1,1,170,0,1.528110," ","integrate(x^3*coth(b*x+a),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \coth\left(b x + a\right) - \frac{1}{2} \, {\left(\frac{x^{4}}{b e^{\left(2 \, b x + 2 \, a\right)} - b} + \frac{x^{4}}{b} - \frac{2 \, {\left(b^{3} x^{3} \log\left(e^{\left(b x + a\right)} + 1\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(-e^{\left(b x + a\right)}\right) - 6 \, b x {\rm Li}_{3}(-e^{\left(b x + a\right)}) + 6 \, {\rm Li}_{4}(-e^{\left(b x + a\right)})\right)}}{b^{5}} - \frac{2 \, {\left(b^{3} x^{3} \log\left(-e^{\left(b x + a\right)} + 1\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(e^{\left(b x + a\right)}\right) - 6 \, b x {\rm Li}_{3}(e^{\left(b x + a\right)}) + 6 \, {\rm Li}_{4}(e^{\left(b x + a\right)})\right)}}{b^{5}}\right)} b"," ",0,"1/4*x^4*coth(b*x + a) - 1/2*(x^4/(b*e^(2*b*x + 2*a) - b) + x^4/b - 2*(b^3*x^3*log(e^(b*x + a) + 1) + 3*b^2*x^2*dilog(-e^(b*x + a)) - 6*b*x*polylog(3, -e^(b*x + a)) + 6*polylog(4, -e^(b*x + a)))/b^5 - 2*(b^3*x^3*log(-e^(b*x + a) + 1) + 3*b^2*x^2*dilog(e^(b*x + a)) - 6*b*x*polylog(3, e^(b*x + a)) + 6*polylog(4, e^(b*x + a)))/b^5)*b","B",0
2,1,138,0,0.696403," ","integrate(x^2*coth(b*x+a),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \coth\left(b x + a\right) - \frac{1}{3} \, {\left(\frac{2 \, x^{3}}{b e^{\left(2 \, b x + 2 \, a\right)} - b} + \frac{2 \, x^{3}}{b} - \frac{3 \, {\left(b^{2} x^{2} \log\left(e^{\left(b x + a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(-e^{\left(b x + a\right)}\right) - 2 \, {\rm Li}_{3}(-e^{\left(b x + a\right)})\right)}}{b^{4}} - \frac{3 \, {\left(b^{2} x^{2} \log\left(-e^{\left(b x + a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(e^{\left(b x + a\right)}\right) - 2 \, {\rm Li}_{3}(e^{\left(b x + a\right)})\right)}}{b^{4}}\right)} b"," ",0,"1/3*x^3*coth(b*x + a) - 1/3*(2*x^3/(b*e^(2*b*x + 2*a) - b) + 2*x^3/b - 3*(b^2*x^2*log(e^(b*x + a) + 1) + 2*b*x*dilog(-e^(b*x + a)) - 2*polylog(3, -e^(b*x + a)))/b^4 - 3*(b^2*x^2*log(-e^(b*x + a) + 1) + 2*b*x*dilog(e^(b*x + a)) - 2*polylog(3, e^(b*x + a)))/b^4)*b","B",0
3,1,98,0,0.503752," ","integrate(x*coth(b*x+a),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \coth\left(b x + a\right) - b {\left(\frac{x^{2}}{b e^{\left(2 \, b x + 2 \, a\right)} - b} + \frac{x^{2}}{b} - \frac{b x \log\left(e^{\left(b x + a\right)} + 1\right) + {\rm Li}_2\left(-e^{\left(b x + a\right)}\right)}{b^{3}} - \frac{b x \log\left(-e^{\left(b x + a\right)} + 1\right) + {\rm Li}_2\left(e^{\left(b x + a\right)}\right)}{b^{3}}\right)}"," ",0,"1/2*x^2*coth(b*x + a) - b*(x^2/(b*e^(2*b*x + 2*a) - b) + x^2/b - (b*x*log(e^(b*x + a) + 1) + dilog(-e^(b*x + a)))/b^3 - (b*x*log(-e^(b*x + a) + 1) + dilog(e^(b*x + a)))/b^3)","B",0
4,0,0,0,0.000000," ","integrate(coth(b*x+a)/x,x, algorithm=""maxima"")","-\int \frac{1}{x e^{\left(b x + a\right)} + x}\,{d x} + \int \frac{1}{x e^{\left(b x + a\right)} - x}\,{d x} + \log\left(x\right)"," ",0,"-integrate(1/(x*e^(b*x + a) + x), x) + integrate(1/(x*e^(b*x + a) - x), x) + log(x)","F",0
5,0,0,0,0.000000," ","integrate(coth(b*x+a)/x^2,x, algorithm=""maxima"")","-\frac{1}{x} - \int \frac{1}{x^{2} e^{\left(b x + a\right)} + x^{2}}\,{d x} + \int \frac{1}{x^{2} e^{\left(b x + a\right)} - x^{2}}\,{d x}"," ",0,"-1/x - integrate(1/(x^2*e^(b*x + a) + x^2), x) + integrate(1/(x^2*e^(b*x + a) - x^2), x)","F",0
6,1,146,0,0.452878," ","integrate(x^3*coth(b*x+a)^2,x, algorithm=""maxima"")","-\frac{2 \, x^{3}}{b} + \frac{b x^{4} e^{\left(2 \, b x + 2 \, a\right)} - b x^{4} - 8 \, x^{3}}{4 \, {\left(b e^{\left(2 \, b x + 2 \, a\right)} - b\right)}} + \frac{3 \, {\left(b^{2} x^{2} \log\left(e^{\left(b x + a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(-e^{\left(b x + a\right)}\right) - 2 \, {\rm Li}_{3}(-e^{\left(b x + a\right)})\right)}}{b^{4}} + \frac{3 \, {\left(b^{2} x^{2} \log\left(-e^{\left(b x + a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(e^{\left(b x + a\right)}\right) - 2 \, {\rm Li}_{3}(e^{\left(b x + a\right)})\right)}}{b^{4}}"," ",0,"-2*x^3/b + 1/4*(b*x^4*e^(2*b*x + 2*a) - b*x^4 - 8*x^3)/(b*e^(2*b*x + 2*a) - b) + 3*(b^2*x^2*log(e^(b*x + a) + 1) + 2*b*x*dilog(-e^(b*x + a)) - 2*polylog(3, -e^(b*x + a)))/b^4 + 3*(b^2*x^2*log(-e^(b*x + a) + 1) + 2*b*x*dilog(e^(b*x + a)) - 2*polylog(3, e^(b*x + a)))/b^4","A",0
7,1,108,0,0.470116," ","integrate(x^2*coth(b*x+a)^2,x, algorithm=""maxima"")","-\frac{2 \, x^{2}}{b} + \frac{b x^{3} e^{\left(2 \, b x + 2 \, a\right)} - b x^{3} - 6 \, x^{2}}{3 \, {\left(b e^{\left(2 \, b x + 2 \, a\right)} - b\right)}} + \frac{2 \, {\left(b x \log\left(e^{\left(b x + a\right)} + 1\right) + {\rm Li}_2\left(-e^{\left(b x + a\right)}\right)\right)}}{b^{3}} + \frac{2 \, {\left(b x \log\left(-e^{\left(b x + a\right)} + 1\right) + {\rm Li}_2\left(e^{\left(b x + a\right)}\right)\right)}}{b^{3}}"," ",0,"-2*x^2/b + 1/3*(b*x^3*e^(2*b*x + 2*a) - b*x^3 - 6*x^2)/(b*e^(2*b*x + 2*a) - b) + 2*(b*x*log(e^(b*x + a) + 1) + dilog(-e^(b*x + a)))/b^3 + 2*(b*x*log(-e^(b*x + a) + 1) + dilog(e^(b*x + a)))/b^3","A",0
8,1,115,0,0.410058," ","integrate(x*coth(b*x+a)^2,x, algorithm=""maxima"")","-\frac{x e^{\left(2 \, b x + 2 \, a\right)}}{b e^{\left(2 \, b x + 2 \, a\right)} - b} - \frac{b x^{2} - {\left(b x^{2} e^{\left(2 \, a\right)} - 2 \, x e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)}}{2 \, {\left(b e^{\left(2 \, b x + 2 \, a\right)} - b\right)}} + \frac{\log\left({\left(e^{\left(b x + a\right)} + 1\right)} e^{\left(-a\right)}\right)}{b^{2}} + \frac{\log\left({\left(e^{\left(b x + a\right)} - 1\right)} e^{\left(-a\right)}\right)}{b^{2}}"," ",0,"-x*e^(2*b*x + 2*a)/(b*e^(2*b*x + 2*a) - b) - 1/2*(b*x^2 - (b*x^2*e^(2*a) - 2*x*e^(2*a))*e^(2*b*x))/(b*e^(2*b*x + 2*a) - b) + log((e^(b*x + a) + 1)*e^(-a))/b^2 + log((e^(b*x + a) - 1)*e^(-a))/b^2","B",0
9,0,0,0,0.000000," ","integrate(coth(b*x+a)^2/x,x, algorithm=""maxima"")","-\frac{2}{b x e^{\left(2 \, b x + 2 \, a\right)} - b x} + \int \frac{1}{b x^{2} e^{\left(b x + a\right)} + b x^{2}}\,{d x} - \int \frac{1}{b x^{2} e^{\left(b x + a\right)} - b x^{2}}\,{d x} + \log\left(x\right)"," ",0,"-2/(b*x*e^(2*b*x + 2*a) - b*x) + integrate(1/(b*x^2*e^(b*x + a) + b*x^2), x) - integrate(1/(b*x^2*e^(b*x + a) - b*x^2), x) + log(x)","F",0
10,0,0,0,0.000000," ","integrate(coth(b*x+a)^2/x^2,x, algorithm=""maxima"")","-\frac{b x e^{\left(2 \, b x + 2 \, a\right)} - b x + 2}{b x^{2} e^{\left(2 \, b x + 2 \, a\right)} - b x^{2}} + 2 \, \int \frac{1}{b x^{3} e^{\left(b x + a\right)} + b x^{3}}\,{d x} - 2 \, \int \frac{1}{b x^{3} e^{\left(b x + a\right)} - b x^{3}}\,{d x}"," ",0,"-(b*x*e^(2*b*x + 2*a) - b*x + 2)/(b*x^2*e^(2*b*x + 2*a) - b*x^2) + 2*integrate(1/(b*x^3*e^(b*x + a) + b*x^3), x) - 2*integrate(1/(b*x^3*e^(b*x + a) - b*x^3), x)","F",0
11,1,302,0,0.442196," ","integrate(x^3*coth(b*x+a)^3,x, algorithm=""maxima"")","\frac{b^{2} x^{4} e^{\left(4 \, b x + 4 \, a\right)} + b^{2} x^{4} + 12 \, x^{2} - 2 \, {\left(b^{2} x^{4} e^{\left(2 \, a\right)} + 4 \, b x^{3} e^{\left(2 \, a\right)} + 6 \, x^{2} e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)}}{4 \, {\left(b^{2} e^{\left(4 \, b x + 4 \, a\right)} - 2 \, b^{2} e^{\left(2 \, b x + 2 \, a\right)} + b^{2}\right)}} - \frac{b^{4} x^{4} + 6 \, b^{2} x^{2}}{2 \, b^{4}} + \frac{b^{3} x^{3} \log\left(e^{\left(b x + a\right)} + 1\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(-e^{\left(b x + a\right)}\right) - 6 \, b x {\rm Li}_{3}(-e^{\left(b x + a\right)}) + 6 \, {\rm Li}_{4}(-e^{\left(b x + a\right)})}{b^{4}} + \frac{b^{3} x^{3} \log\left(-e^{\left(b x + a\right)} + 1\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(e^{\left(b x + a\right)}\right) - 6 \, b x {\rm Li}_{3}(e^{\left(b x + a\right)}) + 6 \, {\rm Li}_{4}(e^{\left(b x + a\right)})}{b^{4}} + \frac{3 \, {\left(b x \log\left(e^{\left(b x + a\right)} + 1\right) + {\rm Li}_2\left(-e^{\left(b x + a\right)}\right)\right)}}{b^{4}} + \frac{3 \, {\left(b x \log\left(-e^{\left(b x + a\right)} + 1\right) + {\rm Li}_2\left(e^{\left(b x + a\right)}\right)\right)}}{b^{4}}"," ",0,"1/4*(b^2*x^4*e^(4*b*x + 4*a) + b^2*x^4 + 12*x^2 - 2*(b^2*x^4*e^(2*a) + 4*b*x^3*e^(2*a) + 6*x^2*e^(2*a))*e^(2*b*x))/(b^2*e^(4*b*x + 4*a) - 2*b^2*e^(2*b*x + 2*a) + b^2) - 1/2*(b^4*x^4 + 6*b^2*x^2)/b^4 + (b^3*x^3*log(e^(b*x + a) + 1) + 3*b^2*x^2*dilog(-e^(b*x + a)) - 6*b*x*polylog(3, -e^(b*x + a)) + 6*polylog(4, -e^(b*x + a)))/b^4 + (b^3*x^3*log(-e^(b*x + a) + 1) + 3*b^2*x^2*dilog(e^(b*x + a)) - 6*b*x*polylog(3, e^(b*x + a)) + 6*polylog(4, e^(b*x + a)))/b^4 + 3*(b*x*log(e^(b*x + a) + 1) + dilog(-e^(b*x + a)))/b^4 + 3*(b*x*log(-e^(b*x + a) + 1) + dilog(e^(b*x + a)))/b^4","A",0
12,1,226,0,0.415933," ","integrate(x^2*coth(b*x+a)^3,x, algorithm=""maxima"")","-\frac{2}{3} \, x^{3} + \frac{b^{2} x^{3} e^{\left(4 \, b x + 4 \, a\right)} + b^{2} x^{3} - 2 \, {\left(b^{2} x^{3} e^{\left(2 \, a\right)} + 3 \, b x^{2} e^{\left(2 \, a\right)} + 3 \, x e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 6 \, x}{3 \, {\left(b^{2} e^{\left(4 \, b x + 4 \, a\right)} - 2 \, b^{2} e^{\left(2 \, b x + 2 \, a\right)} + b^{2}\right)}} - \frac{2 \, x}{b^{2}} + \frac{b^{2} x^{2} \log\left(e^{\left(b x + a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(-e^{\left(b x + a\right)}\right) - 2 \, {\rm Li}_{3}(-e^{\left(b x + a\right)})}{b^{3}} + \frac{b^{2} x^{2} \log\left(-e^{\left(b x + a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(e^{\left(b x + a\right)}\right) - 2 \, {\rm Li}_{3}(e^{\left(b x + a\right)})}{b^{3}} + \frac{\log\left(e^{\left(b x + a\right)} + 1\right)}{b^{3}} + \frac{\log\left(e^{\left(b x + a\right)} - 1\right)}{b^{3}}"," ",0,"-2/3*x^3 + 1/3*(b^2*x^3*e^(4*b*x + 4*a) + b^2*x^3 - 2*(b^2*x^3*e^(2*a) + 3*b*x^2*e^(2*a) + 3*x*e^(2*a))*e^(2*b*x) + 6*x)/(b^2*e^(4*b*x + 4*a) - 2*b^2*e^(2*b*x + 2*a) + b^2) - 2*x/b^2 + (b^2*x^2*log(e^(b*x + a) + 1) + 2*b*x*dilog(-e^(b*x + a)) - 2*polylog(3, -e^(b*x + a)))/b^3 + (b^2*x^2*log(-e^(b*x + a) + 1) + 2*b*x*dilog(e^(b*x + a)) - 2*polylog(3, e^(b*x + a)))/b^3 + log(e^(b*x + a) + 1)/b^3 + log(e^(b*x + a) - 1)/b^3","B",0
13,1,149,0,0.416040," ","integrate(x*coth(b*x+a)^3,x, algorithm=""maxima"")","-x^{2} + \frac{b^{2} x^{2} e^{\left(4 \, b x + 4 \, a\right)} + b^{2} x^{2} - 2 \, {\left(b^{2} x^{2} e^{\left(2 \, a\right)} + 2 \, b x e^{\left(2 \, a\right)} + e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 2}{2 \, {\left(b^{2} e^{\left(4 \, b x + 4 \, a\right)} - 2 \, b^{2} e^{\left(2 \, b x + 2 \, a\right)} + b^{2}\right)}} + \frac{b x \log\left(e^{\left(b x + a\right)} + 1\right) + {\rm Li}_2\left(-e^{\left(b x + a\right)}\right)}{b^{2}} + \frac{b x \log\left(-e^{\left(b x + a\right)} + 1\right) + {\rm Li}_2\left(e^{\left(b x + a\right)}\right)}{b^{2}}"," ",0,"-x^2 + 1/2*(b^2*x^2*e^(4*b*x + 4*a) + b^2*x^2 - 2*(b^2*x^2*e^(2*a) + 2*b*x*e^(2*a) + e^(2*a))*e^(2*b*x) + 2)/(b^2*e^(4*b*x + 4*a) - 2*b^2*e^(2*b*x + 2*a) + b^2) + (b*x*log(e^(b*x + a) + 1) + dilog(-e^(b*x + a)))/b^2 + (b*x*log(-e^(b*x + a) + 1) + dilog(e^(b*x + a)))/b^2","B",0
