1,1,320,0,0.326930," ","integrate(x^3*arctanh(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{artanh}\left(b x + a\right)^{2} + \frac{1}{48} \, b^{2} {\left(\frac{48 \, {\left(a^{3} + a\right)} {\left(\log\left(b x + a - 1\right) \log\left(\frac{1}{2} \, b x + \frac{1}{2} \, a + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, b x - \frac{1}{2} \, a + \frac{1}{2}\right)\right)}}{b^{6}} + \frac{4 \, {\left(13 \, a^{3} + 18 \, a^{2} + 9 \, a + 4\right)} \log\left(b x + a + 1\right)}{b^{6}} + \frac{4 \, b^{2} x^{2} - 40 \, a b x + 3 \, {\left(a^{4} + 4 \, a^{3} + 6 \, a^{2} + 4 \, a + 1\right)} \log\left(b x + a + 1\right)^{2} - 6 \, {\left(a^{4} + 4 \, a^{3} + 6 \, a^{2} + 4 \, a + 1\right)} \log\left(b x + a + 1\right) \log\left(b x + a - 1\right) + 3 \, {\left(a^{4} - 4 \, a^{3} + 6 \, a^{2} - 4 \, a + 1\right)} \log\left(b x + a - 1\right)^{2} - 4 \, {\left(13 \, a^{3} - 18 \, a^{2} + 9 \, a - 4\right)} \log\left(b x + a - 1\right)}{b^{6}}\right)} + \frac{1}{12} \, b {\left(\frac{2 \, {\left(b^{2} x^{3} - 3 \, a b x^{2} + 3 \, {\left(3 \, a^{2} + 1\right)} x\right)}}{b^{4}} - \frac{3 \, {\left(a^{4} + 4 \, a^{3} + 6 \, a^{2} + 4 \, a + 1\right)} \log\left(b x + a + 1\right)}{b^{5}} + \frac{3 \, {\left(a^{4} - 4 \, a^{3} + 6 \, a^{2} - 4 \, a + 1\right)} \log\left(b x + a - 1\right)}{b^{5}}\right)} \operatorname{artanh}\left(b x + a\right)"," ",0,"1/4*x^4*arctanh(b*x + a)^2 + 1/48*b^2*(48*(a^3 + a)*(log(b*x + a - 1)*log(1/2*b*x + 1/2*a + 1/2) + dilog(-1/2*b*x - 1/2*a + 1/2))/b^6 + 4*(13*a^3 + 18*a^2 + 9*a + 4)*log(b*x + a + 1)/b^6 + (4*b^2*x^2 - 40*a*b*x + 3*(a^4 + 4*a^3 + 6*a^2 + 4*a + 1)*log(b*x + a + 1)^2 - 6*(a^4 + 4*a^3 + 6*a^2 + 4*a + 1)*log(b*x + a + 1)*log(b*x + a - 1) + 3*(a^4 - 4*a^3 + 6*a^2 - 4*a + 1)*log(b*x + a - 1)^2 - 4*(13*a^3 - 18*a^2 + 9*a - 4)*log(b*x + a - 1))/b^6) + 1/12*b*(2*(b^2*x^3 - 3*a*b*x^2 + 3*(3*a^2 + 1)*x)/b^4 - 3*(a^4 + 4*a^3 + 6*a^2 + 4*a + 1)*log(b*x + a + 1)/b^5 + 3*(a^4 - 4*a^3 + 6*a^2 - 4*a + 1)*log(b*x + a - 1)/b^5)*arctanh(b*x + a)","A",0
2,1,259,0,0.332400," ","integrate(x^2*arctanh(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{artanh}\left(b x + a\right)^{2} - \frac{1}{12} \, b^{2} {\left(\frac{4 \, {\left(3 \, a^{2} + 1\right)} {\left(\log\left(b x + a - 1\right) \log\left(\frac{1}{2} \, b x + \frac{1}{2} \, a + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, b x - \frac{1}{2} \, a + \frac{1}{2}\right)\right)}}{b^{5}} + \frac{2 \, {\left(5 \, a^{2} + 6 \, a + 1\right)} \log\left(b x + a + 1\right)}{b^{5}} + \frac{{\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} \log\left(b x + a + 1\right)^{2} - 2 \, {\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} \log\left(b x + a + 1\right) \log\left(b x + a - 1\right) + {\left(a^{3} - 3 \, a^{2} + 3 \, a - 1\right)} \log\left(b x + a - 1\right)^{2} - 4 \, b x - 2 \, {\left(5 \, a^{2} - 6 \, a + 1\right)} \log\left(b x + a - 1\right)}{b^{5}}\right)} + \frac{1}{3} \, b {\left(\frac{b x^{2} - 4 \, a x}{b^{3}} + \frac{{\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} \log\left(b x + a + 1\right)}{b^{4}} - \frac{{\left(a^{3} - 3 \, a^{2} + 3 \, a - 1\right)} \log\left(b x + a - 1\right)}{b^{4}}\right)} \operatorname{artanh}\left(b x + a\right)"," ",0,"1/3*x^3*arctanh(b*x + a)^2 - 1/12*b^2*(4*(3*a^2 + 1)*(log(b*x + a - 1)*log(1/2*b*x + 1/2*a + 1/2) + dilog(-1/2*b*x - 1/2*a + 1/2))/b^5 + 2*(5*a^2 + 6*a + 1)*log(b*x + a + 1)/b^5 + ((a^3 + 3*a^2 + 3*a + 1)*log(b*x + a + 1)^2 - 2*(a^3 + 3*a^2 + 3*a + 1)*log(b*x + a + 1)*log(b*x + a - 1) + (a^3 - 3*a^2 + 3*a - 1)*log(b*x + a - 1)^2 - 4*b*x - 2*(5*a^2 - 6*a + 1)*log(b*x + a - 1))/b^5) + 1/3*b*((b*x^2 - 4*a*x)/b^3 + (a^3 + 3*a^2 + 3*a + 1)*log(b*x + a + 1)/b^4 - (a^3 - 3*a^2 + 3*a - 1)*log(b*x + a - 1)/b^4)*arctanh(b*x + a)","A",0
3,1,202,0,0.335757," ","integrate(x*arctanh(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{artanh}\left(b x + a\right)^{2} + \frac{1}{8} \, b^{2} {\left(\frac{8 \, {\left(\log\left(b x + a - 1\right) \log\left(\frac{1}{2} \, b x + \frac{1}{2} \, a + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, b x - \frac{1}{2} \, a + \frac{1}{2}\right)\right)} a}{b^{4}} + \frac{4 \, {\left(a + 1\right)} \log\left(b x + a + 1\right)}{b^{4}} + \frac{{\left(a^{2} + 2 \, a + 1\right)} \log\left(b x + a + 1\right)^{2} - 2 \, {\left(a^{2} + 2 \, a + 1\right)} \log\left(b x + a + 1\right) \log\left(b x + a - 1\right) + {\left(a^{2} - 2 \, a + 1\right)} \log\left(b x + a - 1\right)^{2} - 4 \, {\left(a - 1\right)} \log\left(b x + a - 1\right)}{b^{4}}\right)} + \frac{1}{2} \, b {\left(\frac{2 \, x}{b^{2}} - \frac{{\left(a^{2} + 2 \, a + 1\right)} \log\left(b x + a + 1\right)}{b^{3}} + \frac{{\left(a^{2} - 2 \, a + 1\right)} \log\left(b x + a - 1\right)}{b^{3}}\right)} \operatorname{artanh}\left(b x + a\right)"," ",0,"1/2*x^2*arctanh(b*x + a)^2 + 1/8*b^2*(8*(log(b*x + a - 1)*log(1/2*b*x + 1/2*a + 1/2) + dilog(-1/2*b*x - 1/2*a + 1/2))*a/b^4 + 4*(a + 1)*log(b*x + a + 1)/b^4 + ((a^2 + 2*a + 1)*log(b*x + a + 1)^2 - 2*(a^2 + 2*a + 1)*log(b*x + a + 1)*log(b*x + a - 1) + (a^2 - 2*a + 1)*log(b*x + a - 1)^2 - 4*(a - 1)*log(b*x + a - 1))/b^4) + 1/2*b*(2*x/b^2 - (a^2 + 2*a + 1)*log(b*x + a + 1)/b^3 + (a^2 - 2*a + 1)*log(b*x + a - 1)/b^3)*arctanh(b*x + a)","A",0
4,1,139,0,0.324391," ","integrate(arctanh(b*x+a)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, b^{2} {\left(\frac{{\left(a + 1\right)} \log\left(b x + a + 1\right)^{2} - 2 \, {\left(a + 1\right)} \log\left(b x + a + 1\right) \log\left(b x + a - 1\right) + {\left(a - 1\right)} \log\left(b x + a - 1\right)^{2}}{b^{3}} + \frac{4 \, {\left(\log\left(b x + a - 1\right) \log\left(\frac{1}{2} \, b x + \frac{1}{2} \, a + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, b x - \frac{1}{2} \, a + \frac{1}{2}\right)\right)}}{b^{3}}\right)} + b {\left(\frac{{\left(a + 1\right)} \log\left(b x + a + 1\right)}{b^{2}} - \frac{{\left(a - 1\right)} \log\left(b x + a - 1\right)}{b^{2}}\right)} \operatorname{artanh}\left(b x + a\right) + x \operatorname{artanh}\left(b x + a\right)^{2}"," ",0,"-1/4*b^2*(((a + 1)*log(b*x + a + 1)^2 - 2*(a + 1)*log(b*x + a + 1)*log(b*x + a - 1) + (a - 1)*log(b*x + a - 1)^2)/b^3 + 4*(log(b*x + a - 1)*log(1/2*b*x + 1/2*a + 1/2) + dilog(-1/2*b*x - 1/2*a + 1/2))/b^3) + b*((a + 1)*log(b*x + a + 1)/b^2 - (a - 1)*log(b*x + a - 1)/b^2)*arctanh(b*x + a) + x*arctanh(b*x + a)^2","A",0
5,0,0,0,0.000000," ","integrate(arctanh(b*x+a)^2/x,x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(b x + a\right)^{2}}{x}\,{d x}"," ",0,"integrate(arctanh(b*x + a)^2/x, x)","F",0
6,1,244,0,0.338985," ","integrate(arctanh(b*x+a)^2/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} {\left(\frac{{\left(a - 1\right)} \log\left(b x + a + 1\right)^{2} - 2 \, {\left(a - 1\right)} \log\left(b x + a + 1\right) \log\left(b x + a - 1\right) + {\left(a + 1\right)} \log\left(b x + a - 1\right)^{2}}{a^{2} b - b} - \frac{4 \, {\left(\log\left(b x + a - 1\right) \log\left(\frac{1}{2} \, b x + \frac{1}{2} \, a + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, b x - \frac{1}{2} \, a + \frac{1}{2}\right)\right)}}{a^{2} b - b} + \frac{4 \, {\left(\log\left(\frac{b x}{a + 1} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x}{a + 1}\right)\right)}}{a^{2} b - b} - \frac{4 \, {\left(\log\left(\frac{b x}{a - 1} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x}{a - 1}\right)\right)}}{a^{2} b - b}\right)} - b {\left(\frac{\log\left(b x + a + 1\right)}{a + 1} - \frac{\log\left(b x + a - 1\right)}{a - 1} + \frac{2 \, \log\left(x\right)}{a^{2} - 1}\right)} \operatorname{artanh}\left(b x + a\right) - \frac{\operatorname{artanh}\left(b x + a\right)^{2}}{x}"," ",0,"1/4*b^2*(((a - 1)*log(b*x + a + 1)^2 - 2*(a - 1)*log(b*x + a + 1)*log(b*x + a - 1) + (a + 1)*log(b*x + a - 1)^2)/(a^2*b - b) - 4*(log(b*x + a - 1)*log(1/2*b*x + 1/2*a + 1/2) + dilog(-1/2*b*x - 1/2*a + 1/2))/(a^2*b - b) + 4*(log(b*x/(a + 1) + 1)*log(x) + dilog(-b*x/(a + 1)))/(a^2*b - b) - 4*(log(b*x/(a - 1) + 1)*log(x) + dilog(-b*x/(a - 1)))/(a^2*b - b)) - b*(log(b*x + a + 1)/(a + 1) - log(b*x + a - 1)/(a - 1) + 2*log(x)/(a^2 - 1))*arctanh(b*x + a) - arctanh(b*x + a)^2/x","A",0
7,1,360,0,0.347324," ","integrate(arctanh(b*x+a)^2/x^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{8 \, {\left(\log\left(b x + a - 1\right) \log\left(\frac{1}{2} \, b x + \frac{1}{2} \, a + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, b x - \frac{1}{2} \, a + \frac{1}{2}\right)\right)} a}{a^{4} - 2 \, a^{2} + 1} - \frac{8 \, {\left(\log\left(\frac{b x}{a + 1} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x}{a + 1}\right)\right)} a}{a^{4} - 2 \, a^{2} + 1} + \frac{8 \, {\left(\log\left(\frac{b x}{a - 1} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x}{a - 1}\right)\right)} a}{a^{4} - 2 \, a^{2} + 1} - \frac{{\left(a^{2} - 2 \, a + 1\right)} \log\left(b x + a + 1\right)^{2} - 2 \, {\left(a^{2} - 2 \, a + 1\right)} \log\left(b x + a + 1\right) \log\left(b x + a - 1\right) + {\left(a^{2} + 2 \, a + 1\right)} \log\left(b x + a - 1\right)^{2}}{a^{4} - 2 \, a^{2} + 1} + \frac{4 \, \log\left(b x + a + 1\right)}{a^{3} + a^{2} - a - 1} - \frac{4 \, \log\left(b x + a - 1\right)}{a^{3} - a^{2} - a + 1} + \frac{8 \, \log\left(x\right)}{a^{4} - 2 \, a^{2} + 1}\right)} b^{2} + \frac{1}{2} \, {\left(\frac{4 \, a b \log\left(x\right)}{a^{4} - 2 \, a^{2} + 1} + \frac{b \log\left(b x + a + 1\right)}{a^{2} + 2 \, a + 1} - \frac{b \log\left(b x + a - 1\right)}{a^{2} - 2 \, a + 1} + \frac{2}{{\left(a^{2} - 1\right)} x}\right)} b \operatorname{artanh}\left(b x + a\right) - \frac{\operatorname{artanh}\left(b x + a\right)^{2}}{2 \, x^{2}}"," ",0,"1/8*(8*(log(b*x + a - 1)*log(1/2*b*x + 1/2*a + 1/2) + dilog(-1/2*b*x - 1/2*a + 1/2))*a/(a^4 - 2*a^2 + 1) - 8*(log(b*x/(a + 1) + 1)*log(x) + dilog(-b*x/(a + 1)))*a/(a^4 - 2*a^2 + 1) + 8*(log(b*x/(a - 1) + 1)*log(x) + dilog(-b*x/(a - 1)))*a/(a^4 - 2*a^2 + 1) - ((a^2 - 2*a + 1)*log(b*x + a + 1)^2 - 2*(a^2 - 2*a + 1)*log(b*x + a + 1)*log(b*x + a - 1) + (a^2 + 2*a + 1)*log(b*x + a - 1)^2)/(a^4 - 2*a^2 + 1) + 4*log(b*x + a + 1)/(a^3 + a^2 - a - 1) - 4*log(b*x + a - 1)/(a^3 - a^2 - a + 1) + 8*log(x)/(a^4 - 2*a^2 + 1))*b^2 + 1/2*(4*a*b*log(x)/(a^4 - 2*a^2 + 1) + b*log(b*x + a + 1)/(a^2 + 2*a + 1) - b*log(b*x + a - 1)/(a^2 - 2*a + 1) + 2/((a^2 - 1)*x))*b*arctanh(b*x + a) - 1/2*arctanh(b*x + a)^2/x^2","A",0
8,0,0,0,0.000000," ","integrate(arctanh(b*x+1)^2/x,x, algorithm=""maxima"")","\frac{1}{12} \, \log\left(-b x\right)^{3} + \frac{1}{4} \, \log\left(b x + 2\right)^{2} \log\left(-x\right) - \frac{1}{4} \, \int \frac{2 \, {\left(b x \log\left(b\right) + 2 \, {\left(b x + 1\right)} \log\left(-x\right) + 2 \, \log\left(b\right)\right)} \log\left(b x + 2\right)}{b x^{2} + 2 \, x}\,{d x}"," ",0,"1/12*log(-b*x)^3 + 1/4*log(b*x + 2)^2*log(-x) - 1/4*integrate(2*(b*x*log(b) + 2*(b*x + 1)*log(-x) + 2*log(b))*log(b*x + 2)/(b*x^2 + 2*x), x)","F",0
9,1,357,0,0.330347," ","integrate((d*e*x+c*e)^3*(a+b*arctanh(d*x+c)),x, algorithm=""maxima"")","\frac{1}{4} \, a d^{3} e^{3} x^{4} + a c d^{2} e^{3} x^{3} + \frac{3}{2} \, a c^{2} d e^{3} x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} b c^{2} d e^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} + \frac{{\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{4}} - \frac{{\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(d x + c - 1\right)}{d^{4}}\right)}\right)} b c d^{2} e^{3} + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, {\left(d^{2} x^{3} - 3 \, c d x^{2} + 3 \, {\left(3 \, c^{2} + 1\right)} x\right)}}{d^{4}} - \frac{3 \, {\left(c^{4} + 4 \, c^{3} + 6 \, c^{2} + 4 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{5}} + \frac{3 \, {\left(c^{4} - 4 \, c^{3} + 6 \, c^{2} - 4 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{5}}\right)}\right)} b d^{3} e^{3} + a c^{3} e^{3} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} b c^{3} e^{3}}{2 \, d}"," ",0,"1/4*a*d^3*e^3*x^4 + a*c*d^2*e^3*x^3 + 3/2*a*c^2*d*e^3*x^2 + 3/4*(2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*b*c^2*d*e^3 + 1/2*(2*x^3*arctanh(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 + (c^3 + 3*c^2 + 3*c + 1)*log(d*x + c + 1)/d^4 - (c^3 - 3*c^2 + 3*c - 1)*log(d*x + c - 1)/d^4))*b*c*d^2*e^3 + 1/24*(6*x^4*arctanh(d*x + c) + d*(2*(d^2*x^3 - 3*c*d*x^2 + 3*(3*c^2 + 1)*x)/d^4 - 3*(c^4 + 4*c^3 + 6*c^2 + 4*c + 1)*log(d*x + c + 1)/d^5 + 3*(c^4 - 4*c^3 + 6*c^2 - 4*c + 1)*log(d*x + c - 1)/d^5))*b*d^3*e^3 + a*c^3*e^3*x + 1/2*(2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*b*c^3*e^3/d","B",0
10,1,225,0,0.321315," ","integrate((d*e*x+c*e)^2*(a+b*arctanh(d*x+c)),x, algorithm=""maxima"")","\frac{1}{3} \, a d^{2} e^{2} x^{3} + a c d e^{2} x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} b c d e^{2} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} + \frac{{\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{4}} - \frac{{\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(d x + c - 1\right)}{d^{4}}\right)}\right)} b d^{2} e^{2} + a c^{2} e^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} b c^{2} e^{2}}{2 \, d}"," ",0,"1/3*a*d^2*e^2*x^3 + a*c*d*e^2*x^2 + 1/2*(2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*b*c*d*e^2 + 1/6*(2*x^3*arctanh(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 + (c^3 + 3*c^2 + 3*c + 1)*log(d*x + c + 1)/d^4 - (c^3 - 3*c^2 + 3*c - 1)*log(d*x + c - 1)/d^4))*b*d^2*e^2 + a*c^2*e^2*x + 1/2*(2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*b*c^2*e^2/d","B",0
