - 1\right)}^{2}} - \frac{9 \, {\left(c x + 1\right)} b}{c x - 1} + 2 \, b\right)}}{{\left(c x + 1\right)}^{3} c^{2}}\right)}"," ",0,"1/288*c*(6*(c*x - 1)^3*(3*(c*x + 1)^2*b/(c*x - 1)^2 - 3*(c*x + 1)*b/(c*x - 1) + b)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^3*c^2) + (c*x - 1)^3*(36*(c*x + 1)^2*a/(c*x - 1)^2 - 36*(c*x + 1)*a/(c*x - 1) + 12*a + 18*(c*x + 1)^2*b/(c*x - 1)^2 - 9*(c*x + 1)*b/(c*x - 1) + 2*b)/((c*x + 1)^3*c^2))","B",0
67,0,0,0,0.000000," ","integrate(arctanh(a*x)/(a*c*x^2+c*x),x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)}{a c x^{2} + c x}\,{d x}"," ",0,"integrate(arctanh(a*x)/(a*c*x^2 + c*x), x)","F",0
68,0,0,0,0.000000," ","integrate(x^3*(c*d*x+d)*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\int {\left(c d x + d\right)} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{3}\,{d x}"," ",0,"integrate((c*d*x + d)*(b*arctanh(c*x) + a)^2*x^3, x)","F",0
69,0,0,0,0.000000," ","integrate(x^2*(c*d*x+d)*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\int {\left(c d x + d\right)} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{2}\,{d x}"," ",0,"integrate((c*d*x + d)*(b*arctanh(c*x) + a)^2*x^2, x)","F",0
70,0,0,0,0.000000," ","integrate(x*(c*d*x+d)*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\int {\left(c d x + d\right)} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x\,{d x}"," ",0,"integrate((c*d*x + d)*(b*arctanh(c*x) + a)^2*x, x)","F",0
71,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\int {\left(c d x + d\right)} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((c*d*x + d)*(b*arctanh(c*x) + a)^2, x)","F",0
72,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))^2/x,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x}\,{d x}"," ",0,"integrate((c*d*x + d)*(b*arctanh(c*x) + a)^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=""giac"")","\int \frac{{\left(c d x + d\right)} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x^{2}}\,{d x}"," ",0,"integrate((c*d*x + d)*(b*arctanh(c*x) + a)^2/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=""giac"")","\int \frac{{\left(c d x + d\right)} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x^{3}}\,{d x}"," ",0,"integrate((c*d*x + d)*(b*arctanh(c*x) + a)^2/x^3, x)","F",0
75,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))^2/x^4,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x^{4}}\,{d x}"," ",0,"integrate((c*d*x + d)*(b*arctanh(c*x) + a)^2/x^4, x)","F",0
76,1,1135,0,4.222029," ","integrate(x^3*(c*d*x+d)^2*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\frac{1}{63} \, {\left(\frac{84 \, {\left(\frac{{\left(c x + 1\right)}^{5} b^{2} d^{2}}{{\left(c x - 1\right)}^{5}} + \frac{{\left(c x + 1\right)}^{4} b^{2} d^{2}}{{\left(c x - 1\right)}^{4}} + \frac{{\left(c x + 1\right)}^{3} b^{2} d^{2}}{{\left(c x - 1\right)}^{3}}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{\frac{{\left(c x + 1\right)}^{8} c^{7}}{{\left(c x - 1\right)}^{8}} - \frac{8 \, {\left(c x + 1\right)}^{7} c^{7}}{{\left(c x - 1\right)}^{7}} + \frac{28 \, {\left(c x + 1\right)}^{6} c^{7}}{{\left(c x - 1\right)}^{6}} - \frac{56 \, {\left(c x + 1\right)}^{5} c^{7}}{{\left(c x - 1\right)}^{5}} + \frac{70 \, {\left(c x + 1\right)}^{4} c^{7}}{{\left(c x - 1\right)}^{4}} - \frac{56 \, {\left(c x + 1\right)}^{3} c^{7}}{{\left(c x - 1\right)}^{3}} + \frac{28 \, {\left(c x + 1\right)}^{2} c^{7}}{{\left(c x - 1\right)}^{2}} - \frac{8 \, {\left(c x + 1\right)} c^{7}}{c x - 1} + c^{7}} + \frac{2 \, {\left(\frac{168 \, {\left(c x + 1\right)}^{5} a b d^{2}}{{\left(c x - 1\right)}^{5}} + \frac{168 \, {\left(c x + 1\right)}^{4} a b d^{2}}{{\left(c x - 1\right)}^{4}} + \frac{168 \, {\left(c x + 1\right)}^{3} a b d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{28 \, {\left(c x + 1\right)}^{5} b^{2} d^{2}}{{\left(c x - 1\right)}^{5}} - \frac{35 \, {\left(c x + 1\right)}^{4} b^{2} d^{2}}{{\left(c x - 1\right)}^{4}} + \frac{28 \, {\left(c x + 1\right)}^{3} b^{2} d^{2}}{{\left(c x - 1\right)}^{3}} - \frac{28 \, {\left(c x + 1\right)}^{2} b^{2} d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{8 \, {\left(c x + 1\right)} b^{2} d^{2}}{c x - 1} - b^{2} d^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{8} c^{7}}{{\left(c x - 1\right)}^{8}} - \frac{8 \, {\left(c x + 1\right)}^{7} c^{7}}{{\left(c x - 1\right)}^{7}} + \frac{28 \, {\left(c x + 1\right)}^{6} c^{7}}{{\left(c x - 1\right)}^{6}} - \frac{56 \, {\left(c x + 1\right)}^{5} c^{7}}{{\left(c x - 1\right)}^{5}} + \frac{70 \, {\left(c x + 1\right)}^{4} c^{7}}{{\left(c x - 1\right)}^{4}} - \frac{56 \, {\left(c x + 1\right)}^{3} c^{7}}{{\left(c x - 1\right)}^{3}} + \frac{28 \, {\left(c x + 1\right)}^{2} c^{7}}{{\left(c x - 1\right)}^{2}} - \frac{8 \, {\left(c x + 1\right)} c^{7}}{c x - 1} + c^{7}} + \frac{\frac{336 \, {\left(c x + 1\right)}^{5} a^{2} d^{2}}{{\left(c x - 1\right)}^{5}} + \frac{336 \, {\left(c x + 1\right)}^{4} a^{2} d^{2}}{{\left(c x - 1\right)}^{4}} + \frac{336 \, {\left(c x + 1\right)}^{3} a^{2} d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{112 \, {\left(c x + 1\right)}^{5} a b d^{2}}{{\left(c x - 1\right)}^{5}} - \frac{140 \, {\left(c x + 1\right)}^{4} a b d^{2}}{{\left(c x - 1\right)}^{4}} + \frac{112 \, {\left(c x + 1\right)}^{3} a b d^{2}}{{\left(c x - 1\right)}^{3}} - \frac{112 \, {\left(c x + 1\right)}^{2} a b d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{32 \, {\left(c x + 1\right)} a b d^{2}}{c x - 1} - 4 \, a b d^{2} - \frac{2 \, {\left(c x + 1\right)}^{7} b^{2} d^{2}}{{\left(c x - 1\right)}^{7}} + \frac{15 \, {\left(c x + 1\right)}^{6} b^{2} d^{2}}{{\left(c x - 1\right)}^{6}} - \frac{30 \, {\left(c x + 1\right)}^{5} b^{2} d^{2}}{{\left(c x - 1\right)}^{5}} + \frac{34 \, {\left(c x + 1\right)}^{4} b^{2} d^{2}}{{\left(c x - 1\right)}^{4}} - \frac{30 \, {\left(c x + 1\right)}^{3} b^{2} d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} b^{2} d^{2}}{{\left(c x - 1\right)}^{2}} - \frac{2 \, {\left(c x + 1\right)} b^{2} d^{2}}{c x - 1}}{\frac{{\left(c x + 1\right)}^{8} c^{7}}{{\left(c x - 1\right)}^{8}} - \frac{8 \, {\left(c x + 1\right)}^{7} c^{7}}{{\left(c x - 1\right)}^{7}} + \frac{28 \, {\left(c x + 1\right)}^{6} c^{7}}{{\left(c x - 1\right)}^{6}} - \frac{56 \, {\left(c x + 1\right)}^{5} c^{7}}{{\left(c x - 1\right)}^{5}} + \frac{70 \, {\left(c x + 1\right)}^{4} c^{7}}{{\left(c x - 1\right)}^{4}} - \frac{56 \, {\left(c x + 1\right)}^{3} c^{7}}{{\left(c x - 1\right)}^{3}} + \frac{28 \, {\left(c x + 1\right)}^{2} c^{7}}{{\left(c x - 1\right)}^{2}} - \frac{8 \, {\left(c x + 1\right)} c^{7}}{c x - 1} + c^{7}} - \frac{2 \, b^{2} d^{2} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{7}} + \frac{2 \, b^{2} d^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{7}}\right)} c^{2}"," ",0,"1/63*(84*((c*x + 1)^5*b^2*d^2/(c*x - 1)^5 + (c*x + 1)^4*b^2*d^2/(c*x - 1)^4 + (c*x + 1)^3*b^2*d^2/(c*x - 1)^3)*log(-(c*x + 1)/(c*x - 1))^2/((c*x + 1)^8*c^7/(c*x - 1)^8 - 8*(c*x + 1)^7*c^7/(c*x - 1)^7 + 28*(c*x + 1)^6*c^7/(c*x - 1)^6 - 56*(c*x + 1)^5*c^7/(c*x - 1)^5 + 70*(c*x + 1)^4*c^7/(c*x - 1)^4 - 56*(c*x + 1)^3*c^7/(c*x - 1)^3 + 28*(c*x + 1)^2*c^7/(c*x - 1)^2 - 8*(c*x + 1)*c^7/(c*x - 1) + c^7) + 2*(168*(c*x + 1)^5*a*b*d^2/(c*x - 1)^5 + 168*(c*x + 1)^4*a*b*d^2/(c*x - 1)^4 + 168*(c*x + 1)^3*a*b*d^2/(c*x - 1)^3 + 28*(c*x + 1)^5*b^2*d^2/(c*x - 1)^5 - 35*(c*x + 1)^4*b^2*d^2/(c*x - 1)^4 + 28*(c*x + 1)^3*b^2*d^2/(c*x - 1)^3 - 28*(c*x + 1)^2*b^2*d^2/(c*x - 1)^2 + 8*(c*x + 1)*b^2*d^2/(c*x - 1) - b^2*d^2)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^8*c^7/(c*x - 1)^8 - 8*(c*x + 1)^7*c^7/(c*x - 1)^7 + 28*(c*x + 1)^6*c^7/(c*x - 1)^6 - 56*(c*x + 1)^5*c^7/(c*x - 1)^5 + 70*(c*x + 1)^4*c^7/(c*x - 1)^4 - 56*(c*x + 1)^3*c^7/(c*x - 1)^3 + 28*(c*x + 1)^2*c^7/(c*x - 1)^2 - 8*(c*x + 1)*c^7/(c*x - 1) + c^7) + (336*(c*x + 1)^5*a^2*d^2/(c*x - 1)^5 + 336*(c*x + 1)^4*a^2*d^2/(c*x - 1)^4 + 336*(c*x + 1)^3*a^2*d^2/(c*x - 1)^3 + 112*(c*x + 1)^5*a*b*d^2/(c*x - 1)^5 - 140*(c*x + 1)^4*a*b*d^2/(c*x - 1)^4 + 112*(c*x + 1)^3*a*b*d^2/(c*x - 1)^3 - 112*(c*x + 1)^2*a*b*d^2/(c*x - 1)^2 + 32*(c*x + 1)*a*b*d^2/(c*x - 1) - 4*a*b*d^2 - 2*(c*x + 1)^7*b^2*d^2/(c*x - 1)^7 + 15*(c*x + 1)^6*b^2*d^2/(c*x - 1)^6 - 30*(c*x + 1)^5*b^2*d^2/(c*x - 1)^5 + 34*(c*x + 1)^4*b^2*d^2/(c*x - 1)^4 - 30*(c*x + 1)^3*b^2*d^2/(c*x - 1)^3 + 15*(c*x + 1)^2*b^2*d^2/(c*x - 1)^2 - 2*(c*x + 1)*b^2*d^2/(c*x - 1))/((c*x + 1)^8*c^7/(c*x - 1)^8 - 8*(c*x + 1)^7*c^7/(c*x - 1)^7 + 28*(c*x + 1)^6*c^7/(c*x - 1)^6 - 56*(c*x + 1)^5*c^7/(c*x - 1)^5 + 70*(c*x + 1)^4*c^7/(c*x - 1)^4 - 56*(c*x + 1)^3*c^7/(c*x - 1)^3 + 28*(c*x + 1)^2*c^7/(c*x - 1)^2 - 8*(c*x + 1)*c^7/(c*x - 1) + c^7) - 2*b^2*d^2*log(-(c*x + 1)/(c*x - 1) + 1)/c^7 + 2*b^2*d^2*log(-(c*x + 1)/(c*x - 1))/c^7)*c^2","B",0
77,0,0,0,0.000000," ","integrate(x^2*(c*d*x+d)^2*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\int {\left(c d x + d\right)}^{2} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{2}\,{d x}"," ",0,"integrate((c*d*x + d)^2*(b*arctanh(c*x) + a)^2*x^2, x)","F",0
78,1,761,0,2.363738," ","integrate(x*(c*d*x+d)^2*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\frac{2}{45} \, {\left(\frac{30 \, {\left(c x + 1\right)}^{3} b^{2} d^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{{\left(\frac{{\left(c x + 1\right)}^{6} c^{5}}{{\left(c x - 1\right)}^{6}} - \frac{6 \, {\left(c x + 1\right)}^{5} c^{5}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} - \frac{20 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} c^{5}}{c x - 1} + c^{5}\right)} {\left(c x - 1\right)}^{3}} + \frac{2 \, {\left(\frac{60 \, {\left(c x + 1\right)}^{3} a b d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{10 \, {\left(c x + 1\right)}^{3} b^{2} d^{2}}{{\left(c x - 1\right)}^{3}} - \frac{15 \, {\left(c x + 1\right)}^{2} b^{2} d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{6 \, {\left(c x + 1\right)} b^{2} d^{2}}{c x - 1} - b^{2} d^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{6} c^{5}}{{\left(c x - 1\right)}^{6}} - \frac{6 \, {\left(c x + 1\right)}^{5} c^{5}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} - \frac{20 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} c^{5}}{c x - 1} + c^{5}} + \frac{\frac{120 \, {\left(c x + 1\right)}^{3} a^{2} d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{40 \, {\left(c x + 1\right)}^{3} a b d^{2}}{{\left(c x - 1\right)}^{3}} - \frac{60 \, {\left(c x + 1\right)}^{2} a b d^{2}}{{\left(c x - 1\right)}^{2}} + \frac{24 \, {\left(c x + 1\right)} a b d^{2}}{c x - 1} - 4 \, a b d^{2} - \frac{2 \, {\left(c x + 1\right)}^{5} b^{2} d^{2}}{{\left(c x - 1\right)}^{5}} + \frac{11 \, {\left(c x + 1\right)}^{4} b^{2} d^{2}}{{\left(c x - 1\right)}^{4}} - \frac{18 \, {\left(c x + 1\right)}^{3} b^{2} d^{2}}{{\left(c x - 1\right)}^{3}} + \frac{11 \, {\left(c x + 1\right)}^{2} b^{2} d^{2}}{{\left(c x - 1\right)}^{2}} - \frac{2 \, {\left(c x + 1\right)} b^{2} d^{2}}{c x - 1}}{\frac{{\left(c x + 1\right)}^{6} c^{5}}{{\left(c x - 1\right)}^{6}} - \frac{6 \, {\left(c x + 1\right)}^{5} c^{5}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} - \frac{20 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} c^{5}}{c x - 1} + c^{5}} - \frac{2 \, b^{2} d^{2} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{5}} + \frac{2 \, b^{2} d^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{5}}\right)} c^{2}"," ",0,"2/45*(30*(c*x + 1)^3*b^2*d^2*log(-(c*x + 1)/(c*x - 1))^2/(((c*x + 1)^6*c^5/(c*x - 1)^6 - 6*(c*x + 1)^5*c^5/(c*x - 1)^5 + 15*(c*x + 1)^4*c^5/(c*x - 1)^4 - 20*(c*x + 1)^3*c^5/(c*x - 1)^3 + 15*(c*x + 1)^2*c^5/(c*x - 1)^2 - 6*(c*x + 1)*c^5/(c*x - 1) + c^5)*(c*x - 1)^3) + 2*(60*(c*x + 1)^3*a*b*d^2/(c*x - 1)^3 + 10*(c*x + 1)^3*b^2*d^2/(c*x - 1)^3 - 15*(c*x + 1)^2*b^2*d^2/(c*x - 1)^2 + 6*(c*x + 1)*b^2*d^2/(c*x - 1) - b^2*d^2)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^6*c^5/(c*x - 1)^6 - 6*(c*x + 1)^5*c^5/(c*x - 1)^5 + 15*(c*x + 1)^4*c^5/(c*x - 1)^4 - 20*(c*x + 1)^3*c^5/(c*x - 1)^3 + 15*(c*x + 1)^2*c^5/(c*x - 1)^2 - 6*(c*x + 1)*c^5/(c*x - 1) + c^5) + (120*(c*x + 1)^3*a^2*d^2/(c*x - 1)^3 + 40*(c*x + 1)^3*a*b*d^2/(c*x - 1)^3 - 60*(c*x + 1)^2*a*b*d^2/(c*x - 1)^2 + 24*(c*x + 1)*a*b*d^2/(c*x - 1) - 4*a*b*d^2 - 2*(c*x + 1)^5*b^2*d^2/(c*x - 1)^5 + 11*(c*x + 1)^4*b^2*d^2/(c*x - 1)^4 - 18*(c*x + 1)^3*b^2*d^2/(c*x - 1)^3 + 11*(c*x + 1)^2*b^2*d^2/(c*x - 1)^2 - 2*(c*x + 1)*b^2*d^2/(c*x - 1))/((c*x + 1)^6*c^5/(c*x - 1)^6 - 6*(c*x + 1)^5*c^5/(c*x - 1)^5 + 15*(c*x + 1)^4*c^5/(c*x - 1)^4 - 20*(c*x + 1)^3*c^5/(c*x - 1)^3 + 15*(c*x + 1)^2*c^5/(c*x - 1)^2 - 6*(c*x + 1)*c^5/(c*x - 1) + c^5) - 2*b^2*d^2*log(-(c*x + 1)/(c*x - 1) + 1)/c^5 + 2*b^2*d^2*log(-(c*x + 1)/(c*x - 1))/c^5)*c^2","B",0
79,0,0,0,0.000000," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\int {\left(c d x + d\right)}^{2} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((c*d*x + d)^2*(b*arctanh(c*x) + a)^2, x)","F",0
80,0,0,0,0.000000," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))^2/x,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{2} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x}\,{d x}"," ",0,"integrate((c*d*x + d)^2*(b*arctanh(c*x) + a)^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=""giac"")","\int \frac{{\left(c d x + d\right)}^{2} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x^{2}}\,{d x}"," ",0,"integrate((c*d*x + d)^2*(b*arctanh(c*x) + a)^2/x^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=""giac"")","\int \frac{{\left(c d x + d\right)}^{2} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x^{3}}\,{d x}"," ",0,"integrate((c*d*x + d)^2*(b*arctanh(c*x) + a)^2/x^3, x)","F",0
83,0,0,0,0.000000," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))^2/x^4,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{2} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x^{4}}\,{d x}"," ",0,"integrate((c*d*x + d)^2*(b*arctanh(c*x) + a)^2/x^4, x)","F",0
84,0,0,0,0.000000," ","integrate(x^3*(c*d*x+d)^3*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\int {\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{3}\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)^2*x^3, x)","F",0
85,0,0,0,0.000000," ","integrate(x^2*(c*d*x+d)^3*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\int {\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{2}\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)^2*x^2, x)","F",0
86,0,0,0,0.000000," ","integrate(x*(c*d*x+d)^3*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\int {\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)^2*x, x)","F",0
87,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\int {\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)^2, x)","F",0
88,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x}\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)^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=""giac"")","\int \frac{{\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x^{2}}\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)^2/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=""giac"")","\int \frac{{\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x^{3}}\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)^2/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=""giac"")","\int \frac{{\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x^{4}}\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)^2/x^4, x)","F",0
92,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^5,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x^{5}}\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)^2/x^5, x)","F",0
93,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^6,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x^{6}}\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)^2/x^6, x)","F",0
94,0,0,0,0.000000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^7,x, algorithm=""giac"")","\int \frac{{\left(c d x + d\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x^{7}}\,{d x}"," ",0,"integrate((c*d*x + d)^3*(b*arctanh(c*x) + a)^2/x^7, x)","F",0
95,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x))^2/(c*d*x+d),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{3}}{c d x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*x^3/(c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{2}}{c d x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*x^2/(c*d*x + d), x)","F",0
97,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))^2/(c*d*x+d),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x}{c d x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*x/(c*d*x + d), x)","F",0
98,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/(c*d*x+d),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{c d x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/(c*d*x + d), x)","F",0
99,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x/(c*d*x+d),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{{\left(c d x + d\right)} x}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/((c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{{\left(c d x + d\right)} x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/((c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{{\left(c d x + d\right)} x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/((c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{{\left(c d x + d\right)} x^{4}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/((c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{4}}{{\left(c d x + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*x^4/(c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{3}}{{\left(c d x + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*x^3/(c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{2}}{{\left(c d x + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*x^2/(c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x}{{\left(c d x + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*x/(c*d*x + d)^2, x)","F",0
107,1,119,0,0.160520," ","integrate((a+b*arctanh(c*x))^2/(c*d*x+d)^2,x, algorithm=""giac"")","\frac{1}{8} \, c {\left(\frac{{\left(c x - 1\right)} b^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{{\left(c x + 1\right)} c^{2} d^{2}} + \frac{2 \, {\left(2 \, a b + b^{2}\right)} {\left(c x - 1\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{{\left(c x + 1\right)} c^{2} d^{2}} + \frac{2 \, {\left(2 \, a^{2} + 2 \, a b + b^{2}\right)} {\left(c x - 1\right)}}{{\left(c x + 1\right)} c^{2} d^{2}}\right)}"," ",0,"1/8*c*((c*x - 1)*b^2*log(-(c*x + 1)/(c*x - 1))^2/((c*x + 1)*c^2*d^2) + 2*(2*a*b + b^2)*(c*x - 1)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)*c^2*d^2) + 2*(2*a^2 + 2*a*b + b^2)*(c*x - 1)/((c*x + 1)*c^2*d^2))","A",0
108,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x/(c*d*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{{\left(c d x + d\right)}^{2} x}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/((c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{{\left(c d x + d\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/((c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{{\left(c d x + d\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/((c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{4}}{{\left(c d x + d\right)}^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*x^4/(c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{3}}{{\left(c d x + d\right)}^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*x^3/(c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{2}}{{\left(c d x + d\right)}^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*x^2/(c*d*x + d)^3, x)","F",0
114,1,226,0,0.320178," ","integrate(x*(a+b*arctanh(c*x))^2/(c*d*x+d)^3,x, algorithm=""giac"")","\frac{1}{64} \, c {\left(\frac{2 \, {\left(\frac{2 \, {\left(c x + 1\right)} b^{2}}{c x - 1} + b^{2}\right)} {\left(c x - 1\right)}^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{{\left(c x + 1\right)}^{2} c^{3} d^{3}} + \frac{2 \, {\left(\frac{8 \, {\left(c x + 1\right)} a b}{c x - 1} + 4 \, a b + \frac{4 \, {\left(c x + 1\right)} b^{2}}{c x - 1} + b^{2}\right)} {\left(c x - 1\right)}^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)}{{\left(c x + 1\right)}^{2} c^{3} d^{3}} + \frac{{\left(\frac{16 \, {\left(c x + 1\right)} a^{2}}{c x - 1} + 8 \, a^{2} + \frac{16 \, {\left(c x + 1\right)} a b}{c x - 1} + 4 \, a b + \frac{8 \, {\left(c x + 1\right)} b^{2}}{c x - 1} + b^{2}\right)} {\left(c x - 1\right)}^{2}}{{\left(c x + 1\right)}^{2} c^{3} d^{3}}\right)}"," ",0,"1/64*c*(2*(2*(c*x + 1)*b^2/(c*x - 1) + b^2)*(c*x - 1)^2*log(-(c*x + 1)/(c*x - 1))^2/((c*x + 1)^2*c^3*d^3) + 2*(8*(c*x + 1)*a*b/(c*x - 1) + 4*a*b + 4*(c*x + 1)*b^2/(c*x - 1) + b^2)*(c*x - 1)^2*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^2*c^3*d^3) + (16*(c*x + 1)*a^2/(c*x - 1) + 8*a^2 + 16*(c*x + 1)*a*b/(c*x - 1) + 4*a*b + 8*(c*x + 1)*b^2/(c*x - 1) + b^2)*(c*x - 1)^2/((c*x + 1)^2*c^3*d^3))","A",0