14,0,0,0,0.000000," ","integrate(coth(b*x+a)^3/x,x, algorithm=""maxima"")","-\frac{{\left(2 \, b x e^{\left(2 \, a\right)} - e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 1}{b^{2} x^{2} e^{\left(4 \, b x + 4 \, a\right)} - 2 \, b^{2} x^{2} e^{\left(2 \, b x + 2 \, a\right)} + b^{2} x^{2}} - \int \frac{b^{2} x^{2} + 1}{b^{2} x^{3} e^{\left(b x + a\right)} + b^{2} x^{3}}\,{d x} + \int \frac{b^{2} x^{2} + 1}{b^{2} x^{3} e^{\left(b x + a\right)} - b^{2} x^{3}}\,{d x} + \log\left(x\right)"," ",0,"-((2*b*x*e^(2*a) - e^(2*a))*e^(2*b*x) + 1)/(b^2*x^2*e^(4*b*x + 4*a) - 2*b^2*x^2*e^(2*b*x + 2*a) + b^2*x^2) - integrate((b^2*x^2 + 1)/(b^2*x^3*e^(b*x + a) + b^2*x^3), x) + integrate((b^2*x^2 + 1)/(b^2*x^3*e^(b*x + a) - b^2*x^3), x) + log(x)","F",0
15,0,0,0,0.000000," ","integrate(coth(b*x+a)^3/x^2,x, algorithm=""maxima"")","-\frac{b^{2} x^{2} e^{\left(4 \, b x + 4 \, a\right)} + b^{2} x^{2} - 2 \, {\left(b^{2} x^{2} e^{\left(2 \, a\right)} - b x e^{\left(2 \, a\right)} + e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 2}{b^{2} x^{3} e^{\left(4 \, b x + 4 \, a\right)} - 2 \, b^{2} x^{3} e^{\left(2 \, b x + 2 \, a\right)} + b^{2} x^{3}} - \int \frac{b^{2} x^{2} + 3}{b^{2} x^{4} e^{\left(b x + a\right)} + b^{2} x^{4}}\,{d x} + \int \frac{b^{2} x^{2} + 3}{b^{2} x^{4} e^{\left(b x + a\right)} - b^{2} x^{4}}\,{d x}"," ",0,"-(b^2*x^2*e^(4*b*x + 4*a) + b^2*x^2 - 2*(b^2*x^2*e^(2*a) - b*x*e^(2*a) + e^(2*a))*e^(2*b*x) + 2)/(b^2*x^3*e^(4*b*x + 4*a) - 2*b^2*x^3*e^(2*b*x + 2*a) + b^2*x^3) - integrate((b^2*x^2 + 3)/(b^2*x^4*e^(b*x + a) + b^2*x^4), x) + integrate((b^2*x^2 + 3)/(b^2*x^4*e^(b*x + a) - b^2*x^4), x)","F",0
16,1,183,0,0.459506," ","integrate((d*x+c)^3/(a+a*coth(f*x+e)),x, algorithm=""maxima"")","\frac{1}{4} \, c^{3} {\left(\frac{2 \, {\left(f x + e\right)}}{a f} + \frac{e^{\left(-2 \, f x - 2 \, e\right)}}{a f}\right)} + \frac{3 \, {\left(2 \, f^{2} x^{2} e^{\left(2 \, e\right)} + {\left(2 \, f x + 1\right)} e^{\left(-2 \, f x\right)}\right)} c^{2} d e^{\left(-2 \, e\right)}}{8 \, a f^{2}} + \frac{{\left(4 \, f^{3} x^{3} e^{\left(2 \, e\right)} + 3 \, {\left(2 \, f^{2} x^{2} + 2 \, f x + 1\right)} e^{\left(-2 \, f x\right)}\right)} c d^{2} e^{\left(-2 \, e\right)}}{8 \, a f^{3}} + \frac{{\left(2 \, f^{4} x^{4} e^{\left(2 \, e\right)} + {\left(4 \, f^{3} x^{3} + 6 \, f^{2} x^{2} + 6 \, f x + 3\right)} e^{\left(-2 \, f x\right)}\right)} d^{3} e^{\left(-2 \, e\right)}}{16 \, a f^{4}}"," ",0,"1/4*c^3*(2*(f*x + e)/(a*f) + e^(-2*f*x - 2*e)/(a*f)) + 3/8*(2*f^2*x^2*e^(2*e) + (2*f*x + 1)*e^(-2*f*x))*c^2*d*e^(-2*e)/(a*f^2) + 1/8*(4*f^3*x^3*e^(2*e) + 3*(2*f^2*x^2 + 2*f*x + 1)*e^(-2*f*x))*c*d^2*e^(-2*e)/(a*f^3) + 1/16*(2*f^4*x^4*e^(2*e) + (4*f^3*x^3 + 6*f^2*x^2 + 6*f*x + 3)*e^(-2*f*x))*d^3*e^(-2*e)/(a*f^4)","A",0
17,1,124,0,0.409483," ","integrate((d*x+c)^2/(a+a*coth(f*x+e)),x, algorithm=""maxima"")","\frac{1}{4} \, c^{2} {\left(\frac{2 \, {\left(f x + e\right)}}{a f} + \frac{e^{\left(-2 \, f x - 2 \, e\right)}}{a f}\right)} + \frac{{\left(2 \, f^{2} x^{2} e^{\left(2 \, e\right)} + {\left(2 \, f x + 1\right)} e^{\left(-2 \, f x\right)}\right)} c d e^{\left(-2 \, e\right)}}{4 \, a f^{2}} + \frac{{\left(4 \, f^{3} x^{3} e^{\left(2 \, e\right)} + 3 \, {\left(2 \, f^{2} x^{2} + 2 \, f x + 1\right)} e^{\left(-2 \, f x\right)}\right)} d^{2} e^{\left(-2 \, e\right)}}{24 \, a f^{3}}"," ",0,"1/4*c^2*(2*(f*x + e)/(a*f) + e^(-2*f*x - 2*e)/(a*f)) + 1/4*(2*f^2*x^2*e^(2*e) + (2*f*x + 1)*e^(-2*f*x))*c*d*e^(-2*e)/(a*f^2) + 1/24*(4*f^3*x^3*e^(2*e) + 3*(2*f^2*x^2 + 2*f*x + 1)*e^(-2*f*x))*d^2*e^(-2*e)/(a*f^3)","A",0
18,1,72,0,0.408870," ","integrate((d*x+c)/(a+a*coth(f*x+e)),x, algorithm=""maxima"")","\frac{1}{4} \, c {\left(\frac{2 \, {\left(f x + e\right)}}{a f} + \frac{e^{\left(-2 \, f x - 2 \, e\right)}}{a f}\right)} + \frac{{\left(2 \, f^{2} x^{2} e^{\left(2 \, e\right)} + {\left(2 \, f x + 1\right)} e^{\left(-2 \, f x\right)}\right)} d e^{\left(-2 \, e\right)}}{8 \, a f^{2}}"," ",0,"1/4*c*(2*(f*x + e)/(a*f) + e^(-2*f*x - 2*e)/(a*f)) + 1/8*(2*f^2*x^2*e^(2*e) + (2*f*x + 1)*e^(-2*f*x))*d*e^(-2*e)/(a*f^2)","A",0
19,1,48,0,0.570525," ","integrate(1/(d*x+c)/(a+a*coth(f*x+e)),x, algorithm=""maxima"")","\frac{e^{\left(-2 \, e + \frac{2 \, c f}{d}\right)} E_{1}\left(\frac{2 \, {\left(d x + c\right)} f}{d}\right)}{2 \, a d} + \frac{\log\left(d x + c\right)}{2 \, a d}"," ",0,"1/2*e^(-2*e + 2*c*f/d)*exp_integral_e(1, 2*(d*x + c)*f/d)/(a*d) + 1/2*log(d*x + c)/(a*d)","A",0
20,1,56,0,0.803422," ","integrate(1/(d*x+c)^2/(a+a*coth(f*x+e)),x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(a d^{2} x + a c d\right)}} + \frac{e^{\left(-2 \, e + \frac{2 \, c f}{d}\right)} E_{2}\left(\frac{2 \, {\left(d x + c\right)} f}{d}\right)}{2 \, {\left(d x + c\right)} a d}"," ",0,"-1/2/(a*d^2*x + a*c*d) + 1/2*e^(-2*e + 2*c*f/d)*exp_integral_e(2, 2*(d*x + c)*f/d)/((d*x + c)*a*d)","A",0
21,1,68,0,1.080811," ","integrate(1/(d*x+c)^3/(a+a*coth(f*x+e)),x, algorithm=""maxima"")","-\frac{1}{4 \, {\left(a d^{3} x^{2} + 2 \, a c d^{2} x + a c^{2} d\right)}} + \frac{e^{\left(-2 \, e + \frac{2 \, c f}{d}\right)} E_{3}\left(\frac{2 \, {\left(d x + c\right)} f}{d}\right)}{2 \, {\left(d x + c\right)}^{2} a d}"," ",0,"-1/4/(a*d^3*x^2 + 2*a*c*d^2*x + a*c^2*d) + 1/2*e^(-2*e + 2*c*f/d)*exp_integral_e(3, 2*(d*x + c)*f/d)/((d*x + c)^2*a*d)","A",0
22,1,297,0,0.823699," ","integrate((d*x+c)^3/(a+a*coth(f*x+e))^2,x, algorithm=""maxima"")","\frac{1}{16} \, c^{3} {\left(\frac{4 \, {\left(f x + e\right)}}{a^{2} f} + \frac{4 \, e^{\left(-2 \, f x - 2 \, e\right)} - e^{\left(-4 \, f x - 4 \, e\right)}}{a^{2} f}\right)} + \frac{3 \, {\left(8 \, f^{2} x^{2} e^{\left(4 \, e\right)} + 8 \, {\left(2 \, f x e^{\left(2 \, e\right)} + e^{\left(2 \, e\right)}\right)} e^{\left(-2 \, f x\right)} - {\left(4 \, f x + 1\right)} e^{\left(-4 \, f x\right)}\right)} c^{2} d e^{\left(-4 \, e\right)}}{64 \, a^{2} f^{2}} + \frac{{\left(32 \, f^{3} x^{3} e^{\left(4 \, e\right)} + 48 \, {\left(2 \, f^{2} x^{2} e^{\left(2 \, e\right)} + 2 \, f x e^{\left(2 \, e\right)} + e^{\left(2 \, e\right)}\right)} e^{\left(-2 \, f x\right)} - 3 \, {\left(8 \, f^{2} x^{2} + 4 \, f x + 1\right)} e^{\left(-4 \, f x\right)}\right)} c d^{2} e^{\left(-4 \, e\right)}}{128 \, a^{2} f^{3}} + \frac{{\left(32 \, f^{4} x^{4} e^{\left(4 \, e\right)} + 32 \, {\left(4 \, f^{3} x^{3} e^{\left(2 \, e\right)} + 6 \, f^{2} x^{2} e^{\left(2 \, e\right)} + 6 \, f x e^{\left(2 \, e\right)} + 3 \, e^{\left(2 \, e\right)}\right)} e^{\left(-2 \, f x\right)} - {\left(32 \, f^{3} x^{3} + 24 \, f^{2} x^{2} + 12 \, f x + 3\right)} e^{\left(-4 \, f x\right)}\right)} d^{3} e^{\left(-4 \, e\right)}}{512 \, a^{2} f^{4}}"," ",0,"1/16*c^3*(4*(f*x + e)/(a^2*f) + (4*e^(-2*f*x - 2*e) - e^(-4*f*x - 4*e))/(a^2*f)) + 3/64*(8*f^2*x^2*e^(4*e) + 8*(2*f*x*e^(2*e) + e^(2*e))*e^(-2*f*x) - (4*f*x + 1)*e^(-4*f*x))*c^2*d*e^(-4*e)/(a^2*f^2) + 1/128*(32*f^3*x^3*e^(4*e) + 48*(2*f^2*x^2*e^(2*e) + 2*f*x*e^(2*e) + e^(2*e))*e^(-2*f*x) - 3*(8*f^2*x^2 + 4*f*x + 1)*e^(-4*f*x))*c*d^2*e^(-4*e)/(a^2*f^3) + 1/512*(32*f^4*x^4*e^(4*e) + 32*(4*f^3*x^3*e^(2*e) + 6*f^2*x^2*e^(2*e) + 6*f*x*e^(2*e) + 3*e^(2*e))*e^(-2*f*x) - (32*f^3*x^3 + 24*f^2*x^2 + 12*f*x + 3)*e^(-4*f*x))*d^3*e^(-4*e)/(a^2*f^4)","A",0
23,1,191,0,0.660610," ","integrate((d*x+c)^2/(a+a*coth(f*x+e))^2,x, algorithm=""maxima"")","\frac{1}{16} \, c^{2} {\left(\frac{4 \, {\left(f x + e\right)}}{a^{2} f} + \frac{4 \, e^{\left(-2 \, f x - 2 \, e\right)} - e^{\left(-4 \, f x - 4 \, e\right)}}{a^{2} f}\right)} + \frac{{\left(8 \, f^{2} x^{2} e^{\left(4 \, e\right)} + 8 \, {\left(2 \, f x e^{\left(2 \, e\right)} + e^{\left(2 \, e\right)}\right)} e^{\left(-2 \, f x\right)} - {\left(4 \, f x + 1\right)} e^{\left(-4 \, f x\right)}\right)} c d e^{\left(-4 \, e\right)}}{32 \, a^{2} f^{2}} + \frac{{\left(32 \, f^{3} x^{3} e^{\left(4 \, e\right)} + 48 \, {\left(2 \, f^{2} x^{2} e^{\left(2 \, e\right)} + 2 \, f x e^{\left(2 \, e\right)} + e^{\left(2 \, e\right)}\right)} e^{\left(-2 \, f x\right)} - 3 \, {\left(8 \, f^{2} x^{2} + 4 \, f x + 1\right)} e^{\left(-4 \, f x\right)}\right)} d^{2} e^{\left(-4 \, e\right)}}{384 \, a^{2} f^{3}}"," ",0,"1/16*c^2*(4*(f*x + e)/(a^2*f) + (4*e^(-2*f*x - 2*e) - e^(-4*f*x - 4*e))/(a^2*f)) + 1/32*(8*f^2*x^2*e^(4*e) + 8*(2*f*x*e^(2*e) + e^(2*e))*e^(-2*f*x) - (4*f*x + 1)*e^(-4*f*x))*c*d*e^(-4*e)/(a^2*f^2) + 1/384*(32*f^3*x^3*e^(4*e) + 48*(2*f^2*x^2*e^(2*e) + 2*f*x*e^(2*e) + e^(2*e))*e^(-2*f*x) - 3*(8*f^2*x^2 + 4*f*x + 1)*e^(-4*f*x))*d^2*e^(-4*e)/(a^2*f^3)","A",0
24,1,107,0,0.525520," ","integrate((d*x+c)/(a+a*coth(f*x+e))^2,x, algorithm=""maxima"")","\frac{1}{16} \, c {\left(\frac{4 \, {\left(f x + e\right)}}{a^{2} f} + \frac{4 \, e^{\left(-2 \, f x - 2 \, e\right)} - e^{\left(-4 \, f x - 4 \, e\right)}}{a^{2} f}\right)} + \frac{{\left(8 \, f^{2} x^{2} e^{\left(4 \, e\right)} + 8 \, {\left(2 \, f x e^{\left(2 \, e\right)} + e^{\left(2 \, e\right)}\right)} e^{\left(-2 \, f x\right)} - {\left(4 \, f x + 1\right)} e^{\left(-4 \, f x\right)}\right)} d e^{\left(-4 \, e\right)}}{64 \, a^{2} f^{2}}"," ",0,"1/16*c*(4*(f*x + e)/(a^2*f) + (4*e^(-2*f*x - 2*e) - e^(-4*f*x - 4*e))/(a^2*f)) + 1/64*(8*f^2*x^2*e^(4*e) + 8*(2*f*x*e^(2*e) + e^(2*e))*e^(-2*f*x) - (4*f*x + 1)*e^(-4*f*x))*d*e^(-4*e)/(a^2*f^2)","A",0
25,1,81,0,1.137784," ","integrate(1/(d*x+c)/(a+a*coth(f*x+e))^2,x, algorithm=""maxima"")","-\frac{e^{\left(-4 \, e + \frac{4 \, c f}{d}\right)} E_{1}\left(\frac{4 \, {\left(d x + c\right)} f}{d}\right)}{4 \, a^{2} d} + \frac{e^{\left(-2 \, e + \frac{2 \, c f}{d}\right)} E_{1}\left(\frac{2 \, {\left(d x + c\right)} f}{d}\right)}{2 \, a^{2} d} + \frac{\log\left(d x + c\right)}{4 \, a^{2} d}"," ",0,"-1/4*e^(-4*e + 4*c*f/d)*exp_integral_e(1, 4*(d*x + c)*f/d)/(a^2*d) + 1/2*e^(-2*e + 2*c*f/d)*exp_integral_e(1, 2*(d*x + c)*f/d)/(a^2*d) + 1/4*log(d*x + c)/(a^2*d)","A",0
26,1,100,0,2.155571," ","integrate(1/(d*x+c)^2/(a+a*coth(f*x+e))^2,x, algorithm=""maxima"")","-\frac{1}{4 \, {\left(a^{2} d^{2} x + a^{2} c d\right)}} - \frac{e^{\left(-4 \, e + \frac{4 \, c f}{d}\right)} E_{2}\left(\frac{4 \, {\left(d x + c\right)} f}{d}\right)}{4 \, {\left(d x + c\right)} a^{2} d} + \frac{e^{\left(-2 \, e + \frac{2 \, c f}{d}\right)} E_{2}\left(\frac{2 \, {\left(d x + c\right)} f}{d}\right)}{2 \, {\left(d x + c\right)} a^{2} d}"," ",0,"-1/4/(a^2*d^2*x + a^2*c*d) - 1/4*e^(-4*e + 4*c*f/d)*exp_integral_e(2, 4*(d*x + c)*f/d)/((d*x + c)*a^2*d) + 1/2*e^(-2*e + 2*c*f/d)*exp_integral_e(2, 2*(d*x + c)*f/d)/((d*x + c)*a^2*d)","A",0