11,1,113,0,0.313751," ","integrate((d*e*x+c*e)*(a+b*arctanh(d*x+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a d e x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} b d e + a c e x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} b c e}{2 \, d}"," ",0,"1/2*a*d*e*x^2 + 1/4*(2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*b*d*e + a*c*e*x + 1/2*(2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*b*c*e/d","B",0
12,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))/(d*e*x+c*e),x, algorithm=""maxima"")","\frac{1}{2} \, b \int \frac{\log\left(d x + c + 1\right) - \log\left(-d x - c + 1\right)}{d e x + c e}\,{d x} + \frac{a \log\left(d e x + c e\right)}{d e}"," ",0,"1/2*b*integrate((log(d*x + c + 1) - log(-d*x - c + 1))/(d*e*x + c*e), x) + a*log(d*e*x + c*e)/(d*e)","F",0
13,1,95,0,0.315046," ","integrate((a+b*arctanh(d*x+c))/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(d {\left(\frac{\log\left(d x + c + 1\right)}{d^{2} e^{2}} - \frac{2 \, \log\left(d x + c\right)}{d^{2} e^{2}} + \frac{\log\left(d x + c - 1\right)}{d^{2} e^{2}}\right)} + \frac{2 \, \operatorname{artanh}\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}}\right)} b - \frac{a}{d^{2} e^{2} x + c d e^{2}}"," ",0,"-1/2*(d*(log(d*x + c + 1)/(d^2*e^2) - 2*log(d*x + c)/(d^2*e^2) + log(d*x + c - 1)/(d^2*e^2)) + 2*arctanh(d*x + c)/(d^2*e^2*x + c*d*e^2))*b - a/(d^2*e^2*x + c*d*e^2)","A",0
14,1,131,0,0.320554," ","integrate((a+b*arctanh(d*x+c))/(d*e*x+c*e)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(d {\left(\frac{2}{d^{3} e^{3} x + c d^{2} e^{3}} - \frac{\log\left(d x + c + 1\right)}{d^{2} e^{3}} + \frac{\log\left(d x + c - 1\right)}{d^{2} e^{3}}\right)} + \frac{2 \, \operatorname{artanh}\left(d x + c\right)}{d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}}\right)} b - \frac{a}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}}"," ",0,"-1/4*(d*(2/(d^3*e^3*x + c*d^2*e^3) - log(d*x + c + 1)/(d^2*e^3) + log(d*x + c - 1)/(d^2*e^3)) + 2*arctanh(d*x + c)/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3))*b - 1/2*a/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)","B",0
15,1,827,0,0.622240," ","integrate((d*e*x+c*e)^3*(a+b*arctanh(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} d^{3} e^{3} x^{4} + a^{2} c d^{2} e^{3} x^{3} + \frac{3}{2} \, a^{2} c^{2} d e^{3} x^{2} + \frac{3}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} a b c^{2} d e^{3} + {\left(2 \, x^{3} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} + \frac{{\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{4}} - \frac{{\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(d x + c - 1\right)}{d^{4}}\right)}\right)} a b c d^{2} e^{3} + \frac{1}{12} \, {\left(6 \, x^{4} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, {\left(d^{2} x^{3} - 3 \, c d x^{2} + 3 \, {\left(3 \, c^{2} + 1\right)} x\right)}}{d^{4}} - \frac{3 \, {\left(c^{4} + 4 \, c^{3} + 6 \, c^{2} + 4 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{5}} + \frac{3 \, {\left(c^{4} - 4 \, c^{3} + 6 \, c^{2} - 4 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{5}}\right)}\right)} a b d^{3} e^{3} + a^{2} c^{3} e^{3} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a b c^{3} e^{3}}{d} + \frac{4 \, b^{2} d^{2} e^{3} x^{2} + 8 \, b^{2} c d e^{3} x + 3 \, {\left(b^{2} d^{4} e^{3} x^{4} + 4 \, b^{2} c d^{3} e^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} e^{3} x^{2} + 4 \, b^{2} c^{3} d e^{3} x + {\left(c^{4} e^{3} - e^{3}\right)} b^{2}\right)} \log\left(d x + c + 1\right)^{2} + 3 \, {\left(b^{2} d^{4} e^{3} x^{4} + 4 \, b^{2} c d^{3} e^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} e^{3} x^{2} + 4 \, b^{2} c^{3} d e^{3} x + {\left(c^{4} e^{3} - e^{3}\right)} b^{2}\right)} \log\left(-d x - c + 1\right)^{2} + 4 \, {\left(b^{2} d^{3} e^{3} x^{3} + 3 \, b^{2} c d^{2} e^{3} x^{2} + 3 \, {\left(c^{2} d e^{3} + d e^{3}\right)} b^{2} x + {\left(c^{3} e^{3} + 3 \, c e^{3} + 4 \, e^{3}\right)} b^{2}\right)} \log\left(d x + c + 1\right) - 2 \, {\left(2 \, b^{2} d^{3} e^{3} x^{3} + 6 \, b^{2} c d^{2} e^{3} x^{2} + 6 \, {\left(c^{2} d e^{3} + d e^{3}\right)} b^{2} x + 2 \, {\left(c^{3} e^{3} + 3 \, c e^{3} - 4 \, e^{3}\right)} b^{2} + 3 \, {\left(b^{2} d^{4} e^{3} x^{4} + 4 \, b^{2} c d^{3} e^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} e^{3} x^{2} + 4 \, b^{2} c^{3} d e^{3} x + {\left(c^{4} e^{3} - e^{3}\right)} b^{2}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{48 \, d}"," ",0,"1/4*a^2*d^3*e^3*x^4 + a^2*c*d^2*e^3*x^3 + 3/2*a^2*c^2*d*e^3*x^2 + 3/2*(2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*a*b*c^2*d*e^3 + (2*x^3*arctanh(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 + (c^3 + 3*c^2 + 3*c + 1)*log(d*x + c + 1)/d^4 - (c^3 - 3*c^2 + 3*c - 1)*log(d*x + c - 1)/d^4))*a*b*c*d^2*e^3 + 1/12*(6*x^4*arctanh(d*x + c) + d*(2*(d^2*x^3 - 3*c*d*x^2 + 3*(3*c^2 + 1)*x)/d^4 - 3*(c^4 + 4*c^3 + 6*c^2 + 4*c + 1)*log(d*x + c + 1)/d^5 + 3*(c^4 - 4*c^3 + 6*c^2 - 4*c + 1)*log(d*x + c - 1)/d^5))*a*b*d^3*e^3 + a^2*c^3*e^3*x + (2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*a*b*c^3*e^3/d + 1/48*(4*b^2*d^2*e^3*x^2 + 8*b^2*c*d*e^3*x + 3*(b^2*d^4*e^3*x^4 + 4*b^2*c*d^3*e^3*x^3 + 6*b^2*c^2*d^2*e^3*x^2 + 4*b^2*c^3*d*e^3*x + (c^4*e^3 - e^3)*b^2)*log(d*x + c + 1)^2 + 3*(b^2*d^4*e^3*x^4 + 4*b^2*c*d^3*e^3*x^3 + 6*b^2*c^2*d^2*e^3*x^2 + 4*b^2*c^3*d*e^3*x + (c^4*e^3 - e^3)*b^2)*log(-d*x - c + 1)^2 + 4*(b^2*d^3*e^3*x^3 + 3*b^2*c*d^2*e^3*x^2 + 3*(c^2*d*e^3 + d*e^3)*b^2*x + (c^3*e^3 + 3*c*e^3 + 4*e^3)*b^2)*log(d*x + c + 1) - 2*(2*b^2*d^3*e^3*x^3 + 6*b^2*c*d^2*e^3*x^2 + 6*(c^2*d*e^3 + d*e^3)*b^2*x + 2*(c^3*e^3 + 3*c*e^3 - 4*e^3)*b^2 + 3*(b^2*d^4*e^3*x^4 + 4*b^2*c*d^3*e^3*x^3 + 6*b^2*c^2*d^2*e^3*x^2 + 4*b^2*c^3*d*e^3*x + (c^4*e^3 - e^3)*b^2)*log(d*x + c + 1))*log(-d*x - c + 1))/d","B",0
16,1,619,0,0.627841," ","integrate((d*e*x+c*e)^2*(a+b*arctanh(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} d^{2} e^{2} x^{3} + a^{2} c d e^{2} x^{2} + {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} a b c d e^{2} + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} + \frac{{\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{4}} - \frac{{\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(d x + c - 1\right)}{d^{4}}\right)}\right)} a b d^{2} e^{2} + a^{2} c^{2} e^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a b c^{2} e^{2}}{d} + \frac{{\left(\log\left(d x + c + 1\right) \log\left(-\frac{1}{2} \, d x - \frac{1}{2} \, c + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, d x + \frac{1}{2} \, c + \frac{1}{2}\right)\right)} b^{2} e^{2}}{3 \, d} + \frac{{\left(c^{2} e^{2} - e^{2}\right)} b^{2} \log\left(d x + c + 1\right)}{6 \, d} - \frac{{\left(c^{2} e^{2} - e^{2}\right)} b^{2} \log\left(d x + c - 1\right)}{6 \, d} + \frac{4 \, b^{2} d e^{2} x + {\left(b^{2} d^{3} e^{2} x^{3} + 3 \, b^{2} c d^{2} e^{2} x^{2} + 3 \, b^{2} c^{2} d e^{2} x + {\left(c^{3} e^{2} + e^{2}\right)} b^{2}\right)} \log\left(d x + c + 1\right)^{2} + {\left(b^{2} d^{3} e^{2} x^{3} + 3 \, b^{2} c d^{2} e^{2} x^{2} + 3 \, b^{2} c^{2} d e^{2} x + {\left(c^{3} e^{2} - e^{2}\right)} b^{2}\right)} \log\left(-d x - c + 1\right)^{2} + 2 \, {\left(b^{2} d^{2} e^{2} x^{2} + 2 \, b^{2} c d e^{2} x\right)} \log\left(d x + c + 1\right) - 2 \, {\left(b^{2} d^{2} e^{2} x^{2} + 2 \, b^{2} c d e^{2} x + {\left(b^{2} d^{3} e^{2} x^{3} + 3 \, b^{2} c d^{2} e^{2} x^{2} + 3 \, b^{2} c^{2} d e^{2} x + {\left(c^{3} e^{2} + e^{2}\right)} b^{2}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{12 \, d}"," ",0,"1/3*a^2*d^2*e^2*x^3 + a^2*c*d*e^2*x^2 + (2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*a*b*c*d*e^2 + 1/3*(2*x^3*arctanh(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 + (c^3 + 3*c^2 + 3*c + 1)*log(d*x + c + 1)/d^4 - (c^3 - 3*c^2 + 3*c - 1)*log(d*x + c - 1)/d^4))*a*b*d^2*e^2 + a^2*c^2*e^2*x + (2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*a*b*c^2*e^2/d + 1/3*(log(d*x + c + 1)*log(-1/2*d*x - 1/2*c + 1/2) + dilog(1/2*d*x + 1/2*c + 1/2))*b^2*e^2/d + 1/6*(c^2*e^2 - e^2)*b^2*log(d*x + c + 1)/d - 1/6*(c^2*e^2 - e^2)*b^2*log(d*x + c - 1)/d + 1/12*(4*b^2*d*e^2*x + (b^2*d^3*e^2*x^3 + 3*b^2*c*d^2*e^2*x^2 + 3*b^2*c^2*d*e^2*x + (c^3*e^2 + e^2)*b^2)*log(d*x + c + 1)^2 + (b^2*d^3*e^2*x^3 + 3*b^2*c*d^2*e^2*x^2 + 3*b^2*c^2*d*e^2*x + (c^3*e^2 - e^2)*b^2)*log(-d*x - c + 1)^2 + 2*(b^2*d^2*e^2*x^2 + 2*b^2*c*d*e^2*x)*log(d*x + c + 1) - 2*(b^2*d^2*e^2*x^2 + 2*b^2*c*d*e^2*x + (b^2*d^3*e^2*x^3 + 3*b^2*c*d^2*e^2*x^2 + 3*b^2*c^2*d*e^2*x + (c^3*e^2 + e^2)*b^2)*log(d*x + c + 1))*log(-d*x - c + 1))/d","B",0
17,1,316,0,0.604892," ","integrate((d*e*x+c*e)*(a+b*arctanh(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} d e x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} a b d e + a^{2} c e x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a b c e}{d} + \frac{{\left(b^{2} d^{2} e x^{2} + 2 \, b^{2} c d e x + {\left(c^{2} e - e\right)} b^{2}\right)} \log\left(d x + c + 1\right)^{2} + {\left(b^{2} d^{2} e x^{2} + 2 \, b^{2} c d e x + {\left(c^{2} e - e\right)} b^{2}\right)} \log\left(-d x - c + 1\right)^{2} + 4 \, {\left(b^{2} d e x + {\left(c e + e\right)} b^{2}\right)} \log\left(d x + c + 1\right) - 2 \, {\left(2 \, b^{2} d e x + 2 \, {\left(c e - e\right)} b^{2} + {\left(b^{2} d^{2} e x^{2} + 2 \, b^{2} c d e x + {\left(c^{2} e - e\right)} b^{2}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{8 \, d}"," ",0,"1/2*a^2*d*e*x^2 + 1/2*(2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*a*b*d*e + a^2*c*e*x + (2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*a*b*c*e/d + 1/8*((b^2*d^2*e*x^2 + 2*b^2*c*d*e*x + (c^2*e - e)*b^2)*log(d*x + c + 1)^2 + (b^2*d^2*e*x^2 + 2*b^2*c*d*e*x + (c^2*e - e)*b^2)*log(-d*x - c + 1)^2 + 4*(b^2*d*e*x + (c*e + e)*b^2)*log(d*x + c + 1) - 2*(2*b^2*d*e*x + 2*(c*e - e)*b^2 + (b^2*d^2*e*x^2 + 2*b^2*c*d*e*x + (c^2*e - e)*b^2)*log(d*x + c + 1))*log(-d*x - c + 1))/d","B",0
18,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))^2/(d*e*x+c*e),x, algorithm=""maxima"")","\frac{a^{2} \log\left(d e x + c e\right)}{d e} + \int \frac{b^{2} {\left(\log\left(d x + c + 1\right) - \log\left(-d x - c + 1\right)\right)}^{2}}{4 \, {\left(d e x + c e\right)}} + \frac{a b {\left(\log\left(d x + c + 1\right) - \log\left(-d x - c + 1\right)\right)}}{d e x + c e}\,{d x}"," ",0,"a^2*log(d*e*x + c*e)/(d*e) + integrate(1/4*b^2*(log(d*x + c + 1) - log(-d*x - c + 1))^2/(d*e*x + c*e) + a*b*(log(d*x + c + 1) - log(-d*x - c + 1))/(d*e*x + c*e), x)","F",0
19,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))^2/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-{\left(d {\left(\frac{\log\left(d x + c + 1\right)}{d^{2} e^{2}} - \frac{2 \, \log\left(d x + c\right)}{d^{2} e^{2}} + \frac{\log\left(d x + c - 1\right)}{d^{2} e^{2}}\right)} + \frac{2 \, \operatorname{artanh}\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}}\right)} a b - \frac{1}{4} \, b^{2} {\left(\frac{\log\left(-d x - c + 1\right)^{2}}{d^{2} e^{2} x + c d e^{2}} + \int -\frac{{\left(d x + c - 1\right)} \log\left(d x + c + 1\right)^{2} + 2 \, {\left(d x - {\left(d x + c - 1\right)} \log\left(d x + c + 1\right) + c\right)} \log\left(-d x - c + 1\right)}{d^{3} e^{2} x^{3} + c^{3} e^{2} - c^{2} e^{2} + {\left(3 \, c d^{2} e^{2} - d^{2} e^{2}\right)} x^{2} + {\left(3 \, c^{2} d e^{2} - 2 \, c d e^{2}\right)} x}\,{d x}\right)} - \frac{a^{2}}{d^{2} e^{2} x + c d e^{2}}"," ",0,"-(d*(log(d*x + c + 1)/(d^2*e^2) - 2*log(d*x + c)/(d^2*e^2) + log(d*x + c - 1)/(d^2*e^2)) + 2*arctanh(d*x + c)/(d^2*e^2*x + c*d*e^2))*a*b - 1/4*b^2*(log(-d*x - c + 1)^2/(d^2*e^2*x + c*d*e^2) + integrate(-((d*x + c - 1)*log(d*x + c + 1)^2 + 2*(d*x - (d*x + c - 1)*log(d*x + c + 1) + c)*log(-d*x - c + 1))/(d^3*e^2*x^3 + c^3*e^2 - c^2*e^2 + (3*c*d^2*e^2 - d^2*e^2)*x^2 + (3*c^2*d*e^2 - 2*c*d*e^2)*x), x)) - a^2/(d^2*e^2*x + c*d*e^2)","F",0