115,1,232,0,0.190722," ","integrate((a+b*arctanh(c*x))^2/(c*d*x+d)^3,x, algorithm=""giac"")","\frac{1}{64} \, c {\left(\frac{2 \, {\left(\frac{2 \, {\left(c x + 1\right)} b^{2}}{c x - 1} - b^{2}\right)} {\left(c x - 1\right)}^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{{\left(c x + 1\right)}^{2} c^{2} d^{3}} + \frac{2 \, {\left(\frac{8 \, {\left(c x + 1\right)} a b}{c x - 1} - 4 \, a b + \frac{4 \, {\left(c x + 1\right)} b^{2}}{c x - 1} - b^{2}\right)} {\left(c x - 1\right)}^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)}{{\left(c x + 1\right)}^{2} c^{2} d^{3}} + \frac{{\left(\frac{16 \, {\left(c x + 1\right)} a^{2}}{c x - 1} - 8 \, a^{2} + \frac{16 \, {\left(c x + 1\right)} a b}{c x - 1} - 4 \, a b + \frac{8 \, {\left(c x + 1\right)} b^{2}}{c x - 1} - b^{2}\right)} {\left(c x - 1\right)}^{2}}{{\left(c x + 1\right)}^{2} c^{2} d^{3}}\right)}"," ",0,"1/64*c*(2*(2*(c*x + 1)*b^2/(c*x - 1) - b^2)*(c*x - 1)^2*log(-(c*x + 1)/(c*x - 1))^2/((c*x + 1)^2*c^2*d^3) + 2*(8*(c*x + 1)*a*b/(c*x - 1) - 4*a*b + 4*(c*x + 1)*b^2/(c*x - 1) - b^2)*(c*x - 1)^2*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^2*c^2*d^3) + (16*(c*x + 1)*a^2/(c*x - 1) - 8*a^2 + 16*(c*x + 1)*a*b/(c*x - 1) - 4*a*b + 8*(c*x + 1)*b^2/(c*x - 1) - b^2)*(c*x - 1)^2/((c*x + 1)^2*c^2*d^3))","A",0
116,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x/(c*d*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{{\left(c d x + d\right)}^{3} x}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/((c*d*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{{\left(c d x + d\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/((c*d*x + d)^3*x^2), x)","F",0
118,1,333,0,0.471720," ","integrate((a+b*arctanh(c*x))^2/(c*x+1)^4,x, algorithm=""giac"")","\frac{1}{1728} \, c {\left(\frac{18 \, {\left(\frac{3 \, {\left(c x + 1\right)}^{2} b^{2}}{{\left(c x - 1\right)}^{2}} - \frac{3 \, {\left(c x + 1\right)} b^{2}}{c x - 1} + b^{2}\right)} {\left(c x - 1\right)}^{3} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{{\left(c x + 1\right)}^{3} c^{2}} + \frac{6 \, {\left(\frac{36 \, {\left(c x + 1\right)}^{2} a b}{{\left(c x - 1\right)}^{2}} - \frac{36 \, {\left(c x + 1\right)} a b}{c x - 1} + 12 \, a b + \frac{18 \, {\left(c x + 1\right)}^{2} b^{2}}{{\left(c x - 1\right)}^{2}} - \frac{9 \, {\left(c x + 1\right)} b^{2}}{c x - 1} + 2 \, b^{2}\right)} {\left(c x - 1\right)}^{3} \log\left(-\frac{c x + 1}{c x - 1}\right)}{{\left(c x + 1\right)}^{3} c^{2}} + \frac{{\left(\frac{216 \, {\left(c x + 1\right)}^{2} a^{2}}{{\left(c x - 1\right)}^{2}} - \frac{216 \, {\left(c x + 1\right)} a^{2}}{c x - 1} + 72 \, a^{2} + \frac{216 \, {\left(c x + 1\right)}^{2} a b}{{\left(c x - 1\right)}^{2}} - \frac{108 \, {\left(c x + 1\right)} a b}{c x - 1} + 24 \, a b + \frac{108 \, {\left(c x + 1\right)}^{2} b^{2}}{{\left(c x - 1\right)}^{2}} - \frac{27 \, {\left(c x + 1\right)} b^{2}}{c x - 1} + 4 \, b^{2}\right)} {\left(c x - 1\right)}^{3}}{{\left(c x + 1\right)}^{3} c^{2}}\right)}"," ",0,"1/1728*c*(18*(3*(c*x + 1)^2*b^2/(c*x - 1)^2 - 3*(c*x + 1)*b^2/(c*x - 1) + b^2)*(c*x - 1)^3*log(-(c*x + 1)/(c*x - 1))^2/((c*x + 1)^3*c^2) + 6*(36*(c*x + 1)^2*a*b/(c*x - 1)^2 - 36*(c*x + 1)*a*b/(c*x - 1) + 12*a*b + 18*(c*x + 1)^2*b^2/(c*x - 1)^2 - 9*(c*x + 1)*b^2/(c*x - 1) + 2*b^2)*(c*x - 1)^3*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^3*c^2) + (216*(c*x + 1)^2*a^2/(c*x - 1)^2 - 216*(c*x + 1)*a^2/(c*x - 1) + 72*a^2 + 216*(c*x + 1)^2*a*b/(c*x - 1)^2 - 108*(c*x + 1)*a*b/(c*x - 1) + 24*a*b + 108*(c*x + 1)^2*b^2/(c*x - 1)^2 - 27*(c*x + 1)*b^2/(c*x - 1) + 4*b^2)*(c*x - 1)^3/((c*x + 1)^3*c^2))","B",0
119,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/(-a*c*x^2+c*x),x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{2}}{a c x^{2} - c x}\,{d x}"," ",0,"integrate(-arctanh(a*x)^2/(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=""giac"")","\int {\left(c x + 1\right)}^{3} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((c*x + 1)^3*(b*arctanh(c*x) + a)^3, x)","F",0
121,0,0,0,0.000000," ","integrate((c*x+1)^2*(a+b*arctanh(c*x))^3,x, algorithm=""giac"")","\int {\left(c x + 1\right)}^{2} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((c*x + 1)^2*(b*arctanh(c*x) + a)^3, x)","F",0
122,0,0,0,0.000000," ","integrate((c*x+1)*(a+b*arctanh(c*x))^3,x, algorithm=""giac"")","\int {\left(c x + 1\right)} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((c*x + 1)*(b*arctanh(c*x) + a)^3, x)","F",0
123,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/(c*x+1),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3}}{c x + 1}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^3/(c*x + 1), x)","F",0
124,1,172,0,0.206051," ","integrate((a+b*arctanh(c*x))^3/(c*x+1)^2,x, algorithm=""giac"")","\frac{1}{16} \, {\left(\frac{{\left(c x - 1\right)} b^{3} \log\left(-\frac{c x + 1}{c x - 1}\right)^{3}}{{\left(c x + 1\right)} c^{2}} + \frac{3 \, {\left(2 \, a b^{2} + b^{3}\right)} {\left(c x - 1\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{{\left(c x + 1\right)} c^{2}} + \frac{6 \, {\left(2 \, a^{2} b + 2 \, a b^{2} + b^{3}\right)} {\left(c x - 1\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{{\left(c x + 1\right)} c^{2}} + \frac{2 \, {\left(4 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 3 \, b^{3}\right)} {\left(c x - 1\right)}}{{\left(c x + 1\right)} c^{2}}\right)} c"," ",0,"1/16*((c*x - 1)*b^3*log(-(c*x + 1)/(c*x - 1))^3/((c*x + 1)*c^2) + 3*(2*a*b^2 + b^3)*(c*x - 1)*log(-(c*x + 1)/(c*x - 1))^2/((c*x + 1)*c^2) + 6*(2*a^2*b + 2*a*b^2 + b^3)*(c*x - 1)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)*c^2) + 2*(4*a^3 + 6*a^2*b + 6*a*b^2 + 3*b^3)*(c*x - 1)/((c*x + 1)*c^2))*c","A",0
125,1,362,0,0.286984," ","integrate((a+b*arctanh(c*x))^3/(c*x+1)^3,x, algorithm=""giac"")","\frac{1}{256} \, {\left(\frac{4 \, {\left(\frac{2 \, {\left(c x + 1\right)} b^{3}}{c x - 1} - b^{3}\right)} {\left(c x - 1\right)}^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)^{3}}{{\left(c x + 1\right)}^{2} c^{2}} + \frac{6 \, {\left(\frac{8 \, {\left(c x + 1\right)} a b^{2}}{c x - 1} - 4 \, a b^{2} + \frac{4 \, {\left(c x + 1\right)} b^{3}}{c x - 1} - b^{3}\right)} {\left(c x - 1\right)}^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{{\left(c x + 1\right)}^{2} c^{2}} + \frac{6 \, {\left(\frac{16 \, {\left(c x + 1\right)} a^{2} b}{c x - 1} - 8 \, a^{2} b + \frac{16 \, {\left(c x + 1\right)} a b^{2}}{c x - 1} - 4 \, a b^{2} + \frac{8 \, {\left(c x + 1\right)} b^{3}}{c x - 1} - b^{3}\right)} {\left(c x - 1\right)}^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)}{{\left(c x + 1\right)}^{2} c^{2}} + \frac{{\left(\frac{64 \, {\left(c x + 1\right)} a^{3}}{c x - 1} - 32 \, a^{3} + \frac{96 \, {\left(c x + 1\right)} a^{2} b}{c x - 1} - 24 \, a^{2} b + \frac{96 \, {\left(c x + 1\right)} a b^{2}}{c x - 1} - 12 \, a b^{2} + \frac{48 \, {\left(c x + 1\right)} b^{3}}{c x - 1} - 3 \, b^{3}\right)} {\left(c x - 1\right)}^{2}}{{\left(c x + 1\right)}^{2} c^{2}}\right)} c"," ",0,"1/256*(4*(2*(c*x + 1)*b^3/(c*x - 1) - b^3)*(c*x - 1)^2*log(-(c*x + 1)/(c*x - 1))^3/((c*x + 1)^2*c^2) + 6*(8*(c*x + 1)*a*b^2/(c*x - 1) - 4*a*b^2 + 4*(c*x + 1)*b^3/(c*x - 1) - b^3)*(c*x - 1)^2*log(-(c*x + 1)/(c*x - 1))^2/((c*x + 1)^2*c^2) + 6*(16*(c*x + 1)*a^2*b/(c*x - 1) - 8*a^2*b + 16*(c*x + 1)*a*b^2/(c*x - 1) - 4*a*b^2 + 8*(c*x + 1)*b^3/(c*x - 1) - b^3)*(c*x - 1)^2*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^2*c^2) + (64*(c*x + 1)*a^3/(c*x - 1) - 32*a^3 + 96*(c*x + 1)*a^2*b/(c*x - 1) - 24*a^2*b + 96*(c*x + 1)*a*b^2/(c*x - 1) - 12*a*b^2 + 48*(c*x + 1)*b^3/(c*x - 1) - 3*b^3)*(c*x - 1)^2/((c*x + 1)^2*c^2))*c","A",0
126,1,555,0,0.228032," ","integrate((a+b*arctanh(c*x))^3/(c*x+1)^4,x, algorithm=""giac"")","\frac{1}{6912} \, {\left(\frac{36 \, {\left(\frac{3 \, {\left(c x + 1\right)}^{2} b^{3}}{{\left(c x - 1\right)}^{2}} - \frac{3 \, {\left(c x + 1\right)} b^{3}}{c x - 1} + b^{3}\right)} {\left(c x - 1\right)}^{3} \log\left(-\frac{c x + 1}{c x - 1}\right)^{3}}{{\left(c x + 1\right)}^{3} c^{2}} + \frac{18 \, {\left(\frac{36 \, {\left(c x + 1\right)}^{2} a b^{2}}{{\left(c x - 1\right)}^{2}} - \frac{36 \, {\left(c x + 1\right)} a b^{2}}{c x - 1} + 12 \, a b^{2} + \frac{18 \, {\left(c x + 1\right)}^{2} b^{3}}{{\left(c x - 1\right)}^{2}} - \frac{9 \, {\left(c x + 1\right)} b^{3}}{c x - 1} + 2 \, b^{3}\right)} {\left(c x - 1\right)}^{3} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{{\left(c x + 1\right)}^{3} c^{2}} + \frac{6 \, {\left(\frac{216 \, {\left(c x + 1\right)}^{2} a^{2} b}{{\left(c x - 1\right)}^{2}} - \frac{216 \, {\left(c x + 1\right)} a^{2} b}{c x - 1} + 72 \, a^{2} b + \frac{216 \, {\left(c x + 1\right)}^{2} a b^{2}}{{\left(c x - 1\right)}^{2}} - \frac{108 \, {\left(c x + 1\right)} a b^{2}}{c x - 1} + 24 \, a b^{2} + \frac{108 \, {\left(c x + 1\right)}^{2} b^{3}}{{\left(c x - 1\right)}^{2}} - \frac{27 \, {\left(c x + 1\right)} b^{3}}{c x - 1} + 4 \, b^{3}\right)} {\left(c x - 1\right)}^{3} \log\left(-\frac{c x + 1}{c x - 1}\right)}{{\left(c x + 1\right)}^{3} c^{2}} + \frac{{\left(\frac{864 \, {\left(c x + 1\right)}^{2} a^{3}}{{\left(c x - 1\right)}^{2}} - \frac{864 \, {\left(c x + 1\right)} a^{3}}{c x - 1} + 288 \, a^{3} + \frac{1296 \, {\left(c x + 1\right)}^{2} a^{2} b}{{\left(c x - 1\right)}^{2}} - \frac{648 \, {\left(c x + 1\right)} a^{2} b}{c x - 1} + 144 \, a^{2} b + \frac{1296 \, {\left(c x + 1\right)}^{2} a b^{2}}{{\left(c x - 1\right)}^{2}} - \frac{324 \, {\left(c x + 1\right)} a b^{2}}{c x - 1} + 48 \, a b^{2} + \frac{648 \, {\left(c x + 1\right)}^{2} b^{3}}{{\left(c x - 1\right)}^{2}} - \frac{81 \, {\left(c x + 1\right)} b^{3}}{c x - 1} + 8 \, b^{3}\right)} {\left(c x - 1\right)}^{3}}{{\left(c x + 1\right)}^{3} c^{2}}\right)} c"," ",0,"1/6912*(36*(3*(c*x + 1)^2*b^3/(c*x - 1)^2 - 3*(c*x + 1)*b^3/(c*x - 1) + b^3)*(c*x - 1)^3*log(-(c*x + 1)/(c*x - 1))^3/((c*x + 1)^3*c^2) + 18*(36*(c*x + 1)^2*a*b^2/(c*x - 1)^2 - 36*(c*x + 1)*a*b^2/(c*x - 1) + 12*a*b^2 + 18*(c*x + 1)^2*b^3/(c*x - 1)^2 - 9*(c*x + 1)*b^3/(c*x - 1) + 2*b^3)*(c*x - 1)^3*log(-(c*x + 1)/(c*x - 1))^2/((c*x + 1)^3*c^2) + 6*(216*(c*x + 1)^2*a^2*b/(c*x - 1)^2 - 216*(c*x + 1)*a^2*b/(c*x - 1) + 72*a^2*b + 216*(c*x + 1)^2*a*b^2/(c*x - 1)^2 - 108*(c*x + 1)*a*b^2/(c*x - 1) + 24*a*b^2 + 108*(c*x + 1)^2*b^3/(c*x - 1)^2 - 27*(c*x + 1)*b^3/(c*x - 1) + 4*b^3)*(c*x - 1)^3*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^3*c^2) + (864*(c*x + 1)^2*a^3/(c*x - 1)^2 - 864*(c*x + 1)*a^3/(c*x - 1) + 288*a^3 + 1296*(c*x + 1)^2*a^2*b/(c*x - 1)^2 - 648*(c*x + 1)*a^2*b/(c*x - 1) + 144*a^2*b + 1296*(c*x + 1)^2*a*b^2/(c*x - 1)^2 - 324*(c*x + 1)*a*b^2/(c*x - 1) + 48*a*b^2 + 648*(c*x + 1)^2*b^3/(c*x - 1)^2 - 81*(c*x + 1)*b^3/(c*x - 1) + 8*b^3)*(c*x - 1)^3/((c*x + 1)^3*c^2))*c","B",0
127,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^3/(a*c*x+c),x, algorithm=""giac"")","\int \frac{x^{2} \operatorname{artanh}\left(a x\right)^{3}}{a c x + c}\,{d x}"," ",0,"integrate(x^2*arctanh(a*x)^3/(a*c*x + c), x)","F",0
128,0,0,0,0.000000," ","integrate(x*arctanh(a*x)^3/(a*c*x+c),x, algorithm=""giac"")","\int \frac{x \operatorname{artanh}\left(a x\right)^{3}}{a c x + c}\,{d x}"," ",0,"integrate(x*arctanh(a*x)^3/(a*c*x + c), x)","F",0
129,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/(a*c*x+c),x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{a c x + c}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/(a*c*x + c), x)","F",0
130,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x/(a*c*x+c),x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(a c x + c\right)} x}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/((a*c*x + c)*x), x)","F",0
131,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/(a*c*x^2+c*x),x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{a c x^{2} + c x}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/(a*c*x^2 + c*x), x)","F",0
132,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^2/(a*c*x+c),x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(a c x + c\right)} x^{2}}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/((a*c*x + 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=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(a c x + c\right)} x^{3}}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/((a*c*x + 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=""giac"")","\int -\frac{x^{2} \operatorname{artanh}\left(a x\right)^{4}}{a c x - c}\,{d x}"," ",0,"integrate(-x^2*arctanh(a*x)^4/(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=""giac"")","\int -\frac{x \operatorname{artanh}\left(a x\right)^{4}}{a c x - c}\,{d x}"," ",0,"integrate(-x*arctanh(a*x)^4/(a*c*x - c), x)","F",0
136,0,0,0,0.000000," ","integrate(arctanh(a*x)^4/(-a*c*x+c),x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{4}}{a c x - c}\,{d x}"," ",0,"integrate(-arctanh(a*x)^4/(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=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{4}}{{\left(a c x - c\right)} x}\,{d x}"," ",0,"integrate(-arctanh(a*x)^4/((a*c*x - c)*x), x)","F",0
138,0,0,0,0.000000," ","integrate(arctanh(a*x)^4/(-a*c*x^2+c*x),x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{4}}{a c x^{2} - c x}\,{d x}"," ",0,"integrate(-arctanh(a*x)^4/(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=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{4}}{{\left(a c x - c\right)} x^{2}}\,{d x}"," ",0,"integrate(-arctanh(a*x)^4/((a*c*x - 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=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{4}}{{\left(a c x - c\right)} x^{3}}\,{d x}"," ",0,"integrate(-arctanh(a*x)^4/((a*c*x - c)*x^3), x)","F",0
141,0,0,0,0.000000," ","integrate(x/(a*c*x+c)/arctanh(a*x),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\int \frac{x}{{\left(a c x + c\right)} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x/((a*c*x + c)*arctanh(a*x)^2), x)","F",0
145,0,0,0,0.000000," ","integrate(1/(a*c*x+c)/arctanh(a*x)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a c x + c\right)} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a*c*x + c)*arctanh(a*x)^2), x)","F",0
146,0,0,0,0.000000," ","integrate(1/x/(a*c*x+c)/arctanh(a*x)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a c x + c\right)} x \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a*c*x + c)*x*arctanh(a*x)^2), x)","F",0
147,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x))/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} x^{3}}{e x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*x^3/(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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} x^{2}}{e x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*x^2/(e*x + d), x)","F",0
149,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} x}{e x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*x/(e*x + d), x)","F",0
150,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/(e*x+d),x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{e x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/(e*x + d), x)","F",0
151,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x/(e*x+d),x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{{\left(e x + d\right)} x}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/((e*x + d)*x), x)","F",0
152,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x^2/(e*x+d),x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{{\left(e x + d\right)} x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/((e*x + 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=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{{\left(e x + d\right)} x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/((e*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{2}}{e x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*x^2/(e*x + d), x)","F",0
155,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))^2/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x}{e x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*x/(e*x + d), x)","F",0
156,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{e x + d}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/(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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{{\left(e x + d\right)} x}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/((e*x + 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{{\left(e x + d\right)} x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/((e*x + d)*x^2), x)","F",0
159,0,0,0,0.000000," ","integrate(arctanh(c*x)^2/x/(e*x+d),x, algorithm=""giac"")","\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=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
161,1,335,0,0.226705," ","integrate(x^4*(-a^2*x^2+1)*arctanh(a*x),x, algorithm=""giac"")","\frac{2}{105} \, a {\left(\frac{3 \, \log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right)}{a^{6}} - \frac{3 \, \log\left({\left| -\frac{a x + 1}{a x - 1} + 1 \right|}\right)}{a^{6}} - \frac{\frac{3 \, {\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} + \frac{36 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{2 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{36 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{3 \, {\left(a x + 1\right)}}{a x - 1}}{a^{6} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{6}} - \frac{3 \, {\left(\frac{35 \, {\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} + \frac{35 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{70 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{14 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{7 \, {\left(a x + 1\right)}}{a x - 1} - 1\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{a^{6} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{7}}\right)}"," ",0,"2/105*a*(3*log(abs(-a*x - 1)/abs(a*x - 1))/a^6 - 3*log(abs(-(a*x + 1)/(a*x - 1) + 1))/a^6 - (3*(a*x + 1)^5/(a*x - 1)^5 + 36*(a*x + 1)^4/(a*x - 1)^4 + 2*(a*x + 1)^3/(a*x - 1)^3 + 36*(a*x + 1)^2/(a*x - 1)^2 + 3*(a*x + 1)/(a*x - 1))/(a^6*((a*x + 1)/(a*x - 1) - 1)^6) - 3*(35*(a*x + 1)^5/(a*x - 1)^5 + 35*(a*x + 1)^4/(a*x - 1)^4 + 70*(a*x + 1)^3/(a*x - 1)^3 + 14*(a*x + 1)^2/(a*x - 1)^2 + 7*(a*x + 1)/(a*x - 1) - 1)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/(a^6*((a*x + 1)/(a*x - 1) - 1)^7))","B",0
162,1,227,0,0.210292," ","integrate(x^3*(-a^2*x^2+1)*arctanh(a*x),x, algorithm=""giac"")","-\frac{1}{45} \, a {\left(\frac{\frac{45 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} - \frac{25 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{35 \, {\left(a x + 1\right)}}{a x - 1} - 7}{a^{5} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{5}} + \frac{30 \, {\left(\frac{3 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{2 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{3 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}}\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{a^{5} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{6}}\right)}"," ",0,"-1/45*a*((45*(a*x + 1)^3/(a*x - 1)^3 - 25*(a*x + 1)^2/(a*x - 1)^2 + 35*(a*x + 1)/(a*x - 1) - 7)/(a^5*((a*x + 1)/(a*x - 1) - 1)^5) + 30*(3*(a*x + 1)^4/(a*x - 1)^4 + 2*(a*x + 1)^3/(a*x - 1)^3 + 3*(a*x + 1)^2/(a*x - 1)^2)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/(a^5*((a*x + 1)/(a*x - 1) - 1)^6))","B",0
163,1,268,0,0.156596," ","integrate(x^2*(-a^2*x^2+1)*arctanh(a*x),x, algorithm=""giac"")","\frac{2}{15} \, a {\left(\frac{\log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right)}{a^{4}} - \frac{\log\left({\left| -\frac{a x + 1}{a x - 1} + 1 \right|}\right)}{a^{4}} - \frac{\frac{{\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{4 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{a x + 1}{a x - 1}}{a^{4} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{4}} - \frac{{\left(\frac{15 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{5 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{5 \, {\left(a x + 1\right)}}{a x - 1} - 1\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{a^{4} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{5}}\right)}"," ",0,"2/15*a*(log(abs(-a*x - 1)/abs(a*x - 1))/a^4 - log(abs(-(a*x + 1)/(a*x - 1) + 1))/a^4 - ((a*x + 1)^3/(a*x - 1)^3 + 4*(a*x + 1)^2/(a*x - 1)^2 + (a*x + 1)/(a*x - 1))/(a^4*((a*x + 1)/(a*x - 1) - 1)^4) - (15*(a*x + 1)^3/(a*x - 1)^3 + 5*(a*x + 1)^2/(a*x - 1)^2 + 5*(a*x + 1)/(a*x - 1) - 1)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/(a^4*((a*x + 1)/(a*x - 1) - 1)^5))","B",0
164,1,160,0,0.292745," ","integrate(x*(-a^2*x^2+1)*arctanh(a*x),x, algorithm=""giac"")","-\frac{1}{3} \, a {\left(\frac{\frac{3 \, {\left(a x + 1\right)}}{a x - 1} - 1}{a^{3} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{3}} + \frac{6 \, {\left(a x + 1\right)}^{2} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{{\left(a x - 1\right)}^{2} a^{3} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{4}}\right)}"," ",0,"-1/3*a*((3*(a*x + 1)/(a*x - 1) - 1)/(a^3*((a*x + 1)/(a*x - 1) - 1)^3) + 6*(a*x + 1)^2*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/((a*x - 1)^2*a^3*((a*x + 1)/(a*x - 1) - 1)^4))","B",0