27,1,406,0,2.856422," ","integrate((d*x+c)^3/(a+a*coth(f*x+e))^3,x, algorithm=""maxima"")","\frac{1}{96} \, c^{3} {\left(\frac{12 \, {\left(f x + e\right)}}{a^{3} f} + \frac{18 \, e^{\left(-2 \, f x - 2 \, e\right)} - 9 \, e^{\left(-4 \, f x - 4 \, e\right)} + 2 \, e^{\left(-6 \, f x - 6 \, e\right)}}{a^{3} f}\right)} + \frac{{\left(72 \, f^{2} x^{2} e^{\left(6 \, e\right)} + 108 \, {\left(2 \, f x e^{\left(4 \, e\right)} + e^{\left(4 \, e\right)}\right)} e^{\left(-2 \, f x\right)} - 27 \, {\left(4 \, f x e^{\left(2 \, e\right)} + e^{\left(2 \, e\right)}\right)} e^{\left(-4 \, f x\right)} + 4 \, {\left(6 \, f x + 1\right)} e^{\left(-6 \, f x\right)}\right)} c^{2} d e^{\left(-6 \, e\right)}}{384 \, a^{3} f^{2}} + \frac{{\left(288 \, f^{3} x^{3} e^{\left(6 \, e\right)} + 648 \, {\left(2 \, f^{2} x^{2} e^{\left(4 \, e\right)} + 2 \, f x e^{\left(4 \, e\right)} + e^{\left(4 \, e\right)}\right)} e^{\left(-2 \, f x\right)} - 81 \, {\left(8 \, f^{2} x^{2} e^{\left(2 \, e\right)} + 4 \, f x e^{\left(2 \, e\right)} + e^{\left(2 \, e\right)}\right)} e^{\left(-4 \, f x\right)} + 8 \, {\left(18 \, f^{2} x^{2} + 6 \, f x + 1\right)} e^{\left(-6 \, f x\right)}\right)} c d^{2} e^{\left(-6 \, e\right)}}{2304 \, a^{3} f^{3}} + \frac{{\left(864 \, f^{4} x^{4} e^{\left(6 \, e\right)} + 1296 \, {\left(4 \, f^{3} x^{3} e^{\left(4 \, e\right)} + 6 \, f^{2} x^{2} e^{\left(4 \, e\right)} + 6 \, f x e^{\left(4 \, e\right)} + 3 \, e^{\left(4 \, e\right)}\right)} e^{\left(-2 \, f x\right)} - 81 \, {\left(32 \, f^{3} x^{3} e^{\left(2 \, e\right)} + 24 \, f^{2} x^{2} e^{\left(2 \, e\right)} + 12 \, f x e^{\left(2 \, e\right)} + 3 \, e^{\left(2 \, e\right)}\right)} e^{\left(-4 \, f x\right)} + 16 \, {\left(36 \, f^{3} x^{3} + 18 \, f^{2} x^{2} + 6 \, f x + 1\right)} e^{\left(-6 \, f x\right)}\right)} d^{3} e^{\left(-6 \, e\right)}}{27648 \, a^{3} f^{4}}"," ",0,"1/96*c^3*(12*(f*x + e)/(a^3*f) + (18*e^(-2*f*x - 2*e) - 9*e^(-4*f*x - 4*e) + 2*e^(-6*f*x - 6*e))/(a^3*f)) + 1/384*(72*f^2*x^2*e^(6*e) + 108*(2*f*x*e^(4*e) + e^(4*e))*e^(-2*f*x) - 27*(4*f*x*e^(2*e) + e^(2*e))*e^(-4*f*x) + 4*(6*f*x + 1)*e^(-6*f*x))*c^2*d*e^(-6*e)/(a^3*f^2) + 1/2304*(288*f^3*x^3*e^(6*e) + 648*(2*f^2*x^2*e^(4*e) + 2*f*x*e^(4*e) + e^(4*e))*e^(-2*f*x) - 81*(8*f^2*x^2*e^(2*e) + 4*f*x*e^(2*e) + e^(2*e))*e^(-4*f*x) + 8*(18*f^2*x^2 + 6*f*x + 1)*e^(-6*f*x))*c*d^2*e^(-6*e)/(a^3*f^3) + 1/27648*(864*f^4*x^4*e^(6*e) + 1296*(4*f^3*x^3*e^(4*e) + 6*f^2*x^2*e^(4*e) + 6*f*x*e^(4*e) + 3*e^(4*e))*e^(-2*f*x) - 81*(32*f^3*x^3*e^(2*e) + 24*f^2*x^2*e^(2*e) + 12*f*x*e^(2*e) + 3*e^(2*e))*e^(-4*f*x) + 16*(36*f^3*x^3 + 18*f^2*x^2 + 6*f*x + 1)*e^(-6*f*x))*d^3*e^(-6*e)/(a^3*f^4)","A",0
28,1,254,0,2.083350," ","integrate((d*x+c)^2/(a+a*coth(f*x+e))^3,x, algorithm=""maxima"")","\frac{1}{96} \, c^{2} {\left(\frac{12 \, {\left(f x + e\right)}}{a^{3} f} + \frac{18 \, e^{\left(-2 \, f x - 2 \, e\right)} - 9 \, e^{\left(-4 \, f x - 4 \, e\right)} + 2 \, e^{\left(-6 \, f x - 6 \, e\right)}}{a^{3} f}\right)} + \frac{{\left(72 \, f^{2} x^{2} e^{\left(6 \, e\right)} + 108 \, {\left(2 \, f x e^{\left(4 \, e\right)} + e^{\left(4 \, e\right)}\right)} e^{\left(-2 \, f x\right)} - 27 \, {\left(4 \, f x e^{\left(2 \, e\right)} + e^{\left(2 \, e\right)}\right)} e^{\left(-4 \, f x\right)} + 4 \, {\left(6 \, f x + 1\right)} e^{\left(-6 \, f x\right)}\right)} c d e^{\left(-6 \, e\right)}}{576 \, a^{3} f^{2}} + \frac{{\left(288 \, f^{3} x^{3} e^{\left(6 \, e\right)} + 648 \, {\left(2 \, f^{2} x^{2} e^{\left(4 \, e\right)} + 2 \, f x e^{\left(4 \, e\right)} + e^{\left(4 \, e\right)}\right)} e^{\left(-2 \, f x\right)} - 81 \, {\left(8 \, f^{2} x^{2} e^{\left(2 \, e\right)} + 4 \, f x e^{\left(2 \, e\right)} + e^{\left(2 \, e\right)}\right)} e^{\left(-4 \, f x\right)} + 8 \, {\left(18 \, f^{2} x^{2} + 6 \, f x + 1\right)} e^{\left(-6 \, f x\right)}\right)} d^{2} e^{\left(-6 \, e\right)}}{6912 \, a^{3} f^{3}}"," ",0,"1/96*c^2*(12*(f*x + e)/(a^3*f) + (18*e^(-2*f*x - 2*e) - 9*e^(-4*f*x - 4*e) + 2*e^(-6*f*x - 6*e))/(a^3*f)) + 1/576*(72*f^2*x^2*e^(6*e) + 108*(2*f*x*e^(4*e) + e^(4*e))*e^(-2*f*x) - 27*(4*f*x*e^(2*e) + e^(2*e))*e^(-4*f*x) + 4*(6*f*x + 1)*e^(-6*f*x))*c*d*e^(-6*e)/(a^3*f^2) + 1/6912*(288*f^3*x^3*e^(6*e) + 648*(2*f^2*x^2*e^(4*e) + 2*f*x*e^(4*e) + e^(4*e))*e^(-2*f*x) - 81*(8*f^2*x^2*e^(2*e) + 4*f*x*e^(2*e) + e^(2*e))*e^(-4*f*x) + 8*(18*f^2*x^2 + 6*f*x + 1)*e^(-6*f*x))*d^2*e^(-6*e)/(a^3*f^3)","A",0
29,1,138,0,1.163646," ","integrate((d*x+c)/(a+a*coth(f*x+e))^3,x, algorithm=""maxima"")","\frac{1}{96} \, c {\left(\frac{12 \, {\left(f x + e\right)}}{a^{3} f} + \frac{18 \, e^{\left(-2 \, f x - 2 \, e\right)} - 9 \, e^{\left(-4 \, f x - 4 \, e\right)} + 2 \, e^{\left(-6 \, f x - 6 \, e\right)}}{a^{3} f}\right)} + \frac{{\left(72 \, f^{2} x^{2} e^{\left(6 \, e\right)} + 108 \, {\left(2 \, f x e^{\left(4 \, e\right)} + e^{\left(4 \, e\right)}\right)} e^{\left(-2 \, f x\right)} - 27 \, {\left(4 \, f x e^{\left(2 \, e\right)} + e^{\left(2 \, e\right)}\right)} e^{\left(-4 \, f x\right)} + 4 \, {\left(6 \, f x + 1\right)} e^{\left(-6 \, f x\right)}\right)} d e^{\left(-6 \, e\right)}}{1152 \, a^{3} f^{2}}"," ",0,"1/96*c*(12*(f*x + e)/(a^3*f) + (18*e^(-2*f*x - 2*e) - 9*e^(-4*f*x - 4*e) + 2*e^(-6*f*x - 6*e))/(a^3*f)) + 1/1152*(72*f^2*x^2*e^(6*e) + 108*(2*f*x*e^(4*e) + e^(4*e))*e^(-2*f*x) - 27*(4*f*x*e^(2*e) + e^(2*e))*e^(-4*f*x) + 4*(6*f*x + 1)*e^(-6*f*x))*d*e^(-6*e)/(a^3*f^2)","A",0
30,1,114,0,4.112984," ","integrate(1/(d*x+c)/(a+a*coth(f*x+e))^3,x, algorithm=""maxima"")","\frac{e^{\left(-6 \, e + \frac{6 \, c f}{d}\right)} E_{1}\left(\frac{6 \, {\left(d x + c\right)} f}{d}\right)}{8 \, a^{3} d} - \frac{3 \, e^{\left(-4 \, e + \frac{4 \, c f}{d}\right)} E_{1}\left(\frac{4 \, {\left(d x + c\right)} f}{d}\right)}{8 \, a^{3} d} + \frac{3 \, e^{\left(-2 \, e + \frac{2 \, c f}{d}\right)} E_{1}\left(\frac{2 \, {\left(d x + c\right)} f}{d}\right)}{8 \, a^{3} d} + \frac{\log\left(d x + c\right)}{8 \, a^{3} d}"," ",0,"1/8*e^(-6*e + 6*c*f/d)*exp_integral_e(1, 6*(d*x + c)*f/d)/(a^3*d) - 3/8*e^(-4*e + 4*c*f/d)*exp_integral_e(1, 4*(d*x + c)*f/d)/(a^3*d) + 3/8*e^(-2*e + 2*c*f/d)*exp_integral_e(1, 2*(d*x + c)*f/d)/(a^3*d) + 1/8*log(d*x + c)/(a^3*d)","A",0
31,1,140,0,9.928294," ","integrate(1/(d*x+c)^2/(a+a*coth(f*x+e))^3,x, algorithm=""maxima"")","-\frac{1}{8 \, {\left(a^{3} d^{2} x + a^{3} c d\right)}} + \frac{e^{\left(-6 \, e + \frac{6 \, c f}{d}\right)} E_{2}\left(\frac{6 \, {\left(d x + c\right)} f}{d}\right)}{8 \, {\left(d x + c\right)} a^{3} d} - \frac{3 \, e^{\left(-4 \, e + \frac{4 \, c f}{d}\right)} E_{2}\left(\frac{4 \, {\left(d x + c\right)} f}{d}\right)}{8 \, {\left(d x + c\right)} a^{3} d} + \frac{3 \, e^{\left(-2 \, e + \frac{2 \, c f}{d}\right)} E_{2}\left(\frac{2 \, {\left(d x + c\right)} f}{d}\right)}{8 \, {\left(d x + c\right)} a^{3} d}"," ",0,"-1/8/(a^3*d^2*x + a^3*c*d) + 1/8*e^(-6*e + 6*c*f/d)*exp_integral_e(2, 6*(d*x + c)*f/d)/((d*x + c)*a^3*d) - 3/8*e^(-4*e + 4*c*f/d)*exp_integral_e(2, 4*(d*x + c)*f/d)/((d*x + c)*a^3*d) + 3/8*e^(-2*e + 2*c*f/d)*exp_integral_e(2, 2*(d*x + c)*f/d)/((d*x + c)*a^3*d)","A",0
32,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+a*coth(f*x+e))^2,x, algorithm=""maxima"")","\frac{{\left(d x + c\right)}^{m + 1} a^{2}}{d {\left(m + 1\right)}} + \int \frac{{\left(d x + c\right)}^{m} a^{2} {\left(e^{\left(f x + e\right)} + e^{\left(-f x - e\right)}\right)}^{2}}{{\left(e^{\left(f x + e\right)} - e^{\left(-f x - e\right)}\right)}^{2}} + \frac{2 \, {\left(d x + c\right)}^{m} a^{2} {\left(e^{\left(f x + e\right)} + e^{\left(-f x - e\right)}\right)}}{e^{\left(f x + e\right)} - e^{\left(-f x - e\right)}}\,{d x}"," ",0,"(d*x + c)^(m + 1)*a^2/(d*(m + 1)) + integrate((d*x + c)^m*a^2*(e^(f*x + e) + e^(-f*x - e))^2/(e^(f*x + e) - e^(-f*x - e))^2 + 2*(d*x + c)^m*a^2*(e^(f*x + e) + e^(-f*x - e))/(e^(f*x + e) - e^(-f*x - e)), x)","F",0
33,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+a*coth(f*x+e)),x, algorithm=""maxima"")","a \int \frac{{\left(d x + c\right)}^{m} {\left(e^{\left(f x + e\right)} + e^{\left(-f x - e\right)}\right)}}{e^{\left(f x + e\right)} - e^{\left(-f x - e\right)}}\,{d x} + \frac{{\left(d x + c\right)}^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"a*integrate((d*x + c)^m*(e^(f*x + e) + e^(-f*x - e))/(e^(f*x + e) - e^(-f*x - e)), x) + (d*x + c)^(m + 1)*a/(d*(m + 1))","F",0
34,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+a*coth(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(d x + c\right)}^{m}}{a \coth\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*x + c)^m/(a*coth(f*x + e) + a), x)","F",0
35,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+a*coth(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(d x + c\right)}^{m}}{{\left(a \coth\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x + c)^m/(a*coth(f*x + e) + a)^2, x)","F",0
36,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+a*coth(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{{\left(d x + c\right)}^{m}}{{\left(a \coth\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*x + c)^m/(a*coth(f*x + e) + a)^3, x)","F",0
37,1,419,0,0.477504," ","integrate((d*x+c)^3*(a+b*coth(f*x+e)),x, algorithm=""maxima"")","\frac{1}{4} \, a d^{3} x^{4} + \frac{1}{4} \, b d^{3} x^{4} + a c d^{2} x^{3} + b c d^{2} x^{3} + \frac{3}{2} \, a c^{2} d x^{2} + \frac{3}{2} \, b c^{2} d x^{2} + a c^{3} x + \frac{b c^{3} \log\left(\sinh\left(f x + e\right)\right)}{f} + \frac{3 \, {\left(f x \log\left(e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(-e^{\left(f x + e\right)}\right)\right)} b c^{2} d}{f^{2}} + \frac{3 \, {\left(f x \log\left(-e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(e^{\left(f x + e\right)}\right)\right)} b c^{2} d}{f^{2}} + \frac{3 \, {\left(f^{2} x^{2} \log\left(e^{\left(f x + e\right)} + 1\right) + 2 \, f x {\rm Li}_2\left(-e^{\left(f x + e\right)}\right) - 2 \, {\rm Li}_{3}(-e^{\left(f x + e\right)})\right)} b c d^{2}}{f^{3}} + \frac{3 \, {\left(f^{2} x^{2} \log\left(-e^{\left(f x + e\right)} + 1\right) + 2 \, f x {\rm Li}_2\left(e^{\left(f x + e\right)}\right) - 2 \, {\rm Li}_{3}(e^{\left(f x + e\right)})\right)} b c d^{2}}{f^{3}} + \frac{{\left(f^{3} x^{3} \log\left(e^{\left(f x + e\right)} + 1\right) + 3 \, f^{2} x^{2} {\rm Li}_2\left(-e^{\left(f x + e\right)}\right) - 6 \, f x {\rm Li}_{3}(-e^{\left(f x + e\right)}) + 6 \, {\rm Li}_{4}(-e^{\left(f x + e\right)})\right)} b d^{3}}{f^{4}} + \frac{{\left(f^{3} x^{3} \log\left(-e^{\left(f x + e\right)} + 1\right) + 3 \, f^{2} x^{2} {\rm Li}_2\left(e^{\left(f x + e\right)}\right) - 6 \, f x {\rm Li}_{3}(e^{\left(f x + e\right)}) + 6 \, {\rm Li}_{4}(e^{\left(f x + e\right)})\right)} b d^{3}}{f^{4}} - \frac{b d^{3} f^{4} x^{4} + 4 \, b c d^{2} f^{4} x^{3} + 6 \, b c^{2} d f^{4} x^{2}}{2 \, f^{4}}"," ",0,"1/4*a*d^3*x^4 + 1/4*b*d^3*x^4 + a*c*d^2*x^3 + b*c*d^2*x^3 + 3/2*a*c^2*d*x^2 + 3/2*b*c^2*d*x^2 + a*c^3*x + b*c^3*log(sinh(f*x + e))/f + 3*(f*x*log(e^(f*x + e) + 1) + dilog(-e^(f*x + e)))*b*c^2*d/f^2 + 3*(f*x*log(-e^(f*x + e) + 1) + dilog(e^(f*x + e)))*b*c^2*d/f^2 + 3*(f^2*x^2*log(e^(f*x + e) + 1) + 2*f*x*dilog(-e^(f*x + e)) - 2*polylog(3, -e^(f*x + e)))*b*c*d^2/f^3 + 3*(f^2*x^2*log(-e^(f*x + e) + 1) + 2*f*x*dilog(e^(f*x + e)) - 2*polylog(3, e^(f*x + e)))*b*c*d^2/f^3 + (f^3*x^3*log(e^(f*x + e) + 1) + 3*f^2*x^2*dilog(-e^(f*x + e)) - 6*f*x*polylog(3, -e^(f*x + e)) + 6*polylog(4, -e^(f*x + e)))*b*d^3/f^4 + (f^3*x^3*log(-e^(f*x + e) + 1) + 3*f^2*x^2*dilog(e^(f*x + e)) - 6*f*x*polylog(3, e^(f*x + e)) + 6*polylog(4, e^(f*x + e)))*b*d^3/f^4 - 1/2*(b*d^3*f^4*x^4 + 4*b*c*d^2*f^4*x^3 + 6*b*c^2*d*f^4*x^2)/f^4","B",0
38,1,240,0,0.486964," ","integrate((d*x+c)^2*(a+b*coth(f*x+e)),x, algorithm=""maxima"")","\frac{1}{3} \, a d^{2} x^{3} + \frac{1}{3} \, b d^{2} x^{3} + a c d x^{2} + b c d x^{2} + a c^{2} x + \frac{b c^{2} \log\left(\sinh\left(f x + e\right)\right)}{f} + \frac{2 \, {\left(f x \log\left(e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(-e^{\left(f x + e\right)}\right)\right)} b c d}{f^{2}} + \frac{2 \, {\left(f x \log\left(-e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(e^{\left(f x + e\right)}\right)\right)} b c d}{f^{2}} + \frac{{\left(f^{2} x^{2} \log\left(e^{\left(f x + e\right)} + 1\right) + 2 \, f x {\rm Li}_2\left(-e^{\left(f x + e\right)}\right) - 2 \, {\rm Li}_{3}(-e^{\left(f x + e\right)})\right)} b d^{2}}{f^{3}} + \frac{{\left(f^{2} x^{2} \log\left(-e^{\left(f x + e\right)} + 1\right) + 2 \, f x {\rm Li}_2\left(e^{\left(f x + e\right)}\right) - 2 \, {\rm Li}_{3}(e^{\left(f x + e\right)})\right)} b d^{2}}{f^{3}} - \frac{2 \, {\left(b d^{2} f^{3} x^{3} + 3 \, b c d f^{3} x^{2}\right)}}{3 \, f^{3}}"," ",0,"1/3*a*d^2*x^3 + 1/3*b*d^2*x^3 + a*c*d*x^2 + b*c*d*x^2 + a*c^2*x + b*c^2*log(sinh(f*x + e))/f + 2*(f*x*log(e^(f*x + e) + 1) + dilog(-e^(f*x + e)))*b*c*d/f^2 + 2*(f*x*log(-e^(f*x + e) + 1) + dilog(e^(f*x + e)))*b*c*d/f^2 + (f^2*x^2*log(e^(f*x + e) + 1) + 2*f*x*dilog(-e^(f*x + e)) - 2*polylog(3, -e^(f*x + e)))*b*d^2/f^3 + (f^2*x^2*log(-e^(f*x + e) + 1) + 2*f*x*dilog(e^(f*x + e)) - 2*polylog(3, e^(f*x + e)))*b*d^2/f^3 - 2/3*(b*d^2*f^3*x^3 + 3*b*c*d*f^3*x^2)/f^3","B",0