20,1,329,0,0.358815," ","integrate((a+b*arctanh(d*x+c))^2/(d*e*x+c*e)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(d {\left(\frac{2}{d^{3} e^{3} x + c d^{2} e^{3}} - \frac{\log\left(d x + c + 1\right)}{d^{2} e^{3}} + \frac{\log\left(d x + c - 1\right)}{d^{2} e^{3}}\right)} + \frac{2 \, \operatorname{artanh}\left(d x + c\right)}{d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}}\right)} a b - \frac{1}{8} \, {\left(d^{2} {\left(\frac{\log\left(d x + c + 1\right)^{2} - 2 \, \log\left(d x + c + 1\right) \log\left(d x + c - 1\right) + \log\left(d x + c - 1\right)^{2} + 4 \, \log\left(d x + c - 1\right)}{d^{3} e^{3}} + \frac{4 \, \log\left(d x + c + 1\right)}{d^{3} e^{3}} - \frac{8 \, \log\left(d x + c\right)}{d^{3} e^{3}}\right)} + 4 \, d {\left(\frac{2}{d^{3} e^{3} x + c d^{2} e^{3}} - \frac{\log\left(d x + c + 1\right)}{d^{2} e^{3}} + \frac{\log\left(d x + c - 1\right)}{d^{2} e^{3}}\right)} \operatorname{artanh}\left(d x + c\right)\right)} b^{2} - \frac{b^{2} \operatorname{artanh}\left(d x + c\right)^{2}}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}} - \frac{a^{2}}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}}"," ",0,"-1/2*(d*(2/(d^3*e^3*x + c*d^2*e^3) - log(d*x + c + 1)/(d^2*e^3) + log(d*x + c - 1)/(d^2*e^3)) + 2*arctanh(d*x + c)/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3))*a*b - 1/8*(d^2*((log(d*x + c + 1)^2 - 2*log(d*x + c + 1)*log(d*x + c - 1) + log(d*x + c - 1)^2 + 4*log(d*x + c - 1))/(d^3*e^3) + 4*log(d*x + c + 1)/(d^3*e^3) - 8*log(d*x + c)/(d^3*e^3)) + 4*d*(2/(d^3*e^3*x + c*d^2*e^3) - log(d*x + c + 1)/(d^2*e^3) + log(d*x + c - 1)/(d^2*e^3))*arctanh(d*x + c))*b^2 - 1/2*b^2*arctanh(d*x + c)^2/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3) - 1/2*a^2/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)","B",0
21,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))^2/(d*e*x+c*e)^4,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(d {\left(\frac{1}{d^{4} e^{4} x^{2} + 2 \, c d^{3} e^{4} x + c^{2} d^{2} e^{4}} + \frac{\log\left(d x + c + 1\right)}{d^{2} e^{4}} - \frac{2 \, \log\left(d x + c\right)}{d^{2} e^{4}} + \frac{\log\left(d x + c - 1\right)}{d^{2} e^{4}}\right)} + \frac{2 \, \operatorname{artanh}\left(d x + c\right)}{d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}}\right)} a b - \frac{1}{12} \, b^{2} {\left(\frac{\log\left(-d x - c + 1\right)^{2}}{d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}} + 3 \, \int -\frac{3 \, {\left(d x + c - 1\right)} \log\left(d x + c + 1\right)^{2} + 2 \, {\left(d x - 3 \, {\left(d x + c - 1\right)} \log\left(d x + c + 1\right) + c\right)} \log\left(-d x - c + 1\right)}{3 \, {\left(d^{5} e^{4} x^{5} + c^{5} e^{4} - c^{4} e^{4} + {\left(5 \, c d^{4} e^{4} - d^{4} e^{4}\right)} x^{4} + 2 \, {\left(5 \, c^{2} d^{3} e^{4} - 2 \, c d^{3} e^{4}\right)} x^{3} + 2 \, {\left(5 \, c^{3} d^{2} e^{4} - 3 \, c^{2} d^{2} e^{4}\right)} x^{2} + {\left(5 \, c^{4} d e^{4} - 4 \, c^{3} d e^{4}\right)} x\right)}}\,{d x}\right)} - \frac{a^{2}}{3 \, {\left(d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}\right)}}"," ",0,"-1/3*(d*(1/(d^4*e^4*x^2 + 2*c*d^3*e^4*x + c^2*d^2*e^4) + log(d*x + c + 1)/(d^2*e^4) - 2*log(d*x + c)/(d^2*e^4) + log(d*x + c - 1)/(d^2*e^4)) + 2*arctanh(d*x + c)/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4))*a*b - 1/12*b^2*(log(-d*x - c + 1)^2/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4) + 3*integrate(-1/3*(3*(d*x + c - 1)*log(d*x + c + 1)^2 + 2*(d*x - 3*(d*x + c - 1)*log(d*x + c + 1) + c)*log(-d*x - c + 1))/(d^5*e^4*x^5 + c^5*e^4 - c^4*e^4 + (5*c*d^4*e^4 - d^4*e^4)*x^4 + 2*(5*c^2*d^3*e^4 - 2*c*d^3*e^4)*x^3 + 2*(5*c^3*d^2*e^4 - 3*c^2*d^2*e^4)*x^2 + (5*c^4*d*e^4 - 4*c^3*d*e^4)*x), x)) - 1/3*a^2/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4)","F",0
22,1,613,0,0.377344," ","integrate((a+b*arctanh(d*x+c))^2/(d*e*x+c*e)^5,x, algorithm=""maxima"")","-\frac{1}{12} \, {\left(d {\left(\frac{2 \, {\left(3 \, d^{2} x^{2} + 6 \, c d x + 3 \, c^{2} + 1\right)}}{d^{5} e^{5} x^{3} + 3 \, c d^{4} e^{5} x^{2} + 3 \, c^{2} d^{3} e^{5} x + c^{3} d^{2} e^{5}} - \frac{3 \, \log\left(d x + c + 1\right)}{d^{2} e^{5}} + \frac{3 \, \log\left(d x + c - 1\right)}{d^{2} e^{5}}\right)} + \frac{6 \, \operatorname{artanh}\left(d x + c\right)}{d^{5} e^{5} x^{4} + 4 \, c d^{4} e^{5} x^{3} + 6 \, c^{2} d^{3} e^{5} x^{2} + 4 \, c^{3} d^{2} e^{5} x + c^{4} d e^{5}}\right)} a b - \frac{1}{48} \, {\left(d^{2} {\left(\frac{3 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \log\left(d x + c + 1\right)^{2} + 3 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \log\left(d x + c - 1\right)^{2} + 2 \, {\left(8 \, d^{2} x^{2} + 16 \, c d x + 8 \, c^{2} - 3 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right) + 16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \log\left(d x + c - 1\right) + 4}{d^{5} e^{5} x^{2} + 2 \, c d^{4} e^{5} x + c^{2} d^{3} e^{5}} - \frac{32 \, \log\left(d x + c\right)}{d^{3} e^{5}}\right)} + 4 \, d {\left(\frac{2 \, {\left(3 \, d^{2} x^{2} + 6 \, c d x + 3 \, c^{2} + 1\right)}}{d^{5} e^{5} x^{3} + 3 \, c d^{4} e^{5} x^{2} + 3 \, c^{2} d^{3} e^{5} x + c^{3} d^{2} e^{5}} - \frac{3 \, \log\left(d x + c + 1\right)}{d^{2} e^{5}} + \frac{3 \, \log\left(d x + c - 1\right)}{d^{2} e^{5}}\right)} \operatorname{artanh}\left(d x + c\right)\right)} b^{2} - \frac{b^{2} \operatorname{artanh}\left(d x + c\right)^{2}}{4 \, {\left(d^{5} e^{5} x^{4} + 4 \, c d^{4} e^{5} x^{3} + 6 \, c^{2} d^{3} e^{5} x^{2} + 4 \, c^{3} d^{2} e^{5} x + c^{4} d e^{5}\right)}} - \frac{a^{2}}{4 \, {\left(d^{5} e^{5} x^{4} + 4 \, c d^{4} e^{5} x^{3} + 6 \, c^{2} d^{3} e^{5} x^{2} + 4 \, c^{3} d^{2} e^{5} x + c^{4} d e^{5}\right)}}"," ",0,"-1/12*(d*(2*(3*d^2*x^2 + 6*c*d*x + 3*c^2 + 1)/(d^5*e^5*x^3 + 3*c*d^4*e^5*x^2 + 3*c^2*d^3*e^5*x + c^3*d^2*e^5) - 3*log(d*x + c + 1)/(d^2*e^5) + 3*log(d*x + c - 1)/(d^2*e^5)) + 6*arctanh(d*x + c)/(d^5*e^5*x^4 + 4*c*d^4*e^5*x^3 + 6*c^2*d^3*e^5*x^2 + 4*c^3*d^2*e^5*x + c^4*d*e^5))*a*b - 1/48*(d^2*((3*(d^2*x^2 + 2*c*d*x + c^2)*log(d*x + c + 1)^2 + 3*(d^2*x^2 + 2*c*d*x + c^2)*log(d*x + c - 1)^2 + 2*(8*d^2*x^2 + 16*c*d*x + 8*c^2 - 3*(d^2*x^2 + 2*c*d*x + c^2)*log(d*x + c - 1))*log(d*x + c + 1) + 16*(d^2*x^2 + 2*c*d*x + c^2)*log(d*x + c - 1) + 4)/(d^5*e^5*x^2 + 2*c*d^4*e^5*x + c^2*d^3*e^5) - 32*log(d*x + c)/(d^3*e^5)) + 4*d*(2*(3*d^2*x^2 + 6*c*d*x + 3*c^2 + 1)/(d^5*e^5*x^3 + 3*c*d^4*e^5*x^2 + 3*c^2*d^3*e^5*x + c^3*d^2*e^5) - 3*log(d*x + c + 1)/(d^2*e^5) + 3*log(d*x + c - 1)/(d^2*e^5))*arctanh(d*x + c))*b^2 - 1/4*b^2*arctanh(d*x + c)^2/(d^5*e^5*x^4 + 4*c*d^4*e^5*x^3 + 6*c^2*d^3*e^5*x^2 + 4*c^3*d^2*e^5*x + c^4*d*e^5) - 1/4*a^2/(d^5*e^5*x^4 + 4*c*d^4*e^5*x^3 + 6*c^2*d^3*e^5*x^2 + 4*c^3*d^2*e^5*x + c^4*d*e^5)","B",0
23,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arctanh(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} d^{2} e^{2} x^{3} + a^{3} c d e^{2} x^{2} + \frac{3}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} a^{2} b c d e^{2} + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} + \frac{{\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{4}} - \frac{{\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(d x + c - 1\right)}{d^{4}}\right)}\right)} a^{2} b d^{2} e^{2} + a^{3} c^{2} e^{2} x + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b c^{2} e^{2}}{2 \, d} - \frac{{\left(b^{3} d^{3} e^{2} x^{3} + 3 \, b^{3} c d^{2} e^{2} x^{2} + 3 \, b^{3} c^{2} d e^{2} x + {\left(c^{3} e^{2} - e^{2}\right)} b^{3}\right)} \log\left(-d x - c + 1\right)^{3} - 3 \, {\left(2 \, a b^{2} d^{3} e^{2} x^{3} + {\left(6 \, a b^{2} c d^{2} e^{2} + b^{3} d^{2} e^{2}\right)} x^{2} + 2 \, {\left(3 \, a b^{2} c^{2} d e^{2} + b^{3} c d e^{2}\right)} x + {\left(b^{3} d^{3} e^{2} x^{3} + 3 \, b^{3} c d^{2} e^{2} x^{2} + 3 \, b^{3} c^{2} d e^{2} x + {\left(c^{3} e^{2} + e^{2}\right)} b^{3}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)^{2}}{24 \, d} - \int -\frac{{\left(b^{3} d^{3} e^{2} x^{3} + {\left(3 \, c d^{2} e^{2} - d^{2} e^{2}\right)} b^{3} x^{2} + {\left(3 \, c^{2} d e^{2} - 2 \, c d e^{2}\right)} b^{3} x + {\left(c^{3} e^{2} - c^{2} e^{2}\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{3} + 6 \, {\left(a b^{2} d^{3} e^{2} x^{3} + {\left(3 \, c d^{2} e^{2} - d^{2} e^{2}\right)} a b^{2} x^{2} + {\left(3 \, c^{2} d e^{2} - 2 \, c d e^{2}\right)} a b^{2} x + {\left(c^{3} e^{2} - c^{2} e^{2}\right)} a b^{2}\right)} \log\left(d x + c + 1\right)^{2} - {\left(4 \, a b^{2} d^{3} e^{2} x^{3} + 2 \, {\left(6 \, a b^{2} c d^{2} e^{2} + b^{3} d^{2} e^{2}\right)} x^{2} + 3 \, {\left(b^{3} d^{3} e^{2} x^{3} + {\left(3 \, c d^{2} e^{2} - d^{2} e^{2}\right)} b^{3} x^{2} + {\left(3 \, c^{2} d e^{2} - 2 \, c d e^{2}\right)} b^{3} x + {\left(c^{3} e^{2} - c^{2} e^{2}\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{2} + 4 \, {\left(3 \, a b^{2} c^{2} d e^{2} + b^{3} c d e^{2}\right)} x + 2 \, {\left(6 \, {\left(c^{3} e^{2} - c^{2} e^{2}\right)} a b^{2} + {\left(c^{3} e^{2} + e^{2}\right)} b^{3} + {\left(6 \, a b^{2} d^{3} e^{2} + b^{3} d^{3} e^{2}\right)} x^{3} + 3 \, {\left(b^{3} c d^{2} e^{2} + 2 \, {\left(3 \, c d^{2} e^{2} - d^{2} e^{2}\right)} a b^{2}\right)} x^{2} + 3 \, {\left(b^{3} c^{2} d e^{2} + 2 \, {\left(3 \, c^{2} d e^{2} - 2 \, c d e^{2}\right)} a b^{2}\right)} x\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{8 \, {\left(d x + c - 1\right)}}\,{d x}"," ",0,"1/3*a^3*d^2*e^2*x^3 + a^3*c*d*e^2*x^2 + 3/2*(2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*a^2*b*c*d*e^2 + 1/2*(2*x^3*arctanh(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 + (c^3 + 3*c^2 + 3*c + 1)*log(d*x + c + 1)/d^4 - (c^3 - 3*c^2 + 3*c - 1)*log(d*x + c - 1)/d^4))*a^2*b*d^2*e^2 + a^3*c^2*e^2*x + 3/2*(2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*a^2*b*c^2*e^2/d - 1/24*((b^3*d^3*e^2*x^3 + 3*b^3*c*d^2*e^2*x^2 + 3*b^3*c^2*d*e^2*x + (c^3*e^2 - e^2)*b^3)*log(-d*x - c + 1)^3 - 3*(2*a*b^2*d^3*e^2*x^3 + (6*a*b^2*c*d^2*e^2 + b^3*d^2*e^2)*x^2 + 2*(3*a*b^2*c^2*d*e^2 + b^3*c*d*e^2)*x + (b^3*d^3*e^2*x^3 + 3*b^3*c*d^2*e^2*x^2 + 3*b^3*c^2*d*e^2*x + (c^3*e^2 + e^2)*b^3)*log(d*x + c + 1))*log(-d*x - c + 1)^2)/d - integrate(-1/8*((b^3*d^3*e^2*x^3 + (3*c*d^2*e^2 - d^2*e^2)*b^3*x^2 + (3*c^2*d*e^2 - 2*c*d*e^2)*b^3*x + (c^3*e^2 - c^2*e^2)*b^3)*log(d*x + c + 1)^3 + 6*(a*b^2*d^3*e^2*x^3 + (3*c*d^2*e^2 - d^2*e^2)*a*b^2*x^2 + (3*c^2*d*e^2 - 2*c*d*e^2)*a*b^2*x + (c^3*e^2 - c^2*e^2)*a*b^2)*log(d*x + c + 1)^2 - (4*a*b^2*d^3*e^2*x^3 + 2*(6*a*b^2*c*d^2*e^2 + b^3*d^2*e^2)*x^2 + 3*(b^3*d^3*e^2*x^3 + (3*c*d^2*e^2 - d^2*e^2)*b^3*x^2 + (3*c^2*d*e^2 - 2*c*d*e^2)*b^3*x + (c^3*e^2 - c^2*e^2)*b^3)*log(d*x + c + 1)^2 + 4*(3*a*b^2*c^2*d*e^2 + b^3*c*d*e^2)*x + 2*(6*(c^3*e^2 - c^2*e^2)*a*b^2 + (c^3*e^2 + e^2)*b^3 + (6*a*b^2*d^3*e^2 + b^3*d^3*e^2)*x^3 + 3*(b^3*c*d^2*e^2 + 2*(3*c*d^2*e^2 - d^2*e^2)*a*b^2)*x^2 + 3*(b^3*c^2*d*e^2 + 2*(3*c^2*d*e^2 - 2*c*d*e^2)*a*b^2)*x)*log(d*x + c + 1))*log(-d*x - c + 1))/(d*x + c - 1), x)","F",0
24,1,629,0,0.636931," ","integrate((d*e*x+c*e)*(a+b*arctanh(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} d e x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} a^{2} b d e + a^{3} c e x + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b c e}{2 \, d} + \frac{3 \, {\left(\log\left(d x + c + 1\right) \log\left(-\frac{1}{2} \, d x - \frac{1}{2} \, c + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, d x + \frac{1}{2} \, c + \frac{1}{2}\right)\right)} b^{3} e}{2 \, d} + \frac{3 \, {\left(c e + e\right)} a b^{2} \log\left(d x + c + 1\right)}{2 \, d} - \frac{3 \, {\left(c e - e\right)} a b^{2} \log\left(d x + c - 1\right)}{2 \, d} + \frac{24 \, a b^{2} d e x \log\left(d x + c + 1\right) + {\left(b^{3} d^{2} e x^{2} + 2 \, b^{3} c d e x + {\left(c^{2} e - e\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{3} - {\left(b^{3} d^{2} e x^{2} + 2 \, b^{3} c d e x + {\left(c^{2} e - e\right)} b^{3}\right)} \log\left(-d x - c + 1\right)^{3} + 6 \, {\left(a b^{2} d^{2} e x^{2} + {\left(c^{2} e - e\right)} a b^{2} + {\left(c e + e\right)} b^{3} + {\left(2 \, a b^{2} c d e + b^{3} d e\right)} x\right)} \log\left(d x + c + 1\right)^{2} + 3 \, {\left(2 \, a b^{2} d^{2} e x^{2} + 2 \, {\left(c^{2} e - e\right)} a b^{2} + 2 \, {\left(c e - e\right)} b^{3} + 2 \, {\left(2 \, a b^{2} c d e + b^{3} d e\right)} x + {\left(b^{3} d^{2} e x^{2} + 2 \, b^{3} c d e x + {\left(c^{2} e - e\right)} b^{3}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)^{2} - 3 \, {\left(8 \, a b^{2} d e x + {\left(b^{3} d^{2} e x^{2} + 2 \, b^{3} c d e x + {\left(c^{2} e - e\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{2} + 4 \, {\left(a b^{2} d^{2} e x^{2} + {\left(c^{2} e - e\right)} a b^{2} + {\left(c e + e\right)} b^{3} + {\left(2 \, a b^{2} c d e + b^{3} d e\right)} x\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{16 \, d}"," ",0,"1/2*a^3*d*e*x^2 + 3/4*(2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*a^2*b*d*e + a^3*c*e*x + 3/2*(2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*a^2*b*c*e/d + 3/2*(log(d*x + c + 1)*log(-1/2*d*x - 1/2*c + 1/2) + dilog(1/2*d*x + 1/2*c + 1/2))*b^3*e/d + 3/2*(c*e + e)*a*b^2*log(d*x + c + 1)/d - 3/2*(c*e - e)*a*b^2*log(d*x + c - 1)/d + 1/16*(24*a*b^2*d*e*x*log(d*x + c + 1) + (b^3*d^2*e*x^2 + 2*b^3*c*d*e*x + (c^2*e - e)*b^3)*log(d*x + c + 1)^3 - (b^3*d^2*e*x^2 + 2*b^3*c*d*e*x + (c^2*e - e)*b^3)*log(-d*x - c + 1)^3 + 6*(a*b^2*d^2*e*x^2 + (c^2*e - e)*a*b^2 + (c*e + e)*b^3 + (2*a*b^2*c*d*e + b^3*d*e)*x)*log(d*x + c + 1)^2 + 3*(2*a*b^2*d^2*e*x^2 + 2*(c^2*e - e)*a*b^2 + 2*(c*e - e)*b^3 + 2*(2*a*b^2*c*d*e + b^3*d*e)*x + (b^3*d^2*e*x^2 + 2*b^3*c*d*e*x + (c^2*e - e)*b^3)*log(d*x + c + 1))*log(-d*x - c + 1)^2 - 3*(8*a*b^2*d*e*x + (b^3*d^2*e*x^2 + 2*b^3*c*d*e*x + (c^2*e - e)*b^3)*log(d*x + c + 1)^2 + 4*(a*b^2*d^2*e*x^2 + (c^2*e - e)*a*b^2 + (c*e + e)*b^3 + (2*a*b^2*c*d*e + b^3*d*e)*x)*log(d*x + c + 1))*log(-d*x - c + 1))/d","B",0