165,1,203,0,0.177946," ","integrate((-a^2*x^2+1)*arctanh(a*x),x, algorithm=""giac"")","\frac{2}{3} \, a {\left(\frac{\log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right)}{a^{2}} - \frac{\log\left({\left| -\frac{a x + 1}{a x - 1} + 1 \right|}\right)}{a^{2}} - \frac{{\left(\frac{3 \, {\left(a x + 1\right)}}{a x - 1} - 1\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{a^{2} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{3}} - \frac{a x + 1}{{\left(a x - 1\right)} a^{2} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{2}}\right)}"," ",0,"2/3*a*(log(abs(-a*x - 1)/abs(a*x - 1))/a^2 - log(abs(-(a*x + 1)/(a*x - 1) + 1))/a^2 - (3*(a*x + 1)/(a*x - 1) - 1)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/(a^2*((a*x + 1)/(a*x - 1) - 1)^3) - (a*x + 1)/((a*x - 1)*a^2*((a*x + 1)/(a*x - 1) - 1)^2))","B",0
166,0,0,0,0.000000," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x,x, algorithm=""giac"")","\int -\frac{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)}{x}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*arctanh(a*x)/x, x)","F",0
167,1,145,0,0.381046," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^2,x, algorithm=""giac"")","-a {\left(\frac{2 \, \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{\frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} - 1} + \log\left(\frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}}\right) - \log\left({\left| \frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} - 1 \right|}\right)\right)}"," ",0,"-a*(2*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/((a*x + 1)^2/(a*x - 1)^2 - 1) + log((a*x + 1)^2/(a*x - 1)^2) - log(abs((a*x + 1)^2/(a*x - 1)^2 - 1)))","B",0
168,1,330,0,2.180531," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^3,x, algorithm=""giac"")","a^{2} {\left(\frac{\log\left(\frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}}\right)}{a} - \frac{\log\left({\left| \frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} - 1 \right|}\right)}{a} + \frac{\frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} - 2}{a {\left(\frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} - 1\right)}} - \frac{2 \, \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{a - \frac{a {\left(\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1\right)}}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}} - 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{a - \frac{a {\left(\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1\right)}}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}} + 1}\right)}{a {\left(\frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} - 1\right)}^{2}}\right)}"," ",0,"a^2*(log((a*x + 1)^2/(a*x - 1)^2)/a - log(abs((a*x + 1)^2/(a*x - 1)^2 - 1))/a + ((a*x + 1)^2/(a*x - 1)^2 - 2)/(a*((a*x + 1)^2/(a*x - 1)^2 - 1)) - 2*log(-(a*((a*x + 1)/(a*x - 1) + 1)/(a - a*(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1)) - 1)/(a*((a*x + 1)/(a*x - 1) + 1)/(a - a*(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1)) + 1))/(a*((a*x + 1)^2/(a*x - 1)^2 - 1)^2))","B",0
169,1,204,0,0.209101," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^4,x, algorithm=""giac"")","\frac{2}{3} \, {\left(a^{2} \log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right) - a^{2} \log\left({\left| -\frac{a x + 1}{a x - 1} - 1 \right|}\right) + \frac{{\left(a x + 1\right)} a^{2}}{{\left(a x - 1\right)} {\left(\frac{a x + 1}{a x - 1} + 1\right)}^{2}} - \frac{{\left(\frac{3 \, {\left(a x + 1\right)} a^{2}}{a x - 1} + a^{2}\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{{\left(\frac{a x + 1}{a x - 1} + 1\right)}^{3}}\right)} a"," ",0,"2/3*(a^2*log(abs(-a*x - 1)/abs(a*x - 1)) - a^2*log(abs(-(a*x + 1)/(a*x - 1) - 1)) + (a*x + 1)*a^2/((a*x - 1)*((a*x + 1)/(a*x - 1) + 1)^2) - (3*(a*x + 1)*a^2/(a*x - 1) + a^2)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/((a*x + 1)/(a*x - 1) + 1)^3)*a","B",0
170,1,160,0,0.181478," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^5,x, algorithm=""giac"")","-\frac{1}{3} \, a {\left(\frac{a^{3} {\left(\frac{3 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)}}{{\left(\frac{a x + 1}{a x - 1} + 1\right)}^{3}} + \frac{6 \, {\left(a x + 1\right)}^{2} a^{3} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{{\left(a x - 1\right)}^{2} {\left(\frac{a x + 1}{a x - 1} + 1\right)}^{4}}\right)}"," ",0,"-1/3*a*(a^3*(3*(a*x + 1)/(a*x - 1) + 1)/((a*x + 1)/(a*x - 1) + 1)^3 + 6*(a*x + 1)^2*a^3*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/((a*x - 1)^2*((a*x + 1)/(a*x - 1) + 1)^4))","B",0
171,1,281,0,0.209167," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^6,x, algorithm=""giac"")","\frac{2}{15} \, {\left(a^{4} \log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right) - a^{4} \log\left({\left| -\frac{a x + 1}{a x - 1} - 1 \right|}\right) + \frac{\frac{{\left(a x + 1\right)}^{3} a^{4}}{{\left(a x - 1\right)}^{3}} - \frac{4 \, {\left(a x + 1\right)}^{2} a^{4}}{{\left(a x - 1\right)}^{2}} + \frac{{\left(a x + 1\right)} a^{4}}{a x - 1}}{{\left(\frac{a x + 1}{a x - 1} + 1\right)}^{4}} - \frac{{\left(\frac{15 \, {\left(a x + 1\right)}^{3} a^{4}}{{\left(a x - 1\right)}^{3}} - \frac{5 \, {\left(a x + 1\right)}^{2} a^{4}}{{\left(a x - 1\right)}^{2}} + \frac{5 \, {\left(a x + 1\right)} a^{4}}{a x - 1} + a^{4}\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{{\left(\frac{a x + 1}{a x - 1} + 1\right)}^{5}}\right)} a"," ",0,"2/15*(a^4*log(abs(-a*x - 1)/abs(a*x - 1)) - a^4*log(abs(-(a*x + 1)/(a*x - 1) - 1)) + ((a*x + 1)^3*a^4/(a*x - 1)^3 - 4*(a*x + 1)^2*a^4/(a*x - 1)^2 + (a*x + 1)*a^4/(a*x - 1))/((a*x + 1)/(a*x - 1) + 1)^4 - (15*(a*x + 1)^3*a^4/(a*x - 1)^3 - 5*(a*x + 1)^2*a^4/(a*x - 1)^2 + 5*(a*x + 1)*a^4/(a*x - 1) + a^4)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/((a*x + 1)/(a*x - 1) + 1)^5)*a","B",0
172,0,0,0,0.000000," ","integrate(x^4*(-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""giac"")","\int -{\left(a^{2} x^{2} - 1\right)} x^{4} \operatorname{artanh}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*x^4*arctanh(a*x)^2, x)","F",0
173,1,522,0,0.173095," ","integrate(x^3*(-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""giac"")","-\frac{1}{45} \, {\left(\frac{15 \, {\left(\frac{3 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{2 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{3 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}{\frac{{\left(a x + 1\right)}^{6} a^{5}}{{\left(a x - 1\right)}^{6}} - \frac{6 \, {\left(a x + 1\right)}^{5} a^{5}}{{\left(a x - 1\right)}^{5}} + \frac{15 \, {\left(a x + 1\right)}^{4} a^{5}}{{\left(a x - 1\right)}^{4}} - \frac{20 \, {\left(a x + 1\right)}^{3} a^{5}}{{\left(a x - 1\right)}^{3}} + \frac{15 \, {\left(a x + 1\right)}^{2} a^{5}}{{\left(a x - 1\right)}^{2}} - \frac{6 \, {\left(a x + 1\right)} a^{5}}{a x - 1} + a^{5}} + \frac{{\left(\frac{45 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} - \frac{25 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{35 \, {\left(a x + 1\right)}}{a x - 1} - 7\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{\frac{{\left(a x + 1\right)}^{5} a^{5}}{{\left(a x - 1\right)}^{5}} - \frac{5 \, {\left(a x + 1\right)}^{4} a^{5}}{{\left(a x - 1\right)}^{4}} + \frac{10 \, {\left(a x + 1\right)}^{3} a^{5}}{{\left(a x - 1\right)}^{3}} - \frac{10 \, {\left(a x + 1\right)}^{2} a^{5}}{{\left(a x - 1\right)}^{2}} + \frac{5 \, {\left(a x + 1\right)} a^{5}}{a x - 1} - a^{5}} + \frac{\frac{7 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} - \frac{2 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{7 \, {\left(a x + 1\right)}}{a x - 1}}{\frac{{\left(a x + 1\right)}^{4} a^{5}}{{\left(a x - 1\right)}^{4}} - \frac{4 \, {\left(a x + 1\right)}^{3} a^{5}}{{\left(a x - 1\right)}^{3}} + \frac{6 \, {\left(a x + 1\right)}^{2} a^{5}}{{\left(a x - 1\right)}^{2}} - \frac{4 \, {\left(a x + 1\right)} a^{5}}{a x - 1} + a^{5}} + \frac{7 \, \log\left(-\frac{a x + 1}{a x - 1} + 1\right)}{a^{5}} - \frac{7 \, \log\left(-\frac{a x + 1}{a x - 1}\right)}{a^{5}}\right)} a"," ",0,"-1/45*(15*(3*(a*x + 1)^4/(a*x - 1)^4 + 2*(a*x + 1)^3/(a*x - 1)^3 + 3*(a*x + 1)^2/(a*x - 1)^2)*log(-(a*x + 1)/(a*x - 1))^2/((a*x + 1)^6*a^5/(a*x - 1)^6 - 6*(a*x + 1)^5*a^5/(a*x - 1)^5 + 15*(a*x + 1)^4*a^5/(a*x - 1)^4 - 20*(a*x + 1)^3*a^5/(a*x - 1)^3 + 15*(a*x + 1)^2*a^5/(a*x - 1)^2 - 6*(a*x + 1)*a^5/(a*x - 1) + a^5) + (45*(a*x + 1)^3/(a*x - 1)^3 - 25*(a*x + 1)^2/(a*x - 1)^2 + 35*(a*x + 1)/(a*x - 1) - 7)*log(-(a*x + 1)/(a*x - 1))/((a*x + 1)^5*a^5/(a*x - 1)^5 - 5*(a*x + 1)^4*a^5/(a*x - 1)^4 + 10*(a*x + 1)^3*a^5/(a*x - 1)^3 - 10*(a*x + 1)^2*a^5/(a*x - 1)^2 + 5*(a*x + 1)*a^5/(a*x - 1) - a^5) + (7*(a*x + 1)^3/(a*x - 1)^3 - 2*(a*x + 1)^2/(a*x - 1)^2 + 7*(a*x + 1)/(a*x - 1))/((a*x + 1)^4*a^5/(a*x - 1)^4 - 4*(a*x + 1)^3*a^5/(a*x - 1)^3 + 6*(a*x + 1)^2*a^5/(a*x - 1)^2 - 4*(a*x + 1)*a^5/(a*x - 1) + a^5) + 7*log(-(a*x + 1)/(a*x - 1) + 1)/a^5 - 7*log(-(a*x + 1)/(a*x - 1))/a^5)*a","B",0
174,0,0,0,0.000000," ","integrate(x^2*(-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""giac"")","\int -{\left(a^{2} x^{2} - 1\right)} x^{2} \operatorname{artanh}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*x^2*arctanh(a*x)^2, x)","F",0
175,1,305,0,0.184512," ","integrate(x*(-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""giac"")","-\frac{1}{3} \, a {\left(\frac{{\left(\frac{3 \, {\left(a x + 1\right)}}{a x - 1} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{\frac{{\left(a x + 1\right)}^{3} a^{3}}{{\left(a x - 1\right)}^{3}} - \frac{3 \, {\left(a x + 1\right)}^{2} a^{3}}{{\left(a x - 1\right)}^{2}} + \frac{3 \, {\left(a x + 1\right)} a^{3}}{a x - 1} - a^{3}} + \frac{3 \, {\left(a x + 1\right)}^{2} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}{{\left(\frac{{\left(a x + 1\right)}^{4} a^{3}}{{\left(a x - 1\right)}^{4}} - \frac{4 \, {\left(a x + 1\right)}^{3} a^{3}}{{\left(a x - 1\right)}^{3}} + \frac{6 \, {\left(a x + 1\right)}^{2} a^{3}}{{\left(a x - 1\right)}^{2}} - \frac{4 \, {\left(a x + 1\right)} a^{3}}{a x - 1} + a^{3}\right)} {\left(a x - 1\right)}^{2}} + \frac{a x + 1}{{\left(\frac{{\left(a x + 1\right)}^{2} a^{3}}{{\left(a x - 1\right)}^{2}} - \frac{2 \, {\left(a x + 1\right)} a^{3}}{a x - 1} + a^{3}\right)} {\left(a x - 1\right)}} + \frac{\log\left(-\frac{a x + 1}{a x - 1} + 1\right)}{a^{3}} - \frac{\log\left(-\frac{a x + 1}{a x - 1}\right)}{a^{3}}\right)}"," ",0,"-1/3*a*((3*(a*x + 1)/(a*x - 1) - 1)*log(-(a*x + 1)/(a*x - 1))/((a*x + 1)^3*a^3/(a*x - 1)^3 - 3*(a*x + 1)^2*a^3/(a*x - 1)^2 + 3*(a*x + 1)*a^3/(a*x - 1) - a^3) + 3*(a*x + 1)^2*log(-(a*x + 1)/(a*x - 1))^2/(((a*x + 1)^4*a^3/(a*x - 1)^4 - 4*(a*x + 1)^3*a^3/(a*x - 1)^3 + 6*(a*x + 1)^2*a^3/(a*x - 1)^2 - 4*(a*x + 1)*a^3/(a*x - 1) + a^3)*(a*x - 1)^2) + (a*x + 1)/(((a*x + 1)^2*a^3/(a*x - 1)^2 - 2*(a*x + 1)*a^3/(a*x - 1) + a^3)*(a*x - 1)) + log(-(a*x + 1)/(a*x - 1) + 1)/a^3 - log(-(a*x + 1)/(a*x - 1))/a^3)","B",0
176,0,0,0,0.000000," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""giac"")","\int -{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*arctanh(a*x)^2, x)","F",0
177,0,0,0,0.000000," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x,x, algorithm=""giac"")","\int -\frac{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*arctanh(a*x)^2/x, x)","F",0
178,0,0,0,0.000000," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^2,x, algorithm=""giac"")","\int -\frac{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x^{2}}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*arctanh(a*x)^2/x^2, x)","F",0
179,0,0,0,0.000000," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^3,x, algorithm=""giac"")","\int -\frac{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x^{3}}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*arctanh(a*x)^2/x^3, x)","F",0
180,0,0,0,0.000000," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^4,x, algorithm=""giac"")","\int -\frac{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x^{4}}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*arctanh(a*x)^2/x^4, x)","F",0
181,1,282,0,0.359235," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^5,x, algorithm=""giac"")","-\frac{1}{3} \, {\left(a^{3} \log\left(-\frac{a x + 1}{a x - 1} - 1\right) - a^{3} \log\left(-\frac{a x + 1}{a x - 1}\right) + \frac{3 \, {\left(a x + 1\right)}^{2} a^{3} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}{{\left(a x - 1\right)}^{2} {\left(\frac{{\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{4 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{6 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{4 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)}} - \frac{{\left(a x + 1\right)} a^{3}}{{\left(a x - 1\right)} {\left(\frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{2 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)}} + \frac{{\left(\frac{3 \, {\left(a x + 1\right)} a^{3}}{a x - 1} + a^{3}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{\frac{{\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{3 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{3 \, {\left(a x + 1\right)}}{a x - 1} + 1}\right)} a"," ",0,"-1/3*(a^3*log(-(a*x + 1)/(a*x - 1) - 1) - a^3*log(-(a*x + 1)/(a*x - 1)) + 3*(a*x + 1)^2*a^3*log(-(a*x + 1)/(a*x - 1))^2/((a*x - 1)^2*((a*x + 1)^4/(a*x - 1)^4 + 4*(a*x + 1)^3/(a*x - 1)^3 + 6*(a*x + 1)^2/(a*x - 1)^2 + 4*(a*x + 1)/(a*x - 1) + 1)) - (a*x + 1)*a^3/((a*x - 1)*((a*x + 1)^2/(a*x - 1)^2 + 2*(a*x + 1)/(a*x - 1) + 1)) + (3*(a*x + 1)*a^3/(a*x - 1) + a^3)*log(-(a*x + 1)/(a*x - 1))/((a*x + 1)^3/(a*x - 1)^3 + 3*(a*x + 1)^2/(a*x - 1)^2 + 3*(a*x + 1)/(a*x - 1) + 1))*a","B",0
182,0,0,0,0.000000," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^6,x, algorithm=""giac"")","\int -\frac{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x^{6}}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*arctanh(a*x)^2/x^6, x)","F",0
183,0,0,0,0.000000," ","integrate((-a^2*x^2+1)*arctanh(a*x)^3,x, algorithm=""giac"")","\int -{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{3}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*arctanh(a*x)^3, x)","F",0
184,0,0,0,0.000000," ","integrate(x*arctanh(1/2*x*2^(1/2))/(-x^2+1),x, algorithm=""giac"")","\int -\frac{x \operatorname{artanh}\left(\frac{1}{2} \, \sqrt{2} x\right)}{x^{2} - 1}\,{d x}"," ",0,"integrate(-x*arctanh(1/2*sqrt(2)*x)/(x^2 - 1), x)","F",0
185,0,0,0,0.000000," ","integrate(x*(-a^2*x^2+1)/arctanh(a*x),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\int -\frac{{\left(a^{2} x^{2} - 1\right)} x}{\operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*x/arctanh(a*x)^2, x)","F",0
189,0,0,0,0.000000," ","integrate((-a^2*x^2+1)/arctanh(a*x)^2,x, algorithm=""giac"")","\int -\frac{a^{2} x^{2} - 1}{\operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)/arctanh(a*x)^2, x)","F",0
190,0,0,0,0.000000," ","integrate((-a^2*x^2+1)/x/arctanh(a*x)^2,x, algorithm=""giac"")","\int -\frac{a^{2} x^{2} - 1}{x \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)/(x*arctanh(a*x)^2), x)","F",0
191,0,0,0,0.000000," ","integrate((-a^2*x^2+1)/arctanh(a*x)^3,x, algorithm=""giac"")","\int -\frac{a^{2} x^{2} - 1}{\operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)/arctanh(a*x)^3, x)","F",0
192,1,383,0,0.198561," ","integrate(x^4*(-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""giac"")","\frac{4}{945} \, a {\left(\frac{6 \, \log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right)}{a^{6}} - \frac{6 \, \log\left({\left| -\frac{a x + 1}{a x - 1} + 1 \right|}\right)}{a^{6}} - \frac{\frac{6 \, {\left(a x + 1\right)}^{7}}{{\left(a x - 1\right)}^{7}} - \frac{45 \, {\left(a x + 1\right)}^{6}}{{\left(a x - 1\right)}^{6}} - \frac{274 \, {\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} - \frac{214 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} - \frac{274 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} - \frac{45 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{6 \, {\left(a x + 1\right)}}{a x - 1}}{a^{6} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{8}} + \frac{6 \, {\left(\frac{210 \, {\left(a x + 1\right)}^{6}}{{\left(a x - 1\right)}^{6}} + \frac{315 \, {\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} + \frac{441 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{126 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{36 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} - \frac{9 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{a^{6} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{9}}\right)}"," ",0,"4/945*a*(6*log(abs(-a*x - 1)/abs(a*x - 1))/a^6 - 6*log(abs(-(a*x + 1)/(a*x - 1) + 1))/a^6 - (6*(a*x + 1)^7/(a*x - 1)^7 - 45*(a*x + 1)^6/(a*x - 1)^6 - 274*(a*x + 1)^5/(a*x - 1)^5 - 214*(a*x + 1)^4/(a*x - 1)^4 - 274*(a*x + 1)^3/(a*x - 1)^3 - 45*(a*x + 1)^2/(a*x - 1)^2 + 6*(a*x + 1)/(a*x - 1))/(a^6*((a*x + 1)/(a*x - 1) - 1)^8) + 6*(210*(a*x + 1)^6/(a*x - 1)^6 + 315*(a*x + 1)^5/(a*x - 1)^5 + 441*(a*x + 1)^4/(a*x - 1)^4 + 126*(a*x + 1)^3/(a*x - 1)^3 + 36*(a*x + 1)^2/(a*x - 1)^2 - 9*(a*x + 1)/(a*x - 1) + 1)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/(a^6*((a*x + 1)/(a*x - 1) - 1)^9))","B",0
193,1,240,0,0.196721," ","integrate(x^3*(-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""giac"")","\frac{4}{63} \, a {\left(\frac{\frac{28 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} - \frac{7 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{21 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} - \frac{7 \, {\left(a x + 1\right)}}{a x - 1} + 1}{a^{5} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{7}} + \frac{84 \, {\left(\frac{{\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} + \frac{{\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{{\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}}\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{a^{5} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{8}}\right)}"," ",0,"4/63*a*((28*(a*x + 1)^4/(a*x - 1)^4 - 7*(a*x + 1)^3/(a*x - 1)^3 + 21*(a*x + 1)^2/(a*x - 1)^2 - 7*(a*x + 1)/(a*x - 1) + 1)/(a^5*((a*x + 1)/(a*x - 1) - 1)^7) + 84*((a*x + 1)^5/(a*x - 1)^5 + (a*x + 1)^4/(a*x - 1)^4 + (a*x + 1)^3/(a*x - 1)^3)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/(a^5*((a*x + 1)/(a*x - 1) - 1)^8))","B",0
194,1,319,0,0.231586," ","integrate(x^2*(-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""giac"")","\frac{4}{105} \, a {\left(\frac{2 \, \log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right)}{a^{4}} - \frac{2 \, \log\left({\left| -\frac{a x + 1}{a x - 1} + 1 \right|}\right)}{a^{4}} - \frac{\frac{2 \, {\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} - \frac{11 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} - \frac{22 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} - \frac{11 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{2 \, {\left(a x + 1\right)}}{a x - 1}}{a^{4} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{6}} + \frac{2 \, {\left(\frac{70 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{35 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{21 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} - \frac{7 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{a^{4} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{7}}\right)}"," ",0,"4/105*a*(2*log(abs(-a*x - 1)/abs(a*x - 1))/a^4 - 2*log(abs(-(a*x + 1)/(a*x - 1) + 1))/a^4 - (2*(a*x + 1)^5/(a*x - 1)^5 - 11*(a*x + 1)^4/(a*x - 1)^4 - 22*(a*x + 1)^3/(a*x - 1)^3 - 11*(a*x + 1)^2/(a*x - 1)^2 + 2*(a*x + 1)/(a*x - 1))/(a^4*((a*x + 1)/(a*x - 1) - 1)^6) + 2*(70*(a*x + 1)^4/(a*x - 1)^4 + 35*(a*x + 1)^3/(a*x - 1)^3 + 21*(a*x + 1)^2/(a*x - 1)^2 - 7*(a*x + 1)/(a*x - 1) + 1)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/(a^4*((a*x + 1)/(a*x - 1) - 1)^7))","B",0
195,1,176,0,0.176600," ","integrate(x*(-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""giac"")","\frac{8}{45} \, a {\left(\frac{\frac{10 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} - \frac{5 \, {\left(a x + 1\right)}}{a x - 1} + 1}{a^{3} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{5}} + \frac{30 \, {\left(a x + 1\right)}^{3} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{{\left(a x - 1\right)}^{3} a^{3} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{6}}\right)}"," ",0,"8/45*a*((10*(a*x + 1)^2/(a*x - 1)^2 - 5*(a*x + 1)/(a*x - 1) + 1)/(a^3*((a*x + 1)/(a*x - 1) - 1)^5) + 30*(a*x + 1)^3*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/((a*x - 1)^3*a^3*((a*x + 1)/(a*x - 1) - 1)^6))","B",0
