1,1,273,0,0.334170," ","integrate((e*x+d)^4*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e^{4} x^{5} + a d e^{3} x^{4} + 2 \, a d^{2} e^{2} x^{3} + 2 \, a d^{3} e x^{2} + {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b d^{3} e + {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b d^{2} e^{2} + \frac{1}{6} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b d e^{3} + \frac{1}{20} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b e^{4} + a d^{4} x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d^{4}}{2 \, c}"," ",0,"1/5*a*e^4*x^5 + a*d*e^3*x^4 + 2*a*d^2*e^2*x^3 + 2*a*d^3*e*x^2 + (2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*d^3*e + (2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*d^2*e^2 + 1/6*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*d*e^3 + 1/20*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*e^4 + a*d^4*x + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*d^4/c","A",0
2,1,209,0,0.325615," ","integrate((e*x+d)^3*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a e^{3} x^{4} + a d e^{2} x^{3} + \frac{3}{2} \, a d^{2} e x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b d^{2} e + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b d e^{2} + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b e^{3} + a d^{3} x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d^{3}}{2 \, c}"," ",0,"1/4*a*e^3*x^4 + a*d*e^2*x^3 + 3/2*a*d^2*e*x^2 + 3/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*d^2*e + 1/2*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*d*e^2 + 1/24*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*e^3 + a*d^3*x + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*d^3/c","A",0
3,1,137,0,0.311888," ","integrate((e*x+d)^2*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a e^{2} x^{3} + a d e x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b d e + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b e^{2} + a d^{2} x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d^{2}}{2 \, c}"," ",0,"1/3*a*e^2*x^3 + a*d*e*x^2 + 1/2*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*d*e + 1/6*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*e^2 + a*d^2*x + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*d^2/c","A",0
4,1,83,0,0.315614," ","integrate((e*x+d)*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b e + a d x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d}{2 \, c}"," ",0,"1/2*a*e*x^2 + 1/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*e + a*d*x + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b*d/c","A",0
5,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/(e*x+d),x, algorithm=""maxima"")","\frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{e x + d}\,{d x} + \frac{a \log\left(e x + d\right)}{e}"," ",0,"1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(e*x + d), x) + a*log(e*x + d)/e","F",0
6,1,99,0,0.316549," ","integrate((a+b*arctanh(c*x))/(e*x+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(c {\left(\frac{\log\left(c x + 1\right)}{c d e - e^{2}} - \frac{\log\left(c x - 1\right)}{c d e + e^{2}} - \frac{2 \, \log\left(e x + d\right)}{c^{2} d^{2} - e^{2}}\right)} - \frac{2 \, \operatorname{artanh}\left(c x\right)}{e^{2} x + d e}\right)} b - \frac{a}{e^{2} x + d e}"," ",0,"1/2*(c*(log(c*x + 1)/(c*d*e - e^2) - log(c*x - 1)/(c*d*e + e^2) - 2*log(e*x + d)/(c^2*d^2 - e^2)) - 2*arctanh(c*x)/(e^2*x + d*e))*b - a/(e^2*x + d*e)","A",0
7,1,190,0,0.332212," ","integrate((a+b*arctanh(c*x))/(e*x+d)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left({\left(\frac{4 \, c^{2} d \log\left(e x + d\right)}{c^{4} d^{4} - 2 \, c^{2} d^{2} e^{2} + e^{4}} - \frac{c \log\left(c x + 1\right)}{c^{2} d^{2} e - 2 \, c d e^{2} + e^{3}} + \frac{c \log\left(c x - 1\right)}{c^{2} d^{2} e + 2 \, c d e^{2} + e^{3}} - \frac{2}{c^{2} d^{3} - d e^{2} + {\left(c^{2} d^{2} e - e^{3}\right)} x}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e}\right)} b - \frac{a}{2 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"-1/4*((4*c^2*d*log(e*x + d)/(c^4*d^4 - 2*c^2*d^2*e^2 + e^4) - c*log(c*x + 1)/(c^2*d^2*e - 2*c*d*e^2 + e^3) + c*log(c*x - 1)/(c^2*d^2*e + 2*c*d*e^2 + e^3) - 2/(c^2*d^3 - d*e^2 + (c^2*d^2*e - e^3)*x))*c + 2*arctanh(c*x)/(e^3*x^2 + 2*d*e^2*x + d^2*e))*b - 1/2*a/(e^3*x^2 + 2*d*e^2*x + d^2*e)","A",0
8,1,339,0,0.336379," ","integrate((a+b*arctanh(c*x))/(e*x+d)^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left({\left(\frac{c^{2} \log\left(c x + 1\right)}{c^{3} d^{3} e - 3 \, c^{2} d^{2} e^{2} + 3 \, c d e^{3} - e^{4}} - \frac{c^{2} \log\left(c x - 1\right)}{c^{3} d^{3} e + 3 \, c^{2} d^{2} e^{2} + 3 \, c d e^{3} + e^{4}} - \frac{2 \, {\left(3 \, c^{4} d^{2} + c^{2} e^{2}\right)} \log\left(e x + d\right)}{c^{6} d^{6} - 3 \, c^{4} d^{4} e^{2} + 3 \, c^{2} d^{2} e^{4} - e^{6}} + \frac{4 \, c^{2} d e x + 5 \, c^{2} d^{2} - e^{2}}{c^{4} d^{6} - 2 \, c^{2} d^{4} e^{2} + d^{2} e^{4} + {\left(c^{4} d^{4} e^{2} - 2 \, c^{2} d^{2} e^{4} + e^{6}\right)} x^{2} + 2 \, {\left(c^{4} d^{5} e - 2 \, c^{2} d^{3} e^{3} + d e^{5}\right)} x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e}\right)} b - \frac{a}{3 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}}"," ",0,"1/6*((c^2*log(c*x + 1)/(c^3*d^3*e - 3*c^2*d^2*e^2 + 3*c*d*e^3 - e^4) - c^2*log(c*x - 1)/(c^3*d^3*e + 3*c^2*d^2*e^2 + 3*c*d*e^3 + e^4) - 2*(3*c^4*d^2 + c^2*e^2)*log(e*x + d)/(c^6*d^6 - 3*c^4*d^4*e^2 + 3*c^2*d^2*e^4 - e^6) + (4*c^2*d*e*x + 5*c^2*d^2 - e^2)/(c^4*d^6 - 2*c^2*d^4*e^2 + d^2*e^4 + (c^4*d^4*e^2 - 2*c^2*d^2*e^4 + e^6)*x^2 + 2*(c^4*d^5*e - 2*c^2*d^3*e^3 + d*e^5)*x))*c - 2*arctanh(c*x)/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e))*b - 1/3*a/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e)","B",0
9,1,782,0,0.562487," ","integrate((e*x+d)^3*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} e^{3} x^{4} + a^{2} d e^{2} x^{3} + \frac{3}{2} \, a^{2} d^{2} e x^{2} + \frac{3}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a b d^{2} e + {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a b d e^{2} + \frac{1}{12} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a b e^{3} + a^{2} d^{3} x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a b d^{3}}{c} + \frac{{\left(c^{2} d^{3} + d e^{2}\right)} {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2}}{c^{3}} + \frac{{\left(9 \, c^{2} d^{2} e - 3 \, c d e^{2} + 2 \, e^{3}\right)} b^{2} \log\left(c x + 1\right)}{6 \, c^{4}} + \frac{{\left(9 \, c^{2} d^{2} e + 3 \, c d e^{2} + 2 \, e^{3}\right)} b^{2} \log\left(c x - 1\right)}{6 \, c^{4}} + \frac{4 \, b^{2} c^{2} e^{3} x^{2} + 48 \, b^{2} c^{2} d e^{2} x + 3 \, {\left(b^{2} c^{4} e^{3} x^{4} + 4 \, b^{2} c^{4} d e^{2} x^{3} + 6 \, b^{2} c^{4} d^{2} e x^{2} + 4 \, b^{2} c^{4} d^{3} x + {\left(4 \, c^{3} d^{3} - 6 \, c^{2} d^{2} e + 4 \, c d e^{2} - e^{3}\right)} b^{2}\right)} \log\left(c x + 1\right)^{2} + 3 \, {\left(b^{2} c^{4} e^{3} x^{4} + 4 \, b^{2} c^{4} d e^{2} x^{3} + 6 \, b^{2} c^{4} d^{2} e x^{2} + 4 \, b^{2} c^{4} d^{3} x - {\left(4 \, c^{3} d^{3} + 6 \, c^{2} d^{2} e + 4 \, c d e^{2} + e^{3}\right)} b^{2}\right)} \log\left(-c x + 1\right)^{2} + 4 \, {\left(b^{2} c^{3} e^{3} x^{3} + 6 \, b^{2} c^{3} d e^{2} x^{2} + 3 \, {\left(6 \, c^{3} d^{2} e + c e^{3}\right)} b^{2} x\right)} \log\left(c x + 1\right) - 2 \, {\left(2 \, b^{2} c^{3} e^{3} x^{3} + 12 \, b^{2} c^{3} d e^{2} x^{2} + 6 \, {\left(6 \, c^{3} d^{2} e + c e^{3}\right)} b^{2} x + 3 \, {\left(b^{2} c^{4} e^{3} x^{4} + 4 \, b^{2} c^{4} d e^{2} x^{3} + 6 \, b^{2} c^{4} d^{2} e x^{2} + 4 \, b^{2} c^{4} d^{3} x + {\left(4 \, c^{3} d^{3} - 6 \, c^{2} d^{2} e + 4 \, c d e^{2} - e^{3}\right)} b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{48 \, c^{4}}"," ",0,"1/4*a^2*e^3*x^4 + a^2*d*e^2*x^3 + 3/2*a^2*d^2*e*x^2 + 3/2*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a*b*d^2*e + (2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a*b*d*e^2 + 1/12*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a*b*e^3 + a^2*d^3*x + (2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a*b*d^3/c + (c^2*d^3 + d*e^2)*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2/c^3 + 1/6*(9*c^2*d^2*e - 3*c*d*e^2 + 2*e^3)*b^2*log(c*x + 1)/c^4 + 1/6*(9*c^2*d^2*e + 3*c*d*e^2 + 2*e^3)*b^2*log(c*x - 1)/c^4 + 1/48*(4*b^2*c^2*e^3*x^2 + 48*b^2*c^2*d*e^2*x + 3*(b^2*c^4*e^3*x^4 + 4*b^2*c^4*d*e^2*x^3 + 6*b^2*c^4*d^2*e*x^2 + 4*b^2*c^4*d^3*x + (4*c^3*d^3 - 6*c^2*d^2*e + 4*c*d*e^2 - e^3)*b^2)*log(c*x + 1)^2 + 3*(b^2*c^4*e^3*x^4 + 4*b^2*c^4*d*e^2*x^3 + 6*b^2*c^4*d^2*e*x^2 + 4*b^2*c^4*d^3*x - (4*c^3*d^3 + 6*c^2*d^2*e + 4*c*d*e^2 + e^3)*b^2)*log(-c*x + 1)^2 + 4*(b^2*c^3*e^3*x^3 + 6*b^2*c^3*d*e^2*x^2 + 3*(6*c^3*d^2*e + c*e^3)*b^2*x)*log(c*x + 1) - 2*(2*b^2*c^3*e^3*x^3 + 12*b^2*c^3*d*e^2*x^2 + 6*(6*c^3*d^2*e + c*e^3)*b^2*x + 3*(b^2*c^4*e^3*x^4 + 4*b^2*c^4*d*e^2*x^3 + 6*b^2*c^4*d^2*e*x^2 + 4*b^2*c^4*d^3*x + (4*c^3*d^3 - 6*c^2*d^2*e + 4*c*d*e^2 - e^3)*b^2)*log(c*x + 1))*log(-c*x + 1))/c^4","B",0