25,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))^3/(d*e*x+c*e),x, algorithm=""maxima"")","\frac{a^{3} \log\left(d e x + c e\right)}{d e} + \int \frac{b^{3} {\left(\log\left(d x + c + 1\right) - \log\left(-d x - c + 1\right)\right)}^{3}}{8 \, {\left(d e x + c e\right)}} + \frac{3 \, a b^{2} {\left(\log\left(d x + c + 1\right) - \log\left(-d x - c + 1\right)\right)}^{2}}{4 \, {\left(d e x + c e\right)}} + \frac{3 \, a^{2} b {\left(\log\left(d x + c + 1\right) - \log\left(-d x - c + 1\right)\right)}}{2 \, {\left(d e x + c e\right)}}\,{d x}"," ",0,"a^3*log(d*e*x + c*e)/(d*e) + integrate(1/8*b^3*(log(d*x + c + 1) - log(-d*x - c + 1))^3/(d*e*x + c*e) + 3/4*a*b^2*(log(d*x + c + 1) - log(-d*x - c + 1))^2/(d*e*x + c*e) + 3/2*a^2*b*(log(d*x + c + 1) - log(-d*x - c + 1))/(d*e*x + c*e), x)","F",0
26,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))^3/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-\frac{3}{2} \, {\left(d {\left(\frac{\log\left(d x + c + 1\right)}{d^{2} e^{2}} - \frac{2 \, \log\left(d x + c\right)}{d^{2} e^{2}} + \frac{\log\left(d x + c - 1\right)}{d^{2} e^{2}}\right)} + \frac{2 \, \operatorname{artanh}\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}}\right)} a^{2} b - \frac{a^{3}}{d^{2} e^{2} x + c d e^{2}} - \frac{{\left(b^{3} d x + b^{3} {\left(c - 1\right)}\right)} \log\left(-d x - c + 1\right)^{3} + 3 \, {\left(2 \, a b^{2} + {\left(b^{3} d x + b^{3} {\left(c + 1\right)}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)^{2}}{8 \, {\left(d^{2} e^{2} x + c d e^{2}\right)}} - \int -\frac{{\left(b^{3} d x + b^{3} {\left(c - 1\right)}\right)} \log\left(d x + c + 1\right)^{3} + 6 \, {\left(a b^{2} d x + a b^{2} {\left(c - 1\right)}\right)} \log\left(d x + c + 1\right)^{2} + 3 \, {\left(4 \, a b^{2} d x + 4 \, a b^{2} c - {\left(b^{3} d x + b^{3} {\left(c - 1\right)}\right)} \log\left(d x + c + 1\right)^{2} + 2 \, {\left(b^{3} d^{2} x^{2} + {\left(c^{2} + c\right)} b^{3} - 2 \, a b^{2} {\left(c - 1\right)} + {\left({\left(2 \, c d + d\right)} b^{3} - 2 \, a b^{2} d\right)} x\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{8 \, {\left(d^{3} e^{2} x^{3} + c^{3} e^{2} - c^{2} e^{2} + {\left(3 \, c d^{2} e^{2} - d^{2} e^{2}\right)} x^{2} + {\left(3 \, c^{2} d e^{2} - 2 \, c d e^{2}\right)} x\right)}}\,{d x}"," ",0,"-3/2*(d*(log(d*x + c + 1)/(d^2*e^2) - 2*log(d*x + c)/(d^2*e^2) + log(d*x + c - 1)/(d^2*e^2)) + 2*arctanh(d*x + c)/(d^2*e^2*x + c*d*e^2))*a^2*b - a^3/(d^2*e^2*x + c*d*e^2) - 1/8*((b^3*d*x + b^3*(c - 1))*log(-d*x - c + 1)^3 + 3*(2*a*b^2 + (b^3*d*x + b^3*(c + 1))*log(d*x + c + 1))*log(-d*x - c + 1)^2)/(d^2*e^2*x + c*d*e^2) - integrate(-1/8*((b^3*d*x + b^3*(c - 1))*log(d*x + c + 1)^3 + 6*(a*b^2*d*x + a*b^2*(c - 1))*log(d*x + c + 1)^2 + 3*(4*a*b^2*d*x + 4*a*b^2*c - (b^3*d*x + b^3*(c - 1))*log(d*x + c + 1)^2 + 2*(b^3*d^2*x^2 + (c^2 + c)*b^3 - 2*a*b^2*(c - 1) + ((2*c*d + d)*b^3 - 2*a*b^2*d)*x)*log(d*x + c + 1))*log(-d*x - c + 1))/(d^3*e^2*x^3 + c^3*e^2 - c^2*e^2 + (3*c*d^2*e^2 - d^2*e^2)*x^2 + (3*c^2*d*e^2 - 2*c*d*e^2)*x), x)","F",0
27,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))^3/(d*e*x+c*e)^3,x, algorithm=""maxima"")","-\frac{3}{4} \, {\left(d {\left(\frac{2}{d^{3} e^{3} x + c d^{2} e^{3}} - \frac{\log\left(d x + c + 1\right)}{d^{2} e^{3}} + \frac{\log\left(d x + c - 1\right)}{d^{2} e^{3}}\right)} + \frac{2 \, \operatorname{artanh}\left(d x + c\right)}{d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}}\right)} a^{2} b - \frac{3}{8} \, {\left(d^{2} {\left(\frac{\log\left(d x + c + 1\right)^{2} - 2 \, \log\left(d x + c + 1\right) \log\left(d x + c - 1\right) + \log\left(d x + c - 1\right)^{2} + 4 \, \log\left(d x + c - 1\right)}{d^{3} e^{3}} + \frac{4 \, \log\left(d x + c + 1\right)}{d^{3} e^{3}} - \frac{8 \, \log\left(d x + c\right)}{d^{3} e^{3}}\right)} + 4 \, d {\left(\frac{2}{d^{3} e^{3} x + c d^{2} e^{3}} - \frac{\log\left(d x + c + 1\right)}{d^{2} e^{3}} + \frac{\log\left(d x + c - 1\right)}{d^{2} e^{3}}\right)} \operatorname{artanh}\left(d x + c\right)\right)} a b^{2} - \frac{1}{16} \, b^{3} {\left(\frac{{\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \log\left(-d x - c + 1\right)^{3} + 3 \, {\left(2 \, d x - {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \log\left(d x + c + 1\right) + 2 \, c\right)} \log\left(-d x - c + 1\right)^{2}}{d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}} + 2 \, \int -\frac{{\left(d x + c - 1\right)} \log\left(d x + c + 1\right)^{3} + 3 \, {\left(2 \, d^{2} x^{2} + 4 \, c d x - {\left(d x + c - 1\right)} \log\left(d x + c + 1\right)^{2} + 2 \, c^{2} - {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d - d\right)} x - c\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{d^{4} e^{3} x^{4} + c^{4} e^{3} - c^{3} e^{3} + {\left(4 \, c d^{3} e^{3} - d^{3} e^{3}\right)} x^{3} + 3 \, {\left(2 \, c^{2} d^{2} e^{3} - c d^{2} e^{3}\right)} x^{2} + {\left(4 \, c^{3} d e^{3} - 3 \, c^{2} d e^{3}\right)} x}\,{d x}\right)} - \frac{3 \, a b^{2} \operatorname{artanh}\left(d x + c\right)^{2}}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}} - \frac{a^{3}}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}}"," ",0,"-3/4*(d*(2/(d^3*e^3*x + c*d^2*e^3) - log(d*x + c + 1)/(d^2*e^3) + log(d*x + c - 1)/(d^2*e^3)) + 2*arctanh(d*x + c)/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3))*a^2*b - 3/8*(d^2*((log(d*x + c + 1)^2 - 2*log(d*x + c + 1)*log(d*x + c - 1) + log(d*x + c - 1)^2 + 4*log(d*x + c - 1))/(d^3*e^3) + 4*log(d*x + c + 1)/(d^3*e^3) - 8*log(d*x + c)/(d^3*e^3)) + 4*d*(2/(d^3*e^3*x + c*d^2*e^3) - log(d*x + c + 1)/(d^2*e^3) + log(d*x + c - 1)/(d^2*e^3))*arctanh(d*x + c))*a*b^2 - 1/16*b^3*(((d^2*x^2 + 2*c*d*x + c^2 - 1)*log(-d*x - c + 1)^3 + 3*(2*d*x - (d^2*x^2 + 2*c*d*x + c^2 - 1)*log(d*x + c + 1) + 2*c)*log(-d*x - c + 1)^2)/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3) + 2*integrate(-((d*x + c - 1)*log(d*x + c + 1)^3 + 3*(2*d^2*x^2 + 4*c*d*x - (d*x + c - 1)*log(d*x + c + 1)^2 + 2*c^2 - (d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d - d)*x - c)*log(d*x + c + 1))*log(-d*x - c + 1))/(d^4*e^3*x^4 + c^4*e^3 - c^3*e^3 + (4*c*d^3*e^3 - d^3*e^3)*x^3 + 3*(2*c^2*d^2*e^3 - c*d^2*e^3)*x^2 + (4*c^3*d*e^3 - 3*c^2*d*e^3)*x), x)) - 3/2*a*b^2*arctanh(d*x + c)^2/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3) - 1/2*a^3/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)","F",0
28,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))^3/(d*e*x+c*e)^4,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(d {\left(\frac{1}{d^{4} e^{4} x^{2} + 2 \, c d^{3} e^{4} x + c^{2} d^{2} e^{4}} + \frac{\log\left(d x + c + 1\right)}{d^{2} e^{4}} - \frac{2 \, \log\left(d x + c\right)}{d^{2} e^{4}} + \frac{\log\left(d x + c - 1\right)}{d^{2} e^{4}}\right)} + \frac{2 \, \operatorname{artanh}\left(d x + c\right)}{d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}}\right)} a^{2} b - \frac{a^{3}}{3 \, {\left(d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}\right)}} - \frac{{\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + {\left(c^{3} - 1\right)} b^{3}\right)} \log\left(-d x - c + 1\right)^{3} + 3 \, {\left(b^{3} d x + b^{3} c + 2 \, a b^{2} + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + {\left(c^{3} + 1\right)} b^{3}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)^{2}}{24 \, {\left(d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}\right)}} - \int -\frac{{\left(b^{3} d x + b^{3} {\left(c - 1\right)}\right)} \log\left(d x + c + 1\right)^{3} + 6 \, {\left(a b^{2} d x + a b^{2} {\left(c - 1\right)}\right)} \log\left(d x + c + 1\right)^{2} + {\left(2 \, b^{3} d^{2} x^{2} + 2 \, b^{3} c^{2} + 4 \, a b^{2} c - 3 \, {\left(b^{3} d x + b^{3} {\left(c - 1\right)}\right)} \log\left(d x + c + 1\right)^{2} + 4 \, {\left(b^{3} c d + a b^{2} d\right)} x + 2 \, {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + {\left(c^{4} + c\right)} b^{3} - 6 \, a b^{2} {\left(c - 1\right)} + {\left({\left(4 \, c^{3} d + d\right)} b^{3} - 6 \, a b^{2} d\right)} x\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{8 \, {\left(d^{5} e^{4} x^{5} + c^{5} e^{4} - c^{4} e^{4} + {\left(5 \, c d^{4} e^{4} - d^{4} e^{4}\right)} x^{4} + 2 \, {\left(5 \, c^{2} d^{3} e^{4} - 2 \, c d^{3} e^{4}\right)} x^{3} + 2 \, {\left(5 \, c^{3} d^{2} e^{4} - 3 \, c^{2} d^{2} e^{4}\right)} x^{2} + {\left(5 \, c^{4} d e^{4} - 4 \, c^{3} d e^{4}\right)} x\right)}}\,{d x}"," ",0,"-1/2*(d*(1/(d^4*e^4*x^2 + 2*c*d^3*e^4*x + c^2*d^2*e^4) + log(d*x + c + 1)/(d^2*e^4) - 2*log(d*x + c)/(d^2*e^4) + log(d*x + c - 1)/(d^2*e^4)) + 2*arctanh(d*x + c)/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4))*a^2*b - 1/3*a^3/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4) - 1/24*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + (c^3 - 1)*b^3)*log(-d*x - c + 1)^3 + 3*(b^3*d*x + b^3*c + 2*a*b^2 + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + (c^3 + 1)*b^3)*log(d*x + c + 1))*log(-d*x - c + 1)^2)/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4) - integrate(-1/8*((b^3*d*x + b^3*(c - 1))*log(d*x + c + 1)^3 + 6*(a*b^2*d*x + a*b^2*(c - 1))*log(d*x + c + 1)^2 + (2*b^3*d^2*x^2 + 2*b^3*c^2 + 4*a*b^2*c - 3*(b^3*d*x + b^3*(c - 1))*log(d*x + c + 1)^2 + 4*(b^3*c*d + a*b^2*d)*x + 2*(b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + (c^4 + c)*b^3 - 6*a*b^2*(c - 1) + ((4*c^3*d + d)*b^3 - 6*a*b^2*d)*x)*log(d*x + c + 1))*log(-d*x - c + 1))/(d^5*e^4*x^5 + c^5*e^4 - c^4*e^4 + (5*c*d^4*e^4 - d^4*e^4)*x^4 + 2*(5*c^2*d^3*e^4 - 2*c*d^3*e^4)*x^3 + 2*(5*c^3*d^2*e^4 - 3*c^2*d^2*e^4)*x^2 + (5*c^4*d*e^4 - 4*c^3*d*e^4)*x), x)","F",0
29,1,58,0,0.317311," ","integrate(arctanh(1+x)/(2+2*x),x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(\log\left(x + 2\right) - \log\left(x\right)\right)} \log\left(x + 1\right) + \frac{1}{2} \, \operatorname{artanh}\left(x + 1\right) \log\left(x + 1\right) - \frac{1}{4} \, \log\left(x + 1\right) \log\left(x\right) + \frac{1}{4} \, \log\left(x + 2\right) \log\left(-x - 1\right) - \frac{1}{4} \, {\rm Li}_2\left(-x\right) + \frac{1}{4} \, {\rm Li}_2\left(x + 2\right)"," ",0,"-1/4*(log(x + 2) - log(x))*log(x + 1) + 1/2*arctanh(x + 1)*log(x + 1) - 1/4*log(x + 1)*log(x) + 1/4*log(x + 2)*log(-x - 1) - 1/4*dilog(-x) + 1/4*dilog(x + 2)","B",0
30,1,132,0,0.337313," ","integrate(arctanh(b*x+a)/(a*d/b+d*x),x, algorithm=""maxima"")","-\frac{1}{2} \, b {\left(\frac{\log\left(b x + a\right) \log\left(b x + a - 1\right) + {\rm Li}_2\left(-b x - a + 1\right)}{b d} - \frac{\log\left(b x + a + 1\right) \log\left(-b x - a\right) + {\rm Li}_2\left(b x + a + 1\right)}{b d}\right)} - \frac{b {\left(\frac{\log\left(b x + a + 1\right)}{b} - \frac{\log\left(b x + a - 1\right)}{b}\right)} \log\left(d x + \frac{a d}{b}\right)}{2 \, d} + \frac{\operatorname{artanh}\left(b x + a\right) \log\left(d x + \frac{a d}{b}\right)}{d}"," ",0,"-1/2*b*((log(b*x + a)*log(b*x + a - 1) + dilog(-b*x - a + 1))/(b*d) - (log(b*x + a + 1)*log(-b*x - a) + dilog(b*x + a + 1))/(b*d)) - 1/2*b*(log(b*x + a + 1)/b - log(b*x + a - 1)/b)*log(d*x + a*d/b)/d + arctanh(b*x + a)*log(d*x + a*d/b)/d","B",0
31,1,333,0,0.363427," ","integrate((f*x+e)^3*(a+b*arctanh(d*x+c)),x, algorithm=""maxima"")","\frac{1}{4} \, a f^{3} x^{4} + a e f^{2} x^{3} + \frac{3}{2} \, a e^{2} f x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} b e^{2} f + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} + \frac{{\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{4}} - \frac{{\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(d x + c - 1\right)}{d^{4}}\right)}\right)} b e f^{2} + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, {\left(d^{2} x^{3} - 3 \, c d x^{2} + 3 \, {\left(3 \, c^{2} + 1\right)} x\right)}}{d^{4}} - \frac{3 \, {\left(c^{4} + 4 \, c^{3} + 6 \, c^{2} + 4 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{5}} + \frac{3 \, {\left(c^{4} - 4 \, c^{3} + 6 \, c^{2} - 4 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{5}}\right)}\right)} b f^{3} + a e^{3} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} b e^{3}}{2 \, d}"," ",0,"1/4*a*f^3*x^4 + a*e*f^2*x^3 + 3/2*a*e^2*f*x^2 + 3/4*(2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*b*e^2*f + 1/2*(2*x^3*arctanh(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 + (c^3 + 3*c^2 + 3*c + 1)*log(d*x + c + 1)/d^4 - (c^3 - 3*c^2 + 3*c - 1)*log(d*x + c - 1)/d^4))*b*e*f^2 + 1/24*(6*x^4*arctanh(d*x + c) + d*(2*(d^2*x^3 - 3*c*d*x^2 + 3*(3*c^2 + 1)*x)/d^4 - 3*(c^4 + 4*c^3 + 6*c^2 + 4*c + 1)*log(d*x + c + 1)/d^5 + 3*(c^4 - 4*c^3 + 6*c^2 - 4*c + 1)*log(d*x + c - 1)/d^5))*b*f^3 + a*e^3*x + 1/2*(2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*b*e^3/d","B",0
32,1,207,0,0.318700," ","integrate((f*x+e)^2*(a+b*arctanh(d*x+c)),x, algorithm=""maxima"")","\frac{1}{3} \, a f^{2} x^{3} + a e f x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} b e f + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} + \frac{{\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{4}} - \frac{{\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(d x + c - 1\right)}{d^{4}}\right)}\right)} b f^{2} + a e^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} b e^{2}}{2 \, d}"," ",0,"1/3*a*f^2*x^3 + a*e*f*x^2 + 1/2*(2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*b*e*f + 1/6*(2*x^3*arctanh(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 + (c^3 + 3*c^2 + 3*c + 1)*log(d*x + c + 1)/d^4 - (c^3 - 3*c^2 + 3*c - 1)*log(d*x + c - 1)/d^4))*b*f^2 + a*e^2*x + 1/2*(2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*b*e^2/d","A",0