196,1,255,0,0.377325," ","integrate((-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""giac"")","\frac{4}{15} \, a {\left(\frac{2 \, \log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right)}{a^{2}} - \frac{2 \, \log\left({\left| -\frac{a x + 1}{a x - 1} + 1 \right|}\right)}{a^{2}} - \frac{\frac{2 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} - \frac{7 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{2 \, {\left(a x + 1\right)}}{a x - 1}}{a^{2} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{4}} + \frac{2 \, {\left(\frac{10 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} - \frac{5 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{a^{2} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{5}}\right)}"," ",0,"4/15*a*(2*log(abs(-a*x - 1)/abs(a*x - 1))/a^2 - 2*log(abs(-(a*x + 1)/(a*x - 1) + 1))/a^2 - (2*(a*x + 1)^3/(a*x - 1)^3 - 7*(a*x + 1)^2/(a*x - 1)^2 + 2*(a*x + 1)/(a*x - 1))/(a^2*((a*x + 1)/(a*x - 1) - 1)^4) + 2*(10*(a*x + 1)^2/(a*x - 1)^2 - 5*(a*x + 1)/(a*x - 1) + 1)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/(a^2*((a*x + 1)/(a*x - 1) - 1)^5))","B",0
197,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x,x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)}{x}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*arctanh(a*x)/x, x)","F",0
198,1,249,0,0.262544," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^2,x, algorithm=""giac"")","\frac{1}{3} \, {\left({\left(\frac{3}{\frac{a x + 1}{a x - 1} + 1} - \frac{\frac{3 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} - \frac{12 \, {\left(a x + 1\right)}}{a x - 1} + 5}{{\left(\frac{a x + 1}{a x - 1} - 1\right)}^{3}}\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right) + \frac{2 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{2}} - 8 \, \log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right) + 5 \, \log\left({\left| -\frac{a x + 1}{a x - 1} + 1 \right|}\right) + 3 \, \log\left({\left| -\frac{a x + 1}{a x - 1} - 1 \right|}\right)\right)} a"," ",0,"1/3*((3/((a*x + 1)/(a*x - 1) + 1) - (3*(a*x + 1)^2/(a*x - 1)^2 - 12*(a*x + 1)/(a*x - 1) + 5)/((a*x + 1)/(a*x - 1) - 1)^3)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1)) + 2*(a*x + 1)/((a*x - 1)*((a*x + 1)/(a*x - 1) - 1)^2) - 8*log(abs(-a*x - 1)/abs(a*x - 1)) + 5*log(abs(-(a*x + 1)/(a*x - 1) + 1)) + 3*log(abs(-(a*x + 1)/(a*x - 1) - 1)))*a","B",0
199,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^3,x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)}{x^{3}}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*arctanh(a*x)/x^3, x)","F",0
200,1,274,0,0.232477," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^4,x, algorithm=""giac"")","\frac{1}{3} \, {\left(8 \, a^{2} \log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right) - 3 \, a^{2} \log\left({\left| -\frac{a x + 1}{a x - 1} + 1 \right|}\right) - 5 \, a^{2} \log\left({\left| -\frac{a x + 1}{a x - 1} - 1 \right|}\right) + {\left(\frac{3 \, a^{2}}{\frac{a x + 1}{a x - 1} - 1} - \frac{\frac{3 \, {\left(a x + 1\right)}^{2} a^{2}}{{\left(a x - 1\right)}^{2}} + \frac{12 \, {\left(a x + 1\right)} a^{2}}{a x - 1} + 5 \, a^{2}}{{\left(\frac{a x + 1}{a x - 1} + 1\right)}^{3}}\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right) + \frac{2 \, {\left(a x + 1\right)} a^{2}}{{\left(a x - 1\right)} {\left(\frac{a x + 1}{a x - 1} + 1\right)}^{2}}\right)} a"," ",0,"1/3*(8*a^2*log(abs(-a*x - 1)/abs(a*x - 1)) - 3*a^2*log(abs(-(a*x + 1)/(a*x - 1) + 1)) - 5*a^2*log(abs(-(a*x + 1)/(a*x - 1) - 1)) + (3*a^2/((a*x + 1)/(a*x - 1) - 1) - (3*(a*x + 1)^2*a^2/(a*x - 1)^2 + 12*(a*x + 1)*a^2/(a*x - 1) + 5*a^2)/((a*x + 1)/(a*x - 1) + 1)^3)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1)) + 2*(a*x + 1)*a^2/((a*x - 1)*((a*x + 1)/(a*x - 1) + 1)^2))*a","B",0
201,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^5,x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)}{x^{5}}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*arctanh(a*x)/x^5, x)","F",0
202,1,265,0,0.178463," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^6,x, algorithm=""giac"")","-\frac{4}{15} \, {\left(2 \, a^{4} \log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right) - 2 \, a^{4} \log\left({\left| -\frac{a x + 1}{a x - 1} - 1 \right|}\right) + \frac{\frac{2 \, {\left(a x + 1\right)}^{3} a^{4}}{{\left(a x - 1\right)}^{3}} + \frac{7 \, {\left(a x + 1\right)}^{2} a^{4}}{{\left(a x - 1\right)}^{2}} + \frac{2 \, {\left(a x + 1\right)} a^{4}}{a x - 1}}{{\left(\frac{a x + 1}{a x - 1} + 1\right)}^{4}} - \frac{2 \, {\left(\frac{10 \, {\left(a x + 1\right)}^{2} a^{4}}{{\left(a x - 1\right)}^{2}} + \frac{5 \, {\left(a x + 1\right)} a^{4}}{a x - 1} + a^{4}\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{{\left(\frac{a x + 1}{a x - 1} + 1\right)}^{5}}\right)} a"," ",0,"-4/15*(2*a^4*log(abs(-a*x - 1)/abs(a*x - 1)) - 2*a^4*log(abs(-(a*x + 1)/(a*x - 1) - 1)) + (2*(a*x + 1)^3*a^4/(a*x - 1)^3 + 7*(a*x + 1)^2*a^4/(a*x - 1)^2 + 2*(a*x + 1)*a^4/(a*x - 1))/((a*x + 1)/(a*x - 1) + 1)^4 - 2*(10*(a*x + 1)^2*a^4/(a*x - 1)^2 + 5*(a*x + 1)*a^4/(a*x - 1) + a^4)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/((a*x + 1)/(a*x - 1) + 1)^5)*a","B",0
203,0,0,0,0.000000," ","integrate(x^4*(-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""giac"")","\int {\left(a^{2} x^{2} - 1\right)}^{2} x^{4} \operatorname{artanh}\left(a x\right)^{2}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*x^4*arctanh(a*x)^2, x)","F",0
204,1,683,0,0.228301," ","integrate(x^3*(-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""giac"")","\frac{2}{63} \, {\left(\frac{84 \, {\left(\frac{{\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} + \frac{{\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{{\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}{\frac{{\left(a x + 1\right)}^{8} a^{5}}{{\left(a x - 1\right)}^{8}} - \frac{8 \, {\left(a x + 1\right)}^{7} a^{5}}{{\left(a x - 1\right)}^{7}} + \frac{28 \, {\left(a x + 1\right)}^{6} a^{5}}{{\left(a x - 1\right)}^{6}} - \frac{56 \, {\left(a x + 1\right)}^{5} a^{5}}{{\left(a x - 1\right)}^{5}} + \frac{70 \, {\left(a x + 1\right)}^{4} a^{5}}{{\left(a x - 1\right)}^{4}} - \frac{56 \, {\left(a x + 1\right)}^{3} a^{5}}{{\left(a x - 1\right)}^{3}} + \frac{28 \, {\left(a x + 1\right)}^{2} a^{5}}{{\left(a x - 1\right)}^{2}} - \frac{8 \, {\left(a x + 1\right)} a^{5}}{a x - 1} + a^{5}} + \frac{2 \, {\left(\frac{28 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} - \frac{7 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{21 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} - \frac{7 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{\frac{{\left(a x + 1\right)}^{7} a^{5}}{{\left(a x - 1\right)}^{7}} - \frac{7 \, {\left(a x + 1\right)}^{6} a^{5}}{{\left(a x - 1\right)}^{6}} + \frac{21 \, {\left(a x + 1\right)}^{5} a^{5}}{{\left(a x - 1\right)}^{5}} - \frac{35 \, {\left(a x + 1\right)}^{4} a^{5}}{{\left(a x - 1\right)}^{4}} + \frac{35 \, {\left(a x + 1\right)}^{3} a^{5}}{{\left(a x - 1\right)}^{3}} - \frac{21 \, {\left(a x + 1\right)}^{2} a^{5}}{{\left(a x - 1\right)}^{2}} + \frac{7 \, {\left(a x + 1\right)} a^{5}}{a x - 1} - a^{5}} - \frac{\frac{2 \, {\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} - \frac{11 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{6 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} - \frac{11 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{2 \, {\left(a x + 1\right)}}{a x - 1}}{\frac{{\left(a x + 1\right)}^{6} a^{5}}{{\left(a x - 1\right)}^{6}} - \frac{6 \, {\left(a x + 1\right)}^{5} a^{5}}{{\left(a x - 1\right)}^{5}} + \frac{15 \, {\left(a x + 1\right)}^{4} a^{5}}{{\left(a x - 1\right)}^{4}} - \frac{20 \, {\left(a x + 1\right)}^{3} a^{5}}{{\left(a x - 1\right)}^{3}} + \frac{15 \, {\left(a x + 1\right)}^{2} a^{5}}{{\left(a x - 1\right)}^{2}} - \frac{6 \, {\left(a x + 1\right)} a^{5}}{a x - 1} + a^{5}} - \frac{2 \, \log\left(-\frac{a x + 1}{a x - 1} + 1\right)}{a^{5}} + \frac{2 \, \log\left(-\frac{a x + 1}{a x - 1}\right)}{a^{5}}\right)} a"," ",0,"2/63*(84*((a*x + 1)^5/(a*x - 1)^5 + (a*x + 1)^4/(a*x - 1)^4 + (a*x + 1)^3/(a*x - 1)^3)*log(-(a*x + 1)/(a*x - 1))^2/((a*x + 1)^8*a^5/(a*x - 1)^8 - 8*(a*x + 1)^7*a^5/(a*x - 1)^7 + 28*(a*x + 1)^6*a^5/(a*x - 1)^6 - 56*(a*x + 1)^5*a^5/(a*x - 1)^5 + 70*(a*x + 1)^4*a^5/(a*x - 1)^4 - 56*(a*x + 1)^3*a^5/(a*x - 1)^3 + 28*(a*x + 1)^2*a^5/(a*x - 1)^2 - 8*(a*x + 1)*a^5/(a*x - 1) + a^5) + 2*(28*(a*x + 1)^4/(a*x - 1)^4 - 7*(a*x + 1)^3/(a*x - 1)^3 + 21*(a*x + 1)^2/(a*x - 1)^2 - 7*(a*x + 1)/(a*x - 1) + 1)*log(-(a*x + 1)/(a*x - 1))/((a*x + 1)^7*a^5/(a*x - 1)^7 - 7*(a*x + 1)^6*a^5/(a*x - 1)^6 + 21*(a*x + 1)^5*a^5/(a*x - 1)^5 - 35*(a*x + 1)^4*a^5/(a*x - 1)^4 + 35*(a*x + 1)^3*a^5/(a*x - 1)^3 - 21*(a*x + 1)^2*a^5/(a*x - 1)^2 + 7*(a*x + 1)*a^5/(a*x - 1) - a^5) - (2*(a*x + 1)^5/(a*x - 1)^5 - 11*(a*x + 1)^4/(a*x - 1)^4 + 6*(a*x + 1)^3/(a*x - 1)^3 - 11*(a*x + 1)^2/(a*x - 1)^2 + 2*(a*x + 1)/(a*x - 1))/((a*x + 1)^6*a^5/(a*x - 1)^6 - 6*(a*x + 1)^5*a^5/(a*x - 1)^5 + 15*(a*x + 1)^4*a^5/(a*x - 1)^4 - 20*(a*x + 1)^3*a^5/(a*x - 1)^3 + 15*(a*x + 1)^2*a^5/(a*x - 1)^2 - 6*(a*x + 1)*a^5/(a*x - 1) + a^5) - 2*log(-(a*x + 1)/(a*x - 1) + 1)/a^5 + 2*log(-(a*x + 1)/(a*x - 1))/a^5)*a","B",0
205,0,0,0,0.000000," ","integrate(x^2*(-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""giac"")","\int {\left(a^{2} x^{2} - 1\right)}^{2} x^{2} \operatorname{artanh}\left(a x\right)^{2}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*x^2*arctanh(a*x)^2, x)","F",0
206,1,473,0,0.189780," ","integrate(x*(-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""giac"")","\frac{4}{45} \, a {\left(\frac{2 \, {\left(\frac{10 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} - \frac{5 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{\frac{{\left(a x + 1\right)}^{5} a^{3}}{{\left(a x - 1\right)}^{5}} - \frac{5 \, {\left(a x + 1\right)}^{4} a^{3}}{{\left(a x - 1\right)}^{4}} + \frac{10 \, {\left(a x + 1\right)}^{3} a^{3}}{{\left(a x - 1\right)}^{3}} - \frac{10 \, {\left(a x + 1\right)}^{2} a^{3}}{{\left(a x - 1\right)}^{2}} + \frac{5 \, {\left(a x + 1\right)} a^{3}}{a x - 1} - a^{3}} + \frac{30 \, {\left(a x + 1\right)}^{3} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}{{\left(\frac{{\left(a x + 1\right)}^{6} a^{3}}{{\left(a x - 1\right)}^{6}} - \frac{6 \, {\left(a x + 1\right)}^{5} a^{3}}{{\left(a x - 1\right)}^{5}} + \frac{15 \, {\left(a x + 1\right)}^{4} a^{3}}{{\left(a x - 1\right)}^{4}} - \frac{20 \, {\left(a x + 1\right)}^{3} a^{3}}{{\left(a x - 1\right)}^{3}} + \frac{15 \, {\left(a x + 1\right)}^{2} a^{3}}{{\left(a x - 1\right)}^{2}} - \frac{6 \, {\left(a x + 1\right)} a^{3}}{a x - 1} + a^{3}\right)} {\left(a x - 1\right)}^{3}} - \frac{\frac{2 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} - \frac{7 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{2 \, {\left(a x + 1\right)}}{a x - 1}}{\frac{{\left(a x + 1\right)}^{4} a^{3}}{{\left(a x - 1\right)}^{4}} - \frac{4 \, {\left(a x + 1\right)}^{3} a^{3}}{{\left(a x - 1\right)}^{3}} + \frac{6 \, {\left(a x + 1\right)}^{2} a^{3}}{{\left(a x - 1\right)}^{2}} - \frac{4 \, {\left(a x + 1\right)} a^{3}}{a x - 1} + a^{3}} - \frac{2 \, \log\left(-\frac{a x + 1}{a x - 1} + 1\right)}{a^{3}} + \frac{2 \, \log\left(-\frac{a x + 1}{a x - 1}\right)}{a^{3}}\right)}"," ",0,"4/45*a*(2*(10*(a*x + 1)^2/(a*x - 1)^2 - 5*(a*x + 1)/(a*x - 1) + 1)*log(-(a*x + 1)/(a*x - 1))/((a*x + 1)^5*a^3/(a*x - 1)^5 - 5*(a*x + 1)^4*a^3/(a*x - 1)^4 + 10*(a*x + 1)^3*a^3/(a*x - 1)^3 - 10*(a*x + 1)^2*a^3/(a*x - 1)^2 + 5*(a*x + 1)*a^3/(a*x - 1) - a^3) + 30*(a*x + 1)^3*log(-(a*x + 1)/(a*x - 1))^2/(((a*x + 1)^6*a^3/(a*x - 1)^6 - 6*(a*x + 1)^5*a^3/(a*x - 1)^5 + 15*(a*x + 1)^4*a^3/(a*x - 1)^4 - 20*(a*x + 1)^3*a^3/(a*x - 1)^3 + 15*(a*x + 1)^2*a^3/(a*x - 1)^2 - 6*(a*x + 1)*a^3/(a*x - 1) + a^3)*(a*x - 1)^3) - (2*(a*x + 1)^3/(a*x - 1)^3 - 7*(a*x + 1)^2/(a*x - 1)^2 + 2*(a*x + 1)/(a*x - 1))/((a*x + 1)^4*a^3/(a*x - 1)^4 - 4*(a*x + 1)^3*a^3/(a*x - 1)^3 + 6*(a*x + 1)^2*a^3/(a*x - 1)^2 - 4*(a*x + 1)*a^3/(a*x - 1) + a^3) - 2*log(-(a*x + 1)/(a*x - 1) + 1)/a^3 + 2*log(-(a*x + 1)/(a*x - 1))/a^3)","B",0
207,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""giac"")","\int {\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{2}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*arctanh(a*x)^2, x)","F",0
208,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x,x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{2}}{x}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*arctanh(a*x)^2/x, x)","F",0
209,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^2,x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{2}}{x^{2}}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*arctanh(a*x)^2/x^2, x)","F",0
210,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^3,x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{2}}{x^{3}}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*arctanh(a*x)^2/x^3, x)","F",0
211,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^4,x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{2}}{x^{4}}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*arctanh(a*x)^2/x^4, x)","F",0
212,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^5,x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{2}}{x^{5}}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*arctanh(a*x)^2/x^5, x)","F",0
213,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^6,x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{2}}{x^{6}}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*arctanh(a*x)^2/x^6, x)","F",0
214,1,440,0,0.220656," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^7,x, algorithm=""giac"")","\frac{4}{45} \, {\left(2 \, a^{5} \log\left(-\frac{a x + 1}{a x - 1} - 1\right) - 2 \, a^{5} \log\left(-\frac{a x + 1}{a x - 1}\right) + \frac{30 \, {\left(a x + 1\right)}^{3} a^{5} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}{{\left(a x - 1\right)}^{3} {\left(\frac{{\left(a x + 1\right)}^{6}}{{\left(a x - 1\right)}^{6}} + \frac{6 \, {\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} + \frac{15 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{20 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{15 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{6 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)}} + \frac{2 \, {\left(\frac{10 \, {\left(a x + 1\right)}^{2} a^{5}}{{\left(a x - 1\right)}^{2}} + \frac{5 \, {\left(a x + 1\right)} a^{5}}{a x - 1} + a^{5}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{\frac{{\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} + \frac{5 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{10 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{10 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{5 \, {\left(a x + 1\right)}}{a x - 1} + 1} - \frac{\frac{2 \, {\left(a x + 1\right)}^{3} a^{5}}{{\left(a x - 1\right)}^{3}} + \frac{7 \, {\left(a x + 1\right)}^{2} a^{5}}{{\left(a x - 1\right)}^{2}} + \frac{2 \, {\left(a x + 1\right)} a^{5}}{a x - 1}}{\frac{{\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{4 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{6 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{4 \, {\left(a x + 1\right)}}{a x - 1} + 1}\right)} a"," ",0,"4/45*(2*a^5*log(-(a*x + 1)/(a*x - 1) - 1) - 2*a^5*log(-(a*x + 1)/(a*x - 1)) + 30*(a*x + 1)^3*a^5*log(-(a*x + 1)/(a*x - 1))^2/((a*x - 1)^3*((a*x + 1)^6/(a*x - 1)^6 + 6*(a*x + 1)^5/(a*x - 1)^5 + 15*(a*x + 1)^4/(a*x - 1)^4 + 20*(a*x + 1)^3/(a*x - 1)^3 + 15*(a*x + 1)^2/(a*x - 1)^2 + 6*(a*x + 1)/(a*x - 1) + 1)) + 2*(10*(a*x + 1)^2*a^5/(a*x - 1)^2 + 5*(a*x + 1)*a^5/(a*x - 1) + a^5)*log(-(a*x + 1)/(a*x - 1))/((a*x + 1)^5/(a*x - 1)^5 + 5*(a*x + 1)^4/(a*x - 1)^4 + 10*(a*x + 1)^3/(a*x - 1)^3 + 10*(a*x + 1)^2/(a*x - 1)^2 + 5*(a*x + 1)/(a*x - 1) + 1) - (2*(a*x + 1)^3*a^5/(a*x - 1)^3 + 7*(a*x + 1)^2*a^5/(a*x - 1)^2 + 2*(a*x + 1)*a^5/(a*x - 1))/((a*x + 1)^4/(a*x - 1)^4 + 4*(a*x + 1)^3/(a*x - 1)^3 + 6*(a*x + 1)^2/(a*x - 1)^2 + 4*(a*x + 1)/(a*x - 1) + 1))*a","B",0
215,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^8,x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{2}}{x^{8}}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*arctanh(a*x)^2/x^8, x)","F",0
216,1,651,0,0.235150," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^9,x, algorithm=""giac"")","\frac{2}{63} \, {\left(2 \, a^{7} \log\left(-\frac{a x + 1}{a x - 1} - 1\right) - 2 \, a^{7} \log\left(-\frac{a x + 1}{a x - 1}\right) + \frac{84 \, {\left(\frac{{\left(a x + 1\right)}^{5} a^{7}}{{\left(a x - 1\right)}^{5}} - \frac{{\left(a x + 1\right)}^{4} a^{7}}{{\left(a x - 1\right)}^{4}} + \frac{{\left(a x + 1\right)}^{3} a^{7}}{{\left(a x - 1\right)}^{3}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}{\frac{{\left(a x + 1\right)}^{8}}{{\left(a x - 1\right)}^{8}} + \frac{8 \, {\left(a x + 1\right)}^{7}}{{\left(a x - 1\right)}^{7}} + \frac{28 \, {\left(a x + 1\right)}^{6}}{{\left(a x - 1\right)}^{6}} + \frac{56 \, {\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} + \frac{70 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{56 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{28 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{8 \, {\left(a x + 1\right)}}{a x - 1} + 1} + \frac{2 \, {\left(\frac{28 \, {\left(a x + 1\right)}^{4} a^{7}}{{\left(a x - 1\right)}^{4}} + \frac{7 \, {\left(a x + 1\right)}^{3} a^{7}}{{\left(a x - 1\right)}^{3}} + \frac{21 \, {\left(a x + 1\right)}^{2} a^{7}}{{\left(a x - 1\right)}^{2}} + \frac{7 \, {\left(a x + 1\right)} a^{7}}{a x - 1} + a^{7}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{\frac{{\left(a x + 1\right)}^{7}}{{\left(a x - 1\right)}^{7}} + \frac{7 \, {\left(a x + 1\right)}^{6}}{{\left(a x - 1\right)}^{6}} + \frac{21 \, {\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} + \frac{35 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{35 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{21 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{7 \, {\left(a x + 1\right)}}{a x - 1} + 1} - \frac{\frac{2 \, {\left(a x + 1\right)}^{5} a^{7}}{{\left(a x - 1\right)}^{5}} + \frac{11 \, {\left(a x + 1\right)}^{4} a^{7}}{{\left(a x - 1\right)}^{4}} + \frac{6 \, {\left(a x + 1\right)}^{3} a^{7}}{{\left(a x - 1\right)}^{3}} + \frac{11 \, {\left(a x + 1\right)}^{2} a^{7}}{{\left(a x - 1\right)}^{2}} + \frac{2 \, {\left(a x + 1\right)} a^{7}}{a x - 1}}{\frac{{\left(a x + 1\right)}^{6}}{{\left(a x - 1\right)}^{6}} + \frac{6 \, {\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} + \frac{15 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{20 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} + \frac{15 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{6 \, {\left(a x + 1\right)}}{a x - 1} + 1}\right)} a"," ",0,"2/63*(2*a^7*log(-(a*x + 1)/(a*x - 1) - 1) - 2*a^7*log(-(a*x + 1)/(a*x - 1)) + 84*((a*x + 1)^5*a^7/(a*x - 1)^5 - (a*x + 1)^4*a^7/(a*x - 1)^4 + (a*x + 1)^3*a^7/(a*x - 1)^3)*log(-(a*x + 1)/(a*x - 1))^2/((a*x + 1)^8/(a*x - 1)^8 + 8*(a*x + 1)^7/(a*x - 1)^7 + 28*(a*x + 1)^6/(a*x - 1)^6 + 56*(a*x + 1)^5/(a*x - 1)^5 + 70*(a*x + 1)^4/(a*x - 1)^4 + 56*(a*x + 1)^3/(a*x - 1)^3 + 28*(a*x + 1)^2/(a*x - 1)^2 + 8*(a*x + 1)/(a*x - 1) + 1) + 2*(28*(a*x + 1)^4*a^7/(a*x - 1)^4 + 7*(a*x + 1)^3*a^7/(a*x - 1)^3 + 21*(a*x + 1)^2*a^7/(a*x - 1)^2 + 7*(a*x + 1)*a^7/(a*x - 1) + a^7)*log(-(a*x + 1)/(a*x - 1))/((a*x + 1)^7/(a*x - 1)^7 + 7*(a*x + 1)^6/(a*x - 1)^6 + 21*(a*x + 1)^5/(a*x - 1)^5 + 35*(a*x + 1)^4/(a*x - 1)^4 + 35*(a*x + 1)^3/(a*x - 1)^3 + 21*(a*x + 1)^2/(a*x - 1)^2 + 7*(a*x + 1)/(a*x - 1) + 1) - (2*(a*x + 1)^5*a^7/(a*x - 1)^5 + 11*(a*x + 1)^4*a^7/(a*x - 1)^4 + 6*(a*x + 1)^3*a^7/(a*x - 1)^3 + 11*(a*x + 1)^2*a^7/(a*x - 1)^2 + 2*(a*x + 1)*a^7/(a*x - 1))/((a*x + 1)^6/(a*x - 1)^6 + 6*(a*x + 1)^5/(a*x - 1)^5 + 15*(a*x + 1)^4/(a*x - 1)^4 + 20*(a*x + 1)^3/(a*x - 1)^3 + 15*(a*x + 1)^2/(a*x - 1)^2 + 6*(a*x + 1)/(a*x - 1) + 1))*a","B",0
217,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^3,x, algorithm=""giac"")","\int {\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{3}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*arctanh(a*x)^3, x)","F",0
218,0,0,0,0.000000," ","integrate(x*(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2} x}{\operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2*x/arctanh(a*x)^2, x)","F",0
222,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2}}{\operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2/arctanh(a*x)^2, x)","F",0
223,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^2/x/arctanh(a*x)^2,x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} - 1\right)}^{2}}{x \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate((a^2*x^2 - 1)^2/(x*arctanh(a*x)^2), x)","F",0