10,1,524,0,0.565043," ","integrate((e*x+d)^2*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} e^{2} x^{3} + a^{2} d e x^{2} + {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a b d e + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a b e^{2} + a^{2} d^{2} x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a b d^{2}}{c} + \frac{{\left(3 \, c^{2} d^{2} + e^{2}\right)} {\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2}}{3 \, c^{3}} + \frac{{\left(6 \, c d e - e^{2}\right)} b^{2} \log\left(c x + 1\right)}{6 \, c^{3}} + \frac{{\left(6 \, c d e + e^{2}\right)} b^{2} \log\left(c x - 1\right)}{6 \, c^{3}} + \frac{4 \, b^{2} c e^{2} x + {\left(b^{2} c^{3} e^{2} x^{3} + 3 \, b^{2} c^{3} d e x^{2} + 3 \, b^{2} c^{3} d^{2} x + {\left(3 \, c^{2} d^{2} - 3 \, c d e + e^{2}\right)} b^{2}\right)} \log\left(c x + 1\right)^{2} + {\left(b^{2} c^{3} e^{2} x^{3} + 3 \, b^{2} c^{3} d e x^{2} + 3 \, b^{2} c^{3} d^{2} x - {\left(3 \, c^{2} d^{2} + 3 \, c d e + e^{2}\right)} b^{2}\right)} \log\left(-c x + 1\right)^{2} + 2 \, {\left(b^{2} c^{2} e^{2} x^{2} + 6 \, b^{2} c^{2} d e x\right)} \log\left(c x + 1\right) - 2 \, {\left(b^{2} c^{2} e^{2} x^{2} + 6 \, b^{2} c^{2} d e x + {\left(b^{2} c^{3} e^{2} x^{3} + 3 \, b^{2} c^{3} d e x^{2} + 3 \, b^{2} c^{3} d^{2} x + {\left(3 \, c^{2} d^{2} - 3 \, c d e + e^{2}\right)} b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{12 \, c^{3}}"," ",0,"1/3*a^2*e^2*x^3 + a^2*d*e*x^2 + (2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a*b*d*e + 1/3*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a*b*e^2 + a^2*d^2*x + (2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a*b*d^2/c + 1/3*(3*c^2*d^2 + e^2)*(log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2/c^3 + 1/6*(6*c*d*e - e^2)*b^2*log(c*x + 1)/c^3 + 1/6*(6*c*d*e + e^2)*b^2*log(c*x - 1)/c^3 + 1/12*(4*b^2*c*e^2*x + (b^2*c^3*e^2*x^3 + 3*b^2*c^3*d*e*x^2 + 3*b^2*c^3*d^2*x + (3*c^2*d^2 - 3*c*d*e + e^2)*b^2)*log(c*x + 1)^2 + (b^2*c^3*e^2*x^3 + 3*b^2*c^3*d*e*x^2 + 3*b^2*c^3*d^2*x - (3*c^2*d^2 + 3*c*d*e + e^2)*b^2)*log(-c*x + 1)^2 + 2*(b^2*c^2*e^2*x^2 + 6*b^2*c^2*d*e*x)*log(c*x + 1) - 2*(b^2*c^2*e^2*x^2 + 6*b^2*c^2*d*e*x + (b^2*c^3*e^2*x^3 + 3*b^2*c^3*d*e*x^2 + 3*b^2*c^3*d^2*x + (3*c^2*d^2 - 3*c*d*e + e^2)*b^2)*log(c*x + 1))*log(-c*x + 1))/c^3","B",0
11,1,313,0,0.557433," ","integrate((e*x+d)*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} e x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a b e + a^{2} d x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a b d}{c} + \frac{{\left(\log\left(c x + 1\right) \log\left(-\frac{1}{2} \, c x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c x + \frac{1}{2}\right)\right)} b^{2} d}{c} + \frac{b^{2} e \log\left(c x + 1\right)}{2 \, c^{2}} + \frac{b^{2} e \log\left(c x - 1\right)}{2 \, c^{2}} + \frac{4 \, b^{2} c e x \log\left(c x + 1\right) + {\left(b^{2} c^{2} e x^{2} + 2 \, b^{2} c^{2} d x + {\left(2 \, c d - e\right)} b^{2}\right)} \log\left(c x + 1\right)^{2} + {\left(b^{2} c^{2} e x^{2} + 2 \, b^{2} c^{2} d x - {\left(2 \, c d + e\right)} b^{2}\right)} \log\left(-c x + 1\right)^{2} - 2 \, {\left(2 \, b^{2} c e x + {\left(b^{2} c^{2} e x^{2} + 2 \, b^{2} c^{2} d x + {\left(2 \, c d - e\right)} b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{8 \, c^{2}}"," ",0,"1/2*a^2*e*x^2 + 1/2*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a*b*e + a^2*d*x + (2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a*b*d/c + (log(c*x + 1)*log(-1/2*c*x + 1/2) + dilog(1/2*c*x + 1/2))*b^2*d/c + 1/2*b^2*e*log(c*x + 1)/c^2 + 1/2*b^2*e*log(c*x - 1)/c^2 + 1/8*(4*b^2*c*e*x*log(c*x + 1) + (b^2*c^2*e*x^2 + 2*b^2*c^2*d*x + (2*c*d - e)*b^2)*log(c*x + 1)^2 + (b^2*c^2*e*x^2 + 2*b^2*c^2*d*x - (2*c*d + e)*b^2)*log(-c*x + 1)^2 - 2*(2*b^2*c*e*x + (b^2*c^2*e*x^2 + 2*b^2*c^2*d*x + (2*c*d - e)*b^2)*log(c*x + 1))*log(-c*x + 1))/c^2","B",0
12,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/(e*x+d),x, algorithm=""maxima"")","\frac{a^{2} \log\left(e x + d\right)}{e} + \int \frac{b^{2} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}^{2}}{4 \, {\left(e x + d\right)}} + \frac{a b {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{e x + d}\,{d x}"," ",0,"a^2*log(e*x + d)/e + integrate(1/4*b^2*(log(c*x + 1) - log(-c*x + 1))^2/(e*x + d) + a*b*(log(c*x + 1) - log(-c*x + 1))/(e*x + d), x)","F",0
13,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/(e*x+d)^2,x, algorithm=""maxima"")","{\left(c {\left(\frac{\log\left(c x + 1\right)}{c d e - e^{2}} - \frac{\log\left(c x - 1\right)}{c d e + e^{2}} - \frac{2 \, \log\left(e x + d\right)}{c^{2} d^{2} - e^{2}}\right)} - \frac{2 \, \operatorname{artanh}\left(c x\right)}{e^{2} x + d e}\right)} a b - \frac{1}{4} \, b^{2} {\left(\frac{\log\left(-c x + 1\right)^{2}}{e^{2} x + d e} + \int -\frac{{\left(c e x - e\right)} \log\left(c x + 1\right)^{2} + 2 \, {\left(c e x + c d - {\left(c e x - e\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{c e^{3} x^{3} - d^{2} e + {\left(2 \, c d e^{2} - e^{3}\right)} x^{2} + {\left(c d^{2} e - 2 \, d e^{2}\right)} x}\,{d x}\right)} - \frac{a^{2}}{e^{2} x + d e}"," ",0,"(c*(log(c*x + 1)/(c*d*e - e^2) - log(c*x - 1)/(c*d*e + e^2) - 2*log(e*x + d)/(c^2*d^2 - e^2)) - 2*arctanh(c*x)/(e^2*x + d*e))*a*b - 1/4*b^2*(log(-c*x + 1)^2/(e^2*x + d*e) + integrate(-((c*e*x - e)*log(c*x + 1)^2 + 2*(c*e*x + c*d - (c*e*x - e)*log(c*x + 1))*log(-c*x + 1))/(c*e^3*x^3 - d^2*e + (2*c*d*e^2 - e^3)*x^2 + (c*d^2*e - 2*d*e^2)*x), x)) - a^2/(e^2*x + d*e)","F",0
14,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/(e*x+d)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left({\left(\frac{4 \, c^{2} d \log\left(e x + d\right)}{c^{4} d^{4} - 2 \, c^{2} d^{2} e^{2} + e^{4}} - \frac{c \log\left(c x + 1\right)}{c^{2} d^{2} e - 2 \, c d e^{2} + e^{3}} + \frac{c \log\left(c x - 1\right)}{c^{2} d^{2} e + 2 \, c d e^{2} + e^{3}} - \frac{2}{c^{2} d^{3} - d e^{2} + {\left(c^{2} d^{2} e - e^{3}\right)} x}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e}\right)} a b - \frac{1}{8} \, b^{2} {\left(\frac{\log\left(-c x + 1\right)^{2}}{e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e} + 2 \, \int -\frac{{\left(c e x - e\right)} \log\left(c x + 1\right)^{2} + {\left(c e x + c d - 2 \, {\left(c e x - e\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{c e^{4} x^{4} - d^{3} e + {\left(3 \, c d e^{3} - e^{4}\right)} x^{3} + 3 \, {\left(c d^{2} e^{2} - d e^{3}\right)} x^{2} + {\left(c d^{3} e - 3 \, d^{2} e^{2}\right)} x}\,{d x}\right)} - \frac{a^{2}}{2 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"-1/2*((4*c^2*d*log(e*x + d)/(c^4*d^4 - 2*c^2*d^2*e^2 + e^4) - c*log(c*x + 1)/(c^2*d^2*e - 2*c*d*e^2 + e^3) + c*log(c*x - 1)/(c^2*d^2*e + 2*c*d*e^2 + e^3) - 2/(c^2*d^3 - d*e^2 + (c^2*d^2*e - e^3)*x))*c + 2*arctanh(c*x)/(e^3*x^2 + 2*d*e^2*x + d^2*e))*a*b - 1/8*b^2*(log(-c*x + 1)^2/(e^3*x^2 + 2*d*e^2*x + d^2*e) + 2*integrate(-((c*e*x - e)*log(c*x + 1)^2 + (c*e*x + c*d - 2*(c*e*x - e)*log(c*x + 1))*log(-c*x + 1))/(c*e^4*x^4 - d^3*e + (3*c*d*e^3 - e^4)*x^3 + 3*(c*d^2*e^2 - d*e^3)*x^2 + (c*d^3*e - 3*d^2*e^2)*x), x)) - 1/2*a^2/(e^3*x^2 + 2*d*e^2*x + d^2*e)","F",0