39,0,0,0,0.000000," ","integrate((d*x+c)*(a+b*coth(f*x+e)),x, algorithm=""maxima"")","\frac{1}{2} \, a d x^{2} + \frac{1}{2} \, {\left(x^{2} - 2 \, \int \frac{x}{e^{\left(f x + e\right)} + 1}\,{d x} + 2 \, \int \frac{x}{e^{\left(f x + e\right)} - 1}\,{d x}\right)} b d + a c x + \frac{b c \log\left(\sinh\left(f x + e\right)\right)}{f}"," ",0,"1/2*a*d*x^2 + 1/2*(x^2 - 2*integrate(x/(e^(f*x + e) + 1), x) + 2*integrate(x/(e^(f*x + e) - 1), x))*b*d + a*c*x + b*c*log(sinh(f*x + e))/f","F",0
40,0,0,0,0.000000," ","integrate((a+b*coth(f*x+e))/(d*x+c),x, algorithm=""maxima"")","b {\left(\frac{\log\left(d x + c\right)}{d} - \int \frac{1}{d x + {\left(d x e^{e} + c e^{e}\right)} e^{\left(f x\right)} + c}\,{d x} + \int -\frac{1}{d x - {\left(d x e^{e} + c e^{e}\right)} e^{\left(f x\right)} + c}\,{d x}\right)} + \frac{a \log\left(d x + c\right)}{d}"," ",0,"b*(log(d*x + c)/d - integrate(1/(d*x + (d*x*e^e + c*e^e)*e^(f*x) + c), x) + integrate(-1/(d*x - (d*x*e^e + c*e^e)*e^(f*x) + c), x)) + a*log(d*x + c)/d","F",0
41,0,0,0,0.000000," ","integrate((a+b*coth(f*x+e))/(d*x+c)^2,x, algorithm=""maxima"")","-b {\left(\frac{1}{d^{2} x + c d} + \int \frac{1}{d^{2} x^{2} + 2 \, c d x + c^{2} + {\left(d^{2} x^{2} e^{e} + 2 \, c d x e^{e} + c^{2} e^{e}\right)} e^{\left(f x\right)}}\,{d x} - \int -\frac{1}{d^{2} x^{2} + 2 \, c d x + c^{2} - {\left(d^{2} x^{2} e^{e} + 2 \, c d x e^{e} + c^{2} e^{e}\right)} e^{\left(f x\right)}}\,{d x}\right)} - \frac{a}{d^{2} x + c d}"," ",0,"-b*(1/(d^2*x + c*d) + integrate(1/(d^2*x^2 + 2*c*d*x + c^2 + (d^2*x^2*e^e + 2*c*d*x*e^e + c^2*e^e)*e^(f*x)), x) - integrate(-1/(d^2*x^2 + 2*c*d*x + c^2 - (d^2*x^2*e^e + 2*c*d*x*e^e + c^2*e^e)*e^(f*x)), x)) - a/(d^2*x + c*d)","F",0
42,1,781,0,0.501054," ","integrate((d*x+c)^3*(a+b*coth(f*x+e))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} d^{3} x^{4} + a^{2} c d^{2} x^{3} + \frac{3}{2} \, a^{2} c^{2} d x^{2} + a^{2} c^{3} x - \frac{6 \, b^{2} c^{2} d x}{f} + \frac{2 \, a b c^{3} \log\left(\sinh\left(f x + e\right)\right)}{f} + \frac{3 \, b^{2} c^{2} d \log\left(e^{\left(f x + e\right)} + 1\right)}{f^{2}} + \frac{3 \, b^{2} c^{2} d \log\left(e^{\left(f x + e\right)} - 1\right)}{f^{2}} + \frac{2 \, {\left(f^{3} x^{3} \log\left(e^{\left(f x + e\right)} + 1\right) + 3 \, f^{2} x^{2} {\rm Li}_2\left(-e^{\left(f x + e\right)}\right) - 6 \, f x {\rm Li}_{3}(-e^{\left(f x + e\right)}) + 6 \, {\rm Li}_{4}(-e^{\left(f x + e\right)})\right)} a b d^{3}}{f^{4}} + \frac{2 \, {\left(f^{3} x^{3} \log\left(-e^{\left(f x + e\right)} + 1\right) + 3 \, f^{2} x^{2} {\rm Li}_2\left(e^{\left(f x + e\right)}\right) - 6 \, f x {\rm Li}_{3}(e^{\left(f x + e\right)}) + 6 \, {\rm Li}_{4}(e^{\left(f x + e\right)})\right)} a b d^{3}}{f^{4}} - \frac{8 \, b^{2} c^{3} + {\left(2 \, a b d^{3} f + b^{2} d^{3} f\right)} x^{4} + 4 \, {\left(c^{3} f + 6 \, c^{2} d\right)} b^{2} x + 4 \, {\left(2 \, a b c d^{2} f + {\left(c d^{2} f + 2 \, d^{3}\right)} b^{2}\right)} x^{3} + 6 \, {\left(2 \, a b c^{2} d f + {\left(c^{2} d f + 4 \, c d^{2}\right)} b^{2}\right)} x^{2} - {\left(4 \, b^{2} c^{3} f x e^{\left(2 \, e\right)} + {\left(2 \, a b d^{3} f e^{\left(2 \, e\right)} + b^{2} d^{3} f e^{\left(2 \, e\right)}\right)} x^{4} + 4 \, {\left(2 \, a b c d^{2} f e^{\left(2 \, e\right)} + b^{2} c d^{2} f e^{\left(2 \, e\right)}\right)} x^{3} + 6 \, {\left(2 \, a b c^{2} d f e^{\left(2 \, e\right)} + b^{2} c^{2} d f e^{\left(2 \, e\right)}\right)} x^{2}\right)} e^{\left(2 \, f x\right)}}{4 \, {\left(f e^{\left(2 \, f x + 2 \, e\right)} - f\right)}} + \frac{6 \, {\left(a b c^{2} d f + b^{2} c d^{2}\right)} {\left(f x \log\left(e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(-e^{\left(f x + e\right)}\right)\right)}}{f^{3}} + \frac{6 \, {\left(a b c^{2} d f + b^{2} c d^{2}\right)} {\left(f x \log\left(-e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(e^{\left(f x + e\right)}\right)\right)}}{f^{3}} + \frac{3 \, {\left(2 \, a b c d^{2} f + b^{2} d^{3}\right)} {\left(f^{2} x^{2} \log\left(e^{\left(f x + e\right)} + 1\right) + 2 \, f x {\rm Li}_2\left(-e^{\left(f x + e\right)}\right) - 2 \, {\rm Li}_{3}(-e^{\left(f x + e\right)})\right)}}{f^{4}} + \frac{3 \, {\left(2 \, a b c d^{2} f + b^{2} d^{3}\right)} {\left(f^{2} x^{2} \log\left(-e^{\left(f x + e\right)} + 1\right) + 2 \, f x {\rm Li}_2\left(e^{\left(f x + e\right)}\right) - 2 \, {\rm Li}_{3}(e^{\left(f x + e\right)})\right)}}{f^{4}} - \frac{a b d^{3} f^{4} x^{4} + 2 \, {\left(2 \, a b c d^{2} f + b^{2} d^{3}\right)} f^{3} x^{3} + 6 \, {\left(a b c^{2} d f^{2} + b^{2} c d^{2} f\right)} f^{2} x^{2}}{f^{4}}"," ",0,"1/4*a^2*d^3*x^4 + a^2*c*d^2*x^3 + 3/2*a^2*c^2*d*x^2 + a^2*c^3*x - 6*b^2*c^2*d*x/f + 2*a*b*c^3*log(sinh(f*x + e))/f + 3*b^2*c^2*d*log(e^(f*x + e) + 1)/f^2 + 3*b^2*c^2*d*log(e^(f*x + e) - 1)/f^2 + 2*(f^3*x^3*log(e^(f*x + e) + 1) + 3*f^2*x^2*dilog(-e^(f*x + e)) - 6*f*x*polylog(3, -e^(f*x + e)) + 6*polylog(4, -e^(f*x + e)))*a*b*d^3/f^4 + 2*(f^3*x^3*log(-e^(f*x + e) + 1) + 3*f^2*x^2*dilog(e^(f*x + e)) - 6*f*x*polylog(3, e^(f*x + e)) + 6*polylog(4, e^(f*x + e)))*a*b*d^3/f^4 - 1/4*(8*b^2*c^3 + (2*a*b*d^3*f + b^2*d^3*f)*x^4 + 4*(c^3*f + 6*c^2*d)*b^2*x + 4*(2*a*b*c*d^2*f + (c*d^2*f + 2*d^3)*b^2)*x^3 + 6*(2*a*b*c^2*d*f + (c^2*d*f + 4*c*d^2)*b^2)*x^2 - (4*b^2*c^3*f*x*e^(2*e) + (2*a*b*d^3*f*e^(2*e) + b^2*d^3*f*e^(2*e))*x^4 + 4*(2*a*b*c*d^2*f*e^(2*e) + b^2*c*d^2*f*e^(2*e))*x^3 + 6*(2*a*b*c^2*d*f*e^(2*e) + b^2*c^2*d*f*e^(2*e))*x^2)*e^(2*f*x))/(f*e^(2*f*x + 2*e) - f) + 6*(a*b*c^2*d*f + b^2*c*d^2)*(f*x*log(e^(f*x + e) + 1) + dilog(-e^(f*x + e)))/f^3 + 6*(a*b*c^2*d*f + b^2*c*d^2)*(f*x*log(-e^(f*x + e) + 1) + dilog(e^(f*x + e)))/f^3 + 3*(2*a*b*c*d^2*f + b^2*d^3)*(f^2*x^2*log(e^(f*x + e) + 1) + 2*f*x*dilog(-e^(f*x + e)) - 2*polylog(3, -e^(f*x + e)))/f^4 + 3*(2*a*b*c*d^2*f + b^2*d^3)*(f^2*x^2*log(-e^(f*x + e) + 1) + 2*f*x*dilog(e^(f*x + e)) - 2*polylog(3, e^(f*x + e)))/f^4 - (a*b*d^3*f^4*x^4 + 2*(2*a*b*c*d^2*f + b^2*d^3)*f^3*x^3 + 6*(a*b*c^2*d*f^2 + b^2*c*d^2*f)*f^2*x^2)/f^4","B",0
43,1,494,0,0.476799," ","integrate((d*x+c)^2*(a+b*coth(f*x+e))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} d^{2} x^{3} + a^{2} c d x^{2} + a^{2} c^{2} x - \frac{4 \, b^{2} c d x}{f} + \frac{2 \, a b c^{2} \log\left(\sinh\left(f x + e\right)\right)}{f} + \frac{2 \, b^{2} c d \log\left(e^{\left(f x + e\right)} + 1\right)}{f^{2}} + \frac{2 \, b^{2} c d \log\left(e^{\left(f x + e\right)} - 1\right)}{f^{2}} + \frac{2 \, {\left(f^{2} x^{2} \log\left(e^{\left(f x + e\right)} + 1\right) + 2 \, f x {\rm Li}_2\left(-e^{\left(f x + e\right)}\right) - 2 \, {\rm Li}_{3}(-e^{\left(f x + e\right)})\right)} a b d^{2}}{f^{3}} + \frac{2 \, {\left(f^{2} x^{2} \log\left(-e^{\left(f x + e\right)} + 1\right) + 2 \, f x {\rm Li}_2\left(e^{\left(f x + e\right)}\right) - 2 \, {\rm Li}_{3}(e^{\left(f x + e\right)})\right)} a b d^{2}}{f^{3}} - \frac{6 \, b^{2} c^{2} + 3 \, {\left(c^{2} f + 4 \, c d\right)} b^{2} x + {\left(2 \, a b d^{2} f + b^{2} d^{2} f\right)} x^{3} + 3 \, {\left(2 \, a b c d f + {\left(c d f + 2 \, d^{2}\right)} b^{2}\right)} x^{2} - {\left(3 \, b^{2} c^{2} f x e^{\left(2 \, e\right)} + {\left(2 \, a b d^{2} f e^{\left(2 \, e\right)} + b^{2} d^{2} f e^{\left(2 \, e\right)}\right)} x^{3} + 3 \, {\left(2 \, a b c d f e^{\left(2 \, e\right)} + b^{2} c d f e^{\left(2 \, e\right)}\right)} x^{2}\right)} e^{\left(2 \, f x\right)}}{3 \, {\left(f e^{\left(2 \, f x + 2 \, e\right)} - f\right)}} + \frac{2 \, {\left(2 \, a b c d f + b^{2} d^{2}\right)} {\left(f x \log\left(e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(-e^{\left(f x + e\right)}\right)\right)}}{f^{3}} + \frac{2 \, {\left(2 \, a b c d f + b^{2} d^{2}\right)} {\left(f x \log\left(-e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(e^{\left(f x + e\right)}\right)\right)}}{f^{3}} - \frac{2 \, {\left(2 \, a b d^{2} f^{3} x^{3} + 3 \, {\left(2 \, a b c d f + b^{2} d^{2}\right)} f^{2} x^{2}\right)}}{3 \, f^{3}}"," ",0,"1/3*a^2*d^2*x^3 + a^2*c*d*x^2 + a^2*c^2*x - 4*b^2*c*d*x/f + 2*a*b*c^2*log(sinh(f*x + e))/f + 2*b^2*c*d*log(e^(f*x + e) + 1)/f^2 + 2*b^2*c*d*log(e^(f*x + e) - 1)/f^2 + 2*(f^2*x^2*log(e^(f*x + e) + 1) + 2*f*x*dilog(-e^(f*x + e)) - 2*polylog(3, -e^(f*x + e)))*a*b*d^2/f^3 + 2*(f^2*x^2*log(-e^(f*x + e) + 1) + 2*f*x*dilog(e^(f*x + e)) - 2*polylog(3, e^(f*x + e)))*a*b*d^2/f^3 - 1/3*(6*b^2*c^2 + 3*(c^2*f + 4*c*d)*b^2*x + (2*a*b*d^2*f + b^2*d^2*f)*x^3 + 3*(2*a*b*c*d*f + (c*d*f + 2*d^2)*b^2)*x^2 - (3*b^2*c^2*f*x*e^(2*e) + (2*a*b*d^2*f*e^(2*e) + b^2*d^2*f*e^(2*e))*x^3 + 3*(2*a*b*c*d*f*e^(2*e) + b^2*c*d*f*e^(2*e))*x^2)*e^(2*f*x))/(f*e^(2*f*x + 2*e) - f) + 2*(2*a*b*c*d*f + b^2*d^2)*(f*x*log(e^(f*x + e) + 1) + dilog(-e^(f*x + e)))/f^3 + 2*(2*a*b*c*d*f + b^2*d^2)*(f*x*log(-e^(f*x + e) + 1) + dilog(e^(f*x + e)))/f^3 - 2/3*(2*a*b*d^2*f^3*x^3 + 3*(2*a*b*c*d*f + b^2*d^2)*f^2*x^2)/f^3","B",0
44,1,244,0,0.496226," ","integrate((d*x+c)*(a+b*coth(f*x+e))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} d x^{2} - 2 \, a b d x^{2} + a^{2} c x - \frac{2 \, b^{2} d x}{f} + \frac{2 \, a b c \log\left(\sinh\left(f x + e\right)\right)}{f} + \frac{2 \, {\left(f x \log\left(e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(-e^{\left(f x + e\right)}\right)\right)} a b d}{f^{2}} + \frac{2 \, {\left(f x \log\left(-e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(e^{\left(f x + e\right)}\right)\right)} a b d}{f^{2}} + \frac{b^{2} d \log\left(e^{\left(f x + e\right)} + 1\right)}{f^{2}} + \frac{b^{2} d \log\left(e^{\left(f x + e\right)} - 1\right)}{f^{2}} - \frac{2 \, {\left(c f + 2 \, d\right)} b^{2} x + 4 \, b^{2} c + {\left(2 \, a b d f + b^{2} d f\right)} x^{2} - {\left(2 \, b^{2} c f x e^{\left(2 \, e\right)} + {\left(2 \, a b d f e^{\left(2 \, e\right)} + b^{2} d f e^{\left(2 \, e\right)}\right)} x^{2}\right)} e^{\left(2 \, f x\right)}}{2 \, {\left(f e^{\left(2 \, f x + 2 \, e\right)} - f\right)}}"," ",0,"1/2*a^2*d*x^2 - 2*a*b*d*x^2 + a^2*c*x - 2*b^2*d*x/f + 2*a*b*c*log(sinh(f*x + e))/f + 2*(f*x*log(e^(f*x + e) + 1) + dilog(-e^(f*x + e)))*a*b*d/f^2 + 2*(f*x*log(-e^(f*x + e) + 1) + dilog(e^(f*x + e)))*a*b*d/f^2 + b^2*d*log(e^(f*x + e) + 1)/f^2 + b^2*d*log(e^(f*x + e) - 1)/f^2 - 1/2*(2*(c*f + 2*d)*b^2*x + 4*b^2*c + (2*a*b*d*f + b^2*d*f)*x^2 - (2*b^2*c*f*x*e^(2*e) + (2*a*b*d*f*e^(2*e) + b^2*d*f*e^(2*e))*x^2)*e^(2*f*x))/(f*e^(2*f*x + 2*e) - f)","A",0