224,1,303,0,0.194473," ","integrate((-a^2*x^2+1)^3*arctanh(a*x),x, algorithm=""giac"")","\frac{8}{105} \, a {\left(\frac{6 \, \log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right)}{a^{2}} - \frac{6 \, \log\left({\left| -\frac{a x + 1}{a x - 1} + 1 \right|}\right)}{a^{2}} - \frac{\frac{6 \, {\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} - \frac{33 \, {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{74 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} - \frac{33 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{6 \, {\left(a x + 1\right)}}{a x - 1}}{a^{2} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{6}} - \frac{6 \, {\left(\frac{35 \, {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} - \frac{21 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{7 \, {\left(a x + 1\right)}}{a x - 1} - 1\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{a^{2} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{7}}\right)}"," ",0,"8/105*a*(6*log(abs(-a*x - 1)/abs(a*x - 1))/a^2 - 6*log(abs(-(a*x + 1)/(a*x - 1) + 1))/a^2 - (6*(a*x + 1)^5/(a*x - 1)^5 - 33*(a*x + 1)^4/(a*x - 1)^4 + 74*(a*x + 1)^3/(a*x - 1)^3 - 33*(a*x + 1)^2/(a*x - 1)^2 + 6*(a*x + 1)/(a*x - 1))/(a^2*((a*x + 1)/(a*x - 1) - 1)^6) - 6*(35*(a*x + 1)^3/(a*x - 1)^3 - 21*(a*x + 1)^2/(a*x - 1)^2 + 7*(a*x + 1)/(a*x - 1) - 1)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/(a^2*((a*x + 1)/(a*x - 1) - 1)^7))","B",0
225,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^3*arctanh(a*x)^2,x, algorithm=""giac"")","\int -{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)^3*arctanh(a*x)^2, x)","F",0
226,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^3*arctanh(a*x)^3,x, algorithm=""giac"")","\int -{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{3}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)^3*arctanh(a*x)^3, x)","F",0
227,0,0,0,0.000000," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{x^{3} \operatorname{artanh}\left(a x\right)}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-x^3*arctanh(a*x)/(a^2*x^2 - 1), x)","F",0
228,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{x^{2} \operatorname{artanh}\left(a x\right)}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-x^2*arctanh(a*x)/(a^2*x^2 - 1), x)","F",0
229,0,0,0,0.000000," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{x \operatorname{artanh}\left(a x\right)}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-x*arctanh(a*x)/(a^2*x^2 - 1), x)","F",0
230,1,22,0,0.214260," ","integrate(arctanh(a*x)/(-a^2*x^2+1),x, algorithm=""giac"")","\frac{\log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}{8 \, a}"," ",0,"1/8*log(-(a*x + 1)/(a*x - 1))^2/a","A",0
231,0,0,0,0.000000," ","integrate(arctanh(a*x)/x/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)}{{\left(a^{2} x^{2} - 1\right)} x}\,{d x}"," ",0,"integrate(-arctanh(a*x)/((a^2*x^2 - 1)*x), x)","F",0
232,0,0,0,0.000000," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)}{{\left(a^{2} x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate(-arctanh(a*x)/((a^2*x^2 - 1)*x^2), x)","F",0
233,0,0,0,0.000000," ","integrate(arctanh(a*x)/x^3/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)}{{\left(a^{2} x^{2} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate(-arctanh(a*x)/((a^2*x^2 - 1)*x^3), x)","F",0
234,0,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{x^{3} \operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-x^3*arctanh(a*x)^2/(a^2*x^2 - 1), x)","F",0
235,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{x^{2} \operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-x^2*arctanh(a*x)^2/(a^2*x^2 - 1), x)","F",0
236,0,0,0,0.000000," ","integrate(x*arctanh(a*x)^2/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{x \operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-x*arctanh(a*x)^2/(a^2*x^2 - 1), x)","F",0
237,1,22,0,0.191999," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1),x, algorithm=""giac"")","\frac{\log\left(-\frac{a x + 1}{a x - 1}\right)^{3}}{24 \, a}"," ",0,"1/24*log(-(a*x + 1)/(a*x - 1))^3/a","A",0
238,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(a^{2} x^{2} - 1\right)} x}\,{d x}"," ",0,"integrate(-arctanh(a*x)^2/((a^2*x^2 - 1)*x), x)","F",0
239,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x^2/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(a^{2} x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate(-arctanh(a*x)^2/((a^2*x^2 - 1)*x^2), x)","F",0
240,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x^3/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(a^{2} x^{2} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate(-arctanh(a*x)^2/((a^2*x^2 - 1)*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=""giac"")","\int -\frac{x^{3} \operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-x^3*arctanh(a*x)^3/(a^2*x^2 - 1), x)","F",0
242,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{x^{2} \operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-x^2*arctanh(a*x)^3/(a^2*x^2 - 1), x)","F",0
243,0,0,0,0.000000," ","integrate(x*arctanh(a*x)^3/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{x \operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-x*arctanh(a*x)^3/(a^2*x^2 - 1), x)","F",0
244,1,22,0,0.141396," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1),x, algorithm=""giac"")","\frac{\log\left(-\frac{a x + 1}{a x - 1}\right)^{4}}{64 \, a}"," ",0,"1/64*log(-(a*x + 1)/(a*x - 1))^4/a","A",0
245,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(a^{2} x^{2} - 1\right)} x}\,{d x}"," ",0,"integrate(-arctanh(a*x)^3/((a^2*x^2 - 1)*x), x)","F",0
246,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^2/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(a^{2} x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate(-arctanh(a*x)^3/((a^2*x^2 - 1)*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=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(a^{2} x^{2} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate(-arctanh(a*x)^3/((a^2*x^2 - 1)*x^3), x)","F",0
248,0,0,0,0.000000," ","integrate(arctanh(a*x)^(1/2)/(-a^2*x^2+1),x, algorithm=""giac"")","\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=""giac"")","\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
250,1,21,0,0.220799," ","integrate(1/(-a^2*x^2+1)/arctanh(a*x),x, algorithm=""giac"")","\frac{\log\left({\left| \log\left(-\frac{a x + 1}{a x - 1}\right) \right|}\right)}{a}"," ",0,"log(abs(log(-(a*x + 1)/(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=""giac"")","\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=""giac"")","\int -\frac{x}{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(-x/((a^2*x^2 - 1)*arctanh(a*x)^2), x)","F",0
253,1,22,0,0.193398," ","integrate(1/(-a^2*x^2+1)/arctanh(a*x)^2,x, algorithm=""giac"")","-\frac{2}{a \log\left(-\frac{a x + 1}{a x - 1}\right)}"," ",0,"-2/(a*log(-(a*x + 1)/(a*x - 1)))","A",0
254,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)/arctanh(a*x)^2,x, algorithm=""giac"")","\int -\frac{1}{{\left(a^{2} x^{2} - 1\right)} x \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(-1/((a^2*x^2 - 1)*x*arctanh(a*x)^2), x)","F",0
255,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)/arctanh(a*x)^3,x, algorithm=""giac"")","\int -\frac{x}{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(-x/((a^2*x^2 - 1)*arctanh(a*x)^3), x)","F",0
256,1,22,0,0.151644," ","integrate(1/(-a^2*x^2+1)/arctanh(a*x)^3,x, algorithm=""giac"")","-\frac{2}{a \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}"," ",0,"-2/(a*log(-(a*x + 1)/(a*x - 1))^2)","A",0
257,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)/arctanh(a*x)^3,x, algorithm=""giac"")","\int -\frac{1}{{\left(a^{2} x^{2} - 1\right)} x \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(-1/((a^2*x^2 - 1)*x*arctanh(a*x)^3), x)","F",0
258,0,0,0,0.000000," ","integrate(arctanh(a*x)^p/(-a^2*x^2+1),x, algorithm=""giac"")","\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
259,0,0,0,0.000000," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{x^{3} \operatorname{artanh}\left(a x\right)}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate(x^3*arctanh(a*x)/(a^2*x^2 - 1)^2, x)","F",0
260,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{x^{2} \operatorname{artanh}\left(a x\right)}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate(x^2*arctanh(a*x)/(a^2*x^2 - 1)^2, x)","F",0
261,1,154,0,0.183590," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1)^2,x, algorithm=""giac"")","-\frac{1}{16} \, {\left({\left(\frac{a x + 1}{{\left(a x - 1\right)} a^{3}} + \frac{a x - 1}{{\left(a x + 1\right)} a^{3}}\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right) - \frac{a x + 1}{{\left(a x - 1\right)} a^{3}} + \frac{a x - 1}{{\left(a x + 1\right)} a^{3}}\right)} a"," ",0,"-1/16*(((a*x + 1)/((a*x - 1)*a^3) + (a*x - 1)/((a*x + 1)*a^3))*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1)) - (a*x + 1)/((a*x - 1)*a^3) + (a*x - 1)/((a*x + 1)*a^3))*a","B",0
262,1,255,0,2.011536," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\frac{1}{8} \, a^{2} {\left(\frac{{\left(a x - 1\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{a - \frac{a {\left(\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1\right)}}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}} - 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{a - \frac{a {\left(\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1\right)}}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}} + 1}\right)}{{\left(a x + 1\right)} a^{4}} + \frac{a x - 1}{{\left(a x + 1\right)} a^{4}}\right)}"," ",0,"1/8*a^2*((a*x - 1)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/(a - a*(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1)) - 1)/(a*((a*x + 1)/(a*x - 1) + 1)/(a - a*(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1)) + 1))/((a*x + 1)*a^4) + (a*x - 1)/((a*x + 1)*a^4))","B",0
263,0,0,0,0.000000," ","integrate(arctanh(a*x)/x/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)}{{\left(a^{2} x^{2} - 1\right)}^{2} x}\,{d x}"," ",0,"integrate(arctanh(a*x)/((a^2*x^2 - 1)^2*x), x)","F",0
264,0,0,0,0.000000," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)}{{\left(a^{2} x^{2} - 1\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate(arctanh(a*x)/((a^2*x^2 - 1)^2*x^2), x)","F",0
265,0,0,0,0.000000," ","integrate(arctanh(a*x)/x^3/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)}{{\left(a^{2} x^{2} - 1\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate(arctanh(a*x)/((a^2*x^2 - 1)^2*x^3), x)","F",0
266,0,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{x^{3} \operatorname{artanh}\left(a x\right)^{2}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate(x^3*arctanh(a*x)^2/(a^2*x^2 - 1)^2, x)","F",0
267,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{x^{2} \operatorname{artanh}\left(a x\right)^{2}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate(x^2*arctanh(a*x)^2/(a^2*x^2 - 1)^2, x)","F",0
268,1,140,0,0.173932," ","integrate(x*arctanh(a*x)^2/(-a^2*x^2+1)^2,x, algorithm=""giac"")","-\frac{1}{32} \, {\left({\left(\frac{a x + 1}{{\left(a x - 1\right)} a^{3}} + \frac{a x - 1}{{\left(a x + 1\right)} a^{3}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 2 \, {\left(\frac{a x + 1}{{\left(a x - 1\right)} a^{3}} - \frac{a x - 1}{{\left(a x + 1\right)} a^{3}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + \frac{2 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{3}} + \frac{2 \, {\left(a x - 1\right)}}{{\left(a x + 1\right)} a^{3}}\right)} a"," ",0,"-1/32*(((a*x + 1)/((a*x - 1)*a^3) + (a*x - 1)/((a*x + 1)*a^3))*log(-(a*x + 1)/(a*x - 1))^2 - 2*((a*x + 1)/((a*x - 1)*a^3) - (a*x - 1)/((a*x + 1)*a^3))*log(-(a*x + 1)/(a*x - 1)) + 2*(a*x + 1)/((a*x - 1)*a^3) + 2*(a*x - 1)/((a*x + 1)*a^3))*a","A",0
269,1,88,0,2.080123," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\frac{1}{16} \, a^{2} {\left(\frac{{\left(a x - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}{{\left(a x + 1\right)} a^{4}} + \frac{2 \, {\left(a x - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{{\left(a x + 1\right)} a^{4}} + \frac{2 \, {\left(a x - 1\right)}}{{\left(a x + 1\right)} a^{4}}\right)}"," ",0,"1/16*a^2*((a*x - 1)*log(-(a*x + 1)/(a*x - 1))^2/((a*x + 1)*a^4) + 2*(a*x - 1)*log(-(a*x + 1)/(a*x - 1))/((a*x + 1)*a^4) + 2*(a*x - 1)/((a*x + 1)*a^4))","A",0
270,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(a^{2} x^{2} - 1\right)}^{2} x}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/((a^2*x^2 - 1)^2*x), x)","F",0
271,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x^2/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(a^{2} x^{2} - 1\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/((a^2*x^2 - 1)^2*x^2), x)","F",0
272,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x^3/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(a^{2} x^{2} - 1\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/((a^2*x^2 - 1)^2*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=""giac"")","\int \frac{x^{3} \operatorname{artanh}\left(a x\right)^{3}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate(x^3*arctanh(a*x)^3/(a^2*x^2 - 1)^2, x)","F",0
274,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{x^{2} \operatorname{artanh}\left(a x\right)^{3}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate(x^2*arctanh(a*x)^3/(a^2*x^2 - 1)^2, x)","F",0
275,1,192,0,0.192056," ","integrate(x*arctanh(a*x)^3/(-a^2*x^2+1)^2,x, algorithm=""giac"")","-\frac{1}{64} \, {\left({\left(\frac{a x + 1}{{\left(a x - 1\right)} a^{3}} + \frac{a x - 1}{{\left(a x + 1\right)} a^{3}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} - 3 \, {\left(\frac{a x + 1}{{\left(a x - 1\right)} a^{3}} - \frac{a x - 1}{{\left(a x + 1\right)} a^{3}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 6 \, {\left(\frac{a x + 1}{{\left(a x - 1\right)} a^{3}} + \frac{a x - 1}{{\left(a x + 1\right)} a^{3}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - \frac{6 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{3}} + \frac{6 \, {\left(a x - 1\right)}}{{\left(a x + 1\right)} a^{3}}\right)} a"," ",0,"-1/64*(((a*x + 1)/((a*x - 1)*a^3) + (a*x - 1)/((a*x + 1)*a^3))*log(-(a*x + 1)/(a*x - 1))^3 - 3*((a*x + 1)/((a*x - 1)*a^3) - (a*x - 1)/((a*x + 1)*a^3))*log(-(a*x + 1)/(a*x - 1))^2 + 6*((a*x + 1)/((a*x - 1)*a^3) + (a*x - 1)/((a*x + 1)*a^3))*log(-(a*x + 1)/(a*x - 1)) - 6*(a*x + 1)/((a*x - 1)*a^3) + 6*(a*x - 1)/((a*x + 1)*a^3))*a","A",0
276,1,122,0,2.750195," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\frac{1}{32} \, a^{2} {\left(\frac{{\left(a x - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3}}{{\left(a x + 1\right)} a^{4}} + \frac{3 \, {\left(a x - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}{{\left(a x + 1\right)} a^{4}} + \frac{6 \, {\left(a x - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{{\left(a x + 1\right)} a^{4}} + \frac{6 \, {\left(a x - 1\right)}}{{\left(a x + 1\right)} a^{4}}\right)}"," ",0,"1/32*a^2*((a*x - 1)*log(-(a*x + 1)/(a*x - 1))^3/((a*x + 1)*a^4) + 3*(a*x - 1)*log(-(a*x + 1)/(a*x - 1))^2/((a*x + 1)*a^4) + 6*(a*x - 1)*log(-(a*x + 1)/(a*x - 1))/((a*x + 1)*a^4) + 6*(a*x - 1)/((a*x + 1)*a^4))","A",0
277,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(a^{2} x^{2} - 1\right)}^{2} x}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/((a^2*x^2 - 1)^2*x), x)","F",0
278,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^2/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(a^{2} x^{2} - 1\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/((a^2*x^2 - 1)^2*x^2), x)","F",0
279,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^3/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(a^{2} x^{2} - 1\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/((a^2*x^2 - 1)^2*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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\int \frac{x^{3}}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x^3/((a^2*x^2 - 1)^2*arctanh(a*x)^2), x)","F",0
288,0,0,0,0.000000," ","integrate(x^2/(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x^2/((a^2*x^2 - 1)^2*arctanh(a*x)^2), x)","F",0
289,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""giac"")","\int \frac{x}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x/((a^2*x^2 - 1)^2*arctanh(a*x)^2), x)","F",0
290,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^2*arctanh(a*x)^2), x)","F",0
291,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{2} x \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^2*x*arctanh(a*x)^2), x)","F",0
292,0,0,0,0.000000," ","integrate(x^3/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x^3/((a^2*x^2 - 1)^2*arctanh(a*x)^3), x)","F",0
293,0,0,0,0.000000," ","integrate(x^2/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x^2/((a^2*x^2 - 1)^2*arctanh(a*x)^3), x)","F",0
294,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""giac"")","\int \frac{x}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x/((a^2*x^2 - 1)^2*arctanh(a*x)^3), x)","F",0
295,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^2*arctanh(a*x)^3), x)","F",0
296,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{2} x \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^2*x*arctanh(a*x)^3), x)","F",0
297,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^4,x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{4}}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^2*arctanh(a*x)^4), x)","F",0
298,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^5,x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{5}}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^2*arctanh(a*x)^5), x)","F",0
299,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^6,x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{6}}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^2*arctanh(a*x)^6), x)","F",0
300,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^7,x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{7}}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^2*arctanh(a*x)^7), x)","F",0
301,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^8,x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{2} \operatorname{artanh}\left(a x\right)^{8}}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^2*arctanh(a*x)^8), x)","F",0
302,1,239,0,0.189545," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\frac{1}{256} \, {\left(2 \, {\left(\frac{{\left(a x - 1\right)}^{2} {\left(\frac{4 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)}}{{\left(a x + 1\right)}^{2} a^{5}} + \frac{\frac{{\left(a x + 1\right)}^{2} a^{5}}{{\left(a x - 1\right)}^{2}} + \frac{4 \, {\left(a x + 1\right)} a^{5}}{a x - 1}}{a^{10}}\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right) + \frac{{\left(a x - 1\right)}^{2} {\left(\frac{8 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)}}{{\left(a x + 1\right)}^{2} a^{5}} - \frac{\frac{{\left(a x + 1\right)}^{2} a^{5}}{{\left(a x - 1\right)}^{2}} + \frac{8 \, {\left(a x + 1\right)} a^{5}}{a x - 1}}{a^{10}}\right)} a"," ",0,"1/256*(2*((a*x - 1)^2*(4*(a*x + 1)/(a*x - 1) + 1)/((a*x + 1)^2*a^5) + ((a*x + 1)^2*a^5/(a*x - 1)^2 + 4*(a*x + 1)*a^5/(a*x - 1))/a^10)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1)) + (a*x - 1)^2*(8*(a*x + 1)/(a*x - 1) + 1)/((a*x + 1)^2*a^5) - ((a*x + 1)^2*a^5/(a*x - 1)^2 + 8*(a*x + 1)*a^5/(a*x - 1))/a^10)*a","B",0
303,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\int -\frac{x^{2} \operatorname{artanh}\left(a x\right)}{{\left(a^{2} x^{2} - 1\right)}^{3}}\,{d x}"," ",0,"integrate(-x^2*arctanh(a*x)/(a^2*x^2 - 1)^3, x)","F",0
304,1,239,0,0.251528," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1)^3,x, algorithm=""giac"")","-\frac{1}{256} \, {\left(2 \, {\left(\frac{{\left(a x - 1\right)}^{2} {\left(\frac{4 \, {\left(a x + 1\right)}}{a x - 1} - 1\right)}}{{\left(a x + 1\right)}^{2} a^{3}} - \frac{\frac{{\left(a x + 1\right)}^{2} a^{3}}{{\left(a x - 1\right)}^{2}} - \frac{4 \, {\left(a x + 1\right)} a^{3}}{a x - 1}}{a^{6}}\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right) + \frac{{\left(a x - 1\right)}^{2} {\left(\frac{8 \, {\left(a x + 1\right)}}{a x - 1} - 1\right)}}{{\left(a x + 1\right)}^{2} a^{3}} + \frac{\frac{{\left(a x + 1\right)}^{2} a^{3}}{{\left(a x - 1\right)}^{2}} - \frac{8 \, {\left(a x + 1\right)} a^{3}}{a x - 1}}{a^{6}}\right)} a"," ",0,"-1/256*(2*((a*x - 1)^2*(4*(a*x + 1)/(a*x - 1) - 1)/((a*x + 1)^2*a^3) - ((a*x + 1)^2*a^3/(a*x - 1)^2 - 4*(a*x + 1)*a^3/(a*x - 1))/a^6)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1)) + (a*x - 1)^2*(8*(a*x + 1)/(a*x - 1) - 1)/((a*x + 1)^2*a^3) + ((a*x + 1)^2*a^3/(a*x - 1)^2 - 8*(a*x + 1)*a^3/(a*x - 1))/a^6)*a","B",0
305,0,0,0,0.000000," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)}{{\left(a^{2} x^{2} - 1\right)}^{3}}\,{d x}"," ",0,"integrate(-arctanh(a*x)/(a^2*x^2 - 1)^3, x)","F",0
306,0,0,0,0.000000," ","integrate(arctanh(a*x)/x/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)}{{\left(a^{2} x^{2} - 1\right)}^{3} x}\,{d x}"," ",0,"integrate(-arctanh(a*x)/((a^2*x^2 - 1)^3*x), x)","F",0
307,0,0,0,0.000000," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)}{{\left(a^{2} x^{2} - 1\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate(-arctanh(a*x)/((a^2*x^2 - 1)^3*x^2), x)","F",0