33,1,109,0,0.324129," ","integrate((f*x+e)*(a+b*arctanh(d*x+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a f x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} b f + a e x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} b e}{2 \, d}"," ",0,"1/2*a*f*x^2 + 1/4*(2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*b*f + a*e*x + 1/2*(2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*b*e/d","A",0
34,1,36,0,0.318477," ","integrate(a+b*arctanh(d*x+c),x, algorithm=""maxima"")","a x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} b}{2 \, d}"," ",0,"a*x + 1/2*(2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*b/d","A",0
35,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))/(f*x+e),x, algorithm=""maxima"")","\frac{1}{2} \, b \int \frac{\log\left(d x + c + 1\right) - \log\left(-d x - c + 1\right)}{f x + e}\,{d x} + \frac{a \log\left(f x + e\right)}{f}"," ",0,"1/2*b*integrate((log(d*x + c + 1) - log(-d*x - c + 1))/(f*x + e), x) + a*log(f*x + e)/f","F",0
36,1,121,0,0.321514," ","integrate((a+b*arctanh(d*x+c))/(f*x+e)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(d {\left(\frac{\log\left(d x + c + 1\right)}{d e f - {\left(c + 1\right)} f^{2}} - \frac{\log\left(d x + c - 1\right)}{d e f - {\left(c - 1\right)} f^{2}} - \frac{2 \, \log\left(f x + e\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} - 1\right)} f^{2}}\right)} - \frac{2 \, \operatorname{artanh}\left(d x + c\right)}{f^{2} x + e f}\right)} b - \frac{a}{f^{2} x + e f}"," ",0,"1/2*(d*(log(d*x + c + 1)/(d*e*f - (c + 1)*f^2) - log(d*x + c - 1)/(d*e*f - (c - 1)*f^2) - 2*log(f*x + e)/(d^2*e^2 - 2*c*d*e*f + (c^2 - 1)*f^2)) - 2*arctanh(d*x + c)/(f^2*x + e*f))*b - a/(f^2*x + e*f)","A",0
37,1,291,0,0.336315," ","integrate((a+b*arctanh(d*x+c))/(f*x+e)^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(d {\left(\frac{d \log\left(d x + c + 1\right)}{d^{2} e^{2} f - 2 \, {\left(c + 1\right)} d e f^{2} + {\left(c^{2} + 2 \, c + 1\right)} f^{3}} - \frac{d \log\left(d x + c - 1\right)}{d^{2} e^{2} f - 2 \, {\left(c - 1\right)} d e f^{2} + {\left(c^{2} - 2 \, c + 1\right)} f^{3}} - \frac{4 \, {\left(d^{2} e - c d f\right)} \log\left(f x + e\right)}{d^{4} e^{4} - 4 \, c d^{3} e^{3} f + 2 \, {\left(3 \, c^{2} - 1\right)} d^{2} e^{2} f^{2} - 4 \, {\left(c^{3} - c\right)} d e f^{3} + {\left(c^{4} - 2 \, c^{2} + 1\right)} f^{4}} + \frac{2}{d^{2} e^{3} - 2 \, c d e^{2} f + {\left(c^{2} - 1\right)} e f^{2} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} - 1\right)} f^{3}\right)} x}\right)} - \frac{2 \, \operatorname{artanh}\left(d x + c\right)}{f^{3} x^{2} + 2 \, e f^{2} x + e^{2} f}\right)} b - \frac{a}{2 \, {\left(f^{3} x^{2} + 2 \, e f^{2} x + e^{2} f\right)}}"," ",0,"1/4*(d*(d*log(d*x + c + 1)/(d^2*e^2*f - 2*(c + 1)*d*e*f^2 + (c^2 + 2*c + 1)*f^3) - d*log(d*x + c - 1)/(d^2*e^2*f - 2*(c - 1)*d*e*f^2 + (c^2 - 2*c + 1)*f^3) - 4*(d^2*e - c*d*f)*log(f*x + e)/(d^4*e^4 - 4*c*d^3*e^3*f + 2*(3*c^2 - 1)*d^2*e^2*f^2 - 4*(c^3 - c)*d*e*f^3 + (c^4 - 2*c^2 + 1)*f^4) + 2/(d^2*e^3 - 2*c*d*e^2*f + (c^2 - 1)*e*f^2 + (d^2*e^2*f - 2*c*d*e*f^2 + (c^2 - 1)*f^3)*x)) - 2*arctanh(d*x + c)/(f^3*x^2 + 2*e*f^2*x + e^2*f))*b - 1/2*a/(f^3*x^2 + 2*e*f^2*x + e^2*f)","A",0
38,1,1363,0,0.647183," ","integrate((f*x+e)^3*(a+b*arctanh(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} f^{3} x^{4} + a^{2} e f^{2} x^{3} + \frac{3}{2} \, a^{2} e^{2} f x^{2} + \frac{3}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} a b e^{2} f + {\left(2 \, x^{3} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} + \frac{{\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{4}} - \frac{{\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(d x + c - 1\right)}{d^{4}}\right)}\right)} a b e f^{2} + \frac{1}{12} \, {\left(6 \, x^{4} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, {\left(d^{2} x^{3} - 3 \, c d x^{2} + 3 \, {\left(3 \, c^{2} + 1\right)} x\right)}}{d^{4}} - \frac{3 \, {\left(c^{4} + 4 \, c^{3} + 6 \, c^{2} + 4 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{5}} + \frac{3 \, {\left(c^{4} - 4 \, c^{3} + 6 \, c^{2} - 4 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{5}}\right)}\right)} a b f^{3} + a^{2} e^{3} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a b e^{3}}{d} + \frac{{\left(d^{3} e^{3} + 3 \, c^{2} d e f^{2} - c^{3} f^{3} + d e f^{2} - {\left(3 \, d^{2} e^{2} f + f^{3}\right)} c\right)} {\left(\log\left(d x + c + 1\right) \log\left(-\frac{1}{2} \, d x - \frac{1}{2} \, c + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, d x + \frac{1}{2} \, c + \frac{1}{2}\right)\right)} b^{2}}{d^{4}} + \frac{{\left(13 \, c^{3} f^{3} + 18 \, d^{2} e^{2} f - 6 \, d e f^{2} - 6 \, {\left(5 \, d e f^{2} - 3 \, f^{3}\right)} c^{2} + 4 \, f^{3} + 9 \, {\left(2 \, d^{2} e^{2} f - 4 \, d e f^{2} + f^{3}\right)} c\right)} b^{2} \log\left(d x + c + 1\right)}{12 \, d^{4}} - \frac{{\left(13 \, c^{3} f^{3} - 18 \, d^{2} e^{2} f - 6 \, d e f^{2} - 6 \, {\left(5 \, d e f^{2} + 3 \, f^{3}\right)} c^{2} - 4 \, f^{3} + 9 \, {\left(2 \, d^{2} e^{2} f + 4 \, d e f^{2} + f^{3}\right)} c\right)} b^{2} \log\left(d x + c - 1\right)}{12 \, d^{4}} + \frac{4 \, b^{2} d^{2} f^{3} x^{2} + 8 \, {\left(6 \, d^{2} e f^{2} - 5 \, c d f^{3}\right)} b^{2} x + 3 \, {\left(b^{2} d^{4} f^{3} x^{4} + 4 \, b^{2} d^{4} e f^{2} x^{3} + 6 \, b^{2} d^{4} e^{2} f x^{2} + 4 \, b^{2} d^{4} e^{3} x - {\left(c^{4} f^{3} - 4 \, d^{3} e^{3} + 6 \, d^{2} e^{2} f - 4 \, {\left(d e f^{2} - f^{3}\right)} c^{3} - 4 \, d e f^{2} + 6 \, {\left(d^{2} e^{2} f - 2 \, d e f^{2} + f^{3}\right)} c^{2} + f^{3} - 4 \, {\left(d^{3} e^{3} - 3 \, d^{2} e^{2} f + 3 \, d e f^{2} - f^{3}\right)} c\right)} b^{2}\right)} \log\left(d x + c + 1\right)^{2} + 3 \, {\left(b^{2} d^{4} f^{3} x^{4} + 4 \, b^{2} d^{4} e f^{2} x^{3} + 6 \, b^{2} d^{4} e^{2} f x^{2} + 4 \, b^{2} d^{4} e^{3} x - {\left(c^{4} f^{3} + 4 \, d^{3} e^{3} + 6 \, d^{2} e^{2} f - 4 \, {\left(d e f^{2} + f^{3}\right)} c^{3} + 4 \, d e f^{2} + 6 \, {\left(d^{2} e^{2} f + 2 \, d e f^{2} + f^{3}\right)} c^{2} + f^{3} - 4 \, {\left(d^{3} e^{3} + 3 \, d^{2} e^{2} f + 3 \, d e f^{2} + f^{3}\right)} c\right)} b^{2}\right)} \log\left(-d x - c + 1\right)^{2} + 4 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, {\left(2 \, d^{3} e f^{2} - c d^{2} f^{3}\right)} b^{2} x^{2} + 3 \, {\left(6 \, d^{3} e^{2} f - 8 \, c d^{2} e f^{2} + 3 \, c^{2} d f^{3} + d f^{3}\right)} b^{2} x\right)} \log\left(d x + c + 1\right) - 2 \, {\left(2 \, b^{2} d^{3} f^{3} x^{3} + 6 \, {\left(2 \, d^{3} e f^{2} - c d^{2} f^{3}\right)} b^{2} x^{2} + 6 \, {\left(6 \, d^{3} e^{2} f - 8 \, c d^{2} e f^{2} + 3 \, c^{2} d f^{3} + d f^{3}\right)} b^{2} x + 3 \, {\left(b^{2} d^{4} f^{3} x^{4} + 4 \, b^{2} d^{4} e f^{2} x^{3} + 6 \, b^{2} d^{4} e^{2} f x^{2} + 4 \, b^{2} d^{4} e^{3} x - {\left(c^{4} f^{3} - 4 \, d^{3} e^{3} + 6 \, d^{2} e^{2} f - 4 \, {\left(d e f^{2} - f^{3}\right)} c^{3} - 4 \, d e f^{2} + 6 \, {\left(d^{2} e^{2} f - 2 \, d e f^{2} + f^{3}\right)} c^{2} + f^{3} - 4 \, {\left(d^{3} e^{3} - 3 \, d^{2} e^{2} f + 3 \, d e f^{2} - f^{3}\right)} c\right)} b^{2}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{48 \, d^{4}}"," ",0,"1/4*a^2*f^3*x^4 + a^2*e*f^2*x^3 + 3/2*a^2*e^2*f*x^2 + 3/2*(2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*a*b*e^2*f + (2*x^3*arctanh(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 + (c^3 + 3*c^2 + 3*c + 1)*log(d*x + c + 1)/d^4 - (c^3 - 3*c^2 + 3*c - 1)*log(d*x + c - 1)/d^4))*a*b*e*f^2 + 1/12*(6*x^4*arctanh(d*x + c) + d*(2*(d^2*x^3 - 3*c*d*x^2 + 3*(3*c^2 + 1)*x)/d^4 - 3*(c^4 + 4*c^3 + 6*c^2 + 4*c + 1)*log(d*x + c + 1)/d^5 + 3*(c^4 - 4*c^3 + 6*c^2 - 4*c + 1)*log(d*x + c - 1)/d^5))*a*b*f^3 + a^2*e^3*x + (2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*a*b*e^3/d + (d^3*e^3 + 3*c^2*d*e*f^2 - c^3*f^3 + d*e*f^2 - (3*d^2*e^2*f + f^3)*c)*(log(d*x + c + 1)*log(-1/2*d*x - 1/2*c + 1/2) + dilog(1/2*d*x + 1/2*c + 1/2))*b^2/d^4 + 1/12*(13*c^3*f^3 + 18*d^2*e^2*f - 6*d*e*f^2 - 6*(5*d*e*f^2 - 3*f^3)*c^2 + 4*f^3 + 9*(2*d^2*e^2*f - 4*d*e*f^2 + f^3)*c)*b^2*log(d*x + c + 1)/d^4 - 1/12*(13*c^3*f^3 - 18*d^2*e^2*f - 6*d*e*f^2 - 6*(5*d*e*f^2 + 3*f^3)*c^2 - 4*f^3 + 9*(2*d^2*e^2*f + 4*d*e*f^2 + f^3)*c)*b^2*log(d*x + c - 1)/d^4 + 1/48*(4*b^2*d^2*f^3*x^2 + 8*(6*d^2*e*f^2 - 5*c*d*f^3)*b^2*x + 3*(b^2*d^4*f^3*x^4 + 4*b^2*d^4*e*f^2*x^3 + 6*b^2*d^4*e^2*f*x^2 + 4*b^2*d^4*e^3*x - (c^4*f^3 - 4*d^3*e^3 + 6*d^2*e^2*f - 4*(d*e*f^2 - f^3)*c^3 - 4*d*e*f^2 + 6*(d^2*e^2*f - 2*d*e*f^2 + f^3)*c^2 + f^3 - 4*(d^3*e^3 - 3*d^2*e^2*f + 3*d*e*f^2 - f^3)*c)*b^2)*log(d*x + c + 1)^2 + 3*(b^2*d^4*f^3*x^4 + 4*b^2*d^4*e*f^2*x^3 + 6*b^2*d^4*e^2*f*x^2 + 4*b^2*d^4*e^3*x - (c^4*f^3 + 4*d^3*e^3 + 6*d^2*e^2*f - 4*(d*e*f^2 + f^3)*c^3 + 4*d*e*f^2 + 6*(d^2*e^2*f + 2*d*e*f^2 + f^3)*c^2 + f^3 - 4*(d^3*e^3 + 3*d^2*e^2*f + 3*d*e*f^2 + f^3)*c)*b^2)*log(-d*x - c + 1)^2 + 4*(b^2*d^3*f^3*x^3 + 3*(2*d^3*e*f^2 - c*d^2*f^3)*b^2*x^2 + 3*(6*d^3*e^2*f - 8*c*d^2*e*f^2 + 3*c^2*d*f^3 + d*f^3)*b^2*x)*log(d*x + c + 1) - 2*(2*b^2*d^3*f^3*x^3 + 6*(2*d^3*e*f^2 - c*d^2*f^3)*b^2*x^2 + 6*(6*d^3*e^2*f - 8*c*d^2*e*f^2 + 3*c^2*d*f^3 + d*f^3)*b^2*x + 3*(b^2*d^4*f^3*x^4 + 4*b^2*d^4*e*f^2*x^3 + 6*b^2*d^4*e^2*f*x^2 + 4*b^2*d^4*e^3*x - (c^4*f^3 - 4*d^3*e^3 + 6*d^2*e^2*f - 4*(d*e*f^2 - f^3)*c^3 - 4*d*e*f^2 + 6*(d^2*e^2*f - 2*d*e*f^2 + f^3)*c^2 + f^3 - 4*(d^3*e^3 - 3*d^2*e^2*f + 3*d*e*f^2 - f^3)*c)*b^2)*log(d*x + c + 1))*log(-d*x - c + 1))/d^4","B",0
39,1,806,0,0.623566," ","integrate((f*x+e)^2*(a+b*arctanh(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} f^{2} x^{3} + a^{2} e f x^{2} + {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} a b e f + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} + \frac{{\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{4}} - \frac{{\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(d x + c - 1\right)}{d^{4}}\right)}\right)} a b f^{2} + a^{2} e^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a b e^{2}}{d} + \frac{{\left(3 \, d^{2} e^{2} - 6 \, c d e f + 3 \, c^{2} f^{2} + f^{2}\right)} {\left(\log\left(d x + c + 1\right) \log\left(-\frac{1}{2} \, d x - \frac{1}{2} \, c + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, d x + \frac{1}{2} \, c + \frac{1}{2}\right)\right)} b^{2}}{3 \, d^{3}} - \frac{{\left(5 \, c^{2} f^{2} - 6 \, d e f - 6 \, {\left(d e f - f^{2}\right)} c + f^{2}\right)} b^{2} \log\left(d x + c + 1\right)}{6 \, d^{3}} + \frac{{\left(5 \, c^{2} f^{2} + 6 \, d e f - 6 \, {\left(d e f + f^{2}\right)} c + f^{2}\right)} b^{2} \log\left(d x + c - 1\right)}{6 \, d^{3}} + \frac{4 \, b^{2} d f^{2} x + {\left(b^{2} d^{3} f^{2} x^{3} + 3 \, b^{2} d^{3} e f x^{2} + 3 \, b^{2} d^{3} e^{2} x + {\left(c^{3} f^{2} + 3 \, d^{2} e^{2} - 3 \, {\left(d e f - f^{2}\right)} c^{2} - 3 \, d e f + 3 \, {\left(d^{2} e^{2} - 2 \, d e f + f^{2}\right)} c + f^{2}\right)} b^{2}\right)} \log\left(d x + c + 1\right)^{2} + {\left(b^{2} d^{3} f^{2} x^{3} + 3 \, b^{2} d^{3} e f x^{2} + 3 \, b^{2} d^{3} e^{2} x + {\left(c^{3} f^{2} - 3 \, d^{2} e^{2} - 3 \, {\left(d e f + f^{2}\right)} c^{2} - 3 \, d e f + 3 \, {\left(d^{2} e^{2} + 2 \, d e f + f^{2}\right)} c - f^{2}\right)} b^{2}\right)} \log\left(-d x - c + 1\right)^{2} + 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, c d f^{2}\right)} b^{2} x\right)} \log\left(d x + c + 1\right) - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, c d f^{2}\right)} b^{2} x + {\left(b^{2} d^{3} f^{2} x^{3} + 3 \, b^{2} d^{3} e f x^{2} + 3 \, b^{2} d^{3} e^{2} x + {\left(c^{3} f^{2} + 3 \, d^{2} e^{2} - 3 \, {\left(d e f - f^{2}\right)} c^{2} - 3 \, d e f + 3 \, {\left(d^{2} e^{2} - 2 \, d e f + f^{2}\right)} c + f^{2}\right)} b^{2}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{12 \, d^{3}}"," ",0,"1/3*a^2*f^2*x^3 + a^2*e*f*x^2 + (2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*a*b*e*f + 1/3*(2*x^3*arctanh(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 + (c^3 + 3*c^2 + 3*c + 1)*log(d*x + c + 1)/d^4 - (c^3 - 3*c^2 + 3*c - 1)*log(d*x + c - 1)/d^4))*a*b*f^2 + a^2*e^2*x + (2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*a*b*e^2/d + 1/3*(3*d^2*e^2 - 6*c*d*e*f + 3*c^2*f^2 + f^2)*(log(d*x + c + 1)*log(-1/2*d*x - 1/2*c + 1/2) + dilog(1/2*d*x + 1/2*c + 1/2))*b^2/d^3 - 1/6*(5*c^2*f^2 - 6*d*e*f - 6*(d*e*f - f^2)*c + f^2)*b^2*log(d*x + c + 1)/d^3 + 1/6*(5*c^2*f^2 + 6*d*e*f - 6*(d*e*f + f^2)*c + f^2)*b^2*log(d*x + c - 1)/d^3 + 1/12*(4*b^2*d*f^2*x + (b^2*d^3*f^2*x^3 + 3*b^2*d^3*e*f*x^2 + 3*b^2*d^3*e^2*x + (c^3*f^2 + 3*d^2*e^2 - 3*(d*e*f - f^2)*c^2 - 3*d*e*f + 3*(d^2*e^2 - 2*d*e*f + f^2)*c + f^2)*b^2)*log(d*x + c + 1)^2 + (b^2*d^3*f^2*x^3 + 3*b^2*d^3*e*f*x^2 + 3*b^2*d^3*e^2*x + (c^3*f^2 - 3*d^2*e^2 - 3*(d*e*f + f^2)*c^2 - 3*d*e*f + 3*(d^2*e^2 + 2*d*e*f + f^2)*c - f^2)*b^2)*log(-d*x - c + 1)^2 + 2*(b^2*d^2*f^2*x^2 + 2*(3*d^2*e*f - 2*c*d*f^2)*b^2*x)*log(d*x + c + 1) - 2*(b^2*d^2*f^2*x^2 + 2*(3*d^2*e*f - 2*c*d*f^2)*b^2*x + (b^2*d^3*f^2*x^3 + 3*b^2*d^3*e*f*x^2 + 3*b^2*d^3*e^2*x + (c^3*f^2 + 3*d^2*e^2 - 3*(d*e*f - f^2)*c^2 - 3*d*e*f + 3*(d^2*e^2 - 2*d*e*f + f^2)*c + f^2)*b^2)*log(d*x + c + 1))*log(-d*x - c + 1))/d^3","B",0