15,0,0,0,0.000000," ","integrate((e*x+d)^3*(a+b*arctanh(c*x))^3,x, algorithm=""maxima"")","\frac{1}{4} \, a^{3} e^{3} x^{4} + a^{3} d e^{2} x^{3} + \frac{3}{2} \, a^{3} d^{2} e x^{2} + \frac{9}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a^{2} b d^{2} e + \frac{3}{2} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a^{2} b d e^{2} + \frac{1}{8} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a^{2} b e^{3} + a^{3} d^{3} x + \frac{3 \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a^{2} b d^{3}}{2 \, c} - \frac{{\left(b^{3} c^{4} e^{3} x^{4} + 4 \, b^{3} c^{4} d e^{2} x^{3} + 6 \, b^{3} c^{4} d^{2} e x^{2} + 4 \, b^{3} c^{4} d^{3} x - {\left(4 \, c^{3} d^{3} + 6 \, c^{2} d^{2} e + 4 \, c d e^{2} + e^{3}\right)} b^{3}\right)} \log\left(-c x + 1\right)^{3} - {\left(6 \, a b^{2} c^{4} e^{3} x^{4} + 2 \, {\left(12 \, a b^{2} c^{4} d e^{2} + b^{3} c^{3} e^{3}\right)} x^{3} + 12 \, {\left(3 \, a b^{2} c^{4} d^{2} e + b^{3} c^{3} d e^{2}\right)} x^{2} + 6 \, {\left(4 \, a b^{2} c^{4} d^{3} + {\left(6 \, c^{3} d^{2} e + c e^{3}\right)} b^{3}\right)} x + 3 \, {\left(b^{3} c^{4} e^{3} x^{4} + 4 \, b^{3} c^{4} d e^{2} x^{3} + 6 \, b^{3} c^{4} d^{2} e x^{2} + 4 \, b^{3} c^{4} d^{3} x + {\left(4 \, c^{3} d^{3} - 6 \, c^{2} d^{2} e + 4 \, c d e^{2} - e^{3}\right)} b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{32 \, c^{4}} - \int -\frac{2 \, {\left(b^{3} c^{4} e^{3} x^{4} - b^{3} c^{3} d^{3} + {\left(3 \, c^{4} d e^{2} - c^{3} e^{3}\right)} b^{3} x^{3} + 3 \, {\left(c^{4} d^{2} e - c^{3} d e^{2}\right)} b^{3} x^{2} + {\left(c^{4} d^{3} - 3 \, c^{3} d^{2} e\right)} b^{3} x\right)} \log\left(c x + 1\right)^{3} + 12 \, {\left(a b^{2} c^{4} e^{3} x^{4} - a b^{2} c^{3} d^{3} + {\left(3 \, c^{4} d e^{2} - c^{3} e^{3}\right)} a b^{2} x^{3} + 3 \, {\left(c^{4} d^{2} e - c^{3} d e^{2}\right)} a b^{2} x^{2} + {\left(c^{4} d^{3} - 3 \, c^{3} d^{2} e\right)} a b^{2} x\right)} \log\left(c x + 1\right)^{2} - {\left(6 \, a b^{2} c^{4} e^{3} x^{4} + 2 \, {\left(12 \, a b^{2} c^{4} d e^{2} + b^{3} c^{3} e^{3}\right)} x^{3} + 12 \, {\left(3 \, a b^{2} c^{4} d^{2} e + b^{3} c^{3} d e^{2}\right)} x^{2} + 6 \, {\left(b^{3} c^{4} e^{3} x^{4} - b^{3} c^{3} d^{3} + {\left(3 \, c^{4} d e^{2} - c^{3} e^{3}\right)} b^{3} x^{3} + 3 \, {\left(c^{4} d^{2} e - c^{3} d e^{2}\right)} b^{3} x^{2} + {\left(c^{4} d^{3} - 3 \, c^{3} d^{2} e\right)} b^{3} x\right)} \log\left(c x + 1\right)^{2} + 6 \, {\left(4 \, a b^{2} c^{4} d^{3} + {\left(6 \, c^{3} d^{2} e + c e^{3}\right)} b^{3}\right)} x - 3 \, {\left(8 \, a b^{2} c^{3} d^{3} - {\left(8 \, a b^{2} c^{4} e^{3} + b^{3} c^{4} e^{3}\right)} x^{4} - {\left(4 \, c^{3} d^{3} - 6 \, c^{2} d^{2} e + 4 \, c d e^{2} - e^{3}\right)} b^{3} - 4 \, {\left(b^{3} c^{4} d e^{2} + 2 \, {\left(3 \, c^{4} d e^{2} - c^{3} e^{3}\right)} a b^{2}\right)} x^{3} - 6 \, {\left(b^{3} c^{4} d^{2} e + 4 \, {\left(c^{4} d^{2} e - c^{3} d e^{2}\right)} a b^{2}\right)} x^{2} - 4 \, {\left(b^{3} c^{4} d^{3} + 2 \, {\left(c^{4} d^{3} - 3 \, c^{3} d^{2} e\right)} a b^{2}\right)} x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{16 \, {\left(c^{4} x - c^{3}\right)}}\,{d x}"," ",0,"1/4*a^3*e^3*x^4 + a^3*d*e^2*x^3 + 3/2*a^3*d^2*e*x^2 + 9/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a^2*b*d^2*e + 3/2*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a^2*b*d*e^2 + 1/8*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a^2*b*e^3 + a^3*d^3*x + 3/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a^2*b*d^3/c - 1/32*((b^3*c^4*e^3*x^4 + 4*b^3*c^4*d*e^2*x^3 + 6*b^3*c^4*d^2*e*x^2 + 4*b^3*c^4*d^3*x - (4*c^3*d^3 + 6*c^2*d^2*e + 4*c*d*e^2 + e^3)*b^3)*log(-c*x + 1)^3 - (6*a*b^2*c^4*e^3*x^4 + 2*(12*a*b^2*c^4*d*e^2 + b^3*c^3*e^3)*x^3 + 12*(3*a*b^2*c^4*d^2*e + b^3*c^3*d*e^2)*x^2 + 6*(4*a*b^2*c^4*d^3 + (6*c^3*d^2*e + c*e^3)*b^3)*x + 3*(b^3*c^4*e^3*x^4 + 4*b^3*c^4*d*e^2*x^3 + 6*b^3*c^4*d^2*e*x^2 + 4*b^3*c^4*d^3*x + (4*c^3*d^3 - 6*c^2*d^2*e + 4*c*d*e^2 - e^3)*b^3)*log(c*x + 1))*log(-c*x + 1)^2)/c^4 - integrate(-1/16*(2*(b^3*c^4*e^3*x^4 - b^3*c^3*d^3 + (3*c^4*d*e^2 - c^3*e^3)*b^3*x^3 + 3*(c^4*d^2*e - c^3*d*e^2)*b^3*x^2 + (c^4*d^3 - 3*c^3*d^2*e)*b^3*x)*log(c*x + 1)^3 + 12*(a*b^2*c^4*e^3*x^4 - a*b^2*c^3*d^3 + (3*c^4*d*e^2 - c^3*e^3)*a*b^2*x^3 + 3*(c^4*d^2*e - c^3*d*e^2)*a*b^2*x^2 + (c^4*d^3 - 3*c^3*d^2*e)*a*b^2*x)*log(c*x + 1)^2 - (6*a*b^2*c^4*e^3*x^4 + 2*(12*a*b^2*c^4*d*e^2 + b^3*c^3*e^3)*x^3 + 12*(3*a*b^2*c^4*d^2*e + b^3*c^3*d*e^2)*x^2 + 6*(b^3*c^4*e^3*x^4 - b^3*c^3*d^3 + (3*c^4*d*e^2 - c^3*e^3)*b^3*x^3 + 3*(c^4*d^2*e - c^3*d*e^2)*b^3*x^2 + (c^4*d^3 - 3*c^3*d^2*e)*b^3*x)*log(c*x + 1)^2 + 6*(4*a*b^2*c^4*d^3 + (6*c^3*d^2*e + c*e^3)*b^3)*x - 3*(8*a*b^2*c^3*d^3 - (8*a*b^2*c^4*e^3 + b^3*c^4*e^3)*x^4 - (4*c^3*d^3 - 6*c^2*d^2*e + 4*c*d*e^2 - e^3)*b^3 - 4*(b^3*c^4*d*e^2 + 2*(3*c^4*d*e^2 - c^3*e^3)*a*b^2)*x^3 - 6*(b^3*c^4*d^2*e + 4*(c^4*d^2*e - c^3*d*e^2)*a*b^2)*x^2 - 4*(b^3*c^4*d^3 + 2*(c^4*d^3 - 3*c^3*d^2*e)*a*b^2)*x)*log(c*x + 1))*log(-c*x + 1))/(c^4*x - c^3), x)","F",0
16,0,0,0,0.000000," ","integrate((e*x+d)^2*(a+b*arctanh(c*x))^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} e^{2} x^{3} + a^{3} d e x^{2} + \frac{3}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a^{2} b d e + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a^{2} b e^{2} + a^{3} d^{2} x + \frac{3 \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a^{2} b d^{2}}{2 \, c} - \frac{{\left(b^{3} c^{3} e^{2} x^{3} + 3 \, b^{3} c^{3} d e x^{2} + 3 \, b^{3} c^{3} d^{2} x - {\left(3 \, c^{2} d^{2} + 3 \, c d e + e^{2}\right)} b^{3}\right)} \log\left(-c x + 1\right)^{3} - 3 \, {\left(2 \, a b^{2} c^{3} e^{2} x^{3} + {\left(6 \, a b^{2} c^{3} d e + b^{3} c^{2} e^{2}\right)} x^{2} + 6 \, {\left(a b^{2} c^{3} d^{2} + b^{3} c^{2} d e\right)} x + {\left(b^{3} c^{3} e^{2} x^{3} + 3 \, b^{3} c^{3} d e x^{2} + 3 \, b^{3} c^{3} d^{2} x + {\left(3 \, c^{2} d^{2} - 3 \, c d e + e^{2}\right)} b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{24 \, c^{3}} - \int -\frac{{\left(b^{3} c^{3} e^{2} x^{3} - b^{3} c^{2} d^{2} + {\left(2 \, c^{3} d e - c^{2} e^{2}\right)} b^{3} x^{2} + {\left(c^{3} d^{2} - 2 \, c^{2} d e\right)} b^{3} x\right)} \log\left(c x + 1\right)^{3} + 6 \, {\left(a b^{2} c^{3} e^{2} x^{3} - a b^{2} c^{2} d^{2} + {\left(2 \, c^{3} d e - c^{2} e^{2}\right)} a b^{2} x^{2} + {\left(c^{3} d^{2} - 2 \, c^{2} d e\right)} a b^{2} x\right)} \log\left(c x + 1\right)^{2} - {\left(4 \, a b^{2} c^{3} e^{2} x^{3} + 2 \, {\left(6 \, a b^{2} c^{3} d e + b^{3} c^{2} e^{2}\right)} x^{2} + 3 \, {\left(b^{3} c^{3} e^{2} x^{3} - b^{3} c^{2} d^{2} + {\left(2 \, c^{3} d e - c^{2} e^{2}\right)} b^{3} x^{2} + {\left(c^{3} d^{2} - 2 \, c^{2} d e\right)} b^{3} x\right)} \log\left(c x + 1\right)^{2} + 12 \, {\left(a b^{2} c^{3} d^{2} + b^{3} c^{2} d e\right)} x - 2 \, {\left(6 \, a b^{2} c^{2} d^{2} - {\left(3 \, c^{2} d^{2} - 3 \, c d e + e^{2}\right)} b^{3} - {\left(6 \, a b^{2} c^{3} e^{2} + b^{3} c^{3} e^{2}\right)} x^{3} - 3 \, {\left(b^{3} c^{3} d e + 2 \, {\left(2 \, c^{3} d e - c^{2} e^{2}\right)} a b^{2}\right)} x^{2} - 3 \, {\left(b^{3} c^{3} d^{2} + 2 \, {\left(c^{3} d^{2} - 2 \, c^{2} d e\right)} a b^{2}\right)} x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{8 \, {\left(c^{3} x - c^{2}\right)}}\,{d x}"," ",0,"1/3*a^3*e^2*x^3 + a^3*d*e*x^2 + 3/2*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a^2*b*d*e + 1/2*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a^2*b*e^2 + a^3*d^2*x + 3/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a^2*b*d^2/c - 1/24*((b^3*c^3*e^2*x^3 + 3*b^3*c^3*d*e*x^2 + 3*b^3*c^3*d^2*x - (3*c^2*d^2 + 3*c*d*e + e^2)*b^3)*log(-c*x + 1)^3 - 3*(2*a*b^2*c^3*e^2*x^3 + (6*a*b^2*c^3*d*e + b^3*c^2*e^2)*x^2 + 6*(a*b^2*c^3*d^2 + b^3*c^2*d*e)*x + (b^3*c^3*e^2*x^3 + 3*b^3*c^3*d*e*x^2 + 3*b^3*c^3*d^2*x + (3*c^2*d^2 - 3*c*d*e + e^2)*b^3)*log(c*x + 1))*log(-c*x + 1)^2)/c^3 - integrate(-1/8*((b^3*c^3*e^2*x^3 - b^3*c^2*d^2 + (2*c^3*d*e - c^2*e^2)*b^3*x^2 + (c^3*d^2 - 2*c^2*d*e)*b^3*x)*log(c*x + 1)^3 + 6*(a*b^2*c^3*e^2*x^3 - a*b^2*c^2*d^2 + (2*c^3*d*e - c^2*e^2)*a*b^2*x^2 + (c^3*d^2 - 2*c^2*d*e)*a*b^2*x)*log(c*x + 1)^2 - (4*a*b^2*c^3*e^2*x^3 + 2*(6*a*b^2*c^3*d*e + b^3*c^2*e^2)*x^2 + 3*(b^3*c^3*e^2*x^3 - b^3*c^2*d^2 + (2*c^3*d*e - c^2*e^2)*b^3*x^2 + (c^3*d^2 - 2*c^2*d*e)*b^3*x)*log(c*x + 1)^2 + 12*(a*b^2*c^3*d^2 + b^3*c^2*d*e)*x - 2*(6*a*b^2*c^2*d^2 - (3*c^2*d^2 - 3*c*d*e + e^2)*b^3 - (6*a*b^2*c^3*e^2 + b^3*c^3*e^2)*x^3 - 3*(b^3*c^3*d*e + 2*(2*c^3*d*e - c^2*e^2)*a*b^2)*x^2 - 3*(b^3*c^3*d^2 + 2*(c^3*d^2 - 2*c^2*d*e)*a*b^2)*x)*log(c*x + 1))*log(-c*x + 1))/(c^3*x - c^2), x)","F",0