308,1,250,0,0.174617," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\frac{1}{512} \, {\left(2 \, {\left(\frac{{\left(a x - 1\right)}^{2} {\left(\frac{4 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)}}{{\left(a x + 1\right)}^{2} a^{5}} + \frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2} a^{5}} + \frac{4 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{5}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 2 \, {\left(\frac{{\left(a x - 1\right)}^{2} {\left(\frac{8 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)}}{{\left(a x + 1\right)}^{2} a^{5}} - \frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2} a^{5}} - \frac{8 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{5}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + \frac{{\left(a x - 1\right)}^{2} {\left(\frac{16 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)}}{{\left(a x + 1\right)}^{2} a^{5}} + \frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2} a^{5}} + \frac{16 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{5}}\right)} a"," ",0,"1/512*(2*((a*x - 1)^2*(4*(a*x + 1)/(a*x - 1) + 1)/((a*x + 1)^2*a^5) + (a*x + 1)^2/((a*x - 1)^2*a^5) + 4*(a*x + 1)/((a*x - 1)*a^5))*log(-(a*x + 1)/(a*x - 1))^2 + 2*((a*x - 1)^2*(8*(a*x + 1)/(a*x - 1) + 1)/((a*x + 1)^2*a^5) - (a*x + 1)^2/((a*x - 1)^2*a^5) - 8*(a*x + 1)/((a*x - 1)*a^5))*log(-(a*x + 1)/(a*x - 1)) + (a*x - 1)^2*(16*(a*x + 1)/(a*x - 1) + 1)/((a*x + 1)^2*a^5) + (a*x + 1)^2/((a*x - 1)^2*a^5) + 16*(a*x + 1)/((a*x - 1)*a^5))*a","B",0
309,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\int -\frac{x^{2} \operatorname{artanh}\left(a x\right)^{2}}{{\left(a^{2} x^{2} - 1\right)}^{3}}\,{d x}"," ",0,"integrate(-x^2*arctanh(a*x)^2/(a^2*x^2 - 1)^3, x)","F",0
310,1,251,0,0.252679," ","integrate(x*arctanh(a*x)^2/(-a^2*x^2+1)^3,x, algorithm=""giac"")","-\frac{1}{512} \, {\left(2 \, {\left(\frac{{\left(a x - 1\right)}^{2} {\left(\frac{4 \, {\left(a x + 1\right)}}{a x - 1} - 1\right)}}{{\left(a x + 1\right)}^{2} a^{3}} - \frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2} a^{3}} + \frac{4 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{3}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 2 \, {\left(\frac{{\left(a x - 1\right)}^{2} {\left(\frac{8 \, {\left(a x + 1\right)}}{a x - 1} - 1\right)}}{{\left(a x + 1\right)}^{2} a^{3}} + \frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2} a^{3}} - \frac{8 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{3}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + \frac{{\left(a x - 1\right)}^{2} {\left(\frac{16 \, {\left(a x + 1\right)}}{a x - 1} - 1\right)}}{{\left(a x + 1\right)}^{2} a^{3}} - \frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2} a^{3}} + \frac{16 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{3}}\right)} a"," ",0,"-1/512*(2*((a*x - 1)^2*(4*(a*x + 1)/(a*x - 1) - 1)/((a*x + 1)^2*a^3) - (a*x + 1)^2/((a*x - 1)^2*a^3) + 4*(a*x + 1)/((a*x - 1)*a^3))*log(-(a*x + 1)/(a*x - 1))^2 + 2*((a*x - 1)^2*(8*(a*x + 1)/(a*x - 1) - 1)/((a*x + 1)^2*a^3) + (a*x + 1)^2/((a*x - 1)^2*a^3) - 8*(a*x + 1)/((a*x - 1)*a^3))*log(-(a*x + 1)/(a*x - 1)) + (a*x - 1)^2*(16*(a*x + 1)/(a*x - 1) - 1)/((a*x + 1)^2*a^3) - (a*x + 1)^2/((a*x - 1)^2*a^3) + 16*(a*x + 1)/((a*x - 1)*a^3))*a","B",0
311,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(a^{2} x^{2} - 1\right)}^{3}}\,{d x}"," ",0,"integrate(-arctanh(a*x)^2/(a^2*x^2 - 1)^3, x)","F",0
312,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(a^{2} x^{2} - 1\right)}^{3} x}\,{d x}"," ",0,"integrate(-arctanh(a*x)^2/((a^2*x^2 - 1)^3*x), x)","F",0
313,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x^2/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(a^{2} x^{2} - 1\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate(-arctanh(a*x)^2/((a^2*x^2 - 1)^3*x^2), x)","F",0
314,1,341,0,0.210613," ","integrate(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\frac{1}{2048} \, {\left(4 \, {\left(\frac{{\left(a x - 1\right)}^{2} {\left(\frac{4 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)}}{{\left(a x + 1\right)}^{2} a^{5}} + \frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2} a^{5}} + \frac{4 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{5}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 6 \, {\left(\frac{{\left(a x - 1\right)}^{2} {\left(\frac{8 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)}}{{\left(a x + 1\right)}^{2} a^{5}} - \frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2} a^{5}} - \frac{8 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{5}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 6 \, {\left(\frac{{\left(a x - 1\right)}^{2} {\left(\frac{16 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)}}{{\left(a x + 1\right)}^{2} a^{5}} + \frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2} a^{5}} + \frac{16 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{5}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + \frac{3 \, {\left(a x - 1\right)}^{2} {\left(\frac{32 \, {\left(a x + 1\right)}}{a x - 1} + 1\right)}}{{\left(a x + 1\right)}^{2} a^{5}} - \frac{3 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2} a^{5}} - \frac{96 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{5}}\right)} a"," ",0,"1/2048*(4*((a*x - 1)^2*(4*(a*x + 1)/(a*x - 1) + 1)/((a*x + 1)^2*a^5) + (a*x + 1)^2/((a*x - 1)^2*a^5) + 4*(a*x + 1)/((a*x - 1)*a^5))*log(-(a*x + 1)/(a*x - 1))^3 + 6*((a*x - 1)^2*(8*(a*x + 1)/(a*x - 1) + 1)/((a*x + 1)^2*a^5) - (a*x + 1)^2/((a*x - 1)^2*a^5) - 8*(a*x + 1)/((a*x - 1)*a^5))*log(-(a*x + 1)/(a*x - 1))^2 + 6*((a*x - 1)^2*(16*(a*x + 1)/(a*x - 1) + 1)/((a*x + 1)^2*a^5) + (a*x + 1)^2/((a*x - 1)^2*a^5) + 16*(a*x + 1)/((a*x - 1)*a^5))*log(-(a*x + 1)/(a*x - 1)) + 3*(a*x - 1)^2*(32*(a*x + 1)/(a*x - 1) + 1)/((a*x + 1)^2*a^5) - 3*(a*x + 1)^2/((a*x - 1)^2*a^5) - 96*(a*x + 1)/((a*x - 1)*a^5))*a","B",0
315,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\int -\frac{x^{2} \operatorname{artanh}\left(a x\right)^{3}}{{\left(a^{2} x^{2} - 1\right)}^{3}}\,{d x}"," ",0,"integrate(-x^2*arctanh(a*x)^3/(a^2*x^2 - 1)^3, x)","F",0
316,1,342,0,0.294595," ","integrate(x*arctanh(a*x)^3/(-a^2*x^2+1)^3,x, algorithm=""giac"")","-\frac{1}{2048} \, {\left(4 \, {\left(\frac{{\left(a x - 1\right)}^{2} {\left(\frac{4 \, {\left(a x + 1\right)}}{a x - 1} - 1\right)}}{{\left(a x + 1\right)}^{2} a^{3}} - \frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2} a^{3}} + \frac{4 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{3}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 6 \, {\left(\frac{{\left(a x - 1\right)}^{2} {\left(\frac{8 \, {\left(a x + 1\right)}}{a x - 1} - 1\right)}}{{\left(a x + 1\right)}^{2} a^{3}} + \frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2} a^{3}} - \frac{8 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{3}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 6 \, {\left(\frac{{\left(a x - 1\right)}^{2} {\left(\frac{16 \, {\left(a x + 1\right)}}{a x - 1} - 1\right)}}{{\left(a x + 1\right)}^{2} a^{3}} - \frac{{\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2} a^{3}} + \frac{16 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{3}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + \frac{3 \, {\left(a x - 1\right)}^{2} {\left(\frac{32 \, {\left(a x + 1\right)}}{a x - 1} - 1\right)}}{{\left(a x + 1\right)}^{2} a^{3}} + \frac{3 \, {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2} a^{3}} - \frac{96 \, {\left(a x + 1\right)}}{{\left(a x - 1\right)} a^{3}}\right)} a"," ",0,"-1/2048*(4*((a*x - 1)^2*(4*(a*x + 1)/(a*x - 1) - 1)/((a*x + 1)^2*a^3) - (a*x + 1)^2/((a*x - 1)^2*a^3) + 4*(a*x + 1)/((a*x - 1)*a^3))*log(-(a*x + 1)/(a*x - 1))^3 + 6*((a*x - 1)^2*(8*(a*x + 1)/(a*x - 1) - 1)/((a*x + 1)^2*a^3) + (a*x + 1)^2/((a*x - 1)^2*a^3) - 8*(a*x + 1)/((a*x - 1)*a^3))*log(-(a*x + 1)/(a*x - 1))^2 + 6*((a*x - 1)^2*(16*(a*x + 1)/(a*x - 1) - 1)/((a*x + 1)^2*a^3) - (a*x + 1)^2/((a*x - 1)^2*a^3) + 16*(a*x + 1)/((a*x - 1)*a^3))*log(-(a*x + 1)/(a*x - 1)) + 3*(a*x - 1)^2*(32*(a*x + 1)/(a*x - 1) - 1)/((a*x + 1)^2*a^3) + 3*(a*x + 1)^2/((a*x - 1)^2*a^3) - 96*(a*x + 1)/((a*x - 1)*a^3))*a","B",0
317,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(a^{2} x^{2} - 1\right)}^{3}}\,{d x}"," ",0,"integrate(-arctanh(a*x)^3/(a^2*x^2 - 1)^3, x)","F",0
318,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(a^{2} x^{2} - 1\right)}^{3} x}\,{d x}"," ",0,"integrate(-arctanh(a*x)^3/((a^2*x^2 - 1)^3*x), x)","F",0
319,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x^2/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(a^{2} x^{2} - 1\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate(-arctanh(a*x)^3/((a^2*x^2 - 1)^3*x^2), x)","F",0
320,0,0,0,0.000000," ","integrate(arctanh(a*x)^(1/2)/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\int -\frac{x^{5}}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(-x^5/((a^2*x^2 - 1)^3*arctanh(a*x)^2), x)","F",0
330,0,0,0,0.000000," ","integrate(x^4/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""giac"")","\int -\frac{x^{4}}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(-x^4/((a^2*x^2 - 1)^3*arctanh(a*x)^2), x)","F",0
331,0,0,0,0.000000," ","integrate(x^3/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""giac"")","\int -\frac{x^{3}}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(-x^3/((a^2*x^2 - 1)^3*arctanh(a*x)^2), x)","F",0
332,0,0,0,0.000000," ","integrate(x^2/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""giac"")","\int -\frac{x^{2}}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(-x^2/((a^2*x^2 - 1)^3*arctanh(a*x)^2), x)","F",0
333,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""giac"")","\int -\frac{x}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(-x/((a^2*x^2 - 1)^3*arctanh(a*x)^2), x)","F",0
334,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""giac"")","\int -\frac{1}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(-1/((a^2*x^2 - 1)^3*arctanh(a*x)^2), x)","F",0
335,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""giac"")","\int -\frac{1}{{\left(a^{2} x^{2} - 1\right)}^{3} x \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(-1/((a^2*x^2 - 1)^3*x*arctanh(a*x)^2), x)","F",0
336,0,0,0,0.000000," ","integrate(x^4/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""giac"")","\int -\frac{x^{4}}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(-x^4/((a^2*x^2 - 1)^3*arctanh(a*x)^3), x)","F",0
337,0,0,0,0.000000," ","integrate(x^3/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""giac"")","\int -\frac{x^{3}}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(-x^3/((a^2*x^2 - 1)^3*arctanh(a*x)^3), x)","F",0
338,0,0,0,0.000000," ","integrate(x^2/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""giac"")","\int -\frac{x^{2}}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(-x^2/((a^2*x^2 - 1)^3*arctanh(a*x)^3), x)","F",0
339,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""giac"")","\int -\frac{x}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(-x/((a^2*x^2 - 1)^3*arctanh(a*x)^3), x)","F",0
340,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""giac"")","\int -\frac{1}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(-1/((a^2*x^2 - 1)^3*arctanh(a*x)^3), x)","F",0
341,0,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""giac"")","\int -\frac{1}{{\left(a^{2} x^{2} - 1\right)}^{3} x \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(-1/((a^2*x^2 - 1)^3*x*arctanh(a*x)^3), x)","F",0
342,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^4,x, algorithm=""giac"")","\int -\frac{1}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{4}}\,{d x}"," ",0,"integrate(-1/((a^2*x^2 - 1)^3*arctanh(a*x)^4), x)","F",0
343,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^5,x, algorithm=""giac"")","\int -\frac{1}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{5}}\,{d x}"," ",0,"integrate(-1/((a^2*x^2 - 1)^3*arctanh(a*x)^5), x)","F",0
344,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^6,x, algorithm=""giac"")","\int -\frac{1}{{\left(a^{2} x^{2} - 1\right)}^{3} \operatorname{artanh}\left(a x\right)^{6}}\,{d x}"," ",0,"integrate(-1/((a^2*x^2 - 1)^3*arctanh(a*x)^6), x)","F",0
345,0,0,0,0.000000," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^4,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)}{{\left(a^{2} x^{2} - 1\right)}^{4}}\,{d x}"," ",0,"integrate(arctanh(a*x)/(a^2*x^2 - 1)^4, x)","F",0
346,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^4,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(a^{2} x^{2} - 1\right)}^{4}}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/(a^2*x^2 - 1)^4, x)","F",0
347,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^4,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(a^{2} x^{2} - 1\right)}^{4}}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/(a^2*x^2 - 1)^4, x)","F",0
348,0,0,0,0.000000," ","integrate(arctanh(a*x)^(1/2)/(-a^2*x^2+1)^4,x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\int \frac{x}{{\left(a^{2} x^{2} - 1\right)}^{4} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x/((a^2*x^2 - 1)^4*arctanh(a*x)^2), x)","F",0
361,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^4/arctanh(a*x)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{4} \operatorname{artanh}\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^4*arctanh(a*x)^2), x)","F",0
362,0,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^4/arctanh(a*x)^3,x, algorithm=""giac"")","\int \frac{x}{{\left(a^{2} x^{2} - 1\right)}^{4} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x/((a^2*x^2 - 1)^4*arctanh(a*x)^3), x)","F",0
363,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^4/arctanh(a*x)^3,x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{2} - 1\right)}^{4} \operatorname{artanh}\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - 1)^4*arctanh(a*x)^3), x)","F",0
364,-2,0,0,0.000000," ","integrate(x^5*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
365,0,0,0,0.000000," ","integrate(x^4*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\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,-2,0,0,0.000000," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
367,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\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
368,1,47,0,0.222858," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{a {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} \log\left(-\frac{a x + 1}{a x - 1}\right)}{2 \, a^{2}}"," ",0,"arcsin(a*x)*sgn(a)/(a*abs(a)) - 1/2*sqrt(-a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))/a^2","A",0
369,0,0,0,0.000000," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\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=""giac"")","\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
371,1,111,0,0.265647," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, a {\left(\log\left(\sqrt{-a^{2} x^{2} + 1} + 1\right) - \log\left(-\sqrt{-a^{2} x^{2} + 1} + 1\right)\right)} + \frac{1}{4} \, {\left(\frac{a^{4} x}{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{x {\left| a \right|}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)"," ",0,"-1/2*a*(log(sqrt(-a^2*x^2 + 1) + 1) - log(-sqrt(-a^2*x^2 + 1) + 1)) + 1/4*(a^4*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) - (sqrt(-a^2*x^2 + 1)*abs(a) + a)/(x*abs(a)))*log(-(a*x + 1)/(a*x - 1))","B",0
372,0,0,0,0.000000," ","integrate(arctanh(a*x)/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\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,-2,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
374,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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,-2,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
381,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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,-2,0,0,0.000000," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
389,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\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
390,1,61,0,0.287831," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\frac{\sqrt{-a^{2} x^{2} + 1} x}{{\left(a^{2} x^{2} - 1\right)} a} + \frac{\log\left(-\frac{a x + 1}{a x - 1}\right)}{2 \, \sqrt{-a^{2} x^{2} + 1} a^{2}}"," ",0,"sqrt(-a^2*x^2 + 1)*x/((a^2*x^2 - 1)*a) + 1/2*log(-(a*x + 1)/(a*x - 1))/(sqrt(-a^2*x^2 + 1)*a^2)","A",0
391,1,59,0,0.326566," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{-a^{2} x^{2} + 1} x \log\left(-\frac{a x + 1}{a x - 1}\right)}{2 \, {\left(a^{2} x^{2} - 1\right)}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} a}"," ",0,"-1/2*sqrt(-a^2*x^2 + 1)*x*log(-(a*x + 1)/(a*x - 1))/(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=""giac"")","\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
393,1,155,0,0.314788," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{1}{2} \, a \log\left(\sqrt{-a^{2} x^{2} + 1} + 1\right) + \frac{1}{2} \, a \log\left(-\sqrt{-a^{2} x^{2} + 1} + 1\right) + \frac{1}{4} \, {\left(\frac{a^{4} x}{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} a^{2} x}{a^{2} x^{2} - 1} - \frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{x {\left| a \right|}}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - \frac{a}{\sqrt{-a^{2} x^{2} + 1}}"," ",0,"-1/2*a*log(sqrt(-a^2*x^2 + 1) + 1) + 1/2*a*log(-sqrt(-a^2*x^2 + 1) + 1) + 1/4*(a^4*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) - 2*sqrt(-a^2*x^2 + 1)*a^2*x/(a^2*x^2 - 1) - (sqrt(-a^2*x^2 + 1)*abs(a) + a)/(x*abs(a)))*log(-(a*x + 1)/(a*x - 1)) - a/sqrt(-a^2*x^2 + 1)","B",0
394,0,0,0,0.000000," ","integrate(arctanh(a*x)/x^3/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\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=""giac"")","\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,-2,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
397,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\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
398,0,0,0,0.000000," ","integrate(x*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{x \operatorname{artanh}\left(a x\right)^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x*arctanh(a*x)^2/(-a^2*x^2 + 1)^(3/2), x)","F",0
399,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/(-a^2*x^2 + 1)^(3/2), x)","F",0
400,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/x/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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,-2,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
405,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\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
406,0,0,0,0.000000," ","integrate(x*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{x \operatorname{artanh}\left(a x\right)^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x*arctanh(a*x)^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
407,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arctanh(a*x)^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
408,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/x/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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,-2,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
414,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""giac"")","\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,-2,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
416,0,0,0,0.000000," ","integrate(x^m/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""giac"")","\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=""giac"")","\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,-2,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
419,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""giac"")","\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,-2,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
421,0,0,0,0.000000," ","integrate(x^m/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""giac"")","\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=""giac"")","\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,-2,0,0,0.000000," ","integrate(x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
424,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""giac"")","\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,-2,0,0,0.000000," ","integrate(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
426,0,0,0,0.000000," ","integrate(x^4*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\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,-2,0,0,0.000000," ","integrate(x^3*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
428,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\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,-2,0,0,0.000000," ","integrate(x*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
430,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
431,-2,0,0,0.000000," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
432,-2,0,0,0.000000," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
433,-2,0,0,0.000000," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