40,1,415,0,0.616505," ","integrate((f*x+e)*(a+b*arctanh(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} f x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} a b f + a^{2} e x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a b e}{d} + \frac{{\left(d e - c f\right)} {\left(\log\left(d x + c + 1\right) \log\left(-\frac{1}{2} \, d x - \frac{1}{2} \, c + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, d x + \frac{1}{2} \, c + \frac{1}{2}\right)\right)} b^{2}}{d^{2}} + \frac{{\left(c f + f\right)} b^{2} \log\left(d x + c + 1\right)}{2 \, d^{2}} - \frac{{\left(c f - f\right)} b^{2} \log\left(d x + c - 1\right)}{2 \, d^{2}} + \frac{4 \, b^{2} d f x \log\left(d x + c + 1\right) + {\left(b^{2} d^{2} f x^{2} + 2 \, b^{2} d^{2} e x - {\left(c^{2} f - 2 \, {\left(d e - f\right)} c - 2 \, d e + f\right)} b^{2}\right)} \log\left(d x + c + 1\right)^{2} + {\left(b^{2} d^{2} f x^{2} + 2 \, b^{2} d^{2} e x - {\left(c^{2} f - 2 \, {\left(d e + f\right)} c + 2 \, d e + f\right)} b^{2}\right)} \log\left(-d x - c + 1\right)^{2} - 2 \, {\left(2 \, b^{2} d f x + {\left(b^{2} d^{2} f x^{2} + 2 \, b^{2} d^{2} e x - {\left(c^{2} f - 2 \, {\left(d e - f\right)} c - 2 \, d e + f\right)} b^{2}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{8 \, d^{2}}"," ",0,"1/2*a^2*f*x^2 + 1/2*(2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*a*b*f + a^2*e*x + (2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*a*b*e/d + (d*e - c*f)*(log(d*x + c + 1)*log(-1/2*d*x - 1/2*c + 1/2) + dilog(1/2*d*x + 1/2*c + 1/2))*b^2/d^2 + 1/2*(c*f + f)*b^2*log(d*x + c + 1)/d^2 - 1/2*(c*f - f)*b^2*log(d*x + c - 1)/d^2 + 1/8*(4*b^2*d*f*x*log(d*x + c + 1) + (b^2*d^2*f*x^2 + 2*b^2*d^2*e*x - (c^2*f - 2*(d*e - f)*c - 2*d*e + f)*b^2)*log(d*x + c + 1)^2 + (b^2*d^2*f*x^2 + 2*b^2*d^2*e*x - (c^2*f - 2*(d*e + f)*c + 2*d*e + f)*b^2)*log(-d*x - c + 1)^2 - 2*(2*b^2*d*f*x + (b^2*d^2*f*x^2 + 2*b^2*d^2*e*x - (c^2*f - 2*(d*e - f)*c - 2*d*e + f)*b^2)*log(d*x + c + 1))*log(-d*x - c + 1))/d^2","B",0
41,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(c d {\left(\frac{{\left(c + 1\right)} \log\left(d x + c + 1\right)}{d^{2}} - \frac{{\left(c - 1\right)} \log\left(d x + c - 1\right)}{d^{2}}\right)} + d^{2} {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)} - 2 \, c d \int \frac{x \log\left(d x + c + 1\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} - 2 \, c^{2} \int \frac{\log\left(d x + c + 1\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + d {\left(\frac{{\left(c + 1\right)} \log\left(d x + c + 1\right)}{d^{2}} - \frac{{\left(c - 1\right)} \log\left(d x + c - 1\right)}{d^{2}}\right)} - 6 \, d \int \frac{x \log\left(d x + c + 1\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} - 4 \, c \int \frac{\log\left(d x + c + 1\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} - \frac{{\left(d x + c - 1\right)} {\left(\log\left(-d x - c + 1\right)^{2} - 2 \, \log\left(-d x - c + 1\right) + 2\right)}}{d} - \frac{d x \log\left(d x + c + 1\right)^{2} + 2 \, {\left(d x - {\left(d x + c + 1\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{d} - 2 \, \int \frac{\log\left(d x + c + 1\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x}\right)} b^{2} + a^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a b}{d}"," ",0,"-1/4*(c*d*((c + 1)*log(d*x + c + 1)/d^2 - (c - 1)*log(d*x + c - 1)/d^2) + d^2*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3) - 2*c*d*integrate(x*log(d*x + c + 1)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 2*c^2*integrate(log(d*x + c + 1)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + d*((c + 1)*log(d*x + c + 1)/d^2 - (c - 1)*log(d*x + c - 1)/d^2) - 6*d*integrate(x*log(d*x + c + 1)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 4*c*integrate(log(d*x + c + 1)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - (d*x + c - 1)*(log(-d*x - c + 1)^2 - 2*log(-d*x - c + 1) + 2)/d - (d*x*log(d*x + c + 1)^2 + 2*(d*x - (d*x + c + 1)*log(d*x + c + 1))*log(-d*x - c + 1))/d - 2*integrate(log(d*x + c + 1)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x))*b^2 + a^2*x + (2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*a*b/d","F",0
42,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))^2/(f*x+e),x, algorithm=""maxima"")","\frac{a^{2} \log\left(f x + e\right)}{f} + \int \frac{b^{2} {\left(\log\left(d x + c + 1\right) - \log\left(-d x - c + 1\right)\right)}^{2}}{4 \, {\left(f x + e\right)}} + \frac{a b {\left(\log\left(d x + c + 1\right) - \log\left(-d x - c + 1\right)\right)}}{f x + e}\,{d x}"," ",0,"a^2*log(f*x + e)/f + integrate(1/4*b^2*(log(d*x + c + 1) - log(-d*x - c + 1))^2/(f*x + e) + a*b*(log(d*x + c + 1) - log(-d*x - c + 1))/(f*x + e), x)","F",0
43,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))^2/(f*x+e)^2,x, algorithm=""maxima"")","{\left(d {\left(\frac{\log\left(d x + c + 1\right)}{d e f - {\left(c + 1\right)} f^{2}} - \frac{\log\left(d x + c - 1\right)}{d e f - {\left(c - 1\right)} f^{2}} - \frac{2 \, \log\left(f x + e\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} - 1\right)} f^{2}}\right)} - \frac{2 \, \operatorname{artanh}\left(d x + c\right)}{f^{2} x + e f}\right)} a b - \frac{1}{4} \, b^{2} {\left(\frac{\log\left(-d x - c + 1\right)^{2}}{f^{2} x + e f} + \int -\frac{{\left(d f x + c f - f\right)} \log\left(d x + c + 1\right)^{2} + 2 \, {\left(d f x + d e - {\left(d f x + c f - f\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{d f^{3} x^{3} + c e^{2} f - e^{2} f + {\left(2 \, d e f^{2} + c f^{3} - f^{3}\right)} x^{2} + {\left(d e^{2} f + 2 \, c e f^{2} - 2 \, e f^{2}\right)} x}\,{d x}\right)} - \frac{a^{2}}{f^{2} x + e f}"," ",0,"(d*(log(d*x + c + 1)/(d*e*f - (c + 1)*f^2) - log(d*x + c - 1)/(d*e*f - (c - 1)*f^2) - 2*log(f*x + e)/(d^2*e^2 - 2*c*d*e*f + (c^2 - 1)*f^2)) - 2*arctanh(d*x + c)/(f^2*x + e*f))*a*b - 1/4*b^2*(log(-d*x - c + 1)^2/(f^2*x + e*f) + integrate(-((d*f*x + c*f - f)*log(d*x + c + 1)^2 + 2*(d*f*x + d*e - (d*f*x + c*f - f)*log(d*x + c + 1))*log(-d*x - c + 1))/(d*f^3*x^3 + c*e^2*f - e^2*f + (2*d*e*f^2 + c*f^3 - f^3)*x^2 + (d*e^2*f + 2*c*e*f^2 - 2*e*f^2)*x), x)) - a^2/(f^2*x + e*f)","F",0
44,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))^2/(f*x+e)^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(d {\left(\frac{d \log\left(d x + c + 1\right)}{d^{2} e^{2} f - 2 \, {\left(c + 1\right)} d e f^{2} + {\left(c^{2} + 2 \, c + 1\right)} f^{3}} - \frac{d \log\left(d x + c - 1\right)}{d^{2} e^{2} f - 2 \, {\left(c - 1\right)} d e f^{2} + {\left(c^{2} - 2 \, c + 1\right)} f^{3}} - \frac{4 \, {\left(d^{2} e - c d f\right)} \log\left(f x + e\right)}{d^{4} e^{4} - 4 \, c d^{3} e^{3} f + 2 \, {\left(3 \, c^{2} - 1\right)} d^{2} e^{2} f^{2} - 4 \, {\left(c^{3} - c\right)} d e f^{3} + {\left(c^{4} - 2 \, c^{2} + 1\right)} f^{4}} + \frac{2}{d^{2} e^{3} - 2 \, c d e^{2} f + {\left(c^{2} - 1\right)} e f^{2} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} - 1\right)} f^{3}\right)} x}\right)} - \frac{2 \, \operatorname{artanh}\left(d x + c\right)}{f^{3} x^{2} + 2 \, e f^{2} x + e^{2} f}\right)} a b - \frac{1}{8} \, b^{2} {\left(\frac{\log\left(-d x - c + 1\right)^{2}}{f^{3} x^{2} + 2 \, e f^{2} x + e^{2} f} + 2 \, \int -\frac{{\left(d f x + c f - f\right)} \log\left(d x + c + 1\right)^{2} + {\left(d f x + d e - 2 \, {\left(d f x + c f - f\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{d f^{4} x^{4} + c e^{3} f - e^{3} f + {\left(3 \, d e f^{3} + c f^{4} - f^{4}\right)} x^{3} + 3 \, {\left(d e^{2} f^{2} + c e f^{3} - e f^{3}\right)} x^{2} + {\left(d e^{3} f + 3 \, c e^{2} f^{2} - 3 \, e^{2} f^{2}\right)} x}\,{d x}\right)} - \frac{a^{2}}{2 \, {\left(f^{3} x^{2} + 2 \, e f^{2} x + e^{2} f\right)}}"," ",0,"1/2*(d*(d*log(d*x + c + 1)/(d^2*e^2*f - 2*(c + 1)*d*e*f^2 + (c^2 + 2*c + 1)*f^3) - d*log(d*x + c - 1)/(d^2*e^2*f - 2*(c - 1)*d*e*f^2 + (c^2 - 2*c + 1)*f^3) - 4*(d^2*e - c*d*f)*log(f*x + e)/(d^4*e^4 - 4*c*d^3*e^3*f + 2*(3*c^2 - 1)*d^2*e^2*f^2 - 4*(c^3 - c)*d*e*f^3 + (c^4 - 2*c^2 + 1)*f^4) + 2/(d^2*e^3 - 2*c*d*e^2*f + (c^2 - 1)*e*f^2 + (d^2*e^2*f - 2*c*d*e*f^2 + (c^2 - 1)*f^3)*x)) - 2*arctanh(d*x + c)/(f^3*x^2 + 2*e*f^2*x + e^2*f))*a*b - 1/8*b^2*(log(-d*x - c + 1)^2/(f^3*x^2 + 2*e*f^2*x + e^2*f) + 2*integrate(-((d*f*x + c*f - f)*log(d*x + c + 1)^2 + (d*f*x + d*e - 2*(d*f*x + c*f - f)*log(d*x + c + 1))*log(-d*x - c + 1))/(d*f^4*x^4 + c*e^3*f - e^3*f + (3*d*e*f^3 + c*f^4 - f^4)*x^3 + 3*(d*e^2*f^2 + c*e*f^3 - e*f^3)*x^2 + (d*e^3*f + 3*c*e^2*f^2 - 3*e^2*f^2)*x), x)) - 1/2*a^2/(f^3*x^2 + 2*e*f^2*x + e^2*f)","F",0
45,0,0,0,0.000000," ","integrate((f*x+e)^2*(a+b*arctanh(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} f^{2} x^{3} + a^{3} e f x^{2} + \frac{3}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} a^{2} b e f + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} + \frac{{\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{4}} - \frac{{\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(d x + c - 1\right)}{d^{4}}\right)}\right)} a^{2} b f^{2} + a^{3} e^{2} x + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b e^{2}}{2 \, d} - \frac{{\left(b^{3} d^{3} f^{2} x^{3} + 3 \, b^{3} d^{3} e f x^{2} + 3 \, b^{3} d^{3} e^{2} x + {\left(c^{3} f^{2} - 3 \, d^{2} e^{2} - 3 \, {\left(d e f + f^{2}\right)} c^{2} - 3 \, d e f + 3 \, {\left(d^{2} e^{2} + 2 \, d e f + f^{2}\right)} c - f^{2}\right)} b^{3}\right)} \log\left(-d x - c + 1\right)^{3} - 3 \, {\left(2 \, a b^{2} d^{3} f^{2} x^{3} + {\left(6 \, a b^{2} d^{3} e f + b^{3} d^{2} f^{2}\right)} x^{2} + 2 \, {\left(3 \, a b^{2} d^{3} e^{2} + {\left(3 \, d^{2} e f - 2 \, c d f^{2}\right)} b^{3}\right)} x + {\left(b^{3} d^{3} f^{2} x^{3} + 3 \, b^{3} d^{3} e f x^{2} + 3 \, b^{3} d^{3} e^{2} x + {\left(c^{3} f^{2} + 3 \, d^{2} e^{2} - 3 \, {\left(d e f - f^{2}\right)} c^{2} - 3 \, d e f + 3 \, {\left(d^{2} e^{2} - 2 \, d e f + f^{2}\right)} c + f^{2}\right)} b^{3}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)^{2}}{24 \, d^{3}} - \int -\frac{{\left(b^{3} d^{3} f^{2} x^{3} + {\left(2 \, d^{3} e f + c d^{2} f^{2} - d^{2} f^{2}\right)} b^{3} x^{2} + {\left(d^{3} e^{2} + 2 \, c d^{2} e f - 2 \, d^{2} e f\right)} b^{3} x + {\left(c d^{2} e^{2} - d^{2} e^{2}\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{3} + 6 \, {\left(a b^{2} d^{3} f^{2} x^{3} + {\left(2 \, d^{3} e f + c d^{2} f^{2} - d^{2} f^{2}\right)} a b^{2} x^{2} + {\left(d^{3} e^{2} + 2 \, c d^{2} e f - 2 \, d^{2} e f\right)} a b^{2} x + {\left(c d^{2} e^{2} - d^{2} e^{2}\right)} a b^{2}\right)} \log\left(d x + c + 1\right)^{2} - {\left(4 \, a b^{2} d^{3} f^{2} x^{3} + 2 \, {\left(6 \, a b^{2} d^{3} e f + b^{3} d^{2} f^{2}\right)} x^{2} + 3 \, {\left(b^{3} d^{3} f^{2} x^{3} + {\left(2 \, d^{3} e f + c d^{2} f^{2} - d^{2} f^{2}\right)} b^{3} x^{2} + {\left(d^{3} e^{2} + 2 \, c d^{2} e f - 2 \, d^{2} e f\right)} b^{3} x + {\left(c d^{2} e^{2} - d^{2} e^{2}\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{2} + 4 \, {\left(3 \, a b^{2} d^{3} e^{2} + {\left(3 \, d^{2} e f - 2 \, c d f^{2}\right)} b^{3}\right)} x + 2 \, {\left(6 \, {\left(c d^{2} e^{2} - d^{2} e^{2}\right)} a b^{2} + {\left(c^{3} f^{2} + 3 \, d^{2} e^{2} - 3 \, {\left(d e f - f^{2}\right)} c^{2} - 3 \, d e f + 3 \, {\left(d^{2} e^{2} - 2 \, d e f + f^{2}\right)} c + f^{2}\right)} b^{3} + {\left(6 \, a b^{2} d^{3} f^{2} + b^{3} d^{3} f^{2}\right)} x^{3} + 3 \, {\left(b^{3} d^{3} e f + 2 \, {\left(2 \, d^{3} e f + c d^{2} f^{2} - d^{2} f^{2}\right)} a b^{2}\right)} x^{2} + 3 \, {\left(b^{3} d^{3} e^{2} + 2 \, {\left(d^{3} e^{2} + 2 \, c d^{2} e f - 2 \, d^{2} e f\right)} a b^{2}\right)} x\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{8 \, {\left(d^{3} x + c d^{2} - d^{2}\right)}}\,{d x}"," ",0,"1/3*a^3*f^2*x^3 + a^3*e*f*x^2 + 3/2*(2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*a^2*b*e*f + 1/2*(2*x^3*arctanh(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 + (c^3 + 3*c^2 + 3*c + 1)*log(d*x + c + 1)/d^4 - (c^3 - 3*c^2 + 3*c - 1)*log(d*x + c - 1)/d^4))*a^2*b*f^2 + a^3*e^2*x + 3/2*(2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*a^2*b*e^2/d - 1/24*((b^3*d^3*f^2*x^3 + 3*b^3*d^3*e*f*x^2 + 3*b^3*d^3*e^2*x + (c^3*f^2 - 3*d^2*e^2 - 3*(d*e*f + f^2)*c^2 - 3*d*e*f + 3*(d^2*e^2 + 2*d*e*f + f^2)*c - f^2)*b^3)*log(-d*x - c + 1)^3 - 3*(2*a*b^2*d^3*f^2*x^3 + (6*a*b^2*d^3*e*f + b^3*d^2*f^2)*x^2 + 2*(3*a*b^2*d^3*e^2 + (3*d^2*e*f - 2*c*d*f^2)*b^3)*x + (b^3*d^3*f^2*x^3 + 3*b^3*d^3*e*f*x^2 + 3*b^3*d^3*e^2*x + (c^3*f^2 + 3*d^2*e^2 - 3*(d*e*f - f^2)*c^2 - 3*d*e*f + 3*(d^2*e^2 - 2*d*e*f + f^2)*c + f^2)*b^3)*log(d*x + c + 1))*log(-d*x - c + 1)^2)/d^3 - integrate(-1/8*((b^3*d^3*f^2*x^3 + (2*d^3*e*f + c*d^2*f^2 - d^2*f^2)*b^3*x^2 + (d^3*e^2 + 2*c*d^2*e*f - 2*d^2*e*f)*b^3*x + (c*d^2*e^2 - d^2*e^2)*b^3)*log(d*x + c + 1)^3 + 6*(a*b^2*d^3*f^2*x^3 + (2*d^3*e*f + c*d^2*f^2 - d^2*f^2)*a*b^2*x^2 + (d^3*e^2 + 2*c*d^2*e*f - 2*d^2*e*f)*a*b^2*x + (c*d^2*e^2 - d^2*e^2)*a*b^2)*log(d*x + c + 1)^2 - (4*a*b^2*d^3*f^2*x^3 + 2*(6*a*b^2*d^3*e*f + b^3*d^2*f^2)*x^2 + 3*(b^3*d^3*f^2*x^3 + (2*d^3*e*f + c*d^2*f^2 - d^2*f^2)*b^3*x^2 + (d^3*e^2 + 2*c*d^2*e*f - 2*d^2*e*f)*b^3*x + (c*d^2*e^2 - d^2*e^2)*b^3)*log(d*x + c + 1)^2 + 4*(3*a*b^2*d^3*e^2 + (3*d^2*e*f - 2*c*d*f^2)*b^3)*x + 2*(6*(c*d^2*e^2 - d^2*e^2)*a*b^2 + (c^3*f^2 + 3*d^2*e^2 - 3*(d*e*f - f^2)*c^2 - 3*d*e*f + 3*(d^2*e^2 - 2*d*e*f + f^2)*c + f^2)*b^3 + (6*a*b^2*d^3*f^2 + b^3*d^3*f^2)*x^3 + 3*(b^3*d^3*e*f + 2*(2*d^3*e*f + c*d^2*f^2 - d^2*f^2)*a*b^2)*x^2 + 3*(b^3*d^3*e^2 + 2*(d^3*e^2 + 2*c*d^2*e*f - 2*d^2*e*f)*a*b^2)*x)*log(d*x + c + 1))*log(-d*x - c + 1))/(d^3*x + c*d^2 - d^2), x)","F",0