17,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*arctanh(c*x))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} e x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a^{2} b e + a^{3} d x + \frac{3 \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a^{2} b d}{2 \, c} - \frac{{\left(b^{3} c^{2} e x^{2} + 2 \, b^{3} c^{2} d x - {\left(2 \, c d + e\right)} b^{3}\right)} \log\left(-c x + 1\right)^{3} - 3 \, {\left(2 \, a b^{2} c^{2} e x^{2} + 2 \, {\left(2 \, a b^{2} c^{2} d + b^{3} c e\right)} x + {\left(b^{3} c^{2} e x^{2} + 2 \, b^{3} c^{2} d x + {\left(2 \, c d - e\right)} b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{16 \, c^{2}} - \int -\frac{{\left(b^{3} c^{2} e x^{2} - b^{3} c d + {\left(c^{2} d - c e\right)} b^{3} x\right)} \log\left(c x + 1\right)^{3} + 6 \, {\left(a b^{2} c^{2} e x^{2} - a b^{2} c d + {\left(c^{2} d - c e\right)} a b^{2} x\right)} \log\left(c x + 1\right)^{2} - 3 \, {\left(2 \, a b^{2} c^{2} e x^{2} + {\left(b^{3} c^{2} e x^{2} - b^{3} c d + {\left(c^{2} d - c e\right)} b^{3} x\right)} \log\left(c x + 1\right)^{2} + 2 \, {\left(2 \, a b^{2} c^{2} d + b^{3} c e\right)} x - {\left(4 \, a b^{2} c d - {\left(2 \, c d - e\right)} b^{3} - {\left(4 \, a b^{2} c^{2} e + b^{3} c^{2} e\right)} x^{2} - 2 \, {\left(b^{3} c^{2} d + 2 \, {\left(c^{2} d - c e\right)} a b^{2}\right)} x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{8 \, {\left(c^{2} x - c\right)}}\,{d x}"," ",0,"1/2*a^3*e*x^2 + 3/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a^2*b*e + a^3*d*x + 3/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a^2*b*d/c - 1/16*((b^3*c^2*e*x^2 + 2*b^3*c^2*d*x - (2*c*d + e)*b^3)*log(-c*x + 1)^3 - 3*(2*a*b^2*c^2*e*x^2 + 2*(2*a*b^2*c^2*d + b^3*c*e)*x + (b^3*c^2*e*x^2 + 2*b^3*c^2*d*x + (2*c*d - e)*b^3)*log(c*x + 1))*log(-c*x + 1)^2)/c^2 - integrate(-1/8*((b^3*c^2*e*x^2 - b^3*c*d + (c^2*d - c*e)*b^3*x)*log(c*x + 1)^3 + 6*(a*b^2*c^2*e*x^2 - a*b^2*c*d + (c^2*d - c*e)*a*b^2*x)*log(c*x + 1)^2 - 3*(2*a*b^2*c^2*e*x^2 + (b^3*c^2*e*x^2 - b^3*c*d + (c^2*d - c*e)*b^3*x)*log(c*x + 1)^2 + 2*(2*a*b^2*c^2*d + b^3*c*e)*x - (4*a*b^2*c*d - (2*c*d - e)*b^3 - (4*a*b^2*c^2*e + b^3*c^2*e)*x^2 - 2*(b^3*c^2*d + 2*(c^2*d - c*e)*a*b^2)*x)*log(c*x + 1))*log(-c*x + 1))/(c^2*x - c), x)","F",0
18,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/(e*x+d),x, algorithm=""maxima"")","\frac{a^{3} \log\left(e x + d\right)}{e} + \int \frac{b^{3} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}^{3}}{8 \, {\left(e x + d\right)}} + \frac{3 \, a b^{2} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}^{2}}{4 \, {\left(e x + d\right)}} + \frac{3 \, a^{2} b {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{2 \, {\left(e x + d\right)}}\,{d x}"," ",0,"a^3*log(e*x + d)/e + integrate(1/8*b^3*(log(c*x + 1) - log(-c*x + 1))^3/(e*x + d) + 3/4*a*b^2*(log(c*x + 1) - log(-c*x + 1))^2/(e*x + d) + 3/2*a^2*b*(log(c*x + 1) - log(-c*x + 1))/(e*x + d), x)","F",0
19,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/(e*x+d)^2,x, algorithm=""maxima"")","\frac{3}{2} \, {\left(c {\left(\frac{\log\left(c x + 1\right)}{c d e - e^{2}} - \frac{\log\left(c x - 1\right)}{c d e + e^{2}} - \frac{2 \, \log\left(e x + d\right)}{c^{2} d^{2} - e^{2}}\right)} - \frac{2 \, \operatorname{artanh}\left(c x\right)}{e^{2} x + d e}\right)} a^{2} b - \frac{a^{3}}{e^{2} x + d e} - \frac{{\left({\left(c^{2} d e - c e^{2}\right)} b^{3} x - {\left(c d e - e^{2}\right)} b^{3}\right)} \log\left(-c x + 1\right)^{3} + 3 \, {\left(2 \, {\left(c^{2} d^{2} - e^{2}\right)} a b^{2} - {\left({\left(c^{2} d e + c e^{2}\right)} b^{3} x + {\left(c d e + e^{2}\right)} b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{8 \, {\left(c^{2} d^{3} e - d e^{3} + {\left(c^{2} d^{2} e^{2} - e^{4}\right)} x\right)}} - \int \frac{{\left({\left(c^{2} d e - c e^{2}\right)} b^{3} x - {\left(c d e - e^{2}\right)} b^{3}\right)} \log\left(c x + 1\right)^{3} + 6 \, {\left({\left(c^{2} d e - c e^{2}\right)} a b^{2} x - {\left(c d e - e^{2}\right)} a b^{2}\right)} \log\left(c x + 1\right)^{2} + 3 \, {\left(4 \, {\left(c^{2} d e - c e^{2}\right)} a b^{2} x + 4 \, {\left(c^{2} d^{2} - c d e\right)} a b^{2} - {\left({\left(c^{2} d e - c e^{2}\right)} b^{3} x - {\left(c d e - e^{2}\right)} b^{3}\right)} \log\left(c x + 1\right)^{2} - 2 \, {\left(b^{3} c^{2} e^{2} x^{2} + b^{3} c d e - 2 \, {\left(c d e - e^{2}\right)} a b^{2} + {\left(2 \, {\left(c^{2} d e - c e^{2}\right)} a b^{2} + {\left(c^{2} d e + c e^{2}\right)} b^{3}\right)} x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{8 \, {\left(c d^{3} e - d^{2} e^{2} - {\left(c^{2} d e^{3} - c e^{4}\right)} x^{3} - {\left(2 \, c^{2} d^{2} e^{2} - 3 \, c d e^{3} + e^{4}\right)} x^{2} - {\left(c^{2} d^{3} e - 3 \, c d^{2} e^{2} + 2 \, d e^{3}\right)} x\right)}}\,{d x}"," ",0,"3/2*(c*(log(c*x + 1)/(c*d*e - e^2) - log(c*x - 1)/(c*d*e + e^2) - 2*log(e*x + d)/(c^2*d^2 - e^2)) - 2*arctanh(c*x)/(e^2*x + d*e))*a^2*b - a^3/(e^2*x + d*e) - 1/8*(((c^2*d*e - c*e^2)*b^3*x - (c*d*e - e^2)*b^3)*log(-c*x + 1)^3 + 3*(2*(c^2*d^2 - e^2)*a*b^2 - ((c^2*d*e + c*e^2)*b^3*x + (c*d*e + e^2)*b^3)*log(c*x + 1))*log(-c*x + 1)^2)/(c^2*d^3*e - d*e^3 + (c^2*d^2*e^2 - e^4)*x) - integrate(1/8*(((c^2*d*e - c*e^2)*b^3*x - (c*d*e - e^2)*b^3)*log(c*x + 1)^3 + 6*((c^2*d*e - c*e^2)*a*b^2*x - (c*d*e - e^2)*a*b^2)*log(c*x + 1)^2 + 3*(4*(c^2*d*e - c*e^2)*a*b^2*x + 4*(c^2*d^2 - c*d*e)*a*b^2 - ((c^2*d*e - c*e^2)*b^3*x - (c*d*e - e^2)*b^3)*log(c*x + 1)^2 - 2*(b^3*c^2*e^2*x^2 + b^3*c*d*e - 2*(c*d*e - e^2)*a*b^2 + (2*(c^2*d*e - c*e^2)*a*b^2 + (c^2*d*e + c*e^2)*b^3)*x)*log(c*x + 1))*log(-c*x + 1))/(c*d^3*e - d^2*e^2 - (c^2*d*e^3 - c*e^4)*x^3 - (2*c^2*d^2*e^2 - 3*c*d*e^3 + e^4)*x^2 - (c^2*d^3*e - 3*c*d^2*e^2 + 2*d*e^3)*x), x)","F",0
20,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/(e*x+d)^3,x, algorithm=""maxima"")","-\frac{3}{4} \, {\left({\left(\frac{4 \, c^{2} d \log\left(e x + d\right)}{c^{4} d^{4} - 2 \, c^{2} d^{2} e^{2} + e^{4}} - \frac{c \log\left(c x + 1\right)}{c^{2} d^{2} e - 2 \, c d e^{2} + e^{3}} + \frac{c \log\left(c x - 1\right)}{c^{2} d^{2} e + 2 \, c d e^{2} + e^{3}} - \frac{2}{c^{2} d^{3} - d e^{2} + {\left(c^{2} d^{2} e - e^{3}\right)} x}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e}\right)} a^{2} b - \frac{a^{3}}{2 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}} - \frac{{\left({\left(c^{4} d^{2} e^{2} - 2 \, c^{3} d e^{3} + c^{2} e^{4}\right)} b^{3} x^{2} + 2 \, {\left(c^{4} d^{3} e - 2 \, c^{3} d^{2} e^{2} + c^{2} d e^{3}\right)} b^{3} x - {\left(2 \, c^{3} d^{3} e - 3 \, c^{2} d^{2} e^{2} + e^{4}\right)} b^{3}\right)} \log\left(-c x + 1\right)^{3} - 3 \, {\left(2 \, {\left(c^{3} d^{2} e^{2} - c e^{4}\right)} b^{3} x - 2 \, {\left(c^{4} d^{4} - 2 \, c^{2} d^{2} e^{2} + e^{4}\right)} a b^{2} + 2 \, {\left(c^{3} d^{3} e - c d e^{3}\right)} b^{3} + {\left({\left(c^{4} d^{2} e^{2} + 2 \, c^{3} d e^{3} + c^{2} e^{4}\right)} b^{3} x^{2} + 2 \, {\left(c^{4} d^{3} e + 2 \, c^{3} d^{2} e^{2} + c^{2} d e^{3}\right)} b^{3} x + {\left(2 \, c^{3} d^{3} e + 3 \, c^{2} d^{2} e^{2} - e^{4}\right)} b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{16 \, {\left(c^{4} d^{6} e - 2 \, c^{2} d^{4} e^{3} + d^{2} e^{5} + {\left(c^{4} d^{4} e^{3} - 2 \, c^{2} d^{2} e^{5} + e^{7}\right)} x^{2} + 2 \, {\left(c^{4} d^{5} e^{2} - 2 \, c^{2} d^{3} e^{4} + d e^{6}\right)} x\right)}} - \int \frac{{\left({\left(c^{4} d^{3} e - c^{3} d^{2} e^{2} - c^{2} d e^{3} + c e^{4}\right)} b^{3} x - {\left(c^{3} d^{3} e - c^{2} d^{2} e^{2} - c d e^{3} + e^{4}\right)} b^{3}\right)} \log\left(c x + 1\right)^{3} + 6 \, {\left({\left(c^{4} d^{3} e - c^{3} d^{2} e^{2} - c^{2} d e^{3} + c e^{4}\right)} a b^{2} x - {\left(c^{3} d^{3} e - c^{2} d^{2} e^{2} - c d e^{3} + e^{4}\right)} a b^{2}\right)} \log\left(c x + 1\right)^{2} - 3 \, {\left(2 \, {\left(c^{3} d e^{3} - c^{2} e^{4}\right)} b^{3} x^{2} - 2 \, {\left(c^{4} d^{4} - c^{3} d^{3} e - c^{2} d^{2} e^{2} + c d e^{3}\right)} a b^{2} + 2 \, {\left(c^{3} d^{3} e - c^{2} d^{2} e^{2}\right)} b^{3} + {\left({\left(c^{4} d^{3} e - c^{3} d^{2} e^{2} - c^{2} d e^{3} + c e^{4}\right)} b^{3} x - {\left(c^{3} d^{3} e - c^{2} d^{2} e^{2} - c d e^{3} + e^{4}\right)} b^{3}\right)} \log\left(c x + 1\right)^{2} - 2 \, {\left({\left(c^{4} d^{3} e - c^{3} d^{2} e^{2} - c^{2} d e^{3} + c e^{4}\right)} a b^{2} - 2 \, {\left(c^{3} d^{2} e^{2} - c^{2} d e^{3}\right)} b^{3}\right)} x + {\left({\left(c^{4} d e^{3} + c^{3} e^{4}\right)} b^{3} x^{3} + 3 \, {\left(c^{4} d^{2} e^{2} + c^{3} d e^{3}\right)} b^{3} x^{2} - 4 \, {\left(c^{3} d^{3} e - c^{2} d^{2} e^{2} - c d e^{3} + e^{4}\right)} a b^{2} + {\left(2 \, c^{3} d^{3} e + c^{2} d^{2} e^{2} - c d e^{3}\right)} b^{3} + {\left(4 \, {\left(c^{4} d^{3} e - c^{3} d^{2} e^{2} - c^{2} d e^{3} + c e^{4}\right)} a b^{2} + {\left(2 \, c^{4} d^{3} e + 4 \, c^{3} d^{2} e^{2} + c^{2} d e^{3} - c e^{4}\right)} b^{3}\right)} x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{8 \, {\left(c^{3} d^{6} e - c^{2} d^{5} e^{2} - c d^{4} e^{3} + d^{3} e^{4} - {\left(c^{4} d^{3} e^{4} - c^{3} d^{2} e^{5} - c^{2} d e^{6} + c e^{7}\right)} x^{4} - {\left(3 \, c^{4} d^{4} e^{3} - 4 \, c^{3} d^{3} e^{4} - 2 \, c^{2} d^{2} e^{5} + 4 \, c d e^{6} - e^{7}\right)} x^{3} - 3 \, {\left(c^{4} d^{5} e^{2} - 2 \, c^{3} d^{4} e^{3} + 2 \, c d^{2} e^{5} - d e^{6}\right)} x^{2} - {\left(c^{4} d^{6} e - 4 \, c^{3} d^{5} e^{2} + 2 \, c^{2} d^{4} e^{3} + 4 \, c d^{3} e^{4} - 3 \, d^{2} e^{5}\right)} x\right)}}\,{d x}"," ",0,"-3/4*((4*c^2*d*log(e*x + d)/(c^4*d^4 - 2*c^2*d^2*e^2 + e^4) - c*log(c*x + 1)/(c^2*d^2*e - 2*c*d*e^2 + e^3) + c*log(c*x - 1)/(c^2*d^2*e + 2*c*d*e^2 + e^3) - 2/(c^2*d^3 - d*e^2 + (c^2*d^2*e - e^3)*x))*c + 2*arctanh(c*x)/(e^3*x^2 + 2*d*e^2*x + d^2*e))*a^2*b - 1/2*a^3/(e^3*x^2 + 2*d*e^2*x + d^2*e) - 1/16*(((c^4*d^2*e^2 - 2*c^3*d*e^3 + c^2*e^4)*b^3*x^2 + 2*(c^4*d^3*e - 2*c^3*d^2*e^2 + c^2*d*e^3)*b^3*x - (2*c^3*d^3*e - 3*c^2*d^2*e^2 + e^4)*b^3)*log(-c*x + 1)^3 - 3*(2*(c^3*d^2*e^2 - c*e^4)*b^3*x - 2*(c^4*d^4 - 2*c^2*d^2*e^2 + e^4)*a*b^2 + 2*(c^3*d^3*e - c*d*e^3)*b^3 + ((c^4*d^2*e^2 + 2*c^3*d*e^3 + c^2*e^4)*b^3*x^2 + 2*(c^4*d^3*e + 2*c^3*d^2*e^2 + c^2*d*e^3)*b^3*x + (2*c^3*d^3*e + 3*c^2*d^2*e^2 - e^4)*b^3)*log(c*x + 1))*log(-c*x + 1)^2)/(c^4*d^6*e - 2*c^2*d^4*e^3 + d^2*e^5 + (c^4*d^4*e^3 - 2*c^2*d^2*e^5 + e^7)*x^2 + 2*(c^4*d^5*e^2 - 2*c^2*d^3*e^4 + d*e^6)*x) - integrate(1/8*(((c^4*d^3*e - c^3*d^2*e^2 - c^2*d*e^3 + c*e^4)*b^3*x - (c^3*d^3*e - c^2*d^2*e^2 - c*d*e^3 + e^4)*b^3)*log(c*x + 1)^3 + 6*((c^4*d^3*e - c^3*d^2*e^2 - c^2*d*e^3 + c*e^4)*a*b^2*x - (c^3*d^3*e - c^2*d^2*e^2 - c*d*e^3 + e^4)*a*b^2)*log(c*x + 1)^2 - 3*(2*(c^3*d*e^3 - c^2*e^4)*b^3*x^2 - 2*(c^4*d^4 - c^3*d^3*e - c^2*d^2*e^2 + c*d*e^3)*a*b^2 + 2*(c^3*d^3*e - c^2*d^2*e^2)*b^3 + ((c^4*d^3*e - c^3*d^2*e^2 - c^2*d*e^3 + c*e^4)*b^3*x - (c^3*d^3*e - c^2*d^2*e^2 - c*d*e^3 + e^4)*b^3)*log(c*x + 1)^2 - 2*((c^4*d^3*e - c^3*d^2*e^2 - c^2*d*e^3 + c*e^4)*a*b^2 - 2*(c^3*d^2*e^2 - c^2*d*e^3)*b^3)*x + ((c^4*d*e^3 + c^3*e^4)*b^3*x^3 + 3*(c^4*d^2*e^2 + c^3*d*e^3)*b^3*x^2 - 4*(c^3*d^3*e - c^2*d^2*e^2 - c*d*e^3 + e^4)*a*b^2 + (2*c^3*d^3*e + c^2*d^2*e^2 - c*d*e^3)*b^3 + (4*(c^4*d^3*e - c^3*d^2*e^2 - c^2*d*e^3 + c*e^4)*a*b^2 + (2*c^4*d^3*e + 4*c^3*d^2*e^2 + c^2*d*e^3 - c*e^4)*b^3)*x)*log(c*x + 1))*log(-c*x + 1))/(c^3*d^6*e - c^2*d^5*e^2 - c*d^4*e^3 + d^3*e^4 - (c^4*d^3*e^4 - c^3*d^2*e^5 - c^2*d*e^6 + c*e^7)*x^4 - (3*c^4*d^4*e^3 - 4*c^3*d^3*e^4 - 2*c^2*d^2*e^5 + 4*c*d*e^6 - e^7)*x^3 - 3*(c^4*d^5*e^2 - 2*c^3*d^4*e^3 + 2*c*d^2*e^5 - d*e^6)*x^2 - (c^4*d^6*e - 4*c^3*d^5*e^2 + 2*c^2*d^4*e^3 + 4*c*d^3*e^4 - 3*d^2*e^5)*x), x)","F",0
21,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/(2*c*x+1),x, algorithm=""maxima"")","\frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{2 \, c x + 1}\,{d x} + \frac{a \log\left(2 \, c x + 1\right)}{2 \, c}"," ",0,"1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/(2*c*x + 1), x) + 1/2*a*log(2*c*x + 1)/c","F",0
22,1,144,0,0.416773," ","integrate(arctanh(x)/(1-x*2^(1/2)),x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{2} {\left(\log\left(x + 1\right) - \log\left(x - 1\right)\right)} \log\left(\sqrt{2} x - 1\right) - \frac{1}{2} \, \sqrt{2} \operatorname{artanh}\left(x\right) \log\left(\sqrt{2} x - 1\right) - \frac{1}{4} \, \sqrt{2} {\left(\log\left(x + 1\right) \log\left(-\frac{\sqrt{2} x + \sqrt{2}}{\sqrt{2} + 1} + 1\right) + {\rm Li}_2\left(\frac{\sqrt{2} x + \sqrt{2}}{\sqrt{2} + 1}\right)\right)} + \frac{1}{4} \, \sqrt{2} {\left(\log\left(x - 1\right) \log\left(\frac{\sqrt{2} x - \sqrt{2}}{\sqrt{2} - 1} + 1\right) + {\rm Li}_2\left(-\frac{\sqrt{2} x - \sqrt{2}}{\sqrt{2} - 1}\right)\right)}"," ",0,"1/4*sqrt(2)*(log(x + 1) - log(x - 1))*log(sqrt(2)*x - 1) - 1/2*sqrt(2)*arctanh(x)*log(sqrt(2)*x - 1) - 1/4*sqrt(2)*(log(x + 1)*log(-(sqrt(2)*x + sqrt(2))/(sqrt(2) + 1) + 1) + dilog((sqrt(2)*x + sqrt(2))/(sqrt(2) + 1))) + 1/4*sqrt(2)*(log(x - 1)*log((sqrt(2)*x - sqrt(2))/(sqrt(2) - 1) + 1) + dilog(-(sqrt(2)*x - sqrt(2))/(sqrt(2) - 1)))","B",0
23,1,240,0,0.424158," ","integrate((e*x+d)^3*(a+b*arctanh(c*x^2)),x, algorithm=""maxima"")","\frac{1}{4} \, a e^{3} x^{4} + a d e^{2} x^{3} + \frac{3}{2} \, a d^{2} e x^{2} + \frac{1}{2} \, {\left(c {\left(\frac{2 \, \arctan\left(\sqrt{c} x\right)}{c^{\frac{3}{2}}} + \frac{\log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{c^{\frac{3}{2}}}\right)} + 2 \, x \operatorname{artanh}\left(c x^{2}\right)\right)} b d^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x^{2}\right) + c {\left(\frac{4 \, x}{c^{2}} - \frac{2 \, \arctan\left(\sqrt{c} x\right)}{c^{\frac{5}{2}}} + \frac{\log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{c^{\frac{5}{2}}}\right)}\right)} b d e^{2} + \frac{1}{8} \, {\left(2 \, x^{4} \operatorname{artanh}\left(c x^{2}\right) + c {\left(\frac{2 \, x^{2}}{c^{2}} - \frac{\log\left(c x^{2} + 1\right)}{c^{3}} + \frac{\log\left(c x^{2} - 1\right)}{c^{3}}\right)}\right)} b e^{3} + a d^{3} x + \frac{3 \, {\left(2 \, c x^{2} \operatorname{artanh}\left(c x^{2}\right) + \log\left(-c^{2} x^{4} + 1\right)\right)} b d^{2} e}{4 \, c}"," ",0,"1/4*a*e^3*x^4 + a*d*e^2*x^3 + 3/2*a*d^2*e*x^2 + 1/2*(c*(2*arctan(sqrt(c)*x)/c^(3/2) + log((c*x - sqrt(c))/(c*x + sqrt(c)))/c^(3/2)) + 2*x*arctanh(c*x^2))*b*d^3 + 1/2*(2*x^3*arctanh(c*x^2) + c*(4*x/c^2 - 2*arctan(sqrt(c)*x)/c^(5/2) + log((c*x - sqrt(c))/(c*x + sqrt(c)))/c^(5/2)))*b*d*e^2 + 1/8*(2*x^4*arctanh(c*x^2) + c*(2*x^2/c^2 - log(c*x^2 + 1)/c^3 + log(c*x^2 - 1)/c^3))*b*e^3 + a*d^3*x + 3/4*(2*c*x^2*arctanh(c*x^2) + log(-c^2*x^4 + 1))*b*d^2*e/c","A",0
24,1,171,0,0.409802," ","integrate((e*x+d)^2*(a+b*arctanh(c*x^2)),x, algorithm=""maxima"")","\frac{1}{3} \, a e^{2} x^{3} + a d e x^{2} + \frac{1}{2} \, {\left(c {\left(\frac{2 \, \arctan\left(\sqrt{c} x\right)}{c^{\frac{3}{2}}} + \frac{\log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{c^{\frac{3}{2}}}\right)} + 2 \, x \operatorname{artanh}\left(c x^{2}\right)\right)} b d^{2} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x^{2}\right) + c {\left(\frac{4 \, x}{c^{2}} - \frac{2 \, \arctan\left(\sqrt{c} x\right)}{c^{\frac{5}{2}}} + \frac{\log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{c^{\frac{5}{2}}}\right)}\right)} b e^{2} + a d^{2} x + \frac{{\left(2 \, c x^{2} \operatorname{artanh}\left(c x^{2}\right) + \log\left(-c^{2} x^{4} + 1\right)\right)} b d e}{2 \, c}"," ",0,"1/3*a*e^2*x^3 + a*d*e*x^2 + 1/2*(c*(2*arctan(sqrt(c)*x)/c^(3/2) + log((c*x - sqrt(c))/(c*x + sqrt(c)))/c^(3/2)) + 2*x*arctanh(c*x^2))*b*d^2 + 1/6*(2*x^3*arctanh(c*x^2) + c*(4*x/c^2 - 2*arctan(sqrt(c)*x)/c^(5/2) + log((c*x - sqrt(c))/(c*x + sqrt(c)))/c^(5/2)))*b*e^2 + a*d^2*x + 1/2*(2*c*x^2*arctanh(c*x^2) + log(-c^2*x^4 + 1))*b*d*e/c","A",0
25,1,95,0,0.415218," ","integrate((e*x+d)*(a+b*arctanh(c*x^2)),x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} + \frac{1}{2} \, {\left(c {\left(\frac{2 \, \arctan\left(\sqrt{c} x\right)}{c^{\frac{3}{2}}} + \frac{\log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{c^{\frac{3}{2}}}\right)} + 2 \, x \operatorname{artanh}\left(c x^{2}\right)\right)} b d + a d x + \frac{{\left(2 \, c x^{2} \operatorname{artanh}\left(c x^{2}\right) + \log\left(-c^{2} x^{4} + 1\right)\right)} b e}{4 \, c}"," ",0,"1/2*a*e*x^2 + 1/2*(c*(2*arctan(sqrt(c)*x)/c^(3/2) + log((c*x - sqrt(c))/(c*x + sqrt(c)))/c^(3/2)) + 2*x*arctanh(c*x^2))*b*d + a*d*x + 1/4*(2*c*x^2*arctanh(c*x^2) + log(-c^2*x^4 + 1))*b*e/c","A",0
26,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))/(e*x+d),x, algorithm=""maxima"")","\frac{1}{2} \, b \int \frac{\log\left(c x^{2} + 1\right) - \log\left(-c x^{2} + 1\right)}{e x + d}\,{d x} + \frac{a \log\left(e x + d\right)}{e}"," ",0,"1/2*b*integrate((log(c*x^2 + 1) - log(-c*x^2 + 1))/(e*x + d), x) + a*log(e*x + d)/e","F",0
27,1,172,0,0.413415," ","integrate((a+b*arctanh(c*x^2))/(e*x+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left({\left(\frac{4 \, d e \log\left(e x + d\right)}{c^{2} d^{4} - e^{4}} + \frac{d \log\left(c x^{2} + 1\right)}{c d^{2} e + e^{3}} - \frac{d \log\left(c x^{2} - 1\right)}{c d^{2} e - e^{3}} + \frac{2 \, \arctan\left(\sqrt{c} x\right)}{{\left(c d^{2} + e^{2}\right)} \sqrt{c}} + \frac{\log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{{\left(c d^{2} - e^{2}\right)} \sqrt{c}}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x^{2}\right)}{e^{2} x + d e}\right)} b - \frac{a}{e^{2} x + d e}"," ",0,"1/2*((4*d*e*log(e*x + d)/(c^2*d^4 - e^4) + d*log(c*x^2 + 1)/(c*d^2*e + e^3) - d*log(c*x^2 - 1)/(c*d^2*e - e^3) + 2*arctan(sqrt(c)*x)/((c*d^2 + e^2)*sqrt(c)) + log((c*x - sqrt(c))/(c*x + sqrt(c)))/((c*d^2 - e^2)*sqrt(c)))*c - 2*arctanh(c*x^2)/(e^2*x + d*e))*b - a/(e^2*x + d*e)","A",0