45,0,0,0,0.000000," ","integrate((a+b*coth(f*x+e))^2/(d*x+c),x, algorithm=""maxima"")","\frac{a^{2} \log\left(d x + c\right)}{d} + \frac{2 \, b^{2}}{d f x + c f - {\left(d f x e^{\left(2 \, e\right)} + c f e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}} + \frac{{\left(2 \, a b + b^{2}\right)} \log\left(d x + c\right)}{d} - \int \frac{2 \, a b d f x + 2 \, a b c f - b^{2} d}{d^{2} f x^{2} + 2 \, c d f x + c^{2} f + {\left(d^{2} f x^{2} e^{e} + 2 \, c d f x e^{e} + c^{2} f e^{e}\right)} e^{\left(f x\right)}}\,{d x} + \int -\frac{2 \, a b d f x + 2 \, a b c f - b^{2} d}{d^{2} f x^{2} + 2 \, c d f x + c^{2} f - {\left(d^{2} f x^{2} e^{e} + 2 \, c d f x e^{e} + c^{2} f e^{e}\right)} e^{\left(f x\right)}}\,{d x}"," ",0,"a^2*log(d*x + c)/d + 2*b^2/(d*f*x + c*f - (d*f*x*e^(2*e) + c*f*e^(2*e))*e^(2*f*x)) + (2*a*b + b^2)*log(d*x + c)/d - integrate((2*a*b*d*f*x + 2*a*b*c*f - b^2*d)/(d^2*f*x^2 + 2*c*d*f*x + c^2*f + (d^2*f*x^2*e^e + 2*c*d*f*x*e^e + c^2*f*e^e)*e^(f*x)), x) + integrate(-(2*a*b*d*f*x + 2*a*b*c*f - b^2*d)/(d^2*f*x^2 + 2*c*d*f*x + c^2*f - (d^2*f*x^2*e^e + 2*c*d*f*x*e^e + c^2*f*e^e)*e^(f*x)), x)","F",0
46,0,0,0,0.000000," ","integrate((a+b*coth(f*x+e))^2/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{a^{2}}{d^{2} x + c d} - \frac{2 \, a b c f + {\left(c f - 2 \, d\right)} b^{2} + {\left(2 \, a b d f + b^{2} d f\right)} x - {\left(2 \, a b c f e^{\left(2 \, e\right)} + b^{2} c f e^{\left(2 \, e\right)} + {\left(2 \, a b d f e^{\left(2 \, e\right)} + b^{2} d f e^{\left(2 \, e\right)}\right)} x\right)} e^{\left(2 \, f x\right)}}{d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f - {\left(d^{3} f x^{2} e^{\left(2 \, e\right)} + 2 \, c d^{2} f x e^{\left(2 \, e\right)} + c^{2} d f e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}} - \int \frac{2 \, {\left(a b d f x + a b c f - b^{2} d\right)}}{d^{3} f x^{3} + 3 \, c d^{2} f x^{2} + 3 \, c^{2} d f x + c^{3} f + {\left(d^{3} f x^{3} e^{e} + 3 \, c d^{2} f x^{2} e^{e} + 3 \, c^{2} d f x e^{e} + c^{3} f e^{e}\right)} e^{\left(f x\right)}}\,{d x} + \int -\frac{2 \, {\left(a b d f x + a b c f - b^{2} d\right)}}{d^{3} f x^{3} + 3 \, c d^{2} f x^{2} + 3 \, c^{2} d f x + c^{3} f - {\left(d^{3} f x^{3} e^{e} + 3 \, c d^{2} f x^{2} e^{e} + 3 \, c^{2} d f x e^{e} + c^{3} f e^{e}\right)} e^{\left(f x\right)}}\,{d x}"," ",0,"-a^2/(d^2*x + c*d) - (2*a*b*c*f + (c*f - 2*d)*b^2 + (2*a*b*d*f + b^2*d*f)*x - (2*a*b*c*f*e^(2*e) + b^2*c*f*e^(2*e) + (2*a*b*d*f*e^(2*e) + b^2*d*f*e^(2*e))*x)*e^(2*f*x))/(d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f - (d^3*f*x^2*e^(2*e) + 2*c*d^2*f*x*e^(2*e) + c^2*d*f*e^(2*e))*e^(2*f*x)) - integrate(2*(a*b*d*f*x + a*b*c*f - b^2*d)/(d^3*f*x^3 + 3*c*d^2*f*x^2 + 3*c^2*d*f*x + c^3*f + (d^3*f*x^3*e^e + 3*c*d^2*f*x^2*e^e + 3*c^2*d*f*x*e^e + c^3*f*e^e)*e^(f*x)), x) + integrate(-2*(a*b*d*f*x + a*b*c*f - b^2*d)/(d^3*f*x^3 + 3*c*d^2*f*x^2 + 3*c^2*d*f*x + c^3*f - (d^3*f*x^3*e^e + 3*c*d^2*f*x^2*e^e + 3*c^2*d*f*x*e^e + c^3*f*e^e)*e^(f*x)), x)","F",0
47,1,1531,0,0.534429," ","integrate((d*x+c)^3*(a+b*coth(f*x+e))^3,x, algorithm=""maxima"")","\frac{1}{4} \, a^{3} d^{3} x^{4} + a^{3} c d^{2} x^{3} + \frac{3}{2} \, a^{3} c^{2} d x^{2} + a^{3} c^{3} x + \frac{3 \, a^{2} b c^{3} \log\left(\sinh\left(f x + e\right)\right)}{f} + \frac{24 \, a b^{2} c^{3} f + 12 \, b^{3} c^{2} d + {\left(3 \, a^{2} b d^{3} f^{2} + 3 \, a b^{2} d^{3} f^{2} + b^{3} d^{3} f^{2}\right)} x^{4} + 4 \, {\left(3 \, a^{2} b c d^{2} f^{2} + b^{3} c d^{2} f^{2} + 3 \, {\left(c d^{2} f^{2} + 2 \, d^{3} f\right)} a b^{2}\right)} x^{3} + 6 \, {\left(3 \, a^{2} b c^{2} d f^{2} + 3 \, {\left(c^{2} d f^{2} + 4 \, c d^{2} f\right)} a b^{2} + {\left(c^{2} d f^{2} + 2 \, d^{3}\right)} b^{3}\right)} x^{2} + 4 \, {\left(3 \, {\left(c^{3} f^{2} + 6 \, c^{2} d f\right)} a b^{2} + {\left(c^{3} f^{2} + 6 \, c d^{2}\right)} b^{3}\right)} x + {\left({\left(3 \, a^{2} b d^{3} f^{2} e^{\left(4 \, e\right)} + 3 \, a b^{2} d^{3} f^{2} e^{\left(4 \, e\right)} + b^{3} d^{3} f^{2} e^{\left(4 \, e\right)}\right)} x^{4} + 4 \, {\left(3 \, a^{2} b c d^{2} f^{2} e^{\left(4 \, e\right)} + 3 \, a b^{2} c d^{2} f^{2} e^{\left(4 \, e\right)} + b^{3} c d^{2} f^{2} e^{\left(4 \, e\right)}\right)} x^{3} + 6 \, {\left(3 \, a^{2} b c^{2} d f^{2} e^{\left(4 \, e\right)} + 3 \, a b^{2} c^{2} d f^{2} e^{\left(4 \, e\right)} + b^{3} c^{2} d f^{2} e^{\left(4 \, e\right)}\right)} x^{2} + 4 \, {\left(3 \, a b^{2} c^{3} f^{2} e^{\left(4 \, e\right)} + b^{3} c^{3} f^{2} e^{\left(4 \, e\right)}\right)} x\right)} e^{\left(4 \, f x\right)} - 2 \, {\left(12 \, a b^{2} c^{3} f e^{\left(2 \, e\right)} + {\left(3 \, a^{2} b d^{3} f^{2} e^{\left(2 \, e\right)} + 3 \, a b^{2} d^{3} f^{2} e^{\left(2 \, e\right)} + b^{3} d^{3} f^{2} e^{\left(2 \, e\right)}\right)} x^{4} + 2 \, {\left(2 \, c^{3} f e^{\left(2 \, e\right)} + 3 \, c^{2} d e^{\left(2 \, e\right)}\right)} b^{3} + 4 \, {\left(3 \, a^{2} b c d^{2} f^{2} e^{\left(2 \, e\right)} + 3 \, {\left(c d^{2} f^{2} e^{\left(2 \, e\right)} + d^{3} f e^{\left(2 \, e\right)}\right)} a b^{2} + {\left(c d^{2} f^{2} e^{\left(2 \, e\right)} + d^{3} f e^{\left(2 \, e\right)}\right)} b^{3}\right)} x^{3} + 6 \, {\left(3 \, a^{2} b c^{2} d f^{2} e^{\left(2 \, e\right)} + 3 \, {\left(c^{2} d f^{2} e^{\left(2 \, e\right)} + 2 \, c d^{2} f e^{\left(2 \, e\right)}\right)} a b^{2} + {\left(c^{2} d f^{2} e^{\left(2 \, e\right)} + 2 \, c d^{2} f e^{\left(2 \, e\right)} + d^{3} e^{\left(2 \, e\right)}\right)} b^{3}\right)} x^{2} + 4 \, {\left(3 \, {\left(c^{3} f^{2} e^{\left(2 \, e\right)} + 3 \, c^{2} d f e^{\left(2 \, e\right)}\right)} a b^{2} + {\left(c^{3} f^{2} e^{\left(2 \, e\right)} + 3 \, c^{2} d f e^{\left(2 \, e\right)} + 3 \, c d^{2} e^{\left(2 \, e\right)}\right)} b^{3}\right)} x\right)} e^{\left(2 \, f x\right)}}{4 \, {\left(f^{2} e^{\left(4 \, f x + 4 \, e\right)} - 2 \, f^{2} e^{\left(2 \, f x + 2 \, e\right)} + f^{2}\right)}} - \frac{2 \, {\left(9 \, a b^{2} c^{2} d f + {\left(c^{3} f^{2} + 3 \, c d^{2}\right)} b^{3}\right)} x}{f^{2}} + \frac{{\left(9 \, a b^{2} c^{2} d f + {\left(c^{3} f^{2} + 3 \, c d^{2}\right)} b^{3}\right)} \log\left(e^{\left(f x + e\right)} + 1\right)}{f^{3}} + \frac{{\left(9 \, a b^{2} c^{2} d f + {\left(c^{3} f^{2} + 3 \, c d^{2}\right)} b^{3}\right)} \log\left(e^{\left(f x + e\right)} - 1\right)}{f^{3}} + \frac{{\left(f^{3} x^{3} \log\left(e^{\left(f x + e\right)} + 1\right) + 3 \, f^{2} x^{2} {\rm Li}_2\left(-e^{\left(f x + e\right)}\right) - 6 \, f x {\rm Li}_{3}(-e^{\left(f x + e\right)}) + 6 \, {\rm Li}_{4}(-e^{\left(f x + e\right)})\right)} {\left(3 \, a^{2} b d^{3} + b^{3} d^{3}\right)}}{f^{4}} + \frac{{\left(f^{3} x^{3} \log\left(-e^{\left(f x + e\right)} + 1\right) + 3 \, f^{2} x^{2} {\rm Li}_2\left(e^{\left(f x + e\right)}\right) - 6 \, f x {\rm Li}_{3}(e^{\left(f x + e\right)}) + 6 \, {\rm Li}_{4}(e^{\left(f x + e\right)})\right)} {\left(3 \, a^{2} b d^{3} + b^{3} d^{3}\right)}}{f^{4}} + \frac{3 \, {\left(3 \, a^{2} b c d^{2} f + b^{3} c d^{2} f + 3 \, a b^{2} d^{3}\right)} {\left(f^{2} x^{2} \log\left(e^{\left(f x + e\right)} + 1\right) + 2 \, f x {\rm Li}_2\left(-e^{\left(f x + e\right)}\right) - 2 \, {\rm Li}_{3}(-e^{\left(f x + e\right)})\right)}}{f^{4}} + \frac{3 \, {\left(3 \, a^{2} b c d^{2} f + b^{3} c d^{2} f + 3 \, a b^{2} d^{3}\right)} {\left(f^{2} x^{2} \log\left(-e^{\left(f x + e\right)} + 1\right) + 2 \, f x {\rm Li}_2\left(e^{\left(f x + e\right)}\right) - 2 \, {\rm Li}_{3}(e^{\left(f x + e\right)})\right)}}{f^{4}} + \frac{3 \, {\left(3 \, a^{2} b c^{2} d f^{2} + 6 \, a b^{2} c d^{2} f + {\left(c^{2} d f^{2} + d^{3}\right)} b^{3}\right)} {\left(f x \log\left(e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(-e^{\left(f x + e\right)}\right)\right)}}{f^{4}} + \frac{3 \, {\left(3 \, a^{2} b c^{2} d f^{2} + 6 \, a b^{2} c d^{2} f + {\left(c^{2} d f^{2} + d^{3}\right)} b^{3}\right)} {\left(f x \log\left(-e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(e^{\left(f x + e\right)}\right)\right)}}{f^{4}} - \frac{{\left(3 \, a^{2} b d^{3} + b^{3} d^{3}\right)} f^{4} x^{4} + 4 \, {\left(3 \, a^{2} b c d^{2} f + b^{3} c d^{2} f + 3 \, a b^{2} d^{3}\right)} f^{3} x^{3} + 6 \, {\left(3 \, a^{2} b c^{2} d f^{2} + 6 \, a b^{2} c d^{2} f + {\left(c^{2} d f^{2} + d^{3}\right)} b^{3}\right)} f^{2} x^{2}}{2 \, f^{4}}"," ",0,"1/4*a^3*d^3*x^4 + a^3*c*d^2*x^3 + 3/2*a^3*c^2*d*x^2 + a^3*c^3*x + 3*a^2*b*c^3*log(sinh(f*x + e))/f + 1/4*(24*a*b^2*c^3*f + 12*b^3*c^2*d + (3*a^2*b*d^3*f^2 + 3*a*b^2*d^3*f^2 + b^3*d^3*f^2)*x^4 + 4*(3*a^2*b*c*d^2*f^2 + b^3*c*d^2*f^2 + 3*(c*d^2*f^2 + 2*d^3*f)*a*b^2)*x^3 + 6*(3*a^2*b*c^2*d*f^2 + 3*(c^2*d*f^2 + 4*c*d^2*f)*a*b^2 + (c^2*d*f^2 + 2*d^3)*b^3)*x^2 + 4*(3*(c^3*f^2 + 6*c^2*d*f)*a*b^2 + (c^3*f^2 + 6*c*d^2)*b^3)*x + ((3*a^2*b*d^3*f^2*e^(4*e) + 3*a*b^2*d^3*f^2*e^(4*e) + b^3*d^3*f^2*e^(4*e))*x^4 + 4*(3*a^2*b*c*d^2*f^2*e^(4*e) + 3*a*b^2*c*d^2*f^2*e^(4*e) + b^3*c*d^2*f^2*e^(4*e))*x^3 + 6*(3*a^2*b*c^2*d*f^2*e^(4*e) + 3*a*b^2*c^2*d*f^2*e^(4*e) + b^3*c^2*d*f^2*e^(4*e))*x^2 + 4*(3*a*b^2*c^3*f^2*e^(4*e) + b^3*c^3*f^2*e^(4*e))*x)*e^(4*f*x) - 2*(12*a*b^2*c^3*f*e^(2*e) + (3*a^2*b*d^3*f^2*e^(2*e) + 3*a*b^2*d^3*f^2*e^(2*e) + b^3*d^3*f^2*e^(2*e))*x^4 + 2*(2*c^3*f*e^(2*e) + 3*c^2*d*e^(2*e))*b^3 + 4*(3*a^2*b*c*d^2*f^2*e^(2*e) + 3*(c*d^2*f^2*e^(2*e) + d^3*f*e^(2*e))*a*b^2 + (c*d^2*f^2*e^(2*e) + d^3*f*e^(2*e))*b^3)*x^3 + 6*(3*a^2*b*c^2*d*f^2*e^(2*e) + 3*(c^2*d*f^2*e^(2*e) + 2*c*d^2*f*e^(2*e))*a*b^2 + (c^2*d*f^2*e^(2*e) + 2*c*d^2*f*e^(2*e) + d^3*e^(2*e))*b^3)*x^2 + 4*(3*(c^3*f^2*e^(2*e) + 3*c^2*d*f*e^(2*e))*a*b^2 + (c^3*f^2*e^(2*e) + 3*c^2*d*f*e^(2*e) + 3*c*d^2*e^(2*e))*b^3)*x)*e^(2*f*x))/(f^2*e^(4*f*x + 4*e) - 2*f^2*e^(2*f*x + 2*e) + f^2) - 2*(9*a*b^2*c^2*d*f + (c^3*f^2 + 3*c*d^2)*b^3)*x/f^2 + (9*a*b^2*c^2*d*f + (c^3*f^2 + 3*c*d^2)*b^3)*log(e^(f*x + e) + 1)/f^3 + (9*a*b^2*c^2*d*f + (c^3*f^2 + 3*c*d^2)*b^3)*log(e^(f*x + e) - 1)/f^3 + (f^3*x^3*log(e^(f*x + e) + 1) + 3*f^2*x^2*dilog(-e^(f*x + e)) - 6*f*x*polylog(3, -e^(f*x + e)) + 6*polylog(4, -e^(f*x + e)))*(3*a^2*b*d^3 + b^3*d^3)/f^4 + (f^3*x^3*log(-e^(f*x + e) + 1) + 3*f^2*x^2*dilog(e^(f*x + e)) - 6*f*x*polylog(3, e^(f*x + e)) + 6*polylog(4, e^(f*x + e)))*(3*a^2*b*d^3 + b^3*d^3)/f^4 + 3*(3*a^2*b*c*d^2*f + b^3*c*d^2*f + 3*a*b^2*d^3)*(f^2*x^2*log(e^(f*x + e) + 1) + 2*f*x*dilog(-e^(f*x + e)) - 2*polylog(3, -e^(f*x + e)))/f^4 + 3*(3*a^2*b*c*d^2*f + b^3*c*d^2*f + 3*a*b^2*d^3)*(f^2*x^2*log(-e^(f*x + e) + 1) + 2*f*x*dilog(e^(f*x + e)) - 2*polylog(3, e^(f*x + e)))/f^4 + 3*(3*a^2*b*c^2*d*f^2 + 6*a*b^2*c*d^2*f + (c^2*d*f^2 + d^3)*b^3)*(f*x*log(e^(f*x + e) + 1) + dilog(-e^(f*x + e)))/f^4 + 3*(3*a^2*b*c^2*d*f^2 + 6*a*b^2*c*d^2*f + (c^2*d*f^2 + d^3)*b^3)*(f*x*log(-e^(f*x + e) + 1) + dilog(e^(f*x + e)))/f^4 - 1/2*((3*a^2*b*d^3 + b^3*d^3)*f^4*x^4 + 4*(3*a^2*b*c*d^2*f + b^3*c*d^2*f + 3*a*b^2*d^3)*f^3*x^3 + 6*(3*a^2*b*c^2*d*f^2 + 6*a*b^2*c*d^2*f + (c^2*d*f^2 + d^3)*b^3)*f^2*x^2)/f^4","B",0