434,-2,0,0,0.000000," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
435,-2,0,0,0.000000," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^5,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
436,-2,0,0,0.000000," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^6,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
437,-2,0,0,0.000000," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^7,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
438,0,0,0,0.000000," ","integrate(x^4*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\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,-2,0,0,0.000000," ","integrate(x^3*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
440,0,0,0,0.000000," ","integrate(x^2*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\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,-2,0,0,0.000000," ","integrate(x*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
442,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
443,-2,0,0,0.000000," ","integrate(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
444,-2,0,0,0.000000," ","integrate(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
445,-2,0,0,0.000000," ","integrate(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
446,-2,0,0,0.000000," ","integrate(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
447,0,0,0,0.000000," ","integrate(x^4*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""giac"")","\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,-2,0,0,0.000000," ","integrate(x^3*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
449,0,0,0,0.000000," ","integrate(x^2*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""giac"")","\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,-2,0,0,0.000000," ","integrate(x*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
451,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
452,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
453,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
454,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
455,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
456,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^5,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
457,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^6,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
458,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^7,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
459,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(5/2)*arctanh(a*x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
460,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
461,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
462,1,90,0,0.706788," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(5/2),x, algorithm=""giac"")","-\frac{{\left(2 \, a^{2} x^{2} - 3\right)} \sqrt{-a^{2} x^{2} + 1} x \log\left(-\frac{a x + 1}{a x - 1}\right)}{6 \, {\left(a^{2} x^{2} - 1\right)}^{2}} - \frac{6 \, a^{2} x^{2} - 7}{9 \, {\left(a^{2} x^{2} - 1\right)} \sqrt{-a^{2} x^{2} + 1} a}"," ",0,"-1/6*(2*a^2*x^2 - 3)*sqrt(-a^2*x^2 + 1)*x*log(-(a*x + 1)/(a*x - 1))/(a^2*x^2 - 1)^2 - 1/9*(6*a^2*x^2 - 7)/((a^2*x^2 - 1)*sqrt(-a^2*x^2 + 1)*a)","A",0
463,1,114,0,0.246953," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(7/2),x, algorithm=""giac"")","-\frac{\sqrt{-a^{2} x^{2} + 1} {\left(4 \, {\left(2 \, a^{4} x^{2} - 5 \, a^{2}\right)} x^{2} + 15\right)} x \log\left(-\frac{a x + 1}{a x - 1}\right)}{30 \, {\left(a^{2} x^{2} - 1\right)}^{3}} + \frac{20 \, a^{2} x^{2} - 120 \, {\left(a^{2} x^{2} - 1\right)}^{2} - 29}{225 \, {\left(a^{2} x^{2} - 1\right)}^{2} \sqrt{-a^{2} x^{2} + 1} a}"," ",0,"-1/30*sqrt(-a^2*x^2 + 1)*(4*(2*a^4*x^2 - 5*a^2)*x^2 + 15)*x*log(-(a*x + 1)/(a*x - 1))/(a^2*x^2 - 1)^3 + 1/225*(20*a^2*x^2 - 120*(a^2*x^2 - 1)^2 - 29)/((a^2*x^2 - 1)^2*sqrt(-a^2*x^2 + 1)*a)","A",0
464,1,138,0,0.231459," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(9/2),x, algorithm=""giac"")","-\frac{\sqrt{-a^{2} x^{2} + 1} {\left(2 \, {\left(4 \, {\left(2 \, a^{6} x^{2} - 7 \, a^{4}\right)} x^{2} + 35 \, a^{2}\right)} x^{2} - 35\right)} x \log\left(-\frac{a x + 1}{a x - 1}\right)}{70 \, {\left(a^{2} x^{2} - 1\right)}^{4}} - \frac{126 \, a^{2} x^{2} + 1680 \, {\left(a^{2} x^{2} - 1\right)}^{3} - 280 \, {\left(a^{2} x^{2} - 1\right)}^{2} - 201}{3675 \, {\left(a^{2} x^{2} - 1\right)}^{3} \sqrt{-a^{2} x^{2} + 1} a}"," ",0,"-1/70*sqrt(-a^2*x^2 + 1)*(2*(4*(2*a^6*x^2 - 7*a^4)*x^2 + 35*a^2)*x^2 - 35)*x*log(-(a*x + 1)/(a*x - 1))/(a^2*x^2 - 1)^4 - 1/3675*(126*a^2*x^2 + 1680*(a^2*x^2 - 1)^3 - 280*(a^2*x^2 - 1)^2 - 201)/((a^2*x^2 - 1)^3*sqrt(-a^2*x^2 + 1)*a)","A",0
465,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)*arctanh(a*x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
466,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*arctanh(a*x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
467,0,0,0,0.000000," ","integrate(arctanh(a*x)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\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
468,1,70,0,0.692040," ","integrate(arctanh(a*x)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{-a^{2} c x^{2} + c} x \log\left(-\frac{a x + 1}{a x - 1}\right)}{2 \, {\left(a^{2} c x^{2} - c\right)} c} - \frac{1}{\sqrt{-a^{2} c x^{2} + c} a c}"," ",0,"-1/2*sqrt(-a^2*c*x^2 + c)*x*log(-(a*x + 1)/(a*x - 1))/((a^2*c*x^2 - c)*c) - 1/(sqrt(-a^2*c*x^2 + c)*a*c)","A",0
469,1,111,0,0.314982," ","integrate(arctanh(a*x)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{-a^{2} c x^{2} + c} {\left(\frac{2 \, a^{2} x^{2}}{c} - \frac{3}{c}\right)} x \log\left(-\frac{a x + 1}{a x - 1}\right)}{6 \, {\left(a^{2} c x^{2} - c\right)}^{2}} - \frac{6 \, a^{2} c x^{2} - 7 \, c}{9 \, {\left(a^{2} c x^{2} - c\right)} \sqrt{-a^{2} c x^{2} + c} a c^{2}}"," ",0,"-1/6*sqrt(-a^2*c*x^2 + c)*(2*a^2*x^2/c - 3/c)*x*log(-(a*x + 1)/(a*x - 1))/(a^2*c*x^2 - c)^2 - 1/9*(6*a^2*c*x^2 - 7*c)/((a^2*c*x^2 - c)*sqrt(-a^2*c*x^2 + c)*a*c^2)","A",0
470,1,149,0,0.313136," ","integrate(arctanh(a*x)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","-\frac{\sqrt{-a^{2} c x^{2} + c} {\left(4 \, {\left(\frac{2 \, a^{4} x^{2}}{c} - \frac{5 \, a^{2}}{c}\right)} x^{2} + \frac{15}{c}\right)} x \log\left(-\frac{a x + 1}{a x - 1}\right)}{30 \, {\left(a^{2} c x^{2} - c\right)}^{3}} - \frac{120 \, {\left(a^{2} c x^{2} - c\right)}^{2} - 20 \, {\left(a^{2} c x^{2} - c\right)} c + 9 \, c^{2}}{225 \, {\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} c x^{2} + c} a c^{3}}"," ",0,"-1/30*sqrt(-a^2*c*x^2 + c)*(4*(2*a^4*x^2/c - 5*a^2/c)*x^2 + 15/c)*x*log(-(a*x + 1)/(a*x - 1))/(a^2*c*x^2 - c)^3 - 1/225*(120*(a^2*c*x^2 - c)^2 - 20*(a^2*c*x^2 - c)*c + 9*c^2)/((a^2*c*x^2 - c)^2*sqrt(-a^2*c*x^2 + c)*a*c^3)","A",0
471,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
472,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^(5/2),x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/(-a^2*x^2 + 1)^(5/2), x)","F",0
473,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^(7/2),x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/(-a^2*x^2 + 1)^(7/2), x)","F",0
474,0,0,0,0.000000," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^(9/2),x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(arctanh(a*x)^2/(-a^2*x^2 + 1)^(9/2), x)","F",0
475,-2,0,0,0.000000," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
476,0,0,0,0.000000," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^(5/2),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\int -\frac{{\left(e x + d\right)} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{c^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-(e*x + d)*(b*arctanh(c*x) + a)^2/(c^2*x^2 - 1), x)","F",0
498,1,1471,0,1.244589," ","integrate((d*x^2+c)^4*arctanh(a*x),x, algorithm=""giac"")","\frac{1}{945} \, a {\left(\frac{3 \, {\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(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right)}{a^{10}} - \frac{3 \, {\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({\left| -\frac{a x + 1}{a x - 1} + 1 \right|}\right)}{a^{10}} + \frac{8 \, {\left(\frac{3 \, {\left(105 \, a^{6} c^{3} d + 189 \, a^{4} c^{2} d^{2} + 135 \, a^{2} c d^{3} + 35 \, d^{4}\right)} {\left(a x + 1\right)}^{7}}{{\left(a x - 1\right)}^{7}} - \frac{45 \, {\left(42 \, a^{6} c^{3} d + 63 \, a^{4} c^{2} d^{2} + 36 \, a^{2} c d^{3} + 7 \, d^{4}\right)} {\left(a x + 1\right)}^{6}}{{\left(a x - 1\right)}^{6}} + \frac{{\left(4725 \, a^{6} c^{3} d + 6237 \, a^{4} c^{2} d^{2} + 3555 \, a^{2} c d^{3} + 875 \, d^{4}\right)} {\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} - \frac{2 \, {\left(3150 \, a^{6} c^{3} d + 3969 \, a^{4} c^{2} d^{2} + 2340 \, a^{2} c d^{3} + 455 \, d^{4}\right)} {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{{\left(4725 \, a^{6} c^{3} d + 6237 \, a^{4} c^{2} d^{2} + 3555 \, a^{2} c d^{3} + 875 \, d^{4}\right)} {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} - \frac{45 \, {\left(42 \, a^{6} c^{3} d + 63 \, a^{4} c^{2} d^{2} + 36 \, a^{2} c d^{3} + 7 \, d^{4}\right)} {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{3 \, {\left(105 \, a^{6} c^{3} d + 189 \, a^{4} c^{2} d^{2} + 135 \, a^{2} c d^{3} + 35 \, d^{4}\right)} {\left(a x + 1\right)}}{a x - 1}\right)}}{a^{10} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{8}} + \frac{3 \, {\left(\frac{315 \, {\left(a x + 1\right)}^{8} a^{8} c^{4}}{{\left(a x - 1\right)}^{8}} - \frac{2520 \, {\left(a x + 1\right)}^{7} a^{8} c^{4}}{{\left(a x - 1\right)}^{7}} + \frac{8820 \, {\left(a x + 1\right)}^{6} a^{8} c^{4}}{{\left(a x - 1\right)}^{6}} - \frac{17640 \, {\left(a x + 1\right)}^{5} a^{8} c^{4}}{{\left(a x - 1\right)}^{5}} + \frac{22050 \, {\left(a x + 1\right)}^{4} a^{8} c^{4}}{{\left(a x - 1\right)}^{4}} - \frac{17640 \, {\left(a x + 1\right)}^{3} a^{8} c^{4}}{{\left(a x - 1\right)}^{3}} + \frac{8820 \, {\left(a x + 1\right)}^{2} a^{8} c^{4}}{{\left(a x - 1\right)}^{2}} - \frac{2520 \, {\left(a x + 1\right)} a^{8} c^{4}}{a x - 1} + 315 \, a^{8} c^{4} + \frac{1260 \, {\left(a x + 1\right)}^{8} a^{6} c^{3} d}{{\left(a x - 1\right)}^{8}} - \frac{7560 \, {\left(a x + 1\right)}^{7} a^{6} c^{3} d}{{\left(a x - 1\right)}^{7}} + \frac{19320 \, {\left(a x + 1\right)}^{6} a^{6} c^{3} d}{{\left(a x - 1\right)}^{6}} - \frac{27720 \, {\left(a x + 1\right)}^{5} a^{6} c^{3} d}{{\left(a x - 1\right)}^{5}} + \frac{25200 \, {\left(a x + 1\right)}^{4} a^{6} c^{3} d}{{\left(a x - 1\right)}^{4}} - \frac{15960 \, {\left(a x + 1\right)}^{3} a^{6} c^{3} d}{{\left(a x - 1\right)}^{3}} + \frac{7560 \, {\left(a x + 1\right)}^{2} a^{6} c^{3} d}{{\left(a x - 1\right)}^{2}} - \frac{2520 \, {\left(a x + 1\right)} a^{6} c^{3} d}{a x - 1} + 420 \, a^{6} c^{3} d + \frac{1890 \, {\left(a x + 1\right)}^{8} a^{4} c^{2} d^{2}}{{\left(a x - 1\right)}^{8}} - \frac{7560 \, {\left(a x + 1\right)}^{7} a^{4} c^{2} d^{2}}{{\left(a x - 1\right)}^{7}} + \frac{15120 \, {\left(a x + 1\right)}^{6} a^{4} c^{2} d^{2}}{{\left(a x - 1\right)}^{6}} - \frac{22680 \, {\left(a x + 1\right)}^{5} a^{4} c^{2} d^{2}}{{\left(a x - 1\right)}^{5}} + \frac{24948 \, {\left(a x + 1\right)}^{4} a^{4} c^{2} d^{2}}{{\left(a x - 1\right)}^{4}} - \frac{16632 \, {\left(a x + 1\right)}^{3} a^{4} c^{2} d^{2}}{{\left(a x - 1\right)}^{3}} + \frac{6048 \, {\left(a x + 1\right)}^{2} a^{4} c^{2} d^{2}}{{\left(a x - 1\right)}^{2}} - \frac{1512 \, {\left(a x + 1\right)} a^{4} c^{2} d^{2}}{a x - 1} + 378 \, a^{4} c^{2} d^{2} + \frac{1260 \, {\left(a x + 1\right)}^{8} a^{2} c d^{3}}{{\left(a x - 1\right)}^{8}} - \frac{2520 \, {\left(a x + 1\right)}^{7} a^{2} c d^{3}}{{\left(a x - 1\right)}^{7}} + \frac{7560 \, {\left(a x + 1\right)}^{6} a^{2} c d^{3}}{{\left(a x - 1\right)}^{6}} - \frac{12600 \, {\left(a x + 1\right)}^{5} a^{2} c d^{3}}{{\left(a x - 1\right)}^{5}} + \frac{10080 \, {\left(a x + 1\right)}^{4} a^{2} c d^{3}}{{\left(a x - 1\right)}^{4}} - \frac{7560 \, {\left(a x + 1\right)}^{3} a^{2} c d^{3}}{{\left(a x - 1\right)}^{3}} + \frac{3960 \, {\left(a x + 1\right)}^{2} a^{2} c d^{3}}{{\left(a x - 1\right)}^{2}} - \frac{360 \, {\left(a x + 1\right)} a^{2} c d^{3}}{a x - 1} + 180 \, a^{2} c d^{3} + \frac{315 \, {\left(a x + 1\right)}^{8} d^{4}}{{\left(a x - 1\right)}^{8}} + \frac{2940 \, {\left(a x + 1\right)}^{6} d^{4}}{{\left(a x - 1\right)}^{6}} + \frac{4410 \, {\left(a x + 1\right)}^{4} d^{4}}{{\left(a x - 1\right)}^{4}} + \frac{1260 \, {\left(a x + 1\right)}^{2} d^{4}}{{\left(a x - 1\right)}^{2}} + 35 \, d^{4}\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{a^{10} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{9}}\right)}"," ",0,"1/945*a*(3*(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(abs(-a*x - 1)/abs(a*x - 1))/a^10 - 3*(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(abs(-(a*x + 1)/(a*x - 1) + 1))/a^10 + 8*(3*(105*a^6*c^3*d + 189*a^4*c^2*d^2 + 135*a^2*c*d^3 + 35*d^4)*(a*x + 1)^7/(a*x - 1)^7 - 45*(42*a^6*c^3*d + 63*a^4*c^2*d^2 + 36*a^2*c*d^3 + 7*d^4)*(a*x + 1)^6/(a*x - 1)^6 + (4725*a^6*c^3*d + 6237*a^4*c^2*d^2 + 3555*a^2*c*d^3 + 875*d^4)*(a*x + 1)^5/(a*x - 1)^5 - 2*(3150*a^6*c^3*d + 3969*a^4*c^2*d^2 + 2340*a^2*c*d^3 + 455*d^4)*(a*x + 1)^4/(a*x - 1)^4 + (4725*a^6*c^3*d + 6237*a^4*c^2*d^2 + 3555*a^2*c*d^3 + 875*d^4)*(a*x + 1)^3/(a*x - 1)^3 - 45*(42*a^6*c^3*d + 63*a^4*c^2*d^2 + 36*a^2*c*d^3 + 7*d^4)*(a*x + 1)^2/(a*x - 1)^2 + 3*(105*a^6*c^3*d + 189*a^4*c^2*d^2 + 135*a^2*c*d^3 + 35*d^4)*(a*x + 1)/(a*x - 1))/(a^10*((a*x + 1)/(a*x - 1) - 1)^8) + 3*(315*(a*x + 1)^8*a^8*c^4/(a*x - 1)^8 - 2520*(a*x + 1)^7*a^8*c^4/(a*x - 1)^7 + 8820*(a*x + 1)^6*a^8*c^4/(a*x - 1)^6 - 17640*(a*x + 1)^5*a^8*c^4/(a*x - 1)^5 + 22050*(a*x + 1)^4*a^8*c^4/(a*x - 1)^4 - 17640*(a*x + 1)^3*a^8*c^4/(a*x - 1)^3 + 8820*(a*x + 1)^2*a^8*c^4/(a*x - 1)^2 - 2520*(a*x + 1)*a^8*c^4/(a*x - 1) + 315*a^8*c^4 + 1260*(a*x + 1)^8*a^6*c^3*d/(a*x - 1)^8 - 7560*(a*x + 1)^7*a^6*c^3*d/(a*x - 1)^7 + 19320*(a*x + 1)^6*a^6*c^3*d/(a*x - 1)^6 - 27720*(a*x + 1)^5*a^6*c^3*d/(a*x - 1)^5 + 25200*(a*x + 1)^4*a^6*c^3*d/(a*x - 1)^4 - 15960*(a*x + 1)^3*a^6*c^3*d/(a*x - 1)^3 + 7560*(a*x + 1)^2*a^6*c^3*d/(a*x - 1)^2 - 2520*(a*x + 1)*a^6*c^3*d/(a*x - 1) + 420*a^6*c^3*d + 1890*(a*x + 1)^8*a^4*c^2*d^2/(a*x - 1)^8 - 7560*(a*x + 1)^7*a^4*c^2*d^2/(a*x - 1)^7 + 15120*(a*x + 1)^6*a^4*c^2*d^2/(a*x - 1)^6 - 22680*(a*x + 1)^5*a^4*c^2*d^2/(a*x - 1)^5 + 24948*(a*x + 1)^4*a^4*c^2*d^2/(a*x - 1)^4 - 16632*(a*x + 1)^3*a^4*c^2*d^2/(a*x - 1)^3 + 6048*(a*x + 1)^2*a^4*c^2*d^2/(a*x - 1)^2 - 1512*(a*x + 1)*a^4*c^2*d^2/(a*x - 1) + 378*a^4*c^2*d^2 + 1260*(a*x + 1)^8*a^2*c*d^3/(a*x - 1)^8 - 2520*(a*x + 1)^7*a^2*c*d^3/(a*x - 1)^7 + 7560*(a*x + 1)^6*a^2*c*d^3/(a*x - 1)^6 - 12600*(a*x + 1)^5*a^2*c*d^3/(a*x - 1)^5 + 10080*(a*x + 1)^4*a^2*c*d^3/(a*x - 1)^4 - 7560*(a*x + 1)^3*a^2*c*d^3/(a*x - 1)^3 + 3960*(a*x + 1)^2*a^2*c*d^3/(a*x - 1)^2 - 360*(a*x + 1)*a^2*c*d^3/(a*x - 1) + 180*a^2*c*d^3 + 315*(a*x + 1)^8*d^4/(a*x - 1)^8 + 2940*(a*x + 1)^6*d^4/(a*x - 1)^6 + 4410*(a*x + 1)^4*d^4/(a*x - 1)^4 + 1260*(a*x + 1)^2*d^4/(a*x - 1)^2 + 35*d^4)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/(a^10*((a*x + 1)/(a*x - 1) - 1)^9))","B",0
499,1,930,0,0.247032," ","integrate((d*x^2+c)^3*arctanh(a*x),x, algorithm=""giac"")","\frac{1}{105} \, a {\left(\frac{3 \, {\left(35 \, a^{6} c^{3} + 35 \, a^{4} c^{2} d + 21 \, a^{2} c d^{2} + 5 \, d^{3}\right)} \log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right)}{a^{8}} - \frac{3 \, {\left(35 \, a^{6} c^{3} + 35 \, a^{4} c^{2} d + 21 \, a^{2} c d^{2} + 5 \, d^{3}\right)} \log\left({\left| -\frac{a x + 1}{a x - 1} + 1 \right|}\right)}{a^{8}} + \frac{2 \, {\left(\frac{3 \, {\left(35 \, a^{4} c^{2} d + 42 \, a^{2} c d^{2} + 15 \, d^{3}\right)} {\left(a x + 1\right)}^{5}}{{\left(a x - 1\right)}^{5}} - \frac{6 \, {\left(70 \, a^{4} c^{2} d + 63 \, a^{2} c d^{2} + 15 \, d^{3}\right)} {\left(a x + 1\right)}^{4}}{{\left(a x - 1\right)}^{4}} + \frac{2 \, {\left(315 \, a^{4} c^{2} d + 252 \, a^{2} c d^{2} + 85 \, d^{3}\right)} {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} - \frac{6 \, {\left(70 \, a^{4} c^{2} d + 63 \, a^{2} c d^{2} + 15 \, d^{3}\right)} {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{3 \, {\left(35 \, a^{4} c^{2} d + 42 \, a^{2} c d^{2} + 15 \, d^{3}\right)} {\left(a x + 1\right)}}{a x - 1}\right)}}{a^{8} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{6}} + \frac{3 \, {\left(\frac{35 \, {\left(a x + 1\right)}^{6} a^{6} c^{3}}{{\left(a x - 1\right)}^{6}} - \frac{210 \, {\left(a x + 1\right)}^{5} a^{6} c^{3}}{{\left(a x - 1\right)}^{5}} + \frac{525 \, {\left(a x + 1\right)}^{4} a^{6} c^{3}}{{\left(a x - 1\right)}^{4}} - \frac{700 \, {\left(a x + 1\right)}^{3} a^{6} c^{3}}{{\left(a x - 1\right)}^{3}} + \frac{525 \, {\left(a x + 1\right)}^{2} a^{6} c^{3}}{{\left(a x - 1\right)}^{2}} - \frac{210 \, {\left(a x + 1\right)} a^{6} c^{3}}{a x - 1} + 35 \, a^{6} c^{3} + \frac{105 \, {\left(a x + 1\right)}^{6} a^{4} c^{2} d}{{\left(a x - 1\right)}^{6}} - \frac{420 \, {\left(a x + 1\right)}^{5} a^{4} c^{2} d}{{\left(a x - 1\right)}^{5}} + \frac{665 \, {\left(a x + 1\right)}^{4} a^{4} c^{2} d}{{\left(a x - 1\right)}^{4}} - \frac{560 \, {\left(a x + 1\right)}^{3} a^{4} c^{2} d}{{\left(a x - 1\right)}^{3}} + \frac{315 \, {\left(a x + 1\right)}^{2} a^{4} c^{2} d}{{\left(a x - 1\right)}^{2}} - \frac{140 \, {\left(a x + 1\right)} a^{4} c^{2} d}{a x - 1} + 35 \, a^{4} c^{2} d + \frac{105 \, {\left(a x + 1\right)}^{6} a^{2} c d^{2}}{{\left(a x - 1\right)}^{6}} - \frac{210 \, {\left(a x + 1\right)}^{5} a^{2} c d^{2}}{{\left(a x - 1\right)}^{5}} + \frac{315 \, {\left(a x + 1\right)}^{4} a^{2} c d^{2}}{{\left(a x - 1\right)}^{4}} - \frac{420 \, {\left(a x + 1\right)}^{3} a^{2} c d^{2}}{{\left(a x - 1\right)}^{3}} + \frac{231 \, {\left(a x + 1\right)}^{2} a^{2} c d^{2}}{{\left(a x - 1\right)}^{2}} - \frac{42 \, {\left(a x + 1\right)} a^{2} c d^{2}}{a x - 1} + 21 \, a^{2} c d^{2} + \frac{35 \, {\left(a x + 1\right)}^{6} d^{3}}{{\left(a x - 1\right)}^{6}} + \frac{175 \, {\left(a x + 1\right)}^{4} d^{3}}{{\left(a x - 1\right)}^{4}} + \frac{105 \, {\left(a x + 1\right)}^{2} d^{3}}{{\left(a x - 1\right)}^{2}} + 5 \, d^{3}\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{a^{8} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{7}}\right)}"," ",0,"1/105*a*(3*(35*a^6*c^3 + 35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*log(abs(-a*x - 1)/abs(a*x - 1))/a^8 - 3*(35*a^6*c^3 + 35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*log(abs(-(a*x + 1)/(a*x - 1) + 1))/a^8 + 2*(3*(35*a^4*c^2*d + 42*a^2*c*d^2 + 15*d^3)*(a*x + 1)^5/(a*x - 1)^5 - 6*(70*a^4*c^2*d + 63*a^2*c*d^2 + 15*d^3)*(a*x + 1)^4/(a*x - 1)^4 + 2*(315*a^4*c^2*d + 252*a^2*c*d^2 + 85*d^3)*(a*x + 1)^3/(a*x - 1)^3 - 6*(70*a^4*c^2*d + 63*a^2*c*d^2 + 15*d^3)*(a*x + 1)^2/(a*x - 1)^2 + 3*(35*a^4*c^2*d + 42*a^2*c*d^2 + 15*d^3)*(a*x + 1)/(a*x - 1))/(a^8*((a*x + 1)/(a*x - 1) - 1)^6) + 3*(35*(a*x + 1)^6*a^6*c^3/(a*x - 1)^6 - 210*(a*x + 1)^5*a^6*c^3/(a*x - 1)^5 + 525*(a*x + 1)^4*a^6*c^3/(a*x - 1)^4 - 700*(a*x + 1)^3*a^6*c^3/(a*x - 1)^3 + 525*(a*x + 1)^2*a^6*c^3/(a*x - 1)^2 - 210*(a*x + 1)*a^6*c^3/(a*x - 1) + 35*a^6*c^3 + 105*(a*x + 1)^6*a^4*c^2*d/(a*x - 1)^6 - 420*(a*x + 1)^5*a^4*c^2*d/(a*x - 1)^5 + 665*(a*x + 1)^4*a^4*c^2*d/(a*x - 1)^4 - 560*(a*x + 1)^3*a^4*c^2*d/(a*x - 1)^3 + 315*(a*x + 1)^2*a^4*c^2*d/(a*x - 1)^2 - 140*(a*x + 1)*a^4*c^2*d/(a*x - 1) + 35*a^4*c^2*d + 105*(a*x + 1)^6*a^2*c*d^2/(a*x - 1)^6 - 210*(a*x + 1)^5*a^2*c*d^2/(a*x - 1)^5 + 315*(a*x + 1)^4*a^2*c*d^2/(a*x - 1)^4 - 420*(a*x + 1)^3*a^2*c*d^2/(a*x - 1)^3 + 231*(a*x + 1)^2*a^2*c*d^2/(a*x - 1)^2 - 42*(a*x + 1)*a^2*c*d^2/(a*x - 1) + 21*a^2*c*d^2 + 35*(a*x + 1)^6*d^3/(a*x - 1)^6 + 175*(a*x + 1)^4*d^3/(a*x - 1)^4 + 105*(a*x + 1)^2*d^3/(a*x - 1)^2 + 5*d^3)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/(a^8*((a*x + 1)/(a*x - 1) - 1)^7))","B",0