28,1,311,0,0.424342," ","integrate((a+b*arctanh(c*x^2))/(e*x+d)^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(\frac{4 \, \sqrt{c} d \arctan\left(\sqrt{c} x\right)}{c^{2} d^{4} + 2 \, c d^{2} e^{2} + e^{4}} + \frac{2 \, \sqrt{c} d \log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{c^{2} d^{4} - 2 \, c d^{2} e^{2} + e^{4}} - \frac{4 \, d e}{c^{2} d^{5} - d e^{4} + {\left(c^{2} d^{4} e - e^{5}\right)} x} + \frac{{\left(c d^{2} - e^{2}\right)} \log\left(c x^{2} + 1\right)}{c^{2} d^{4} e + 2 \, c d^{2} e^{3} + e^{5}} - \frac{{\left(c d^{2} + e^{2}\right)} \log\left(c x^{2} - 1\right)}{c^{2} d^{4} e - 2 \, c d^{2} e^{3} + e^{5}} + \frac{4 \, {\left(3 \, c^{2} d^{4} e + e^{5}\right)} \log\left(e x + d\right)}{c^{4} d^{8} - 2 \, c^{2} d^{4} e^{4} + e^{8}}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x^{2}\right)}{e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e}\right)} b - \frac{a}{2 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"1/4*((4*sqrt(c)*d*arctan(sqrt(c)*x)/(c^2*d^4 + 2*c*d^2*e^2 + e^4) + 2*sqrt(c)*d*log((c*x - sqrt(c))/(c*x + sqrt(c)))/(c^2*d^4 - 2*c*d^2*e^2 + e^4) - 4*d*e/(c^2*d^5 - d*e^4 + (c^2*d^4*e - e^5)*x) + (c*d^2 - e^2)*log(c*x^2 + 1)/(c^2*d^4*e + 2*c*d^2*e^3 + e^5) - (c*d^2 + e^2)*log(c*x^2 - 1)/(c^2*d^4*e - 2*c*d^2*e^3 + e^5) + 4*(3*c^2*d^4*e + e^5)*log(e*x + d)/(c^4*d^8 - 2*c^2*d^4*e^4 + e^8))*c - 2*arctanh(c*x^2)/(e^3*x^2 + 2*d*e^2*x + d^2*e))*b - 1/2*a/(e^3*x^2 + 2*d*e^2*x + d^2*e)","A",0
29,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*arctanh(c*x^2))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} e x^{2} + {\left(c {\left(\frac{2 \, \arctan\left(\sqrt{c} x\right)}{c^{\frac{3}{2}}} + \frac{\log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{c^{\frac{3}{2}}}\right)} + 2 \, x \operatorname{artanh}\left(c x^{2}\right)\right)} a b d + a^{2} d x + \frac{{\left(2 \, c x^{2} \operatorname{artanh}\left(c x^{2}\right) + \log\left(-c^{2} x^{4} + 1\right)\right)} a b e}{2 \, c} + \frac{1}{8} \, {\left(b^{2} e x^{2} + 2 \, b^{2} d x\right)} \log\left(-c x^{2} + 1\right)^{2} - \int -\frac{{\left(b^{2} c e x^{3} + b^{2} c d x^{2} - b^{2} e x - b^{2} d\right)} \log\left(c x^{2} + 1\right)^{2} - 2 \, {\left(b^{2} c e x^{3} + 2 \, b^{2} c d x^{2} + {\left(b^{2} c e x^{3} + b^{2} c d x^{2} - b^{2} e x - b^{2} d\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)}{4 \, {\left(c x^{2} - 1\right)}}\,{d x}"," ",0,"1/2*a^2*e*x^2 + (c*(2*arctan(sqrt(c)*x)/c^(3/2) + log((c*x - sqrt(c))/(c*x + sqrt(c)))/c^(3/2)) + 2*x*arctanh(c*x^2))*a*b*d + a^2*d*x + 1/2*(2*c*x^2*arctanh(c*x^2) + log(-c^2*x^4 + 1))*a*b*e/c + 1/8*(b^2*e*x^2 + 2*b^2*d*x)*log(-c*x^2 + 1)^2 - integrate(-1/4*((b^2*c*e*x^3 + b^2*c*d*x^2 - b^2*e*x - b^2*d)*log(c*x^2 + 1)^2 - 2*(b^2*c*e*x^3 + 2*b^2*c*d*x^2 + (b^2*c*e*x^3 + b^2*c*d*x^2 - b^2*e*x - b^2*d)*log(c*x^2 + 1))*log(-c*x^2 + 1))/(c*x^2 - 1), x)","F",0
30,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/(e*x+d),x, algorithm=""maxima"")","\frac{a^{2} \log\left(e x + d\right)}{e} + \int \frac{b^{2} {\left(\log\left(c x^{2} + 1\right) - \log\left(-c x^{2} + 1\right)\right)}^{2}}{4 \, {\left(e x + d\right)}} + \frac{a b {\left(\log\left(c x^{2} + 1\right) - \log\left(-c x^{2} + 1\right)\right)}}{e x + d}\,{d x}"," ",0,"a^2*log(e*x + d)/e + integrate(1/4*b^2*(log(c*x^2 + 1) - log(-c*x^2 + 1))^2/(e*x + d) + a*b*(log(c*x^2 + 1) - log(-c*x^2 + 1))/(e*x + d), x)","F",0
31,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/(e*x+d)^2,x, algorithm=""maxima"")","{\left({\left(\frac{4 \, d e \log\left(e x + d\right)}{c^{2} d^{4} - e^{4}} + \frac{d \log\left(c x^{2} + 1\right)}{c d^{2} e + e^{3}} - \frac{d \log\left(c x^{2} - 1\right)}{c d^{2} e - e^{3}} + \frac{2 \, \arctan\left(\sqrt{c} x\right)}{{\left(c d^{2} + e^{2}\right)} \sqrt{c}} + \frac{\log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{{\left(c d^{2} - e^{2}\right)} \sqrt{c}}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x^{2}\right)}{e^{2} x + d e}\right)} a b - \frac{1}{4} \, b^{2} {\left(\frac{\log\left(-c x^{2} + 1\right)^{2}}{e^{2} x + d e} + \int -\frac{{\left(c e x^{2} - e\right)} \log\left(c x^{2} + 1\right)^{2} + 2 \, {\left(2 \, c e x^{2} + 2 \, c d x - {\left(c e x^{2} - e\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)}{c e^{3} x^{4} + 2 \, c d e^{2} x^{3} - 2 \, d e^{2} x - d^{2} e + {\left(c d^{2} e - e^{3}\right)} x^{2}}\,{d x}\right)} - \frac{a^{2}}{e^{2} x + d e}"," ",0,"((4*d*e*log(e*x + d)/(c^2*d^4 - e^4) + d*log(c*x^2 + 1)/(c*d^2*e + e^3) - d*log(c*x^2 - 1)/(c*d^2*e - e^3) + 2*arctan(sqrt(c)*x)/((c*d^2 + e^2)*sqrt(c)) + log((c*x - sqrt(c))/(c*x + sqrt(c)))/((c*d^2 - e^2)*sqrt(c)))*c - 2*arctanh(c*x^2)/(e^2*x + d*e))*a*b - 1/4*b^2*(log(-c*x^2 + 1)^2/(e^2*x + d*e) + integrate(-((c*e*x^2 - e)*log(c*x^2 + 1)^2 + 2*(2*c*e*x^2 + 2*c*d*x - (c*e*x^2 - e)*log(c*x^2 + 1))*log(-c*x^2 + 1))/(c*e^3*x^4 + 2*c*d*e^2*x^3 - 2*d*e^2*x - d^2*e + (c*d^2*e - e^3)*x^2), x)) - a^2/(e^2*x + d*e)","F",0
32,1,295,0,0.418052," ","integrate((e*x+d)^2*(a+b*arctanh(c*x^3)),x, algorithm=""maxima"")","\frac{1}{3} \, a e^{2} x^{3} + a d e x^{2} + \frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{4}{3}} x^{2} + c^{\frac{2}{3}}\right)}}{3 \, c^{\frac{2}{3}}}\right)}{c^{\frac{4}{3}}} - \frac{\log\left(c^{\frac{4}{3}} x^{4} + c^{\frac{2}{3}} x^{2} + 1\right)}{c^{\frac{4}{3}}} + \frac{2 \, \log\left(\frac{c^{\frac{2}{3}} x^{2} - 1}{c^{\frac{2}{3}}}\right)}{c^{\frac{4}{3}}}\right)} + 4 \, x \operatorname{artanh}\left(c x^{3}\right)\right)} b d^{2} + \frac{1}{4} \, {\left(4 \, x^{2} \operatorname{artanh}\left(c x^{3}\right) + c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} + \frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x - c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} - \frac{\log\left(c^{\frac{2}{3}} x^{2} + c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} + \frac{\log\left(c^{\frac{2}{3}} x^{2} - c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} - \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} x + 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} + \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} x - 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}}\right)}\right)} b d e + a d^{2} x + \frac{{\left(2 \, c x^{3} \operatorname{artanh}\left(c x^{3}\right) + \log\left(-c^{2} x^{6} + 1\right)\right)} b e^{2}}{6 \, c}"," ",0,"1/3*a*e^2*x^3 + a*d*e*x^2 + 1/4*(c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(4/3)*x^2 + c^(2/3))/c^(2/3))/c^(4/3) - log(c^(4/3)*x^4 + c^(2/3)*x^2 + 1)/c^(4/3) + 2*log((c^(2/3)*x^2 - 1)/c^(2/3))/c^(4/3)) + 4*x*arctanh(c*x^3))*b*d^2 + 1/4*(4*x^2*arctanh(c*x^3) + c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x + c^(1/3))/c^(1/3))/c^(5/3) + 2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x - c^(1/3))/c^(1/3))/c^(5/3) - log(c^(2/3)*x^2 + c^(1/3)*x + 1)/c^(5/3) + log(c^(2/3)*x^2 - c^(1/3)*x + 1)/c^(5/3) - 2*log((c^(1/3)*x + 1)/c^(1/3))/c^(5/3) + 2*log((c^(1/3)*x - 1)/c^(1/3))/c^(5/3)))*b*d*e + a*d^2*x + 1/6*(2*c*x^3*arctanh(c*x^3) + log(-c^2*x^6 + 1))*b*e^2/c","A",0
33,1,248,0,0.421573," ","integrate((e*x+d)*(a+b*arctanh(c*x^3)),x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} + \frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{4}{3}} x^{2} + c^{\frac{2}{3}}\right)}}{3 \, c^{\frac{2}{3}}}\right)}{c^{\frac{4}{3}}} - \frac{\log\left(c^{\frac{4}{3}} x^{4} + c^{\frac{2}{3}} x^{2} + 1\right)}{c^{\frac{4}{3}}} + \frac{2 \, \log\left(\frac{c^{\frac{2}{3}} x^{2} - 1}{c^{\frac{2}{3}}}\right)}{c^{\frac{4}{3}}}\right)} + 4 \, x \operatorname{artanh}\left(c x^{3}\right)\right)} b d + \frac{1}{8} \, {\left(4 \, x^{2} \operatorname{artanh}\left(c x^{3}\right) + c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} + \frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x - c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} - \frac{\log\left(c^{\frac{2}{3}} x^{2} + c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} + \frac{\log\left(c^{\frac{2}{3}} x^{2} - c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} - \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} x + 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} + \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} x - 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}}\right)}\right)} b e + a d x"," ",0,"1/2*a*e*x^2 + 1/4*(c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(4/3)*x^2 + c^(2/3))/c^(2/3))/c^(4/3) - log(c^(4/3)*x^4 + c^(2/3)*x^2 + 1)/c^(4/3) + 2*log((c^(2/3)*x^2 - 1)/c^(2/3))/c^(4/3)) + 4*x*arctanh(c*x^3))*b*d + 1/8*(4*x^2*arctanh(c*x^3) + c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x + c^(1/3))/c^(1/3))/c^(5/3) + 2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x - c^(1/3))/c^(1/3))/c^(5/3) - log(c^(2/3)*x^2 + c^(1/3)*x + 1)/c^(5/3) + log(c^(2/3)*x^2 - c^(1/3)*x + 1)/c^(5/3) - 2*log((c^(1/3)*x + 1)/c^(1/3))/c^(5/3) + 2*log((c^(1/3)*x - 1)/c^(1/3))/c^(5/3)))*b*e + a*d*x","A",0