48,1,997,0,0.505005," ","integrate((d*x+c)^2*(a+b*coth(f*x+e))^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} d^{2} x^{3} + a^{3} c d x^{2} + a^{3} c^{2} x + \frac{3 \, a^{2} b c^{2} \log\left(\sinh\left(f x + e\right)\right)}{f} + \frac{18 \, a b^{2} c^{2} f + 6 \, b^{3} c d + {\left(3 \, a^{2} b d^{2} f^{2} + 3 \, a b^{2} d^{2} f^{2} + b^{3} d^{2} f^{2}\right)} x^{3} + 3 \, {\left(3 \, a^{2} b c d f^{2} + b^{3} c d f^{2} + 3 \, {\left(c d f^{2} + 2 \, d^{2} f\right)} a b^{2}\right)} x^{2} + 3 \, {\left(3 \, {\left(c^{2} f^{2} + 4 \, c d f\right)} a b^{2} + {\left(c^{2} f^{2} + 2 \, d^{2}\right)} b^{3}\right)} x + {\left({\left(3 \, a^{2} b d^{2} f^{2} e^{\left(4 \, e\right)} + 3 \, a b^{2} d^{2} f^{2} e^{\left(4 \, e\right)} + b^{3} d^{2} f^{2} e^{\left(4 \, e\right)}\right)} x^{3} + 3 \, {\left(3 \, a^{2} b c d f^{2} e^{\left(4 \, e\right)} + 3 \, a b^{2} c d f^{2} e^{\left(4 \, e\right)} + b^{3} c d f^{2} e^{\left(4 \, e\right)}\right)} x^{2} + 3 \, {\left(3 \, a b^{2} c^{2} f^{2} e^{\left(4 \, e\right)} + b^{3} c^{2} f^{2} e^{\left(4 \, e\right)}\right)} x\right)} e^{\left(4 \, f x\right)} - 2 \, {\left(9 \, a b^{2} c^{2} f e^{\left(2 \, e\right)} + 3 \, {\left(c^{2} f e^{\left(2 \, e\right)} + c d e^{\left(2 \, e\right)}\right)} b^{3} + {\left(3 \, a^{2} b d^{2} f^{2} e^{\left(2 \, e\right)} + 3 \, a b^{2} d^{2} f^{2} e^{\left(2 \, e\right)} + b^{3} d^{2} f^{2} e^{\left(2 \, e\right)}\right)} x^{3} + 3 \, {\left(3 \, a^{2} b c d f^{2} e^{\left(2 \, e\right)} + 3 \, {\left(c d f^{2} e^{\left(2 \, e\right)} + d^{2} f e^{\left(2 \, e\right)}\right)} a b^{2} + {\left(c d f^{2} e^{\left(2 \, e\right)} + d^{2} f e^{\left(2 \, e\right)}\right)} b^{3}\right)} x^{2} + 3 \, {\left(3 \, {\left(c^{2} f^{2} e^{\left(2 \, e\right)} + 2 \, c d f e^{\left(2 \, e\right)}\right)} a b^{2} + {\left(c^{2} f^{2} e^{\left(2 \, e\right)} + 2 \, c d f e^{\left(2 \, e\right)} + d^{2} e^{\left(2 \, e\right)}\right)} b^{3}\right)} x\right)} e^{\left(2 \, f x\right)}}{3 \, {\left(f^{2} e^{\left(4 \, f x + 4 \, e\right)} - 2 \, f^{2} e^{\left(2 \, f x + 2 \, e\right)} + f^{2}\right)}} - \frac{2 \, {\left(6 \, a b^{2} c d f + {\left(c^{2} f^{2} + d^{2}\right)} b^{3}\right)} x}{f^{2}} + \frac{{\left(3 \, a^{2} b d^{2} + b^{3} d^{2}\right)} {\left(f^{2} x^{2} \log\left(e^{\left(f x + e\right)} + 1\right) + 2 \, f x {\rm Li}_2\left(-e^{\left(f x + e\right)}\right) - 2 \, {\rm Li}_{3}(-e^{\left(f x + e\right)})\right)}}{f^{3}} + \frac{{\left(3 \, a^{2} b d^{2} + b^{3} d^{2}\right)} {\left(f^{2} x^{2} \log\left(-e^{\left(f x + e\right)} + 1\right) + 2 \, f x {\rm Li}_2\left(e^{\left(f x + e\right)}\right) - 2 \, {\rm Li}_{3}(e^{\left(f x + e\right)})\right)}}{f^{3}} + \frac{2 \, {\left(3 \, a^{2} b c d f + b^{3} c d f + 3 \, a b^{2} d^{2}\right)} {\left(f x \log\left(e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(-e^{\left(f x + e\right)}\right)\right)}}{f^{3}} + \frac{2 \, {\left(3 \, a^{2} b c d f + b^{3} c d f + 3 \, a b^{2} d^{2}\right)} {\left(f x \log\left(-e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(e^{\left(f x + e\right)}\right)\right)}}{f^{3}} + \frac{{\left(6 \, a b^{2} c d f + {\left(c^{2} f^{2} + d^{2}\right)} b^{3}\right)} \log\left(e^{\left(f x + e\right)} + 1\right)}{f^{3}} + \frac{{\left(6 \, a b^{2} c d f + {\left(c^{2} f^{2} + d^{2}\right)} b^{3}\right)} \log\left(e^{\left(f x + e\right)} - 1\right)}{f^{3}} - \frac{2 \, {\left({\left(3 \, a^{2} b d^{2} + b^{3} d^{2}\right)} f^{3} x^{3} + 3 \, {\left(3 \, a^{2} b c d f + b^{3} c d f + 3 \, a b^{2} d^{2}\right)} f^{2} x^{2}\right)}}{3 \, f^{3}}"," ",0,"1/3*a^3*d^2*x^3 + a^3*c*d*x^2 + a^3*c^2*x + 3*a^2*b*c^2*log(sinh(f*x + e))/f + 1/3*(18*a*b^2*c^2*f + 6*b^3*c*d + (3*a^2*b*d^2*f^2 + 3*a*b^2*d^2*f^2 + b^3*d^2*f^2)*x^3 + 3*(3*a^2*b*c*d*f^2 + b^3*c*d*f^2 + 3*(c*d*f^2 + 2*d^2*f)*a*b^2)*x^2 + 3*(3*(c^2*f^2 + 4*c*d*f)*a*b^2 + (c^2*f^2 + 2*d^2)*b^3)*x + ((3*a^2*b*d^2*f^2*e^(4*e) + 3*a*b^2*d^2*f^2*e^(4*e) + b^3*d^2*f^2*e^(4*e))*x^3 + 3*(3*a^2*b*c*d*f^2*e^(4*e) + 3*a*b^2*c*d*f^2*e^(4*e) + b^3*c*d*f^2*e^(4*e))*x^2 + 3*(3*a*b^2*c^2*f^2*e^(4*e) + b^3*c^2*f^2*e^(4*e))*x)*e^(4*f*x) - 2*(9*a*b^2*c^2*f*e^(2*e) + 3*(c^2*f*e^(2*e) + c*d*e^(2*e))*b^3 + (3*a^2*b*d^2*f^2*e^(2*e) + 3*a*b^2*d^2*f^2*e^(2*e) + b^3*d^2*f^2*e^(2*e))*x^3 + 3*(3*a^2*b*c*d*f^2*e^(2*e) + 3*(c*d*f^2*e^(2*e) + d^2*f*e^(2*e))*a*b^2 + (c*d*f^2*e^(2*e) + d^2*f*e^(2*e))*b^3)*x^2 + 3*(3*(c^2*f^2*e^(2*e) + 2*c*d*f*e^(2*e))*a*b^2 + (c^2*f^2*e^(2*e) + 2*c*d*f*e^(2*e) + d^2*e^(2*e))*b^3)*x)*e^(2*f*x))/(f^2*e^(4*f*x + 4*e) - 2*f^2*e^(2*f*x + 2*e) + f^2) - 2*(6*a*b^2*c*d*f + (c^2*f^2 + d^2)*b^3)*x/f^2 + (3*a^2*b*d^2 + b^3*d^2)*(f^2*x^2*log(e^(f*x + e) + 1) + 2*f*x*dilog(-e^(f*x + e)) - 2*polylog(3, -e^(f*x + e)))/f^3 + (3*a^2*b*d^2 + b^3*d^2)*(f^2*x^2*log(-e^(f*x + e) + 1) + 2*f*x*dilog(e^(f*x + e)) - 2*polylog(3, e^(f*x + e)))/f^3 + 2*(3*a^2*b*c*d*f + b^3*c*d*f + 3*a*b^2*d^2)*(f*x*log(e^(f*x + e) + 1) + dilog(-e^(f*x + e)))/f^3 + 2*(3*a^2*b*c*d*f + b^3*c*d*f + 3*a*b^2*d^2)*(f*x*log(-e^(f*x + e) + 1) + dilog(e^(f*x + e)))/f^3 + (6*a*b^2*c*d*f + (c^2*f^2 + d^2)*b^3)*log(e^(f*x + e) + 1)/f^3 + (6*a*b^2*c*d*f + (c^2*f^2 + d^2)*b^3)*log(e^(f*x + e) - 1)/f^3 - 2/3*((3*a^2*b*d^2 + b^3*d^2)*f^3*x^3 + 3*(3*a^2*b*c*d*f + b^3*c*d*f + 3*a*b^2*d^2)*f^2*x^2)/f^3","B",0
49,1,528,0,0.468063," ","integrate((d*x+c)*(a+b*coth(f*x+e))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} d x^{2} + a^{3} c x + \frac{3 \, a^{2} b c \log\left(\sinh\left(f x + e\right)\right)}{f} - {\left(3 \, a^{2} b d + b^{3} d\right)} x^{2} - \frac{2 \, {\left(b^{3} c f + 3 \, a b^{2} d\right)} x}{f} + \frac{12 \, a b^{2} c f + 2 \, b^{3} d + {\left(3 \, a^{2} b d f^{2} + 3 \, a b^{2} d f^{2} + b^{3} d f^{2}\right)} x^{2} + 2 \, {\left(b^{3} c f^{2} + 3 \, {\left(c f^{2} + 2 \, d f\right)} a b^{2}\right)} x + {\left({\left(3 \, a^{2} b d f^{2} e^{\left(4 \, e\right)} + 3 \, a b^{2} d f^{2} e^{\left(4 \, e\right)} + b^{3} d f^{2} e^{\left(4 \, e\right)}\right)} x^{2} + 2 \, {\left(3 \, a b^{2} c f^{2} e^{\left(4 \, e\right)} + b^{3} c f^{2} e^{\left(4 \, e\right)}\right)} x\right)} e^{\left(4 \, f x\right)} - 2 \, {\left(6 \, a b^{2} c f e^{\left(2 \, e\right)} + {\left(2 \, c f e^{\left(2 \, e\right)} + d e^{\left(2 \, e\right)}\right)} b^{3} + {\left(3 \, a^{2} b d f^{2} e^{\left(2 \, e\right)} + 3 \, a b^{2} d f^{2} e^{\left(2 \, e\right)} + b^{3} d f^{2} e^{\left(2 \, e\right)}\right)} x^{2} + 2 \, {\left(3 \, {\left(c f^{2} e^{\left(2 \, e\right)} + d f e^{\left(2 \, e\right)}\right)} a b^{2} + {\left(c f^{2} e^{\left(2 \, e\right)} + d f e^{\left(2 \, e\right)}\right)} b^{3}\right)} x\right)} e^{\left(2 \, f x\right)}}{2 \, {\left(f^{2} e^{\left(4 \, f x + 4 \, e\right)} - 2 \, f^{2} e^{\left(2 \, f x + 2 \, e\right)} + f^{2}\right)}} + \frac{{\left(3 \, a^{2} b d + b^{3} d\right)} {\left(f x \log\left(e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(-e^{\left(f x + e\right)}\right)\right)}}{f^{2}} + \frac{{\left(3 \, a^{2} b d + b^{3} d\right)} {\left(f x \log\left(-e^{\left(f x + e\right)} + 1\right) + {\rm Li}_2\left(e^{\left(f x + e\right)}\right)\right)}}{f^{2}} + \frac{{\left(b^{3} c f + 3 \, a b^{2} d\right)} \log\left(e^{\left(f x + e\right)} + 1\right)}{f^{2}} + \frac{{\left(b^{3} c f + 3 \, a b^{2} d\right)} \log\left(e^{\left(f x + e\right)} - 1\right)}{f^{2}}"," ",0,"1/2*a^3*d*x^2 + a^3*c*x + 3*a^2*b*c*log(sinh(f*x + e))/f - (3*a^2*b*d + b^3*d)*x^2 - 2*(b^3*c*f + 3*a*b^2*d)*x/f + 1/2*(12*a*b^2*c*f + 2*b^3*d + (3*a^2*b*d*f^2 + 3*a*b^2*d*f^2 + b^3*d*f^2)*x^2 + 2*(b^3*c*f^2 + 3*(c*f^2 + 2*d*f)*a*b^2)*x + ((3*a^2*b*d*f^2*e^(4*e) + 3*a*b^2*d*f^2*e^(4*e) + b^3*d*f^2*e^(4*e))*x^2 + 2*(3*a*b^2*c*f^2*e^(4*e) + b^3*c*f^2*e^(4*e))*x)*e^(4*f*x) - 2*(6*a*b^2*c*f*e^(2*e) + (2*c*f*e^(2*e) + d*e^(2*e))*b^3 + (3*a^2*b*d*f^2*e^(2*e) + 3*a*b^2*d*f^2*e^(2*e) + b^3*d*f^2*e^(2*e))*x^2 + 2*(3*(c*f^2*e^(2*e) + d*f*e^(2*e))*a*b^2 + (c*f^2*e^(2*e) + d*f*e^(2*e))*b^3)*x)*e^(2*f*x))/(f^2*e^(4*f*x + 4*e) - 2*f^2*e^(2*f*x + 2*e) + f^2) + (3*a^2*b*d + b^3*d)*(f*x*log(e^(f*x + e) + 1) + dilog(-e^(f*x + e)))/f^2 + (3*a^2*b*d + b^3*d)*(f*x*log(-e^(f*x + e) + 1) + dilog(e^(f*x + e)))/f^2 + (b^3*c*f + 3*a*b^2*d)*log(e^(f*x + e) + 1)/f^2 + (b^3*c*f + 3*a*b^2*d)*log(e^(f*x + e) - 1)/f^2","B",0
50,0,0,0,0.000000," ","integrate((a+b*coth(f*x+e))^3/(d*x+c),x, algorithm=""maxima"")","\frac{a^{3} \log\left(d x + c\right)}{d} + \frac{{\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(d x + c\right)}{d} + \frac{6 \, a b^{2} d f x + 6 \, a b^{2} c f - b^{3} d - {\left(6 \, a b^{2} c f e^{\left(2 \, e\right)} + {\left(2 \, c f e^{\left(2 \, e\right)} - d e^{\left(2 \, e\right)}\right)} b^{3} + 2 \, {\left(3 \, a b^{2} d f e^{\left(2 \, e\right)} + b^{3} d f e^{\left(2 \, e\right)}\right)} x\right)} e^{\left(2 \, f x\right)}}{d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + {\left(d^{2} f^{2} x^{2} e^{\left(4 \, e\right)} + 2 \, c d f^{2} x e^{\left(4 \, e\right)} + c^{2} f^{2} e^{\left(4 \, e\right)}\right)} e^{\left(4 \, f x\right)} - 2 \, {\left(d^{2} f^{2} x^{2} e^{\left(2 \, e\right)} + 2 \, c d f^{2} x e^{\left(2 \, e\right)} + c^{2} f^{2} e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}} - \int \frac{3 \, a^{2} b c^{2} f^{2} - 3 \, a b^{2} c d f + {\left(c^{2} f^{2} + d^{2}\right)} b^{3} + {\left(3 \, a^{2} b d^{2} f^{2} + b^{3} d^{2} f^{2}\right)} x^{2} + {\left(6 \, a^{2} b c d f^{2} + 2 \, b^{3} c d f^{2} - 3 \, a b^{2} d^{2} f\right)} x}{d^{3} f^{2} x^{3} + 3 \, c d^{2} f^{2} x^{2} + 3 \, c^{2} d f^{2} x + c^{3} f^{2} + {\left(d^{3} f^{2} x^{3} e^{e} + 3 \, c d^{2} f^{2} x^{2} e^{e} + 3 \, c^{2} d f^{2} x e^{e} + c^{3} f^{2} e^{e}\right)} e^{\left(f x\right)}}\,{d x} + \int -\frac{3 \, a^{2} b c^{2} f^{2} - 3 \, a b^{2} c d f + {\left(c^{2} f^{2} + d^{2}\right)} b^{3} + {\left(3 \, a^{2} b d^{2} f^{2} + b^{3} d^{2} f^{2}\right)} x^{2} + {\left(6 \, a^{2} b c d f^{2} + 2 \, b^{3} c d f^{2} - 3 \, a b^{2} d^{2} f\right)} x}{d^{3} f^{2} x^{3} + 3 \, c d^{2} f^{2} x^{2} + 3 \, c^{2} d f^{2} x + c^{3} f^{2} - {\left(d^{3} f^{2} x^{3} e^{e} + 3 \, c d^{2} f^{2} x^{2} e^{e} + 3 \, c^{2} d f^{2} x e^{e} + c^{3} f^{2} e^{e}\right)} e^{\left(f x\right)}}\,{d x}"," ",0,"a^3*log(d*x + c)/d + (3*a^2*b + 3*a*b^2 + b^3)*log(d*x + c)/d + (6*a*b^2*d*f*x + 6*a*b^2*c*f - b^3*d - (6*a*b^2*c*f*e^(2*e) + (2*c*f*e^(2*e) - d*e^(2*e))*b^3 + 2*(3*a*b^2*d*f*e^(2*e) + b^3*d*f*e^(2*e))*x)*e^(2*f*x))/(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + (d^2*f^2*x^2*e^(4*e) + 2*c*d*f^2*x*e^(4*e) + c^2*f^2*e^(4*e))*e^(4*f*x) - 2*(d^2*f^2*x^2*e^(2*e) + 2*c*d*f^2*x*e^(2*e) + c^2*f^2*e^(2*e))*e^(2*f*x)) - integrate((3*a^2*b*c^2*f^2 - 3*a*b^2*c*d*f + (c^2*f^2 + d^2)*b^3 + (3*a^2*b*d^2*f^2 + b^3*d^2*f^2)*x^2 + (6*a^2*b*c*d*f^2 + 2*b^3*c*d*f^2 - 3*a*b^2*d^2*f)*x)/(d^3*f^2*x^3 + 3*c*d^2*f^2*x^2 + 3*c^2*d*f^2*x + c^3*f^2 + (d^3*f^2*x^3*e^e + 3*c*d^2*f^2*x^2*e^e + 3*c^2*d*f^2*x*e^e + c^3*f^2*e^e)*e^(f*x)), x) + integrate(-(3*a^2*b*c^2*f^2 - 3*a*b^2*c*d*f + (c^2*f^2 + d^2)*b^3 + (3*a^2*b*d^2*f^2 + b^3*d^2*f^2)*x^2 + (6*a^2*b*c*d*f^2 + 2*b^3*c*d*f^2 - 3*a*b^2*d^2*f)*x)/(d^3*f^2*x^3 + 3*c*d^2*f^2*x^2 + 3*c^2*d*f^2*x + c^3*f^2 - (d^3*f^2*x^3*e^e + 3*c*d^2*f^2*x^2*e^e + 3*c^2*d*f^2*x*e^e + c^3*f^2*e^e)*e^(f*x)), x)","F",0