46,0,0,0,0.000000," ","integrate((f*x+e)*(a+b*arctanh(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} f x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} a^{2} b f + a^{3} e x + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b e}{2 \, d} - \frac{{\left(b^{3} d^{2} f x^{2} + 2 \, b^{3} d^{2} e x - {\left(c^{2} f - 2 \, {\left(d e + f\right)} c + 2 \, d e + f\right)} b^{3}\right)} \log\left(-d x - c + 1\right)^{3} - 3 \, {\left(2 \, a b^{2} d^{2} f x^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e + b^{3} d f\right)} x + {\left(b^{3} d^{2} f x^{2} + 2 \, b^{3} d^{2} e x - {\left(c^{2} f - 2 \, {\left(d e - f\right)} c - 2 \, d e + f\right)} b^{3}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)^{2}}{16 \, d^{2}} - \int -\frac{{\left(b^{3} d^{2} f x^{2} + {\left(d^{2} e + c d f - d f\right)} b^{3} x + {\left(c d e - d e\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{3} + 6 \, {\left(a b^{2} d^{2} f x^{2} + {\left(d^{2} e + c d f - d f\right)} a b^{2} x + {\left(c d e - d e\right)} a b^{2}\right)} \log\left(d x + c + 1\right)^{2} - 3 \, {\left(2 \, a b^{2} d^{2} f x^{2} + {\left(b^{3} d^{2} f x^{2} + {\left(d^{2} e + c d f - d f\right)} b^{3} x + {\left(c d e - d e\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e + b^{3} d f\right)} x + {\left(4 \, {\left(c d e - d e\right)} a b^{2} - {\left(c^{2} f - 2 \, {\left(d e - f\right)} c - 2 \, d e + f\right)} b^{3} + {\left(4 \, a b^{2} d^{2} f + b^{3} d^{2} f\right)} x^{2} + 2 \, {\left(b^{3} d^{2} e + 2 \, {\left(d^{2} e + c d f - d f\right)} a b^{2}\right)} x\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{8 \, {\left(d^{2} x + c d - d\right)}}\,{d x}"," ",0,"1/2*a^3*f*x^2 + 3/4*(2*x^2*arctanh(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*a^2*b*f + a^3*e*x + 3/2*(2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*a^2*b*e/d - 1/16*((b^3*d^2*f*x^2 + 2*b^3*d^2*e*x - (c^2*f - 2*(d*e + f)*c + 2*d*e + f)*b^3)*log(-d*x - c + 1)^3 - 3*(2*a*b^2*d^2*f*x^2 + 2*(2*a*b^2*d^2*e + b^3*d*f)*x + (b^3*d^2*f*x^2 + 2*b^3*d^2*e*x - (c^2*f - 2*(d*e - f)*c - 2*d*e + f)*b^3)*log(d*x + c + 1))*log(-d*x - c + 1)^2)/d^2 - integrate(-1/8*((b^3*d^2*f*x^2 + (d^2*e + c*d*f - d*f)*b^3*x + (c*d*e - d*e)*b^3)*log(d*x + c + 1)^3 + 6*(a*b^2*d^2*f*x^2 + (d^2*e + c*d*f - d*f)*a*b^2*x + (c*d*e - d*e)*a*b^2)*log(d*x + c + 1)^2 - 3*(2*a*b^2*d^2*f*x^2 + (b^3*d^2*f*x^2 + (d^2*e + c*d*f - d*f)*b^3*x + (c*d*e - d*e)*b^3)*log(d*x + c + 1)^2 + 2*(2*a*b^2*d^2*e + b^3*d*f)*x + (4*(c*d*e - d*e)*a*b^2 - (c^2*f - 2*(d*e - f)*c - 2*d*e + f)*b^3 + (4*a*b^2*d^2*f + b^3*d^2*f)*x^2 + 2*(b^3*d^2*e + 2*(d^2*e + c*d*f - d*f)*a*b^2)*x)*log(d*x + c + 1))*log(-d*x - c + 1))/(d^2*x + c*d - d), x)","F",0
47,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))^3,x, algorithm=""maxima"")","a^{3} x + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \operatorname{artanh}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b}{2 \, d} - \frac{{\left(b^{3} d x + b^{3} {\left(c - 1\right)}\right)} \log\left(-d x - c + 1\right)^{3} - 3 \, {\left(2 \, a b^{2} d x + {\left(b^{3} d x + b^{3} {\left(c + 1\right)}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)^{2}}{8 \, d} - \int -\frac{{\left(b^{3} d x + b^{3} {\left(c - 1\right)}\right)} \log\left(d x + c + 1\right)^{3} + 6 \, {\left(a b^{2} d x + a b^{2} {\left(c - 1\right)}\right)} \log\left(d x + c + 1\right)^{2} - 3 \, {\left(4 \, a b^{2} d x + {\left(b^{3} d x + b^{3} {\left(c - 1\right)}\right)} \log\left(d x + c + 1\right)^{2} + 2 \, {\left(b^{3} {\left(c + 1\right)} + 2 \, a b^{2} {\left(c - 1\right)} + {\left(2 \, a b^{2} d + b^{3} d\right)} x\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{8 \, {\left(d x + c - 1\right)}}\,{d x}"," ",0,"a^3*x + 3/2*(2*(d*x + c)*arctanh(d*x + c) + log(-(d*x + c)^2 + 1))*a^2*b/d - 1/8*((b^3*d*x + b^3*(c - 1))*log(-d*x - c + 1)^3 - 3*(2*a*b^2*d*x + (b^3*d*x + b^3*(c + 1))*log(d*x + c + 1))*log(-d*x - c + 1)^2)/d - integrate(-1/8*((b^3*d*x + b^3*(c - 1))*log(d*x + c + 1)^3 + 6*(a*b^2*d*x + a*b^2*(c - 1))*log(d*x + c + 1)^2 - 3*(4*a*b^2*d*x + (b^3*d*x + b^3*(c - 1))*log(d*x + c + 1)^2 + 2*(b^3*(c + 1) + 2*a*b^2*(c - 1) + (2*a*b^2*d + b^3*d)*x)*log(d*x + c + 1))*log(-d*x - c + 1))/(d*x + c - 1), x)","F",0
48,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))^3/(f*x+e),x, algorithm=""maxima"")","\frac{a^{3} \log\left(f x + e\right)}{f} + \int \frac{b^{3} {\left(\log\left(d x + c + 1\right) - \log\left(-d x - c + 1\right)\right)}^{3}}{8 \, {\left(f x + e\right)}} + \frac{3 \, a b^{2} {\left(\log\left(d x + c + 1\right) - \log\left(-d x - c + 1\right)\right)}^{2}}{4 \, {\left(f x + e\right)}} + \frac{3 \, a^{2} b {\left(\log\left(d x + c + 1\right) - \log\left(-d x - c + 1\right)\right)}}{2 \, {\left(f x + e\right)}}\,{d x}"," ",0,"a^3*log(f*x + e)/f + integrate(1/8*b^3*(log(d*x + c + 1) - log(-d*x - c + 1))^3/(f*x + e) + 3/4*a*b^2*(log(d*x + c + 1) - log(-d*x - c + 1))^2/(f*x + e) + 3/2*a^2*b*(log(d*x + c + 1) - log(-d*x - c + 1))/(f*x + e), x)","F",0
49,0,0,0,0.000000," ","integrate((a+b*arctanh(d*x+c))^3/(f*x+e)^2,x, algorithm=""maxima"")","\frac{3}{2} \, {\left(d {\left(\frac{\log\left(d x + c + 1\right)}{d e f - {\left(c + 1\right)} f^{2}} - \frac{\log\left(d x + c - 1\right)}{d e f - {\left(c - 1\right)} f^{2}} - \frac{2 \, \log\left(f x + e\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} - 1\right)} f^{2}}\right)} - \frac{2 \, \operatorname{artanh}\left(d x + c\right)}{f^{2} x + e f}\right)} a^{2} b - \frac{a^{3}}{f^{2} x + e f} - \frac{{\left({\left(d^{2} e f - c d f^{2} - d f^{2}\right)} b^{3} x + {\left(c d e f - c^{2} f^{2} - d e f + f^{2}\right)} b^{3}\right)} \log\left(-d x - c + 1\right)^{3} + 3 \, {\left(2 \, {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2} - f^{2}\right)} a b^{2} - {\left({\left(d^{2} e f - c d f^{2} + d f^{2}\right)} b^{3} x + {\left(c d e f - c^{2} f^{2} + d e f + f^{2}\right)} b^{3}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)^{2}}{8 \, {\left(d^{2} e^{3} f - 2 \, c d e^{2} f^{2} + c^{2} e f^{3} - e f^{3} + {\left(d^{2} e^{2} f^{2} - 2 \, c d e f^{3} + c^{2} f^{4} - f^{4}\right)} x\right)}} - \int -\frac{{\left({\left(d^{2} e f - c d f^{2} - d f^{2}\right)} b^{3} x + {\left(c d e f - c^{2} f^{2} - d e f + f^{2}\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{3} + 6 \, {\left({\left(d^{2} e f - c d f^{2} - d f^{2}\right)} a b^{2} x + {\left(c d e f - c^{2} f^{2} - d e f + f^{2}\right)} a b^{2}\right)} \log\left(d x + c + 1\right)^{2} + 3 \, {\left(4 \, {\left(d^{2} e f - c d f^{2} - d f^{2}\right)} a b^{2} x + 4 \, {\left(d^{2} e^{2} - c d e f - d e f\right)} a b^{2} - {\left({\left(d^{2} e f - c d f^{2} - d f^{2}\right)} b^{3} x + {\left(c d e f - c^{2} f^{2} - d e f + f^{2}\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{2} - 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, {\left(c d e f - c^{2} f^{2} - d e f + f^{2}\right)} a b^{2} + {\left(c d e f + d e f\right)} b^{3} + {\left(2 \, {\left(d^{2} e f - c d f^{2} - d f^{2}\right)} a b^{2} + {\left(d^{2} e f + c d f^{2} + d f^{2}\right)} b^{3}\right)} x\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)}{8 \, {\left(c d e^{3} f - c^{2} e^{2} f^{2} - d e^{3} f + e^{2} f^{2} + {\left(d^{2} e f^{3} - c d f^{4} - d f^{4}\right)} x^{3} + {\left(2 \, d^{2} e^{2} f^{2} - c d e f^{3} - c^{2} f^{4} - 3 \, d e f^{3} + f^{4}\right)} x^{2} + {\left(d^{2} e^{3} f + c d e^{2} f^{2} - 2 \, c^{2} e f^{3} - 3 \, d e^{2} f^{2} + 2 \, e f^{3}\right)} x\right)}}\,{d x}"," ",0,"3/2*(d*(log(d*x + c + 1)/(d*e*f - (c + 1)*f^2) - log(d*x + c - 1)/(d*e*f - (c - 1)*f^2) - 2*log(f*x + e)/(d^2*e^2 - 2*c*d*e*f + (c^2 - 1)*f^2)) - 2*arctanh(d*x + c)/(f^2*x + e*f))*a^2*b - a^3/(f^2*x + e*f) - 1/8*(((d^2*e*f - c*d*f^2 - d*f^2)*b^3*x + (c*d*e*f - c^2*f^2 - d*e*f + f^2)*b^3)*log(-d*x - c + 1)^3 + 3*(2*(d^2*e^2 - 2*c*d*e*f + c^2*f^2 - f^2)*a*b^2 - ((d^2*e*f - c*d*f^2 + d*f^2)*b^3*x + (c*d*e*f - c^2*f^2 + d*e*f + f^2)*b^3)*log(d*x + c + 1))*log(-d*x - c + 1)^2)/(d^2*e^3*f - 2*c*d*e^2*f^2 + c^2*e*f^3 - e*f^3 + (d^2*e^2*f^2 - 2*c*d*e*f^3 + c^2*f^4 - f^4)*x) - integrate(-1/8*(((d^2*e*f - c*d*f^2 - d*f^2)*b^3*x + (c*d*e*f - c^2*f^2 - d*e*f + f^2)*b^3)*log(d*x + c + 1)^3 + 6*((d^2*e*f - c*d*f^2 - d*f^2)*a*b^2*x + (c*d*e*f - c^2*f^2 - d*e*f + f^2)*a*b^2)*log(d*x + c + 1)^2 + 3*(4*(d^2*e*f - c*d*f^2 - d*f^2)*a*b^2*x + 4*(d^2*e^2 - c*d*e*f - d*e*f)*a*b^2 - ((d^2*e*f - c*d*f^2 - d*f^2)*b^3*x + (c*d*e*f - c^2*f^2 - d*e*f + f^2)*b^3)*log(d*x + c + 1)^2 - 2*(b^3*d^2*f^2*x^2 + 2*(c*d*e*f - c^2*f^2 - d*e*f + f^2)*a*b^2 + (c*d*e*f + d*e*f)*b^3 + (2*(d^2*e*f - c*d*f^2 - d*f^2)*a*b^2 + (d^2*e*f + c*d*f^2 + d*f^2)*b^3)*x)*log(d*x + c + 1))*log(-d*x - c + 1))/(c*d*e^3*f - c^2*e^2*f^2 - d*e^3*f + e^2*f^2 + (d^2*e*f^3 - c*d*f^4 - d*f^4)*x^3 + (2*d^2*e^2*f^2 - c*d*e*f^3 - c^2*f^4 - 3*d*e*f^3 + f^4)*x^2 + (d^2*e^3*f + c*d*e^2*f^2 - 2*c^2*e*f^3 - 3*d*e^2*f^2 + 2*e*f^3)*x), x)","F",0
50,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arctanh(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(b^{3} f x + b^{3} e\right)} {\left(f x + e\right)}^{m} \log\left(-d x - c + 1\right)^{3}}{8 \, f {\left(m + 1\right)}} + \frac{{\left(f x + e\right)}^{m + 1} a^{3}}{f {\left(m + 1\right)}} + \int \frac{{\left({\left(b^{3} d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{3} + 6 \, {\left(a b^{2} d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)} a b^{2}\right)} \log\left(d x + c + 1\right)^{2} + 3 \, {\left(b^{3} d e + 2 \, {\left(c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)} a b^{2} + {\left(2 \, a b^{2} d f {\left(m + 1\right)} + b^{3} d f\right)} x + {\left(b^{3} d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)} b^{3}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)^{2} + 12 \, {\left(a^{2} b d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)} a^{2} b\right)} \log\left(d x + c + 1\right) - 3 \, {\left(4 \, a^{2} b d f {\left(m + 1\right)} x + 4 \, {\left(c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)} a^{2} b + {\left(b^{3} d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{2} + 4 \, {\left(a b^{2} d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)} a b^{2}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)\right)} {\left(f x + e\right)}^{m}}{8 \, {\left(d f {\left(m + 1\right)} x + c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)}}\,{d x}"," ",0,"-1/8*(b^3*f*x + b^3*e)*(f*x + e)^m*log(-d*x - c + 1)^3/(f*(m + 1)) + (f*x + e)^(m + 1)*a^3/(f*(m + 1)) + integrate(1/8*((b^3*d*f*(m + 1)*x + (c*f*(m + 1) - f*(m + 1))*b^3)*log(d*x + c + 1)^3 + 6*(a*b^2*d*f*(m + 1)*x + (c*f*(m + 1) - f*(m + 1))*a*b^2)*log(d*x + c + 1)^2 + 3*(b^3*d*e + 2*(c*f*(m + 1) - f*(m + 1))*a*b^2 + (2*a*b^2*d*f*(m + 1) + b^3*d*f)*x + (b^3*d*f*(m + 1)*x + (c*f*(m + 1) - f*(m + 1))*b^3)*log(d*x + c + 1))*log(-d*x - c + 1)^2 + 12*(a^2*b*d*f*(m + 1)*x + (c*f*(m + 1) - f*(m + 1))*a^2*b)*log(d*x + c + 1) - 3*(4*a^2*b*d*f*(m + 1)*x + 4*(c*f*(m + 1) - f*(m + 1))*a^2*b + (b^3*d*f*(m + 1)*x + (c*f*(m + 1) - f*(m + 1))*b^3)*log(d*x + c + 1)^2 + 4*(a*b^2*d*f*(m + 1)*x + (c*f*(m + 1) - f*(m + 1))*a*b^2)*log(d*x + c + 1))*log(-d*x - c + 1))*(f*x + e)^m/(d*f*(m + 1)*x + c*f*(m + 1) - f*(m + 1)), x)","F",0
51,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arctanh(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} f x + b^{2} e\right)} {\left(f x + e\right)}^{m} \log\left(-d x - c + 1\right)^{2}}{4 \, f {\left(m + 1\right)}} + \frac{{\left(f x + e\right)}^{m + 1} a^{2}}{f {\left(m + 1\right)}} - \int -\frac{{\left({\left(b^{2} d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)} b^{2}\right)} \log\left(d x + c + 1\right)^{2} + 4 \, {\left(a b d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)} a b\right)} \log\left(d x + c + 1\right) - 2 \, {\left(b^{2} d e + 2 \, {\left(c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)} a b + {\left(2 \, a b d f {\left(m + 1\right)} + b^{2} d f\right)} x + {\left(b^{2} d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)} b^{2}\right)} \log\left(d x + c + 1\right)\right)} \log\left(-d x - c + 1\right)\right)} {\left(f x + e\right)}^{m}}{4 \, {\left(d f {\left(m + 1\right)} x + c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)}}\,{d x}"," ",0,"1/4*(b^2*f*x + b^2*e)*(f*x + e)^m*log(-d*x - c + 1)^2/(f*(m + 1)) + (f*x + e)^(m + 1)*a^2/(f*(m + 1)) - integrate(-1/4*((b^2*d*f*(m + 1)*x + (c*f*(m + 1) - f*(m + 1))*b^2)*log(d*x + c + 1)^2 + 4*(a*b*d*f*(m + 1)*x + (c*f*(m + 1) - f*(m + 1))*a*b)*log(d*x + c + 1) - 2*(b^2*d*e + 2*(c*f*(m + 1) - f*(m + 1))*a*b + (2*a*b*d*f*(m + 1) + b^2*d*f)*x + (b^2*d*f*(m + 1)*x + (c*f*(m + 1) - f*(m + 1))*b^2)*log(d*x + c + 1))*log(-d*x - c + 1))*(f*x + e)^m/(d*f*(m + 1)*x + c*f*(m + 1) - f*(m + 1)), x)","F",0