34,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))/(e*x+d),x, algorithm=""maxima"")","\frac{1}{2} \, b \int \frac{\log\left(c x^{3} + 1\right) - \log\left(-c x^{3} + 1\right)}{e x + d}\,{d x} + \frac{a \log\left(e x + d\right)}{e}"," ",0,"1/2*b*integrate((log(c*x^3 + 1) - log(-c*x^3 + 1))/(e*x + d), x) + a*log(e*x + d)/e","F",0
35,1,394,0,0.426936," ","integrate((a+b*arctanh(c*x^3))/(e*x+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left({\left(\frac{12 \, d^{2} e^{2} \log\left(e x + d\right)}{c^{2} d^{6} - e^{6}} + \frac{2 \, \sqrt{3} {\left(c d e + c^{\frac{2}{3}} e^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{{\left(c^{2} d^{3} e + c e^{4}\right)} c^{\frac{1}{3}}} - \frac{2 \, \sqrt{3} {\left(c d e - c^{\frac{2}{3}} e^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x - c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{{\left(c^{2} d^{3} e - c e^{4}\right)} c^{\frac{1}{3}}} + \frac{{\left(2 \, c d^{2} + c^{\frac{2}{3}} d e - c^{\frac{1}{3}} e^{2}\right)} \log\left(c^{\frac{2}{3}} x^{2} + c^{\frac{1}{3}} x + 1\right)}{c^{2} d^{3} e + c e^{4}} - \frac{{\left(2 \, c d^{2} - c^{\frac{2}{3}} d e - c^{\frac{1}{3}} e^{2}\right)} \log\left(c^{\frac{2}{3}} x^{2} - c^{\frac{1}{3}} x + 1\right)}{c^{2} d^{3} e - c e^{4}} - \frac{2 \, {\left(c d^{2} + c^{\frac{2}{3}} d e + c^{\frac{1}{3}} e^{2}\right)} \log\left(\frac{c^{\frac{1}{3}} x + 1}{c^{\frac{1}{3}}}\right)}{c^{2} d^{3} e - c e^{4}} + \frac{2 \, {\left(c d^{2} - c^{\frac{2}{3}} d e + c^{\frac{1}{3}} e^{2}\right)} \log\left(\frac{c^{\frac{1}{3}} x - 1}{c^{\frac{1}{3}}}\right)}{c^{2} d^{3} e + c e^{4}}\right)} c + \frac{4 \, \operatorname{artanh}\left(c x^{3}\right)}{e^{2} x + d e}\right)} b - \frac{a}{e^{2} x + d e}"," ",0,"-1/4*((12*d^2*e^2*log(e*x + d)/(c^2*d^6 - e^6) + 2*sqrt(3)*(c*d*e + c^(2/3)*e^2)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x + c^(1/3))/c^(1/3))/((c^2*d^3*e + c*e^4)*c^(1/3)) - 2*sqrt(3)*(c*d*e - c^(2/3)*e^2)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x - c^(1/3))/c^(1/3))/((c^2*d^3*e - c*e^4)*c^(1/3)) + (2*c*d^2 + c^(2/3)*d*e - c^(1/3)*e^2)*log(c^(2/3)*x^2 + c^(1/3)*x + 1)/(c^2*d^3*e + c*e^4) - (2*c*d^2 - c^(2/3)*d*e - c^(1/3)*e^2)*log(c^(2/3)*x^2 - c^(1/3)*x + 1)/(c^2*d^3*e - c*e^4) - 2*(c*d^2 + c^(2/3)*d*e + c^(1/3)*e^2)*log((c^(1/3)*x + 1)/c^(1/3))/(c^2*d^3*e - c*e^4) + 2*(c*d^2 - c^(2/3)*d*e + c^(1/3)*e^2)*log((c^(1/3)*x - 1)/c^(1/3))/(c^2*d^3*e + c*e^4))*c + 4*arctanh(c*x^3)/(e^2*x + d*e))*b - a/(e^2*x + d*e)","A",0
36,1,246,0,0.558297," ","integrate(x^3*(a+b*arctanh(c*x^(1/2)))/(-c^2*x+1),x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{2 \, c^{4} x^{3} + 3 \, c^{2} x^{2} + 6 \, x}{c^{6}} + \frac{6 \, \log\left(c^{2} x - 1\right)}{c^{8}}\right)} - \frac{{\left(\log\left(c \sqrt{x} + 1\right) \log\left(-\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right)\right)} b}{c^{8}} + \frac{11 \, b \log\left(c \sqrt{x} + 1\right)}{12 \, c^{8}} - \frac{11 \, b \log\left(c \sqrt{x} - 1\right)}{12 \, c^{8}} - \frac{12 \, b c^{5} x^{\frac{5}{2}} + 50 \, b c^{3} x^{\frac{3}{2}} + 45 \, b \log\left(c \sqrt{x} + 1\right)^{2} - 45 \, b \log\left(-c \sqrt{x} + 1\right)^{2} + 330 \, b c \sqrt{x} + 15 \, {\left(2 \, b c^{6} x^{3} + 3 \, b c^{4} x^{2} + 6 \, b c^{2} x\right)} \log\left(c \sqrt{x} + 1\right) - 15 \, {\left(2 \, b c^{6} x^{3} + 3 \, b c^{4} x^{2} + 6 \, b c^{2} x + 6 \, b \log\left(c \sqrt{x} + 1\right)\right)} \log\left(-c \sqrt{x} + 1\right)}{180 \, c^{8}}"," ",0,"-1/6*a*((2*c^4*x^3 + 3*c^2*x^2 + 6*x)/c^6 + 6*log(c^2*x - 1)/c^8) - (log(c*sqrt(x) + 1)*log(-1/2*c*sqrt(x) + 1/2) + dilog(1/2*c*sqrt(x) + 1/2))*b/c^8 + 11/12*b*log(c*sqrt(x) + 1)/c^8 - 11/12*b*log(c*sqrt(x) - 1)/c^8 - 1/180*(12*b*c^5*x^(5/2) + 50*b*c^3*x^(3/2) + 45*b*log(c*sqrt(x) + 1)^2 - 45*b*log(-c*sqrt(x) + 1)^2 + 330*b*c*sqrt(x) + 15*(2*b*c^6*x^3 + 3*b*c^4*x^2 + 6*b*c^2*x)*log(c*sqrt(x) + 1) - 15*(2*b*c^6*x^3 + 3*b*c^4*x^2 + 6*b*c^2*x + 6*b*log(c*sqrt(x) + 1))*log(-c*sqrt(x) + 1))/c^8","A",0
37,1,208,0,0.555764," ","integrate(x^2*(a+b*arctanh(c*x^(1/2)))/(-c^2*x+1),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{c^{2} x^{2} + 2 \, x}{c^{4}} + \frac{2 \, \log\left(c^{2} x - 1\right)}{c^{6}}\right)} - \frac{{\left(\log\left(c \sqrt{x} + 1\right) \log\left(-\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right)\right)} b}{c^{6}} + \frac{3 \, b \log\left(c \sqrt{x} + 1\right)}{4 \, c^{6}} - \frac{3 \, b \log\left(c \sqrt{x} - 1\right)}{4 \, c^{6}} - \frac{2 \, b c^{3} x^{\frac{3}{2}} + 3 \, b \log\left(c \sqrt{x} + 1\right)^{2} - 3 \, b \log\left(-c \sqrt{x} + 1\right)^{2} + 18 \, b c \sqrt{x} + 3 \, {\left(b c^{4} x^{2} + 2 \, b c^{2} x\right)} \log\left(c \sqrt{x} + 1\right) - 3 \, {\left(b c^{4} x^{2} + 2 \, b c^{2} x + 2 \, b \log\left(c \sqrt{x} + 1\right)\right)} \log\left(-c \sqrt{x} + 1\right)}{12 \, c^{6}}"," ",0,"-1/2*a*((c^2*x^2 + 2*x)/c^4 + 2*log(c^2*x - 1)/c^6) - (log(c*sqrt(x) + 1)*log(-1/2*c*sqrt(x) + 1/2) + dilog(1/2*c*sqrt(x) + 1/2))*b/c^6 + 3/4*b*log(c*sqrt(x) + 1)/c^6 - 3/4*b*log(c*sqrt(x) - 1)/c^6 - 1/12*(2*b*c^3*x^(3/2) + 3*b*log(c*sqrt(x) + 1)^2 - 3*b*log(-c*sqrt(x) + 1)^2 + 18*b*c*sqrt(x) + 3*(b*c^4*x^2 + 2*b*c^2*x)*log(c*sqrt(x) + 1) - 3*(b*c^4*x^2 + 2*b*c^2*x + 2*b*log(c*sqrt(x) + 1))*log(-c*sqrt(x) + 1))/c^6","A",0
38,1,166,0,0.553249," ","integrate(x*(a+b*arctanh(c*x^(1/2)))/(-c^2*x+1),x, algorithm=""maxima"")","-a {\left(\frac{x}{c^{2}} + \frac{\log\left(c^{2} x - 1\right)}{c^{4}}\right)} - \frac{{\left(\log\left(c \sqrt{x} + 1\right) \log\left(-\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right)\right)} b}{c^{4}} + \frac{b \log\left(c \sqrt{x} + 1\right)}{2 \, c^{4}} - \frac{b \log\left(c \sqrt{x} - 1\right)}{2 \, c^{4}} - \frac{2 \, b c^{2} x \log\left(c \sqrt{x} + 1\right) + b \log\left(c \sqrt{x} + 1\right)^{2} - b \log\left(-c \sqrt{x} + 1\right)^{2} + 4 \, b c \sqrt{x} - 2 \, {\left(b c^{2} x + b \log\left(c \sqrt{x} + 1\right)\right)} \log\left(-c \sqrt{x} + 1\right)}{4 \, c^{4}}"," ",0,"-a*(x/c^2 + log(c^2*x - 1)/c^4) - (log(c*sqrt(x) + 1)*log(-1/2*c*sqrt(x) + 1/2) + dilog(1/2*c*sqrt(x) + 1/2))*b/c^4 + 1/2*b*log(c*sqrt(x) + 1)/c^4 - 1/2*b*log(c*sqrt(x) - 1)/c^4 - 1/4*(2*b*c^2*x*log(c*sqrt(x) + 1) + b*log(c*sqrt(x) + 1)^2 - b*log(-c*sqrt(x) + 1)^2 + 4*b*c*sqrt(x) - 2*(b*c^2*x + b*log(c*sqrt(x) + 1))*log(-c*sqrt(x) + 1))/c^4","A",0
39,1,101,0,0.596730," ","integrate((a+b*arctanh(c*x^(1/2)))/(-c^2*x+1),x, algorithm=""maxima"")","-\frac{{\left(\log\left(c \sqrt{x} + 1\right) \log\left(-\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right)\right)} b}{c^{2}} - \frac{a \log\left(c^{2} x - 1\right)}{c^{2}} - \frac{b \log\left(c \sqrt{x} + 1\right)^{2} - 2 \, b \log\left(c \sqrt{x} + 1\right) \log\left(-c \sqrt{x} + 1\right) - b \log\left(-c \sqrt{x} + 1\right)^{2}}{4 \, c^{2}}"," ",0,"-(log(c*sqrt(x) + 1)*log(-1/2*c*sqrt(x) + 1/2) + dilog(1/2*c*sqrt(x) + 1/2))*b/c^2 - a*log(c^2*x - 1)/c^2 - 1/4*(b*log(c*sqrt(x) + 1)^2 - 2*b*log(c*sqrt(x) + 1)*log(-c*sqrt(x) + 1) - b*log(-c*sqrt(x) + 1)^2)/c^2","A",0
40,1,159,0,0.523455," ","integrate((a+b*arctanh(c*x^(1/2)))/x/(-c^2*x+1),x, algorithm=""maxima"")","-\frac{1}{4} \, b \log\left(c \sqrt{x} + 1\right)^{2} + \frac{1}{2} \, b \log\left(c \sqrt{x} + 1\right) \log\left(-c \sqrt{x} + 1\right) + \frac{1}{4} \, b \log\left(-c \sqrt{x} + 1\right)^{2} - {\left(\log\left(c \sqrt{x} + 1\right) \log\left(-\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right)\right)} b - {\left(\log\left(c \sqrt{x}\right) \log\left(-c \sqrt{x} + 1\right) + {\rm Li}_2\left(-c \sqrt{x} + 1\right)\right)} b + {\left(\log\left(c \sqrt{x} + 1\right) \log\left(-c \sqrt{x}\right) + {\rm Li}_2\left(c \sqrt{x} + 1\right)\right)} b - a {\left(\log\left(c \sqrt{x} + 1\right) + \log\left(c \sqrt{x} - 1\right) - \log\left(x\right)\right)}"," ",0,"-1/4*b*log(c*sqrt(x) + 1)^2 + 1/2*b*log(c*sqrt(x) + 1)*log(-c*sqrt(x) + 1) + 1/4*b*log(-c*sqrt(x) + 1)^2 - (log(c*sqrt(x) + 1)*log(-1/2*c*sqrt(x) + 1/2) + dilog(1/2*c*sqrt(x) + 1/2))*b - (log(c*sqrt(x))*log(-c*sqrt(x) + 1) + dilog(-c*sqrt(x) + 1))*b + (log(c*sqrt(x) + 1)*log(-c*sqrt(x)) + dilog(c*sqrt(x) + 1))*b - a*(log(c*sqrt(x) + 1) + log(c*sqrt(x) - 1) - log(x))","B",0