51,0,0,0,0.000000," ","integrate((a+b*coth(f*x+e))^3/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{a^{3}}{d^{2} x + c d} - \frac{3 \, a^{2} b c^{2} f^{2} + 3 \, {\left(c^{2} f^{2} - 2 \, c d f\right)} a b^{2} + {\left(c^{2} f^{2} + 2 \, d^{2}\right)} b^{3} + {\left(3 \, a^{2} b d^{2} f^{2} + 3 \, a b^{2} d^{2} f^{2} + b^{3} d^{2} f^{2}\right)} x^{2} + 2 \, {\left(3 \, a^{2} b c d f^{2} + b^{3} c d f^{2} + 3 \, {\left(c d f^{2} - d^{2} f\right)} a b^{2}\right)} x + {\left(3 \, a^{2} b c^{2} f^{2} e^{\left(4 \, e\right)} + 3 \, a b^{2} c^{2} f^{2} e^{\left(4 \, e\right)} + b^{3} c^{2} f^{2} e^{\left(4 \, e\right)} + {\left(3 \, a^{2} b d^{2} f^{2} e^{\left(4 \, e\right)} + 3 \, a b^{2} d^{2} f^{2} e^{\left(4 \, e\right)} + b^{3} d^{2} f^{2} e^{\left(4 \, e\right)}\right)} x^{2} + 2 \, {\left(3 \, a^{2} b c d f^{2} e^{\left(4 \, e\right)} + 3 \, a b^{2} c d f^{2} e^{\left(4 \, e\right)} + b^{3} c d f^{2} e^{\left(4 \, e\right)}\right)} x\right)} e^{\left(4 \, f x\right)} - 2 \, {\left(3 \, a^{2} b c^{2} f^{2} e^{\left(2 \, e\right)} + 3 \, {\left(c^{2} f^{2} e^{\left(2 \, e\right)} - c d f e^{\left(2 \, e\right)}\right)} a b^{2} + {\left(c^{2} f^{2} e^{\left(2 \, e\right)} - c d f e^{\left(2 \, e\right)} + d^{2} e^{\left(2 \, e\right)}\right)} b^{3} + {\left(3 \, a^{2} b d^{2} f^{2} e^{\left(2 \, e\right)} + 3 \, a b^{2} d^{2} f^{2} e^{\left(2 \, e\right)} + b^{3} d^{2} f^{2} e^{\left(2 \, e\right)}\right)} x^{2} + {\left(6 \, a^{2} b c d f^{2} e^{\left(2 \, e\right)} + 3 \, {\left(2 \, c d f^{2} e^{\left(2 \, e\right)} - d^{2} f e^{\left(2 \, e\right)}\right)} a b^{2} + {\left(2 \, c d f^{2} e^{\left(2 \, e\right)} - d^{2} f e^{\left(2 \, e\right)}\right)} b^{3}\right)} x\right)} e^{\left(2 \, f x\right)}}{d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2} + {\left(d^{4} f^{2} x^{3} e^{\left(4 \, e\right)} + 3 \, c d^{3} f^{2} x^{2} e^{\left(4 \, e\right)} + 3 \, c^{2} d^{2} f^{2} x e^{\left(4 \, e\right)} + c^{3} d f^{2} e^{\left(4 \, e\right)}\right)} e^{\left(4 \, f x\right)} - 2 \, {\left(d^{4} f^{2} x^{3} e^{\left(2 \, e\right)} + 3 \, c d^{3} f^{2} x^{2} e^{\left(2 \, e\right)} + 3 \, c^{2} d^{2} f^{2} x e^{\left(2 \, e\right)} + c^{3} d f^{2} e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}} - \int \frac{3 \, a^{2} b c^{2} f^{2} - 6 \, a b^{2} c d f + {\left(c^{2} f^{2} + 3 \, d^{2}\right)} b^{3} + {\left(3 \, a^{2} b d^{2} f^{2} + b^{3} d^{2} f^{2}\right)} x^{2} + 2 \, {\left(3 \, a^{2} b c d f^{2} + b^{3} c d f^{2} - 3 \, a b^{2} d^{2} f\right)} x}{d^{4} f^{2} x^{4} + 4 \, c d^{3} f^{2} x^{3} + 6 \, c^{2} d^{2} f^{2} x^{2} + 4 \, c^{3} d f^{2} x + c^{4} f^{2} + {\left(d^{4} f^{2} x^{4} e^{e} + 4 \, c d^{3} f^{2} x^{3} e^{e} + 6 \, c^{2} d^{2} f^{2} x^{2} e^{e} + 4 \, c^{3} d f^{2} x e^{e} + c^{4} f^{2} e^{e}\right)} e^{\left(f x\right)}}\,{d x} + \int -\frac{3 \, a^{2} b c^{2} f^{2} - 6 \, a b^{2} c d f + {\left(c^{2} f^{2} + 3 \, d^{2}\right)} b^{3} + {\left(3 \, a^{2} b d^{2} f^{2} + b^{3} d^{2} f^{2}\right)} x^{2} + 2 \, {\left(3 \, a^{2} b c d f^{2} + b^{3} c d f^{2} - 3 \, a b^{2} d^{2} f\right)} x}{d^{4} f^{2} x^{4} + 4 \, c d^{3} f^{2} x^{3} + 6 \, c^{2} d^{2} f^{2} x^{2} + 4 \, c^{3} d f^{2} x + c^{4} f^{2} - {\left(d^{4} f^{2} x^{4} e^{e} + 4 \, c d^{3} f^{2} x^{3} e^{e} + 6 \, c^{2} d^{2} f^{2} x^{2} e^{e} + 4 \, c^{3} d f^{2} x e^{e} + c^{4} f^{2} e^{e}\right)} e^{\left(f x\right)}}\,{d x}"," ",0,"-a^3/(d^2*x + c*d) - (3*a^2*b*c^2*f^2 + 3*(c^2*f^2 - 2*c*d*f)*a*b^2 + (c^2*f^2 + 2*d^2)*b^3 + (3*a^2*b*d^2*f^2 + 3*a*b^2*d^2*f^2 + b^3*d^2*f^2)*x^2 + 2*(3*a^2*b*c*d*f^2 + b^3*c*d*f^2 + 3*(c*d*f^2 - d^2*f)*a*b^2)*x + (3*a^2*b*c^2*f^2*e^(4*e) + 3*a*b^2*c^2*f^2*e^(4*e) + b^3*c^2*f^2*e^(4*e) + (3*a^2*b*d^2*f^2*e^(4*e) + 3*a*b^2*d^2*f^2*e^(4*e) + b^3*d^2*f^2*e^(4*e))*x^2 + 2*(3*a^2*b*c*d*f^2*e^(4*e) + 3*a*b^2*c*d*f^2*e^(4*e) + b^3*c*d*f^2*e^(4*e))*x)*e^(4*f*x) - 2*(3*a^2*b*c^2*f^2*e^(2*e) + 3*(c^2*f^2*e^(2*e) - c*d*f*e^(2*e))*a*b^2 + (c^2*f^2*e^(2*e) - c*d*f*e^(2*e) + d^2*e^(2*e))*b^3 + (3*a^2*b*d^2*f^2*e^(2*e) + 3*a*b^2*d^2*f^2*e^(2*e) + b^3*d^2*f^2*e^(2*e))*x^2 + (6*a^2*b*c*d*f^2*e^(2*e) + 3*(2*c*d*f^2*e^(2*e) - d^2*f*e^(2*e))*a*b^2 + (2*c*d*f^2*e^(2*e) - d^2*f*e^(2*e))*b^3)*x)*e^(2*f*x))/(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2 + (d^4*f^2*x^3*e^(4*e) + 3*c*d^3*f^2*x^2*e^(4*e) + 3*c^2*d^2*f^2*x*e^(4*e) + c^3*d*f^2*e^(4*e))*e^(4*f*x) - 2*(d^4*f^2*x^3*e^(2*e) + 3*c*d^3*f^2*x^2*e^(2*e) + 3*c^2*d^2*f^2*x*e^(2*e) + c^3*d*f^2*e^(2*e))*e^(2*f*x)) - integrate((3*a^2*b*c^2*f^2 - 6*a*b^2*c*d*f + (c^2*f^2 + 3*d^2)*b^3 + (3*a^2*b*d^2*f^2 + b^3*d^2*f^2)*x^2 + 2*(3*a^2*b*c*d*f^2 + b^3*c*d*f^2 - 3*a*b^2*d^2*f)*x)/(d^4*f^2*x^4 + 4*c*d^3*f^2*x^3 + 6*c^2*d^2*f^2*x^2 + 4*c^3*d*f^2*x + c^4*f^2 + (d^4*f^2*x^4*e^e + 4*c*d^3*f^2*x^3*e^e + 6*c^2*d^2*f^2*x^2*e^e + 4*c^3*d*f^2*x*e^e + c^4*f^2*e^e)*e^(f*x)), x) + integrate(-(3*a^2*b*c^2*f^2 - 6*a*b^2*c*d*f + (c^2*f^2 + 3*d^2)*b^3 + (3*a^2*b*d^2*f^2 + b^3*d^2*f^2)*x^2 + 2*(3*a^2*b*c*d*f^2 + b^3*c*d*f^2 - 3*a*b^2*d^2*f)*x)/(d^4*f^2*x^4 + 4*c*d^3*f^2*x^3 + 6*c^2*d^2*f^2*x^2 + 4*c^3*d*f^2*x + c^4*f^2 - (d^4*f^2*x^4*e^e + 4*c*d^3*f^2*x^3*e^e + 6*c^2*d^2*f^2*x^2*e^e + 4*c^3*d*f^2*x*e^e + c^4*f^2*e^e)*e^(f*x)), x)","F",0
52,1,521,0,0.519179," ","integrate((d*x+c)^3/(a+b*coth(f*x+e)),x, algorithm=""maxima"")","-\frac{3 \, {\left(2 \, f x \log\left(-\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b} + 1\right) + {\rm Li}_2\left(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b}\right)\right)} b c^{2} d}{2 \, {\left(a^{2} f^{2} - b^{2} f^{2}\right)}} - \frac{3 \, {\left(2 \, f^{2} x^{2} \log\left(-\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b} + 1\right) + 2 \, f x {\rm Li}_2\left(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b}\right) - {\rm Li}_{3}(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b})\right)} b c d^{2}}{2 \, {\left(a^{2} f^{3} - b^{2} f^{3}\right)}} - \frac{{\left(4 \, f^{3} x^{3} \log\left(-\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b} + 1\right) + 6 \, f^{2} x^{2} {\rm Li}_2\left(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b}\right) - 6 \, f x {\rm Li}_{3}(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b}) + 3 \, {\rm Li}_{4}(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b})\right)} b d^{3}}{3 \, {\left(a^{2} f^{4} - b^{2} f^{4}\right)}} - c^{3} {\left(\frac{b \log\left(-{\left(a - b\right)} e^{\left(-2 \, f x - 2 \, e\right)} + a + b\right)}{{\left(a^{2} - b^{2}\right)} f} - \frac{f x + e}{{\left(a + b\right)} f}\right)} + \frac{b d^{3} f^{4} x^{4} + 4 \, b c d^{2} f^{4} x^{3} + 6 \, b c^{2} d f^{4} x^{2}}{2 \, {\left(a^{2} f^{4} - b^{2} f^{4}\right)}} + \frac{d^{3} x^{4} + 4 \, c d^{2} x^{3} + 6 \, c^{2} d x^{2}}{4 \, {\left(a + b\right)}}"," ",0,"-3/2*(2*f*x*log(-(a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b) + 1) + dilog((a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)))*b*c^2*d/(a^2*f^2 - b^2*f^2) - 3/2*(2*f^2*x^2*log(-(a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b) + 1) + 2*f*x*dilog((a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)) - polylog(3, (a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)))*b*c*d^2/(a^2*f^3 - b^2*f^3) - 1/3*(4*f^3*x^3*log(-(a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b) + 1) + 6*f^2*x^2*dilog((a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)) - 6*f*x*polylog(3, (a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)) + 3*polylog(4, (a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)))*b*d^3/(a^2*f^4 - b^2*f^4) - c^3*(b*log(-(a - b)*e^(-2*f*x - 2*e) + a + b)/((a^2 - b^2)*f) - (f*x + e)/((a + b)*f)) + 1/2*(b*d^3*f^4*x^4 + 4*b*c*d^2*f^4*x^3 + 6*b*c^2*d*f^4*x^2)/(a^2*f^4 - b^2*f^4) + 1/4*(d^3*x^4 + 4*c*d^2*x^3 + 6*c^2*d*x^2)/(a + b)","B",0
53,1,332,0,0.492515," ","integrate((d*x+c)^2/(a+b*coth(f*x+e)),x, algorithm=""maxima"")","-\frac{{\left(2 \, f x \log\left(-\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b} + 1\right) + {\rm Li}_2\left(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b}\right)\right)} b c d}{a^{2} f^{2} - b^{2} f^{2}} - \frac{{\left(2 \, f^{2} x^{2} \log\left(-\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b} + 1\right) + 2 \, f x {\rm Li}_2\left(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b}\right) - {\rm Li}_{3}(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b})\right)} b d^{2}}{2 \, {\left(a^{2} f^{3} - b^{2} f^{3}\right)}} - c^{2} {\left(\frac{b \log\left(-{\left(a - b\right)} e^{\left(-2 \, f x - 2 \, e\right)} + a + b\right)}{{\left(a^{2} - b^{2}\right)} f} - \frac{f x + e}{{\left(a + b\right)} f}\right)} + \frac{2 \, {\left(b d^{2} f^{3} x^{3} + 3 \, b c d f^{3} x^{2}\right)}}{3 \, {\left(a^{2} f^{3} - b^{2} f^{3}\right)}} + \frac{d^{2} x^{3} + 3 \, c d x^{2}}{3 \, {\left(a + b\right)}}"," ",0,"-(2*f*x*log(-(a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b) + 1) + dilog((a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)))*b*c*d/(a^2*f^2 - b^2*f^2) - 1/2*(2*f^2*x^2*log(-(a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b) + 1) + 2*f*x*dilog((a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)) - polylog(3, (a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)))*b*d^2/(a^2*f^3 - b^2*f^3) - c^2*(b*log(-(a - b)*e^(-2*f*x - 2*e) + a + b)/((a^2 - b^2)*f) - (f*x + e)/((a + b)*f)) + 2/3*(b*d^2*f^3*x^3 + 3*b*c*d*f^3*x^2)/(a^2*f^3 - b^2*f^3) + 1/3*(d^2*x^3 + 3*c*d*x^2)/(a + b)","B",0
54,0,0,0,0.000000," ","integrate((d*x+c)/(a+b*coth(f*x+e)),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(4 \, b \int -\frac{x}{a^{2} - b^{2} - {\left(a^{2} e^{\left(2 \, e\right)} + 2 \, a b e^{\left(2 \, e\right)} + b^{2} e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}\,{d x} - \frac{x^{2}}{a + b}\right)} d - c {\left(\frac{b \log\left(-{\left(a - b\right)} e^{\left(-2 \, f x - 2 \, e\right)} + a + b\right)}{{\left(a^{2} - b^{2}\right)} f} - \frac{f x + e}{{\left(a + b\right)} f}\right)}"," ",0,"-1/2*(4*b*integrate(-x/(a^2 - b^2 - (a^2*e^(2*e) + 2*a*b*e^(2*e) + b^2*e^(2*e))*e^(2*f*x)), x) - x^2/(a + b))*d - c*(b*log(-(a - b)*e^(-2*f*x - 2*e) + a + b)/((a^2 - b^2)*f) - (f*x + e)/((a + b)*f))","F",0
55,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+b*coth(f*x+e)),x, algorithm=""maxima"")","-2 \, b \int -\frac{1}{a^{2} c - b^{2} c + {\left(a^{2} d - b^{2} d\right)} x - {\left(a^{2} c e^{\left(2 \, e\right)} + 2 \, a b c e^{\left(2 \, e\right)} + b^{2} c e^{\left(2 \, e\right)} + {\left(a^{2} d e^{\left(2 \, e\right)} + 2 \, a b d e^{\left(2 \, e\right)} + b^{2} d e^{\left(2 \, e\right)}\right)} x\right)} e^{\left(2 \, f x\right)}}\,{d x} + \frac{\log\left(d x + c\right)}{a d + b d}"," ",0,"-2*b*integrate(-1/(a^2*c - b^2*c + (a^2*d - b^2*d)*x - (a^2*c*e^(2*e) + 2*a*b*c*e^(2*e) + b^2*c*e^(2*e) + (a^2*d*e^(2*e) + 2*a*b*d*e^(2*e) + b^2*d*e^(2*e))*x)*e^(2*f*x)), x) + log(d*x + c)/(a*d + b*d)","F",0
56,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+b*coth(f*x+e)),x, algorithm=""maxima"")","-2 \, b \int -\frac{1}{a^{2} c^{2} - b^{2} c^{2} + {\left(a^{2} d^{2} - b^{2} d^{2}\right)} x^{2} + 2 \, {\left(a^{2} c d - b^{2} c d\right)} x - {\left(a^{2} c^{2} e^{\left(2 \, e\right)} + 2 \, a b c^{2} e^{\left(2 \, e\right)} + b^{2} c^{2} e^{\left(2 \, e\right)} + {\left(a^{2} d^{2} e^{\left(2 \, e\right)} + 2 \, a b d^{2} e^{\left(2 \, e\right)} + b^{2} d^{2} e^{\left(2 \, e\right)}\right)} x^{2} + 2 \, {\left(a^{2} c d e^{\left(2 \, e\right)} + 2 \, a b c d e^{\left(2 \, e\right)} + b^{2} c d e^{\left(2 \, e\right)}\right)} x\right)} e^{\left(2 \, f x\right)}}\,{d x} - \frac{1}{a c d + b c d + {\left(a d^{2} + b d^{2}\right)} x}"," ",0,"-2*b*integrate(-1/(a^2*c^2 - b^2*c^2 + (a^2*d^2 - b^2*d^2)*x^2 + 2*(a^2*c*d - b^2*c*d)*x - (a^2*c^2*e^(2*e) + 2*a*b*c^2*e^(2*e) + b^2*c^2*e^(2*e) + (a^2*d^2*e^(2*e) + 2*a*b*d^2*e^(2*e) + b^2*d^2*e^(2*e))*x^2 + 2*(a^2*c*d*e^(2*e) + 2*a*b*c*d*e^(2*e) + b^2*c*d*e^(2*e))*x)*e^(2*f*x)), x) - 1/(a*c*d + b*c*d + (a*d^2 + b*d^2)*x)","F",0