500,1,527,0,0.199298," ","integrate((d*x^2+c)^2*arctanh(a*x),x, algorithm=""giac"")","\frac{1}{15} \, a {\left(\frac{{\left(15 \, a^{4} c^{2} + 10 \, a^{2} c d + 3 \, d^{2}\right)} \log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right)}{a^{6}} - \frac{{\left(15 \, a^{4} c^{2} + 10 \, a^{2} c d + 3 \, d^{2}\right)} \log\left({\left| -\frac{a x + 1}{a x - 1} + 1 \right|}\right)}{a^{6}} + \frac{4 \, {\left(\frac{{\left(5 \, a^{2} c d + 3 \, d^{2}\right)} {\left(a x + 1\right)}^{3}}{{\left(a x - 1\right)}^{3}} - \frac{{\left(10 \, a^{2} c d + 3 \, d^{2}\right)} {\left(a x + 1\right)}^{2}}{{\left(a x - 1\right)}^{2}} + \frac{{\left(5 \, a^{2} c d + 3 \, d^{2}\right)} {\left(a x + 1\right)}}{a x - 1}\right)}}{a^{6} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{4}} + \frac{{\left(\frac{15 \, {\left(a x + 1\right)}^{4} a^{4} c^{2}}{{\left(a x - 1\right)}^{4}} - \frac{60 \, {\left(a x + 1\right)}^{3} a^{4} c^{2}}{{\left(a x - 1\right)}^{3}} + \frac{90 \, {\left(a x + 1\right)}^{2} a^{4} c^{2}}{{\left(a x - 1\right)}^{2}} - \frac{60 \, {\left(a x + 1\right)} a^{4} c^{2}}{a x - 1} + 15 \, a^{4} c^{2} + \frac{30 \, {\left(a x + 1\right)}^{4} a^{2} c d}{{\left(a x - 1\right)}^{4}} - \frac{60 \, {\left(a x + 1\right)}^{3} a^{2} c d}{{\left(a x - 1\right)}^{3}} + \frac{40 \, {\left(a x + 1\right)}^{2} a^{2} c d}{{\left(a x - 1\right)}^{2}} - \frac{20 \, {\left(a x + 1\right)} a^{2} c d}{a x - 1} + 10 \, a^{2} c d + \frac{15 \, {\left(a x + 1\right)}^{4} d^{2}}{{\left(a x - 1\right)}^{4}} + \frac{30 \, {\left(a x + 1\right)}^{2} d^{2}}{{\left(a x - 1\right)}^{2}} + 3 \, d^{2}\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{a^{6} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{5}}\right)}"," ",0,"1/15*a*((15*a^4*c^2 + 10*a^2*c*d + 3*d^2)*log(abs(-a*x - 1)/abs(a*x - 1))/a^6 - (15*a^4*c^2 + 10*a^2*c*d + 3*d^2)*log(abs(-(a*x + 1)/(a*x - 1) + 1))/a^6 + 4*((5*a^2*c*d + 3*d^2)*(a*x + 1)^3/(a*x - 1)^3 - (10*a^2*c*d + 3*d^2)*(a*x + 1)^2/(a*x - 1)^2 + (5*a^2*c*d + 3*d^2)*(a*x + 1)/(a*x - 1))/(a^6*((a*x + 1)/(a*x - 1) - 1)^4) + (15*(a*x + 1)^4*a^4*c^2/(a*x - 1)^4 - 60*(a*x + 1)^3*a^4*c^2/(a*x - 1)^3 + 90*(a*x + 1)^2*a^4*c^2/(a*x - 1)^2 - 60*(a*x + 1)*a^4*c^2/(a*x - 1) + 15*a^4*c^2 + 30*(a*x + 1)^4*a^2*c*d/(a*x - 1)^4 - 60*(a*x + 1)^3*a^2*c*d/(a*x - 1)^3 + 40*(a*x + 1)^2*a^2*c*d/(a*x - 1)^2 - 20*(a*x + 1)*a^2*c*d/(a*x - 1) + 10*a^2*c*d + 15*(a*x + 1)^4*d^2/(a*x - 1)^4 + 30*(a*x + 1)^2*d^2/(a*x - 1)^2 + 3*d^2)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/(a^6*((a*x + 1)/(a*x - 1) - 1)^5))","B",0
501,1,266,0,0.209850," ","integrate((d*x^2+c)*arctanh(a*x),x, algorithm=""giac"")","\frac{1}{3} \, a {\left(\frac{{\left(3 \, a^{2} c + d\right)} \log\left(\frac{{\left| -a x - 1 \right|}}{{\left| a x - 1 \right|}}\right)}{a^{4}} - \frac{{\left(3 \, a^{2} c + d\right)} \log\left({\left| -\frac{a x + 1}{a x - 1} + 1 \right|}\right)}{a^{4}} + \frac{2 \, {\left(a x + 1\right)} d}{{\left(a x - 1\right)} a^{4} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{2}} + \frac{{\left(\frac{3 \, {\left(a x + 1\right)}^{2} a^{2} c}{{\left(a x - 1\right)}^{2}} - \frac{6 \, {\left(a x + 1\right)} a^{2} c}{a x - 1} + 3 \, a^{2} c + \frac{3 \, {\left(a x + 1\right)}^{2} d}{{\left(a x - 1\right)}^{2}} + d\right)} \log\left(-\frac{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} + 1}{\frac{a {\left(\frac{a x + 1}{a x - 1} + 1\right)}}{\frac{{\left(a x + 1\right)} a}{a x - 1} - a} - 1}\right)}{a^{4} {\left(\frac{a x + 1}{a x - 1} - 1\right)}^{3}}\right)}"," ",0,"1/3*a*((3*a^2*c + d)*log(abs(-a*x - 1)/abs(a*x - 1))/a^4 - (3*a^2*c + d)*log(abs(-(a*x + 1)/(a*x - 1) + 1))/a^4 + 2*(a*x + 1)*d/((a*x - 1)*a^4*((a*x + 1)/(a*x - 1) - 1)^2) + (3*(a*x + 1)^2*a^2*c/(a*x - 1)^2 - 6*(a*x + 1)*a^2*c/(a*x - 1) + 3*a^2*c + 3*(a*x + 1)^2*d/(a*x - 1)^2 + d)*log(-(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) + 1)/(a*((a*x + 1)/(a*x - 1) + 1)/((a*x + 1)*a/(a*x - 1) - a) - 1))/(a^4*((a*x + 1)/(a*x - 1) - 1)^3))","B",0
502,0,0,0,0.000000," ","integrate(arctanh(a*x)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)}{d x^{2} + c}\,{d x}"," ",0,"integrate(arctanh(a*x)/(d*x^2 + c), x)","F",0
503,0,0,0,0.000000," ","integrate(arctanh(a*x)/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(arctanh(a*x)/(d*x^2 + c)^2, x)","F",0
504,0,0,0,0.000000," ","integrate(arctanh(a*x)/(d*x^2+c)^3,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x\right)}{{\left(d x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate(arctanh(a*x)/(d*x^2 + c)^3, x)","F",0
505,1,48,0,0.234370," ","integrate(1/(-a*x^2+a)/(b-2*b*arctanh(x)),x, algorithm=""giac"")","-\frac{\log\left(\frac{1}{4} \, \pi^{2} {\left(\mathrm{sgn}\left(x - 1\right) \mathrm{sgn}\left(-x - 1\right) - 1\right)}^{2} + {\left(\log\left(\frac{{\left| -x - 1 \right|}}{{\left| x - 1 \right|}}\right) - 1\right)}^{2}\right)}{4 \, a b}"," ",0,"-1/4*log(1/4*pi^2*(sgn(x - 1)*sgn(-x - 1) - 1)^2 + (log(abs(-x - 1)/abs(x - 1)) - 1)^2)/(a*b)","B",0
506,0,0,0,0.000000," ","integrate(arctanh(b*x)/(-x^2+1),x, algorithm=""giac"")","\int -\frac{\operatorname{artanh}\left(b x\right)}{x^{2} - 1}\,{d x}"," ",0,"integrate(-arctanh(b*x)/(x^2 - 1), x)","F",0
507,-1,0,0,0.000000," ","integrate(arctanh(b*x+a)/(-x^2+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,0,0,0,0.000000," ","integrate(arctanh(x)/(b*x+a),x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(x\right)}{b x + a}\,{d x}"," ",0,"integrate(arctanh(x)/(b*x + a), x)","F",0
509,0,0,0,0.000000," ","integrate(arctanh(x)/(b*x^2+a),x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(x\right)}{b x^{2} + a}\,{d x}"," ",0,"integrate(arctanh(x)/(b*x^2 + a), x)","F",0
510,0,0,0,0.000000," ","integrate(arctanh(x)/(c*x^2+b*x+a),x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(x\right)}{c x^{2} + b x + a}\,{d x}"," ",0,"integrate(arctanh(x)/(c*x^2 + b*x + a), x)","F",0
511,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)*arctanh(a*x),x, algorithm=""giac"")","\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=""giac"")","\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
513,1,71,0,0.179112," ","integrate(arctanh(a*x)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{x \log\left(-\frac{a x + 1}{a x - 1}\right)}{2 \, \sqrt{d x^{2} + c} c} + \frac{\arctan\left(\frac{\sqrt{d x^{2} + c} a}{\sqrt{-a^{2} c - d}}\right)}{\sqrt{-a^{2} c - d} c}"," ",0,"1/2*x*log(-(a*x + 1)/(a*x - 1))/(sqrt(d*x^2 + c)*c) + arctan(sqrt(d*x^2 + c)*a/sqrt(-a^2*c - d))/(sqrt(-a^2*c - d)*c)","A",0
514,1,135,0,0.206767," ","integrate(arctanh(a*x)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{1}{3} \, a {\left(\frac{{\left(3 \, a^{2} c + 2 \, d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} a}{\sqrt{-a^{2} c - d}}\right)}{{\left(a^{2} c^{3} + c^{2} d\right)} \sqrt{-a^{2} c - d} a} + \frac{1}{{\left(a^{2} c^{2} + c d\right)} \sqrt{d x^{2} + c}}\right)} + \frac{x {\left(\frac{2 \, d x^{2}}{c^{2}} + \frac{3}{c}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{6 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}}"," ",0,"1/3*a*((3*a^2*c + 2*d)*arctan(sqrt(d*x^2 + c)*a/sqrt(-a^2*c - d))/((a^2*c^3 + c^2*d)*sqrt(-a^2*c - d)*a) + 1/((a^2*c^2 + c*d)*sqrt(d*x^2 + c))) + 1/6*x*(2*d*x^2/c^2 + 3/c)*log(-(a*x + 1)/(a*x - 1))/(d*x^2 + c)^(3/2)","A",0
515,1,218,0,0.217161," ","integrate(arctanh(a*x)/(d*x^2+c)^(7/2),x, algorithm=""giac"")","\frac{1}{15} \, a {\left(\frac{{\left(15 \, a^{4} c^{2} + 20 \, a^{2} c d + 8 \, d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} a}{\sqrt{-a^{2} c - d}}\right)}{{\left(a^{4} c^{5} + 2 \, a^{2} c^{4} d + c^{3} d^{2}\right)} \sqrt{-a^{2} c - d} a} + \frac{7 \, {\left(d x^{2} + c\right)} a^{2} c + a^{2} c^{2} + 4 \, {\left(d x^{2} + c\right)} d + c d}{{\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)} + \frac{{\left(4 \, x^{2} {\left(\frac{2 \, d^{2} x^{2}}{c^{3}} + \frac{5 \, d}{c^{2}}\right)} + \frac{15}{c}\right)} x \log\left(-\frac{a x + 1}{a x - 1}\right)}{30 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}}}"," ",0,"1/15*a*((15*a^4*c^2 + 20*a^2*c*d + 8*d^2)*arctan(sqrt(d*x^2 + c)*a/sqrt(-a^2*c - d))/((a^4*c^5 + 2*a^2*c^4*d + c^3*d^2)*sqrt(-a^2*c - d)*a) + (7*(d*x^2 + c)*a^2*c + a^2*c^2 + 4*(d*x^2 + c)*d + c*d)/((a^4*c^4 + 2*a^2*c^3*d + c^2*d^2)*(d*x^2 + c)^(3/2))) + 1/30*(4*x^2*(2*d^2*x^2/c^3 + 5*d/c^2) + 15/c)*x*log(-(a*x + 1)/(a*x - 1))/(d*x^2 + c)^(5/2)","A",0
516,1,349,0,0.228076," ","integrate(arctanh(a*x)/(d*x^2+c)^(9/2),x, algorithm=""giac"")","\frac{1}{105} \, a {\left(\frac{3 \, {\left(35 \, a^{6} c^{3} + 70 \, a^{4} c^{2} d + 56 \, a^{2} c d^{2} + 16 \, d^{3}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} a}{\sqrt{-a^{2} c - d}}\right)}{{\left(a^{6} c^{7} + 3 \, a^{4} c^{6} d + 3 \, a^{2} c^{5} d^{2} + c^{4} d^{3}\right)} \sqrt{-a^{2} c - d} a} + \frac{57 \, {\left(d x^{2} + c\right)}^{2} a^{4} c^{2} + 11 \, {\left(d x^{2} + c\right)} a^{4} c^{3} + 3 \, a^{4} c^{4} + 66 \, {\left(d x^{2} + c\right)}^{2} a^{2} c d + 17 \, {\left(d x^{2} + c\right)} a^{2} c^{2} d + 6 \, a^{2} c^{3} d + 24 \, {\left(d x^{2} + c\right)}^{2} d^{2} + 6 \, {\left(d x^{2} + c\right)} c d^{2} + 3 \, c^{2} d^{2}}{{\left(a^{6} c^{6} + 3 \, a^{4} c^{5} d + 3 \, a^{2} c^{4} d^{2} + c^{3} d^{3}\right)} {\left(d x^{2} + c\right)}^{\frac{5}{2}}}\right)} + \frac{{\left(2 \, {\left(4 \, x^{2} {\left(\frac{2 \, d^{3} x^{2}}{c^{4}} + \frac{7 \, d^{2}}{c^{3}}\right)} + \frac{35 \, d}{c^{2}}\right)} x^{2} + \frac{35}{c}\right)} x \log\left(-\frac{a x + 1}{a x - 1}\right)}{70 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}}}"," ",0,"1/105*a*(3*(35*a^6*c^3 + 70*a^4*c^2*d + 56*a^2*c*d^2 + 16*d^3)*arctan(sqrt(d*x^2 + c)*a/sqrt(-a^2*c - d))/((a^6*c^7 + 3*a^4*c^6*d + 3*a^2*c^5*d^2 + c^4*d^3)*sqrt(-a^2*c - d)*a) + (57*(d*x^2 + c)^2*a^4*c^2 + 11*(d*x^2 + c)*a^4*c^3 + 3*a^4*c^4 + 66*(d*x^2 + c)^2*a^2*c*d + 17*(d*x^2 + c)*a^2*c^2*d + 6*a^2*c^3*d + 24*(d*x^2 + c)^2*d^2 + 6*(d*x^2 + c)*c*d^2 + 3*c^2*d^2)/((a^6*c^6 + 3*a^4*c^5*d + 3*a^2*c^4*d^2 + c^3*d^3)*(d*x^2 + c)^(5/2))) + 1/70*(2*(4*x^2*(2*d^3*x^2/c^4 + 7*d^2/c^3) + 35*d/c^2)*x^2 + 35/c)*x*log(-(a*x + 1)/(a*x - 1))/(d*x^2 + c)^(7/2)","A",0
517,0,0,0,0.000000," ","integrate((-a*x^2+a)^(1/2)*arctanh(x),x, algorithm=""giac"")","\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=""giac"")","\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
519,1,54,0,0.196468," ","integrate(arctanh(x)/(-a*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{-a x^{2} + a} x \log\left(-\frac{x + 1}{x - 1}\right)}{2 \, {\left(a x^{2} - a\right)} a} - \frac{1}{\sqrt{-a x^{2} + a} a}"," ",0,"-1/2*sqrt(-a*x^2 + a)*x*log(-(x + 1)/(x - 1))/((a*x^2 - a)*a) - 1/(sqrt(-a*x^2 + a)*a)","A",0
520,1,86,0,0.188236," ","integrate(arctanh(x)/(-a*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{-a x^{2} + a} x {\left(\frac{2 \, x^{2}}{a} - \frac{3}{a}\right)} \log\left(-\frac{x + 1}{x - 1}\right)}{6 \, {\left(a x^{2} - a\right)}^{2}} - \frac{6 \, a x^{2} - 7 \, a}{9 \, {\left(a x^{2} - a\right)} \sqrt{-a x^{2} + a} a^{2}}"," ",0,"-1/6*sqrt(-a*x^2 + a)*x*(2*x^2/a - 3/a)*log(-(x + 1)/(x - 1))/(a*x^2 - a)^2 - 1/9*(6*a*x^2 - 7*a)/((a*x^2 - a)*sqrt(-a*x^2 + a)*a^2)","A",0
521,1,118,0,0.191079," ","integrate(arctanh(x)/(-a*x^2+a)^(7/2),x, algorithm=""giac"")","-\frac{\sqrt{-a x^{2} + a} {\left(4 \, x^{2} {\left(\frac{2 \, x^{2}}{a} - \frac{5}{a}\right)} + \frac{15}{a}\right)} x \log\left(-\frac{x + 1}{x - 1}\right)}{30 \, {\left(a x^{2} - a\right)}^{3}} - \frac{120 \, {\left(a x^{2} - a\right)}^{2} - 20 \, {\left(a x^{2} - a\right)} a + 9 \, a^{2}}{225 \, {\left(a x^{2} - a\right)}^{2} \sqrt{-a x^{2} + a} a^{3}}"," ",0,"-1/30*sqrt(-a*x^2 + a)*(4*x^2*(2*x^2/a - 5/a) + 15/a)*x*log(-(x + 1)/(x - 1))/(a*x^2 - a)^3 - 1/225*(120*(a*x^2 - a)^2 - 20*(a*x^2 - a)*a + 9*a^2)/((a*x^2 - a)^2*sqrt(-a*x^2 + a)*a^3)","A",0
522,1,455,0,0.481678," ","integrate(x^4*(a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""giac"")","\frac{60 \, b c^{5} x^{5} e \log\left(c x + 1\right)^{2} - 60 \, b c^{5} x^{5} e \log\left(-c x + 1\right)^{2} + 120 \, a c^{5} x^{5} e \log\left(c x + 1\right) - 24 \, b c^{5} x^{5} e \log\left(c x + 1\right) + 120 \, a c^{5} x^{5} e \log\left(-c x + 1\right) + 24 \, b c^{5} x^{5} e \log\left(-c x + 1\right) + 60 \, b c^{5} d x^{5} \log\left(-\frac{c x + 1}{c x - 1}\right) + 120 \, a c^{5} d x^{5} - 48 \, a c^{5} x^{5} e + 30 \, b c^{4} x^{4} e \log\left(c x + 1\right) + 30 \, b c^{4} x^{4} e \log\left(-c x + 1\right) + 30 \, b c^{4} d x^{4} - 27 \, b c^{4} x^{4} e - 40 \, b c^{3} x^{3} e \log\left(c x + 1\right) + 40 \, b c^{3} x^{3} e \log\left(-c x + 1\right) - 80 \, a c^{3} x^{3} e + 60 \, b c^{2} x^{2} e \log\left(c x + 1\right) + 60 \, b c^{2} x^{2} e \log\left(-c x + 1\right) + 60 \, b c^{2} d x^{2} - 154 \, b c^{2} x^{2} e - 120 \, b c x e \log\left(c x + 1\right) + 120 \, b c x e \log\left(-c x + 1\right) - 240 \, a c x e + 60 \, b e \log\left(c x + 1\right)^{2} - 60 \, b e \log\left(c x - 1\right)^{2} + 120 \, b e \log\left(c x - 1\right) \log\left(-c x + 1\right) + 60 \, b d \log\left(c^{2} x^{2} - 1\right) + 120 \, a e \log\left(c x + 1\right) - 274 \, b e \log\left(c x + 1\right) - 120 \, a e \log\left(c x - 1\right) - 274 \, b e \log\left(c x - 1\right)}{600 \, c^{5}}"," ",0,"1/600*(60*b*c^5*x^5*e*log(c*x + 1)^2 - 60*b*c^5*x^5*e*log(-c*x + 1)^2 + 120*a*c^5*x^5*e*log(c*x + 1) - 24*b*c^5*x^5*e*log(c*x + 1) + 120*a*c^5*x^5*e*log(-c*x + 1) + 24*b*c^5*x^5*e*log(-c*x + 1) + 60*b*c^5*d*x^5*log(-(c*x + 1)/(c*x - 1)) + 120*a*c^5*d*x^5 - 48*a*c^5*x^5*e + 30*b*c^4*x^4*e*log(c*x + 1) + 30*b*c^4*x^4*e*log(-c*x + 1) + 30*b*c^4*d*x^4 - 27*b*c^4*x^4*e - 40*b*c^3*x^3*e*log(c*x + 1) + 40*b*c^3*x^3*e*log(-c*x + 1) - 80*a*c^3*x^3*e + 60*b*c^2*x^2*e*log(c*x + 1) + 60*b*c^2*x^2*e*log(-c*x + 1) + 60*b*c^2*d*x^2 - 154*b*c^2*x^2*e - 120*b*c*x*e*log(c*x + 1) + 120*b*c*x*e*log(-c*x + 1) - 240*a*c*x*e + 60*b*e*log(c*x + 1)^2 - 60*b*e*log(c*x - 1)^2 + 120*b*e*log(c*x - 1)*log(-c*x + 1) + 60*b*d*log(c^2*x^2 - 1) + 120*a*e*log(c*x + 1) - 274*b*e*log(c*x + 1) - 120*a*e*log(c*x - 1) - 274*b*e*log(c*x - 1))/c^5","A",0
523,-2,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
524,1,353,0,0.399372," ","integrate(x^2*(a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""giac"")","\frac{3 \, b c^{3} x^{3} e \log\left(c x + 1\right)^{2} - 3 \, b c^{3} x^{3} e \log\left(-c x + 1\right)^{2} + 6 \, a c^{3} x^{3} e \log\left(c x + 1\right) - 2 \, b c^{3} x^{3} e \log\left(c x + 1\right) + 6 \, a c^{3} x^{3} e \log\left(-c x + 1\right) + 2 \, b c^{3} x^{3} e \log\left(-c x + 1\right) + 3 \, b c^{3} d x^{3} \log\left(-\frac{c x + 1}{c x - 1}\right) + 6 \, a c^{3} d x^{3} - 4 \, a c^{3} x^{3} e + 3 \, b c^{2} x^{2} e \log\left(c x + 1\right) + 3 \, b c^{2} x^{2} e \log\left(-c x + 1\right) + 3 \, b c^{2} d x^{2} - 5 \, b c^{2} x^{2} e - 6 \, b c x e \log\left(c x + 1\right) + 6 \, b c x e \log\left(-c x + 1\right) - 12 \, a c x e + 3 \, b e \log\left(c x + 1\right)^{2} - 3 \, b e \log\left(c x - 1\right)^{2} + 6 \, b e \log\left(c x - 1\right) \log\left(-c x + 1\right) + 3 \, b d \log\left(c^{2} x^{2} - 1\right) + 6 \, a e \log\left(c x + 1\right) - 11 \, b e \log\left(c x + 1\right) - 6 \, a e \log\left(c x - 1\right) - 11 \, b e \log\left(c x - 1\right)}{18 \, c^{3}}"," ",0,"1/18*(3*b*c^3*x^3*e*log(c*x + 1)^2 - 3*b*c^3*x^3*e*log(-c*x + 1)^2 + 6*a*c^3*x^3*e*log(c*x + 1) - 2*b*c^3*x^3*e*log(c*x + 1) + 6*a*c^3*x^3*e*log(-c*x + 1) + 2*b*c^3*x^3*e*log(-c*x + 1) + 3*b*c^3*d*x^3*log(-(c*x + 1)/(c*x - 1)) + 6*a*c^3*d*x^3 - 4*a*c^3*x^3*e + 3*b*c^2*x^2*e*log(c*x + 1) + 3*b*c^2*x^2*e*log(-c*x + 1) + 3*b*c^2*d*x^2 - 5*b*c^2*x^2*e - 6*b*c*x*e*log(c*x + 1) + 6*b*c*x*e*log(-c*x + 1) - 12*a*c*x*e + 3*b*e*log(c*x + 1)^2 - 3*b*e*log(c*x - 1)^2 + 6*b*e*log(c*x - 1)*log(-c*x + 1) + 3*b*d*log(c^2*x^2 - 1) + 6*a*e*log(c*x + 1) - 11*b*e*log(c*x + 1) - 6*a*e*log(c*x - 1) - 11*b*e*log(c*x - 1))/c^3","A",0
525,1,305,0,0.354291," ","integrate(x*(a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""giac"")","\frac{b c^{2} x^{2} e \log\left(c x + 1\right)^{2} - b c^{2} x^{2} e \log\left(-c x + 1\right)^{2} + 2 \, a c^{2} x^{2} e \log\left(c x + 1\right) - b c^{2} x^{2} e \log\left(c x + 1\right) + 2 \, a c^{2} x^{2} e \log\left(-c x + 1\right) + b c^{2} x^{2} e \log\left(-c x + 1\right) + b c^{2} d x^{2} \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a c^{2} d x^{2} - 2 \, a c^{2} x^{2} e + 2 \, b c x e \log\left(c x + 1\right) + 2 \, b c x e \log\left(-c x + 1\right) + 2 \, b c d x - 6 \, b c x e - b e \log\left(c x + 1\right)^{2} - b e \log\left(c x - 1\right)^{2} + 2 \, b e \log\left(c x - 1\right) \log\left(-c x + 1\right) - b d \log\left(c x + 1\right) - 2 \, a e \log\left(c x + 1\right) + 3 \, b e \log\left(c x + 1\right) + b d \log\left(c x - 1\right) - 2 \, a e \log\left(c x - 1\right) - 3 \, b e \log\left(c x - 1\right)}{4 \, c^{2}}"," ",0,"1/4*(b*c^2*x^2*e*log(c*x + 1)^2 - b*c^2*x^2*e*log(-c*x + 1)^2 + 2*a*c^2*x^2*e*log(c*x + 1) - b*c^2*x^2*e*log(c*x + 1) + 2*a*c^2*x^2*e*log(-c*x + 1) + b*c^2*x^2*e*log(-c*x + 1) + b*c^2*d*x^2*log(-(c*x + 1)/(c*x - 1)) + 2*a*c^2*d*x^2 - 2*a*c^2*x^2*e + 2*b*c*x*e*log(c*x + 1) + 2*b*c*x*e*log(-c*x + 1) + 2*b*c*d*x - 6*b*c*x*e - b*e*log(c*x + 1)^2 - b*e*log(c*x - 1)^2 + 2*b*e*log(c*x - 1)*log(-c*x + 1) - b*d*log(c*x + 1) - 2*a*e*log(c*x + 1) + 3*b*e*log(c*x + 1) + b*d*log(c*x - 1) - 2*a*e*log(c*x - 1) - 3*b*e*log(c*x - 1))/c^2","B",0
526,1,223,0,0.182674," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""giac"")","\frac{b c x e \log\left(c x + 1\right)^{2} - b c x e \log\left(-c x + 1\right)^{2} + 2 \, a c x e \log\left(c x + 1\right) - 2 \, b c x e \log\left(c x + 1\right) + 2 \, a c x e \log\left(-c x + 1\right) + 2 \, b c x e \log\left(-c x + 1\right) + b c d x \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a c d x - 4 \, a c x e + b e \log\left(c x + 1\right)^{2} - b e \log\left(c x - 1\right)^{2} + 2 \, b e \log\left(c x - 1\right) \log\left(-c x + 1\right) + b d \log\left(c^{2} x^{2} - 1\right) + 2 \, a e \log\left(c x + 1\right) - 2 \, b e \log\left(c x + 1\right) - 2 \, a e \log\left(c x - 1\right) - 2 \, b e \log\left(c x - 1\right)}{2 \, c}"," ",0,"1/2*(b*c*x*e*log(c*x + 1)^2 - b*c*x*e*log(-c*x + 1)^2 + 2*a*c*x*e*log(c*x + 1) - 2*b*c*x*e*log(c*x + 1) + 2*a*c*x*e*log(-c*x + 1) + 2*b*c*x*e*log(-c*x + 1) + b*c*d*x*log(-(c*x + 1)/(c*x - 1)) + 2*a*c*d*x - 4*a*c*x*e + b*e*log(c*x + 1)^2 - b*e*log(c*x - 1)^2 + 2*b*e*log(c*x - 1)*log(-c*x + 1) + b*d*log(c^2*x^2 - 1) + 2*a*e*log(c*x + 1) - 2*b*e*log(c*x + 1) - 2*a*e*log(c*x - 1) - 2*b*e*log(c*x - 1))/c","B",0
527,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1))/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} {\left(e \log\left(-c^{2} x^{2} + 1\right) + d\right)}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*(e*log(-c^2*x^2 + 1) + d)/x, x)","F",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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} {\left(e \log\left(-c^{2} x^{2} + 1\right) + d\right)}}{x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*(e*log(-c^2*x^2 + 1) + d)/x^2, 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} {\left(e \log\left(-c^{2} x^{2} + 1\right) + d\right)}}{x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*(e*log(-c^2*x^2 + 1) + d)/x^3, x)","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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} {\left(e \log\left(-c^{2} x^{2} + 1\right) + d\right)}}{x^{4}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*(e*log(-c^2*x^2 + 1) + d)/x^4, x)","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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} {\left(e \log\left(-c^{2} x^{2} + 1\right) + d\right)}}{x^{5}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*(e*log(-c^2*x^2 + 1) + d)/x^5, x)","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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} {\left(e \log\left(-c^{2} x^{2} + 1\right) + d\right)}}{x^{6}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*(e*log(-c^2*x^2 + 1) + d)/x^6, x)","F",0
533,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))*(d+e*log(g*x^2+f)),x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)} {\left(e \log\left(g x^{2} + f\right) + d\right)} x\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*(e*log(g*x^2 + f) + d)*x, x)","F",0
534,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))*(d+e*log(g*x^2+f)),x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)} {\left(e \log\left(g x^{2} + f\right) + d\right)}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*(e*log(g*x^2 + f) + d), x)","F",0
535,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))*(d+e*log(g*x^2+f))/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} {\left(e \log\left(g x^{2} + f\right) + d\right)}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*(e*log(g*x^2 + f) + d)/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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} {\left(e \log\left(g x^{2} + f\right) + d\right)}}{x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*(e*log(g*x^2 + f) + d)/x^2, 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=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)} {\left(e \log\left(g x^{2} + f\right) + d\right)}}{x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*(e*log(g*x^2 + f) + d)/x^3, x)","F",0
538,1,93,0,0.169243," ","integrate(arctanh(c*x)*(a+b*arctanh(c*x))/(c*x+1)^2,x, algorithm=""giac"")","\frac{1}{8} \, c {\left(\frac{{\left(c x - 1\right)} b \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{{\left(c x + 1\right)} c^{2}} + \frac{2 \, {\left(c x - 1\right)} {\left(a + b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{{\left(c x + 1\right)} c^{2}} + \frac{2 \, {\left(c x - 1\right)} {\left(a + b\right)}}{{\left(c x + 1\right)} c^{2}}\right)}"," ",0,"1/8*c*((c*x - 1)*b*log(-(c*x + 1)/(c*x - 1))^2/((c*x + 1)*c^2) + 2*(c*x - 1)*(a + b)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)*c^2) + 2*(c*x - 1)*(a + b)/((c*x + 1)*c^2))","A",0