41,1,248,0,0.565190," ","integrate((a+b*arctanh(c*x^(1/2)))/x^2/(-c^2*x+1),x, algorithm=""maxima"")","-{\left(\log\left(c \sqrt{x} + 1\right) \log\left(-\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right)\right)} b c^{2} - {\left(\log\left(c \sqrt{x}\right) \log\left(-c \sqrt{x} + 1\right) + {\rm Li}_2\left(-c \sqrt{x} + 1\right)\right)} b c^{2} + {\left(\log\left(c \sqrt{x} + 1\right) \log\left(-c \sqrt{x}\right) + {\rm Li}_2\left(c \sqrt{x} + 1\right)\right)} b c^{2} + \frac{1}{2} \, b c^{2} \log\left(c \sqrt{x} + 1\right) - \frac{1}{2} \, b c^{2} \log\left(c \sqrt{x} - 1\right) - {\left(c^{2} \log\left(c \sqrt{x} + 1\right) + c^{2} \log\left(c \sqrt{x} - 1\right) - c^{2} \log\left(x\right) + \frac{1}{x}\right)} a - \frac{b c^{2} x \log\left(c \sqrt{x} + 1\right)^{2} - b c^{2} x \log\left(-c \sqrt{x} + 1\right)^{2} + 4 \, b c \sqrt{x} + 2 \, b \log\left(c \sqrt{x} + 1\right) - 2 \, {\left(b c^{2} x \log\left(c \sqrt{x} + 1\right) + b\right)} \log\left(-c \sqrt{x} + 1\right)}{4 \, x}"," ",0,"-(log(c*sqrt(x) + 1)*log(-1/2*c*sqrt(x) + 1/2) + dilog(1/2*c*sqrt(x) + 1/2))*b*c^2 - (log(c*sqrt(x))*log(-c*sqrt(x) + 1) + dilog(-c*sqrt(x) + 1))*b*c^2 + (log(c*sqrt(x) + 1)*log(-c*sqrt(x)) + dilog(c*sqrt(x) + 1))*b*c^2 + 1/2*b*c^2*log(c*sqrt(x) + 1) - 1/2*b*c^2*log(c*sqrt(x) - 1) - (c^2*log(c*sqrt(x) + 1) + c^2*log(c*sqrt(x) - 1) - c^2*log(x) + 1/x)*a - 1/4*(b*c^2*x*log(c*sqrt(x) + 1)^2 - b*c^2*x*log(-c*sqrt(x) + 1)^2 + 4*b*c*sqrt(x) + 2*b*log(c*sqrt(x) + 1) - 2*(b*c^2*x*log(c*sqrt(x) + 1) + b)*log(-c*sqrt(x) + 1))/x","B",0
42,1,291,0,0.569493," ","integrate((a+b*arctanh(c*x^(1/2)))/x^3/(-c^2*x+1),x, algorithm=""maxima"")","-{\left(\log\left(c \sqrt{x} + 1\right) \log\left(-\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right)\right)} b c^{4} - {\left(\log\left(c \sqrt{x}\right) \log\left(-c \sqrt{x} + 1\right) + {\rm Li}_2\left(-c \sqrt{x} + 1\right)\right)} b c^{4} + {\left(\log\left(c \sqrt{x} + 1\right) \log\left(-c \sqrt{x}\right) + {\rm Li}_2\left(c \sqrt{x} + 1\right)\right)} b c^{4} + \frac{3}{4} \, b c^{4} \log\left(c \sqrt{x} + 1\right) - \frac{3}{4} \, b c^{4} \log\left(c \sqrt{x} - 1\right) - \frac{1}{2} \, {\left(2 \, c^{4} \log\left(c \sqrt{x} + 1\right) + 2 \, c^{4} \log\left(c \sqrt{x} - 1\right) - 2 \, c^{4} \log\left(x\right) + \frac{2 \, c^{2} x + 1}{x^{2}}\right)} a - \frac{3 \, b c^{4} x^{2} \log\left(c \sqrt{x} + 1\right)^{2} - 3 \, b c^{4} x^{2} \log\left(-c \sqrt{x} + 1\right)^{2} + 18 \, b c^{3} x^{\frac{3}{2}} + 2 \, b c \sqrt{x} + 3 \, {\left(2 \, b c^{2} x + b\right)} \log\left(c \sqrt{x} + 1\right) - 3 \, {\left(2 \, b c^{4} x^{2} \log\left(c \sqrt{x} + 1\right) + 2 \, b c^{2} x + b\right)} \log\left(-c \sqrt{x} + 1\right)}{12 \, x^{2}}"," ",0,"-(log(c*sqrt(x) + 1)*log(-1/2*c*sqrt(x) + 1/2) + dilog(1/2*c*sqrt(x) + 1/2))*b*c^4 - (log(c*sqrt(x))*log(-c*sqrt(x) + 1) + dilog(-c*sqrt(x) + 1))*b*c^4 + (log(c*sqrt(x) + 1)*log(-c*sqrt(x)) + dilog(c*sqrt(x) + 1))*b*c^4 + 3/4*b*c^4*log(c*sqrt(x) + 1) - 3/4*b*c^4*log(c*sqrt(x) - 1) - 1/2*(2*c^4*log(c*sqrt(x) + 1) + 2*c^4*log(c*sqrt(x) - 1) - 2*c^4*log(x) + (2*c^2*x + 1)/x^2)*a - 1/12*(3*b*c^4*x^2*log(c*sqrt(x) + 1)^2 - 3*b*c^4*x^2*log(-c*sqrt(x) + 1)^2 + 18*b*c^3*x^(3/2) + 2*b*c*sqrt(x) + 3*(2*b*c^2*x + b)*log(c*sqrt(x) + 1) - 3*(2*b*c^4*x^2*log(c*sqrt(x) + 1) + 2*b*c^2*x + b)*log(-c*sqrt(x) + 1))/x^2","B",0
43,1,330,0,0.562534," ","integrate((a+b*arctanh(c*x^(1/2)))/x^4/(-c^2*x+1),x, algorithm=""maxima"")","-{\left(\log\left(c \sqrt{x} + 1\right) \log\left(-\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right)\right)} b c^{6} - {\left(\log\left(c \sqrt{x}\right) \log\left(-c \sqrt{x} + 1\right) + {\rm Li}_2\left(-c \sqrt{x} + 1\right)\right)} b c^{6} + {\left(\log\left(c \sqrt{x} + 1\right) \log\left(-c \sqrt{x}\right) + {\rm Li}_2\left(c \sqrt{x} + 1\right)\right)} b c^{6} + \frac{11}{12} \, b c^{6} \log\left(c \sqrt{x} + 1\right) - \frac{11}{12} \, b c^{6} \log\left(c \sqrt{x} - 1\right) - \frac{1}{6} \, {\left(6 \, c^{6} \log\left(c \sqrt{x} + 1\right) + 6 \, c^{6} \log\left(c \sqrt{x} - 1\right) - 6 \, c^{6} \log\left(x\right) + \frac{6 \, c^{4} x^{2} + 3 \, c^{2} x + 2}{x^{3}}\right)} a - \frac{45 \, b c^{6} x^{3} \log\left(c \sqrt{x} + 1\right)^{2} - 45 \, b c^{6} x^{3} \log\left(-c \sqrt{x} + 1\right)^{2} + 330 \, b c^{5} x^{\frac{5}{2}} + 50 \, b c^{3} x^{\frac{3}{2}} + 12 \, b c \sqrt{x} + 15 \, {\left(6 \, b c^{4} x^{2} + 3 \, b c^{2} x + 2 \, b\right)} \log\left(c \sqrt{x} + 1\right) - 15 \, {\left(6 \, b c^{6} x^{3} \log\left(c \sqrt{x} + 1\right) + 6 \, b c^{4} x^{2} + 3 \, b c^{2} x + 2 \, b\right)} \log\left(-c \sqrt{x} + 1\right)}{180 \, x^{3}}"," ",0,"-(log(c*sqrt(x) + 1)*log(-1/2*c*sqrt(x) + 1/2) + dilog(1/2*c*sqrt(x) + 1/2))*b*c^6 - (log(c*sqrt(x))*log(-c*sqrt(x) + 1) + dilog(-c*sqrt(x) + 1))*b*c^6 + (log(c*sqrt(x) + 1)*log(-c*sqrt(x)) + dilog(c*sqrt(x) + 1))*b*c^6 + 11/12*b*c^6*log(c*sqrt(x) + 1) - 11/12*b*c^6*log(c*sqrt(x) - 1) - 1/6*(6*c^6*log(c*sqrt(x) + 1) + 6*c^6*log(c*sqrt(x) - 1) - 6*c^6*log(x) + (6*c^4*x^2 + 3*c^2*x + 2)/x^3)*a - 1/180*(45*b*c^6*x^3*log(c*sqrt(x) + 1)^2 - 45*b*c^6*x^3*log(-c*sqrt(x) + 1)^2 + 330*b*c^5*x^(5/2) + 50*b*c^3*x^(3/2) + 12*b*c*sqrt(x) + 15*(6*b*c^4*x^2 + 3*b*c^2*x + 2*b)*log(c*sqrt(x) + 1) - 15*(6*b*c^6*x^3*log(c*sqrt(x) + 1) + 6*b*c^4*x^2 + 3*b*c^2*x + 2*b)*log(-c*sqrt(x) + 1))/x^3","B",0
44,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x^(1/2)))/(e*x+d),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{2 \, d^{2} \log\left(e x + d\right)}{e^{3}} + \frac{e x^{2} - 2 \, d x}{e^{2}}\right)} + b \int \frac{x^{2} \log\left(c \sqrt{x} + 1\right)}{2 \, {\left(e x + d\right)}}\,{d x} - b \int \frac{x^{2} \log\left(-c \sqrt{x} + 1\right)}{2 \, {\left(e x + d\right)}}\,{d x}"," ",0,"1/2*a*(2*d^2*log(e*x + d)/e^3 + (e*x^2 - 2*d*x)/e^2) + b*integrate(1/2*x^2*log(c*sqrt(x) + 1)/(e*x + d), x) - b*integrate(1/2*x^2*log(-c*sqrt(x) + 1)/(e*x + d), x)","F",0
45,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x^(1/2)))/(e*x+d),x, algorithm=""maxima"")","a {\left(\frac{x}{e} - \frac{d \log\left(e x + d\right)}{e^{2}}\right)} + b \int \frac{x \log\left(c \sqrt{x} + 1\right)}{2 \, {\left(e x + d\right)}}\,{d x} - b \int \frac{x \log\left(-c \sqrt{x} + 1\right)}{2 \, {\left(e x + d\right)}}\,{d x}"," ",0,"a*(x/e - d*log(e*x + d)/e^2) + b*integrate(1/2*x*log(c*sqrt(x) + 1)/(e*x + d), x) - b*integrate(1/2*x*log(-c*sqrt(x) + 1)/(e*x + d), x)","F",0
46,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))/(e*x+d),x, algorithm=""maxima"")","b \int \frac{\log\left(c \sqrt{x} + 1\right)}{2 \, {\left(e x + d\right)}}\,{d x} - b \int \frac{\log\left(-c \sqrt{x} + 1\right)}{2 \, {\left(e x + d\right)}}\,{d x} + \frac{a \log\left(e x + d\right)}{e}"," ",0,"b*integrate(1/2*log(c*sqrt(x) + 1)/(e*x + d), x) - b*integrate(1/2*log(-c*sqrt(x) + 1)/(e*x + d), x) + a*log(e*x + d)/e","F",0
47,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))/x/(e*x+d),x, algorithm=""maxima"")","-a {\left(\frac{\log\left(e x + d\right)}{d} - \frac{\log\left(x\right)}{d}\right)} + b \int \frac{\log\left(c \sqrt{x} + 1\right)}{2 \, {\left(e x^{\frac{3}{2}} + d \sqrt{x}\right)} \sqrt{x}}\,{d x} - b \int \frac{\log\left(-c \sqrt{x} + 1\right)}{2 \, {\left(e x^{\frac{3}{2}} + d \sqrt{x}\right)} \sqrt{x}}\,{d x}"," ",0,"-a*(log(e*x + d)/d - log(x)/d) + b*integrate(1/2*log(c*sqrt(x) + 1)/((e*x^(3/2) + d*sqrt(x))*sqrt(x)), x) - b*integrate(1/2*log(-c*sqrt(x) + 1)/((e*x^(3/2) + d*sqrt(x))*sqrt(x)), x)","F",0
48,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))/x^2/(e*x+d),x, algorithm=""maxima"")","a {\left(\frac{e \log\left(e x + d\right)}{d^{2}} - \frac{e \log\left(x\right)}{d^{2}} - \frac{1}{d x}\right)} + b \int \frac{\log\left(c \sqrt{x} + 1\right)}{2 \, {\left(e x^{\frac{5}{2}} + d x^{\frac{3}{2}}\right)} \sqrt{x}}\,{d x} - b \int \frac{\log\left(-c \sqrt{x} + 1\right)}{2 \, {\left(e x^{\frac{5}{2}} + d x^{\frac{3}{2}}\right)} \sqrt{x}}\,{d x}"," ",0,"a*(e*log(e*x + d)/d^2 - e*log(x)/d^2 - 1/(d*x)) + b*integrate(1/2*log(c*sqrt(x) + 1)/((e*x^(5/2) + d*x^(3/2))*sqrt(x)), x) - b*integrate(1/2*log(-c*sqrt(x) + 1)/((e*x^(5/2) + d*x^(3/2))*sqrt(x)), x)","F",0
49,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))/x^3/(e*x+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, e^{2} \log\left(e x + d\right)}{d^{3}} - \frac{2 \, e^{2} \log\left(x\right)}{d^{3}} - \frac{2 \, e x - d}{d^{2} x^{2}}\right)} + b \int \frac{\log\left(c \sqrt{x} + 1\right)}{2 \, {\left(e x^{\frac{7}{2}} + d x^{\frac{5}{2}}\right)} \sqrt{x}}\,{d x} - b \int \frac{\log\left(-c \sqrt{x} + 1\right)}{2 \, {\left(e x^{\frac{7}{2}} + d x^{\frac{5}{2}}\right)} \sqrt{x}}\,{d x}"," ",0,"-1/2*a*(2*e^2*log(e*x + d)/d^3 - 2*e^2*log(x)/d^3 - (2*e*x - d)/(d^2*x^2)) + b*integrate(1/2*log(c*sqrt(x) + 1)/((e*x^(7/2) + d*x^(5/2))*sqrt(x)), x) - b*integrate(1/2*log(-c*sqrt(x) + 1)/((e*x^(7/2) + d*x^(5/2))*sqrt(x)), x)","F",0