52,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arctanh(d*x+c)),x, algorithm=""maxima"")","-\frac{1}{2} \, b {\left(\frac{{\left(f x + e\right)} {\left(f x + e\right)}^{m} \log\left(-d x - c + 1\right)}{f {\left(m + 1\right)}} - \int \frac{{\left(d f x + d e + {\left(d f {\left(m + 1\right)} x + c f {\left(m + 1\right)} - f {\left(m + 1\right)}\right)} \log\left(d x + c + 1\right)\right)} {\left(f x + e\right)}^{m}}{d f {\left(m + 1\right)} x + c f {\left(m + 1\right)} - f {\left(m + 1\right)}}\,{d x}\right)} + \frac{{\left(f x + e\right)}^{m + 1} a}{f {\left(m + 1\right)}}"," ",0,"-1/2*b*((f*x + e)*(f*x + e)^m*log(-d*x - c + 1)/(f*(m + 1)) - integrate((d*f*x + d*e + (d*f*(m + 1)*x + c*f*(m + 1) - f*(m + 1))*log(d*x + c + 1))*(f*x + e)^m/(d*f*(m + 1)*x + c*f*(m + 1) - f*(m + 1)), x)) + (f*x + e)^(m + 1)*a/(f*(m + 1))","F",0
53,0,0,0,0.000000," ","integrate(arctanh(b*x+a)/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(b x + a\right)}{d x^{3} + c}\,{d x}"," ",0,"integrate(arctanh(b*x + a)/(d*x^3 + c), x)","F",0
54,1,589,0,0.586415," ","integrate(arctanh(b*x+a)/(d*x^2+c),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{d x}{\sqrt{c d}}\right) \operatorname{artanh}\left(b x + a\right)}{\sqrt{c d}} + \frac{{\left(\arctan\left(\frac{{\left(b^{2} x + {\left(a + 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c + {\left(a^{2} + 2 \, a + 1\right)} d}, \frac{{\left(a + 1\right)} b d x + {\left(a^{2} + 2 \, a + 1\right)} d}{b^{2} c + {\left(a^{2} + 2 \, a + 1\right)} d}\right) - \arctan\left(\frac{{\left(b^{2} x + {\left(a - 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c + {\left(a^{2} - 2 \, a + 1\right)} d}, \frac{{\left(a - 1\right)} b d x + {\left(a^{2} - 2 \, a + 1\right)} d}{b^{2} c + {\left(a^{2} - 2 \, a + 1\right)} d}\right)\right)} \log\left(d x^{2} + c\right) - \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{b^{2} d x^{2} + 2 \, {\left(a + 1\right)} b d x + {\left(a^{2} + 2 \, a + 1\right)} d}{b^{2} c + {\left(a^{2} + 2 \, a + 1\right)} d}\right) + \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{b^{2} d x^{2} + 2 \, {\left(a - 1\right)} b d x + {\left(a^{2} - 2 \, a + 1\right)} d}{b^{2} c + {\left(a^{2} - 2 \, a + 1\right)} d}\right) - i \, {\rm Li}_2\left(\frac{{\left(a + 1\right)} b d x + b^{2} c - {\left(i \, b^{2} x + {\left(-i \, a - i\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c + {\left(2 i \, a + 2 i\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} + 2 \, a + 1\right)} d}\right) + i \, {\rm Li}_2\left(\frac{{\left(a + 1\right)} b d x + b^{2} c + {\left(i \, b^{2} x + {\left(-i \, a - i\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c - {\left(2 i \, a + 2 i\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} + 2 \, a + 1\right)} d}\right) + i \, {\rm Li}_2\left(\frac{{\left(a - 1\right)} b d x + b^{2} c - {\left(i \, b^{2} x + {\left(-i \, a + i\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c + {\left(2 i \, a - 2 i\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} - 2 \, a + 1\right)} d}\right) - i \, {\rm Li}_2\left(\frac{{\left(a - 1\right)} b d x + b^{2} c + {\left(i \, b^{2} x + {\left(-i \, a + i\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c - {\left(2 i \, a - 2 i\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} - 2 \, a + 1\right)} d}\right)}{4 \, \sqrt{c d}}"," ",0,"arctan(d*x/sqrt(c*d))*arctanh(b*x + a)/sqrt(c*d) + 1/4*((arctan2((b^2*x + (a + 1)*b)*sqrt(c)*sqrt(d)/(b^2*c + (a^2 + 2*a + 1)*d), ((a + 1)*b*d*x + (a^2 + 2*a + 1)*d)/(b^2*c + (a^2 + 2*a + 1)*d)) - arctan2((b^2*x + (a - 1)*b)*sqrt(c)*sqrt(d)/(b^2*c + (a^2 - 2*a + 1)*d), ((a - 1)*b*d*x + (a^2 - 2*a + 1)*d)/(b^2*c + (a^2 - 2*a + 1)*d)))*log(d*x^2 + c) - arctan(sqrt(d)*x/sqrt(c))*log((b^2*d*x^2 + 2*(a + 1)*b*d*x + (a^2 + 2*a + 1)*d)/(b^2*c + (a^2 + 2*a + 1)*d)) + arctan(sqrt(d)*x/sqrt(c))*log((b^2*d*x^2 + 2*(a - 1)*b*d*x + (a^2 - 2*a + 1)*d)/(b^2*c + (a^2 - 2*a + 1)*d)) - I*dilog(((a + 1)*b*d*x + b^2*c - (I*b^2*x + (-I*a - I)*b)*sqrt(c)*sqrt(d))/(b^2*c + (2*I*a + 2*I)*b*sqrt(c)*sqrt(d) - (a^2 + 2*a + 1)*d)) + I*dilog(((a + 1)*b*d*x + b^2*c + (I*b^2*x + (-I*a - I)*b)*sqrt(c)*sqrt(d))/(b^2*c - (2*I*a + 2*I)*b*sqrt(c)*sqrt(d) - (a^2 + 2*a + 1)*d)) + I*dilog(((a - 1)*b*d*x + b^2*c - (I*b^2*x + (-I*a + I)*b)*sqrt(c)*sqrt(d))/(b^2*c + (2*I*a - 2*I)*b*sqrt(c)*sqrt(d) - (a^2 - 2*a + 1)*d)) - I*dilog(((a - 1)*b*d*x + b^2*c + (I*b^2*x + (-I*a + I)*b)*sqrt(c)*sqrt(d))/(b^2*c - (2*I*a - 2*I)*b*sqrt(c)*sqrt(d) - (a^2 - 2*a + 1)*d)))/sqrt(c*d)","C",0
55,1,192,0,0.330558," ","integrate(arctanh(b*x+a)/(d*x+c),x, algorithm=""maxima"")","-\frac{1}{2} \, b {\left(\frac{\log\left(b x + a - 1\right) \log\left(\frac{b d x + a d - d}{b c - a d + d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d - d}{b c - a d + d}\right)}{b d} - \frac{\log\left(b x + a + 1\right) \log\left(\frac{b d x + a d + d}{b c - a d - d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d + d}{b c - a d - d}\right)}{b d}\right)} - \frac{b {\left(\frac{\log\left(b x + a + 1\right)}{b} - \frac{\log\left(b x + a - 1\right)}{b}\right)} \log\left(d x + c\right)}{2 \, d} + \frac{\operatorname{artanh}\left(b x + a\right) \log\left(d x + c\right)}{d}"," ",0,"-1/2*b*((log(b*x + a - 1)*log((b*d*x + a*d - d)/(b*c - a*d + d) + 1) + dilog(-(b*d*x + a*d - d)/(b*c - a*d + d)))/(b*d) - (log(b*x + a + 1)*log((b*d*x + a*d + d)/(b*c - a*d - d) + 1) + dilog(-(b*d*x + a*d + d)/(b*c - a*d - d)))/(b*d)) - 1/2*b*(log(b*x + a + 1)/b - log(b*x + a - 1)/b)*log(d*x + c)/d + arctanh(b*x + a)*log(d*x + c)/d","A",0
56,1,192,0,0.321419," ","integrate(arctanh(b*x+a)/(c+d/x),x, algorithm=""maxima"")","\frac{1}{2} \, b {\left(\frac{{\left(\log\left(c x + d\right) \log\left(\frac{b c x + b d}{a c - b d + c} + 1\right) + {\rm Li}_2\left(-\frac{b c x + b d}{a c - b d + c}\right)\right)} d}{b c^{2}} - \frac{{\left(\log\left(c x + d\right) \log\left(\frac{b c x + b d}{a c - b d - c} + 1\right) + {\rm Li}_2\left(-\frac{b c x + b d}{a c - b d - c}\right)\right)} d}{b c^{2}} + \frac{{\left(a + 1\right)} \log\left(b x + a + 1\right)}{b^{2} c} - \frac{{\left(a - 1\right)} \log\left(b x + a - 1\right)}{b^{2} c}\right)} + {\left(\frac{x}{c} - \frac{d \log\left(c x + d\right)}{c^{2}}\right)} \operatorname{artanh}\left(b x + a\right)"," ",0,"1/2*b*((log(c*x + d)*log((b*c*x + b*d)/(a*c - b*d + c) + 1) + dilog(-(b*c*x + b*d)/(a*c - b*d + c)))*d/(b*c^2) - (log(c*x + d)*log((b*c*x + b*d)/(a*c - b*d - c) + 1) + dilog(-(b*c*x + b*d)/(a*c - b*d - c)))*d/(b*c^2) + (a + 1)*log(b*x + a + 1)/(b^2*c) - (a - 1)*log(b*x + a - 1)/(b^2*c)) + (x/c - d*log(c*x + d)/c^2)*arctanh(b*x + a)","A",0
57,1,647,0,0.550099," ","integrate(arctanh(b*x+a)/(c+d/x^2),x, algorithm=""maxima"")","-{\left(\frac{d \arctan\left(\frac{c x}{\sqrt{c d}}\right)}{\sqrt{c d} c} - \frac{x}{c}\right)} \operatorname{artanh}\left(b x + a\right) + \frac{2 \, {\left(a + 1\right)} c \log\left(b x + a + 1\right) - 2 \, {\left(a - 1\right)} c \log\left(b x + a - 1\right) + {\left(b \arctan\left(\frac{\sqrt{c} x}{\sqrt{d}}\right) \log\left(\frac{b^{2} c x^{2} + 2 \, {\left(a + 1\right)} b c x + {\left(a^{2} + 2 \, a + 1\right)} c}{b^{2} d + {\left(a^{2} + 2 \, a + 1\right)} c}\right) - b \arctan\left(\frac{\sqrt{c} x}{\sqrt{d}}\right) \log\left(\frac{b^{2} c x^{2} + 2 \, {\left(a - 1\right)} b c x + {\left(a^{2} - 2 \, a + 1\right)} c}{b^{2} d + {\left(a^{2} - 2 \, a + 1\right)} c}\right) + i \, b {\rm Li}_2\left(\frac{{\left(a + 1\right)} b c x + b^{2} d - {\left(i \, b^{2} x + {\left(-i \, a - i\right)} b\right)} \sqrt{c} \sqrt{d}}{{\left(2 i \, a + 2 i\right)} b \sqrt{c} \sqrt{d} + b^{2} d - {\left(a^{2} + 2 \, a + 1\right)} c}\right) - i \, b {\rm Li}_2\left(-\frac{{\left(a + 1\right)} b c x + b^{2} d + {\left(i \, b^{2} x + {\left(-i \, a - i\right)} b\right)} \sqrt{c} \sqrt{d}}{{\left(2 i \, a + 2 i\right)} b \sqrt{c} \sqrt{d} - b^{2} d + {\left(a^{2} + 2 \, a + 1\right)} c}\right) - i \, b {\rm Li}_2\left(\frac{{\left(a - 1\right)} b c x + b^{2} d - {\left(i \, b^{2} x + {\left(-i \, a + i\right)} b\right)} \sqrt{c} \sqrt{d}}{{\left(2 i \, a - 2 i\right)} b \sqrt{c} \sqrt{d} + b^{2} d - {\left(a^{2} - 2 \, a + 1\right)} c}\right) + i \, b {\rm Li}_2\left(-\frac{{\left(a - 1\right)} b c x + b^{2} d + {\left(i \, b^{2} x + {\left(-i \, a + i\right)} b\right)} \sqrt{c} \sqrt{d}}{{\left(2 i \, a - 2 i\right)} b \sqrt{c} \sqrt{d} - b^{2} d + {\left(a^{2} - 2 \, a + 1\right)} c}\right) - {\left(b \arctan\left(\frac{{\left(b^{2} x + {\left(a + 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} d + {\left(a^{2} + 2 \, a + 1\right)} c}, \frac{{\left(a + 1\right)} b c x + {\left(a^{2} + 2 \, a + 1\right)} c}{b^{2} d + {\left(a^{2} + 2 \, a + 1\right)} c}\right) - b \arctan\left(\frac{{\left(b^{2} x + {\left(a - 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} d + {\left(a^{2} - 2 \, a + 1\right)} c}, \frac{{\left(a - 1\right)} b c x + {\left(a^{2} - 2 \, a + 1\right)} c}{b^{2} d + {\left(a^{2} - 2 \, a + 1\right)} c}\right)\right)} \log\left(c x^{2} + d\right)\right)} \sqrt{c} \sqrt{d}}{4 \, b c^{2}}"," ",0,"-(d*arctan(c*x/sqrt(c*d))/(sqrt(c*d)*c) - x/c)*arctanh(b*x + a) + 1/4*(2*(a + 1)*c*log(b*x + a + 1) - 2*(a - 1)*c*log(b*x + a - 1) + (b*arctan(sqrt(c)*x/sqrt(d))*log((b^2*c*x^2 + 2*(a + 1)*b*c*x + (a^2 + 2*a + 1)*c)/(b^2*d + (a^2 + 2*a + 1)*c)) - b*arctan(sqrt(c)*x/sqrt(d))*log((b^2*c*x^2 + 2*(a - 1)*b*c*x + (a^2 - 2*a + 1)*c)/(b^2*d + (a^2 - 2*a + 1)*c)) + I*b*dilog(((a + 1)*b*c*x + b^2*d - (I*b^2*x + (-I*a - I)*b)*sqrt(c)*sqrt(d))/((2*I*a + 2*I)*b*sqrt(c)*sqrt(d) + b^2*d - (a^2 + 2*a + 1)*c)) - I*b*dilog(-((a + 1)*b*c*x + b^2*d + (I*b^2*x + (-I*a - I)*b)*sqrt(c)*sqrt(d))/((2*I*a + 2*I)*b*sqrt(c)*sqrt(d) - b^2*d + (a^2 + 2*a + 1)*c)) - I*b*dilog(((a - 1)*b*c*x + b^2*d - (I*b^2*x + (-I*a + I)*b)*sqrt(c)*sqrt(d))/((2*I*a - 2*I)*b*sqrt(c)*sqrt(d) + b^2*d - (a^2 - 2*a + 1)*c)) + I*b*dilog(-((a - 1)*b*c*x + b^2*d + (I*b^2*x + (-I*a + I)*b)*sqrt(c)*sqrt(d))/((2*I*a - 2*I)*b*sqrt(c)*sqrt(d) - b^2*d + (a^2 - 2*a + 1)*c)) - (b*arctan2((b^2*x + (a + 1)*b)*sqrt(c)*sqrt(d)/(b^2*d + (a^2 + 2*a + 1)*c), ((a + 1)*b*c*x + (a^2 + 2*a + 1)*c)/(b^2*d + (a^2 + 2*a + 1)*c)) - b*arctan2((b^2*x + (a - 1)*b)*sqrt(c)*sqrt(d)/(b^2*d + (a^2 - 2*a + 1)*c), ((a - 1)*b*c*x + (a^2 - 2*a + 1)*c)/(b^2*d + (a^2 - 2*a + 1)*c)))*log(c*x^2 + d))*sqrt(c)*sqrt(d))/(b*c^2)","C",0
58,0,0,0,0.000000," ","integrate(arctanh(b*x+a)/(c+d/x^3),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(b x + a\right)}{c + \frac{d}{x^{3}}}\,{d x}"," ",0,"integrate(arctanh(b*x + a)/(c + d/x^3), x)","F",0
59,0,0,0,0.000000," ","integrate(arctanh(b*x+a)/(c+d*x^(1/2)),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(b x + a\right)}{d \sqrt{x} + c}\,{d x}"," ",0,"integrate(arctanh(b*x + a)/(d*sqrt(x) + c), x)","F",0
60,0,0,0,0.000000," ","integrate(arctanh(b*x+a)/(c+d/x^(1/2)),x, algorithm=""maxima"")","\int \frac{\operatorname{artanh}\left(b x + a\right)}{c + \frac{d}{\sqrt{x}}}\,{d x}"," ",0,"integrate(arctanh(b*x + a)/(c + d/sqrt(x)), x)","F",0
61,-2,0,0,0.000000," ","integrate(arctanh(e*x+d)/(c*x^2+b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
62,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arctanh(d*x+c))/(1-(d*x+c)^2),x, algorithm=""maxima"")","\frac{1}{2} \, b c e {\left(\frac{\log\left(d x + c + 1\right)}{d} - \frac{\log\left(d x + c - 1\right)}{d}\right)} \operatorname{artanh}\left(d x + c\right) - \frac{1}{2} \, a d e {\left(\frac{{\left(c + 1\right)} \log\left(d x + c + 1\right)}{d^{2}} - \frac{{\left(c - 1\right)} \log\left(d x + c - 1\right)}{d^{2}}\right)} + \frac{1}{2} \, a c e {\left(\frac{\log\left(d x + c + 1\right)}{d} - \frac{\log\left(d x + c - 1\right)}{d}\right)} + \frac{1}{8} \, b d e {\left(\frac{2 \, {\left(c + 1\right)} \log\left(d x + c + 1\right) \log\left(-d x - c + 1\right) - {\left(c - 1\right)} \log\left(-d x - c + 1\right)^{2}}{d^{2}} - 4 \, \int \frac{{\left(c^{2} + {\left(c d + 3 \, d\right)} x + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{2 \, {\left(d^{3} x^{2} + 2 \, c d^{2} x + c^{2} d - d\right)}}\,{d x}\right)} - \frac{{\left(\log\left(d x + c + 1\right)^{2} - 2 \, \log\left(d x + c + 1\right) \log\left(d x + c - 1\right) + \log\left(d x + c - 1\right)^{2}\right)} b c e}{8 \, d}"," ",0,"1/2*b*c*e*(log(d*x + c + 1)/d - log(d*x + c - 1)/d)*arctanh(d*x + c) - 1/2*a*d*e*((c + 1)*log(d*x + c + 1)/d^2 - (c - 1)*log(d*x + c - 1)/d^2) + 1/2*a*c*e*(log(d*x + c + 1)/d - log(d*x + c - 1)/d) + 1/8*b*d*e*((2*(c + 1)*log(d*x + c + 1)*log(-d*x - c + 1) - (c - 1)*log(-d*x - c + 1)^2)/d^2 - 4*integrate(1/2*(c^2 + (c*d + 3*d)*x + 2*c + 1)*log(d*x + c + 1)/(d^3*x^2 + 2*c*d^2*x + c^2*d - d), x)) - 1/8*(log(d*x + c + 1)^2 - 2*log(d*x + c + 1)*log(d*x + c - 1) + log(d*x + c - 1)^2)*b*c*e/d","F",0