57,1,1056,0,1.034784," ","integrate((d*x+c)^3/(a+b*coth(f*x+e))^2,x, algorithm=""maxima"")","-\frac{6 \, b^{2} c^{2} d f x}{a^{4} f^{2} - 2 \, a^{2} b^{2} f^{2} + b^{4} f^{2}} - \frac{2 \, {\left(4 \, f^{3} x^{3} \log\left(-\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b} + 1\right) + 6 \, f^{2} x^{2} {\rm Li}_2\left(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b}\right) - 6 \, f x {\rm Li}_{3}(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b}) + 3 \, {\rm Li}_{4}(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b})\right)} a b d^{3}}{3 \, {\left(a^{4} f^{4} - 2 \, a^{2} b^{2} f^{4} + b^{4} f^{4}\right)}} + \frac{3 \, b^{2} c^{2} d \log\left({\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)} - a + b\right)}{a^{4} f^{2} - 2 \, a^{2} b^{2} f^{2} + b^{4} f^{2}} - c^{3} {\left(\frac{2 \, a b \log\left(-{\left(a - b\right)} e^{\left(-2 \, f x - 2 \, e\right)} + a + b\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f} + \frac{2 \, b^{2}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - {\left(a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - b^{4}\right)} e^{\left(-2 \, f x - 2 \, e\right)}\right)} f} - \frac{f x + e}{{\left(a^{2} + 2 \, a b + b^{2}\right)} f}\right)} - \frac{3 \, {\left(2 \, a b c d^{2} f - b^{2} d^{3}\right)} {\left(2 \, f^{2} x^{2} \log\left(-\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b} + 1\right) + 2 \, f x {\rm Li}_2\left(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b}\right) - {\rm Li}_{3}(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b})\right)}}{2 \, {\left(a^{4} f^{4} - 2 \, a^{2} b^{2} f^{4} + b^{4} f^{4}\right)}} - \frac{3 \, {\left(a b c^{2} d f - b^{2} c d^{2}\right)} {\left(2 \, f x \log\left(-\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b} + 1\right) + {\rm Li}_2\left(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b}\right)\right)}}{a^{4} f^{3} - 2 \, a^{2} b^{2} f^{3} + b^{4} f^{3}} + \frac{a b d^{3} f^{4} x^{4} + 2 \, {\left(2 \, a b c d^{2} f - b^{2} d^{3}\right)} f^{3} x^{3} + 6 \, {\left(a b c^{2} d f^{2} - b^{2} c d^{2} f\right)} f^{2} x^{2}}{a^{4} f^{4} - 2 \, a^{2} b^{2} f^{4} + b^{4} f^{4}} + \frac{24 \, b^{2} c^{2} d x + {\left(a^{2} d^{3} f - 2 \, a b d^{3} f + b^{2} d^{3} f\right)} x^{4} + 4 \, {\left(a^{2} c d^{2} f - 2 \, a b c d^{2} f + {\left(c d^{2} f + 2 \, d^{3}\right)} b^{2}\right)} x^{3} + 6 \, {\left(a^{2} c^{2} d f - 2 \, a b c^{2} d f + {\left(c^{2} d f + 4 \, c d^{2}\right)} b^{2}\right)} x^{2} - {\left({\left(a^{2} d^{3} f e^{\left(2 \, e\right)} - b^{2} d^{3} f e^{\left(2 \, e\right)}\right)} x^{4} + 4 \, {\left(a^{2} c d^{2} f e^{\left(2 \, e\right)} - b^{2} c d^{2} f e^{\left(2 \, e\right)}\right)} x^{3} + 6 \, {\left(a^{2} c^{2} d f e^{\left(2 \, e\right)} - b^{2} c^{2} d f e^{\left(2 \, e\right)}\right)} x^{2}\right)} e^{\left(2 \, f x\right)}}{4 \, {\left(a^{4} f - 2 \, a^{2} b^{2} f + b^{4} f - {\left(a^{4} f e^{\left(2 \, e\right)} + 2 \, a^{3} b f e^{\left(2 \, e\right)} - 2 \, a b^{3} f e^{\left(2 \, e\right)} - b^{4} f e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}\right)}}"," ",0,"-6*b^2*c^2*d*f*x/(a^4*f^2 - 2*a^2*b^2*f^2 + b^4*f^2) - 2/3*(4*f^3*x^3*log(-(a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b) + 1) + 6*f^2*x^2*dilog((a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)) - 6*f*x*polylog(3, (a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)) + 3*polylog(4, (a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)))*a*b*d^3/(a^4*f^4 - 2*a^2*b^2*f^4 + b^4*f^4) + 3*b^2*c^2*d*log((a*e^(2*e) + b*e^(2*e))*e^(2*f*x) - a + b)/(a^4*f^2 - 2*a^2*b^2*f^2 + b^4*f^2) - c^3*(2*a*b*log(-(a - b)*e^(-2*f*x - 2*e) + a + b)/((a^4 - 2*a^2*b^2 + b^4)*f) + 2*b^2/((a^4 - 2*a^2*b^2 + b^4 - (a^4 - 2*a^3*b + 2*a*b^3 - b^4)*e^(-2*f*x - 2*e))*f) - (f*x + e)/((a^2 + 2*a*b + b^2)*f)) - 3/2*(2*a*b*c*d^2*f - b^2*d^3)*(2*f^2*x^2*log(-(a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b) + 1) + 2*f*x*dilog((a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)) - polylog(3, (a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)))/(a^4*f^4 - 2*a^2*b^2*f^4 + b^4*f^4) - 3*(a*b*c^2*d*f - b^2*c*d^2)*(2*f*x*log(-(a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b) + 1) + dilog((a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)))/(a^4*f^3 - 2*a^2*b^2*f^3 + b^4*f^3) + (a*b*d^3*f^4*x^4 + 2*(2*a*b*c*d^2*f - b^2*d^3)*f^3*x^3 + 6*(a*b*c^2*d*f^2 - b^2*c*d^2*f)*f^2*x^2)/(a^4*f^4 - 2*a^2*b^2*f^4 + b^4*f^4) + 1/4*(24*b^2*c^2*d*x + (a^2*d^3*f - 2*a*b*d^3*f + b^2*d^3*f)*x^4 + 4*(a^2*c*d^2*f - 2*a*b*c*d^2*f + (c*d^2*f + 2*d^3)*b^2)*x^3 + 6*(a^2*c^2*d*f - 2*a*b*c^2*d*f + (c^2*d*f + 4*c*d^2)*b^2)*x^2 - ((a^2*d^3*f*e^(2*e) - b^2*d^3*f*e^(2*e))*x^4 + 4*(a^2*c*d^2*f*e^(2*e) - b^2*c*d^2*f*e^(2*e))*x^3 + 6*(a^2*c^2*d*f*e^(2*e) - b^2*c^2*d*f*e^(2*e))*x^2)*e^(2*f*x))/(a^4*f - 2*a^2*b^2*f + b^4*f - (a^4*f*e^(2*e) + 2*a^3*b*f*e^(2*e) - 2*a*b^3*f*e^(2*e) - b^4*f*e^(2*e))*e^(2*f*x))","A",0
58,1,751,0,0.838068," ","integrate((d*x+c)^2/(a+b*coth(f*x+e))^2,x, algorithm=""maxima"")","-\frac{4 \, b^{2} c d f x}{a^{4} f^{2} - 2 \, a^{2} b^{2} f^{2} + b^{4} f^{2}} - \frac{{\left(2 \, f^{2} x^{2} \log\left(-\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b} + 1\right) + 2 \, f x {\rm Li}_2\left(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b}\right) - {\rm Li}_{3}(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b})\right)} a b d^{2}}{a^{4} f^{3} - 2 \, a^{2} b^{2} f^{3} + b^{4} f^{3}} + \frac{2 \, b^{2} c d \log\left({\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)} - a + b\right)}{a^{4} f^{2} - 2 \, a^{2} b^{2} f^{2} + b^{4} f^{2}} - c^{2} {\left(\frac{2 \, a b \log\left(-{\left(a - b\right)} e^{\left(-2 \, f x - 2 \, e\right)} + a + b\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f} + \frac{2 \, b^{2}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - {\left(a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - b^{4}\right)} e^{\left(-2 \, f x - 2 \, e\right)}\right)} f} - \frac{f x + e}{{\left(a^{2} + 2 \, a b + b^{2}\right)} f}\right)} - \frac{{\left(2 \, a b c d f - b^{2} d^{2}\right)} {\left(2 \, f x \log\left(-\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b} + 1\right) + {\rm Li}_2\left(\frac{{\left(a e^{\left(2 \, e\right)} + b e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}{a - b}\right)\right)}}{a^{4} f^{3} - 2 \, a^{2} b^{2} f^{3} + b^{4} f^{3}} + \frac{2 \, {\left(2 \, a b d^{2} f^{3} x^{3} + 3 \, {\left(2 \, a b c d f - b^{2} d^{2}\right)} f^{2} x^{2}\right)}}{3 \, {\left(a^{4} f^{3} - 2 \, a^{2} b^{2} f^{3} + b^{4} f^{3}\right)}} + \frac{12 \, b^{2} c d x + {\left(a^{2} d^{2} f - 2 \, a b d^{2} f + b^{2} d^{2} f\right)} x^{3} + 3 \, {\left(a^{2} c d f - 2 \, a b c d f + {\left(c d f + 2 \, d^{2}\right)} b^{2}\right)} x^{2} - {\left({\left(a^{2} d^{2} f e^{\left(2 \, e\right)} - b^{2} d^{2} f e^{\left(2 \, e\right)}\right)} x^{3} + 3 \, {\left(a^{2} c d f e^{\left(2 \, e\right)} - b^{2} c d f e^{\left(2 \, e\right)}\right)} x^{2}\right)} e^{\left(2 \, f x\right)}}{3 \, {\left(a^{4} f - 2 \, a^{2} b^{2} f + b^{4} f - {\left(a^{4} f e^{\left(2 \, e\right)} + 2 \, a^{3} b f e^{\left(2 \, e\right)} - 2 \, a b^{3} f e^{\left(2 \, e\right)} - b^{4} f e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}\right)}}"," ",0,"-4*b^2*c*d*f*x/(a^4*f^2 - 2*a^2*b^2*f^2 + b^4*f^2) - (2*f^2*x^2*log(-(a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b) + 1) + 2*f*x*dilog((a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)) - polylog(3, (a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)))*a*b*d^2/(a^4*f^3 - 2*a^2*b^2*f^3 + b^4*f^3) + 2*b^2*c*d*log((a*e^(2*e) + b*e^(2*e))*e^(2*f*x) - a + b)/(a^4*f^2 - 2*a^2*b^2*f^2 + b^4*f^2) - c^2*(2*a*b*log(-(a - b)*e^(-2*f*x - 2*e) + a + b)/((a^4 - 2*a^2*b^2 + b^4)*f) + 2*b^2/((a^4 - 2*a^2*b^2 + b^4 - (a^4 - 2*a^3*b + 2*a*b^3 - b^4)*e^(-2*f*x - 2*e))*f) - (f*x + e)/((a^2 + 2*a*b + b^2)*f)) - (2*a*b*c*d*f - b^2*d^2)*(2*f*x*log(-(a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b) + 1) + dilog((a*e^(2*e) + b*e^(2*e))*e^(2*f*x)/(a - b)))/(a^4*f^3 - 2*a^2*b^2*f^3 + b^4*f^3) + 2/3*(2*a*b*d^2*f^3*x^3 + 3*(2*a*b*c*d*f - b^2*d^2)*f^2*x^2)/(a^4*f^3 - 2*a^2*b^2*f^3 + b^4*f^3) + 1/3*(12*b^2*c*d*x + (a^2*d^2*f - 2*a*b*d^2*f + b^2*d^2*f)*x^3 + 3*(a^2*c*d*f - 2*a*b*c*d*f + (c*d*f + 2*d^2)*b^2)*x^2 - ((a^2*d^2*f*e^(2*e) - b^2*d^2*f*e^(2*e))*x^3 + 3*(a^2*c*d*f*e^(2*e) - b^2*c*d*f*e^(2*e))*x^2)*e^(2*f*x))/(a^4*f - 2*a^2*b^2*f + b^4*f - (a^4*f*e^(2*e) + 2*a^3*b*f*e^(2*e) - 2*a*b^3*f*e^(2*e) - b^4*f*e^(2*e))*e^(2*f*x))","A",0
59,0,0,0,0.000000," ","integrate((d*x+c)/(a+b*coth(f*x+e))^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(8 \, a b f \int \frac{x}{a^{4} f e^{\left(2 \, f x + 2 \, e\right)} + 2 \, a^{3} b f e^{\left(2 \, f x + 2 \, e\right)} - 2 \, a b^{3} f e^{\left(2 \, f x + 2 \, e\right)} - b^{4} f e^{\left(2 \, f x + 2 \, e\right)} - a^{4} f + 2 \, a^{2} b^{2} f - b^{4} f}\,{d x} + 2 \, b^{2} {\left(\frac{2 \, {\left(f x + e\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f^{2}} - \frac{\log\left({\left(a + b\right)} e^{\left(2 \, f x + 2 \, e\right)} - a + b\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f^{2}}\right)} + \frac{{\left(a^{2} f e^{\left(2 \, e\right)} - b^{2} f e^{\left(2 \, e\right)}\right)} x^{2} e^{\left(2 \, f x\right)} - 4 \, b^{2} x - {\left(a^{2} f - 2 \, a b f + b^{2} f\right)} x^{2}}{a^{4} f - 2 \, a^{2} b^{2} f + b^{4} f - {\left(a^{4} f e^{\left(2 \, e\right)} + 2 \, a^{3} b f e^{\left(2 \, e\right)} - 2 \, a b^{3} f e^{\left(2 \, e\right)} - b^{4} f e^{\left(2 \, e\right)}\right)} e^{\left(2 \, f x\right)}}\right)} d - c {\left(\frac{2 \, a b \log\left(-{\left(a - b\right)} e^{\left(-2 \, f x - 2 \, e\right)} + a + b\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f} + \frac{2 \, b^{2}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - {\left(a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - b^{4}\right)} e^{\left(-2 \, f x - 2 \, e\right)}\right)} f} - \frac{f x + e}{{\left(a^{2} + 2 \, a b + b^{2}\right)} f}\right)}"," ",0,"-1/2*(8*a*b*f*integrate(x/(a^4*f*e^(2*f*x + 2*e) + 2*a^3*b*f*e^(2*f*x + 2*e) - 2*a*b^3*f*e^(2*f*x + 2*e) - b^4*f*e^(2*f*x + 2*e) - a^4*f + 2*a^2*b^2*f - b^4*f), x) + 2*b^2*(2*(f*x + e)/((a^4 - 2*a^2*b^2 + b^4)*f^2) - log((a + b)*e^(2*f*x + 2*e) - a + b)/((a^4 - 2*a^2*b^2 + b^4)*f^2)) + ((a^2*f*e^(2*e) - b^2*f*e^(2*e))*x^2*e^(2*f*x) - 4*b^2*x - (a^2*f - 2*a*b*f + b^2*f)*x^2)/(a^4*f - 2*a^2*b^2*f + b^4*f - (a^4*f*e^(2*e) + 2*a^3*b*f*e^(2*e) - 2*a*b^3*f*e^(2*e) - b^4*f*e^(2*e))*e^(2*f*x)))*d - c*(2*a*b*log(-(a - b)*e^(-2*f*x - 2*e) + a + b)/((a^4 - 2*a^2*b^2 + b^4)*f) + 2*b^2/((a^4 - 2*a^2*b^2 + b^4 - (a^4 - 2*a^3*b + 2*a*b^3 - b^4)*e^(-2*f*x - 2*e))*f) - (f*x + e)/((a^2 + 2*a*b + b^2)*f))","F",0
60,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+b*coth(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, b^{2}}{a^{4} c f - 2 \, a^{2} b^{2} c f + b^{4} c f + {\left(a^{4} d f - 2 \, a^{2} b^{2} d f + b^{4} d f\right)} x - {\left(a^{4} c f e^{\left(2 \, e\right)} + 2 \, a^{3} b c f e^{\left(2 \, e\right)} - 2 \, a b^{3} c f e^{\left(2 \, e\right)} - b^{4} c f e^{\left(2 \, e\right)} + {\left(a^{4} d f e^{\left(2 \, e\right)} + 2 \, a^{3} b d f e^{\left(2 \, e\right)} - 2 \, a b^{3} d f e^{\left(2 \, e\right)} - b^{4} d f e^{\left(2 \, e\right)}\right)} x\right)} e^{\left(2 \, f x\right)}} + \frac{\log\left(d x + c\right)}{a^{2} d + 2 \, a b d + b^{2} d} - \int -\frac{2 \, {\left(2 \, a b d f x + 2 \, a b c f + b^{2} d\right)}}{a^{4} c^{2} f - 2 \, a^{2} b^{2} c^{2} f + b^{4} c^{2} f + {\left(a^{4} d^{2} f - 2 \, a^{2} b^{2} d^{2} f + b^{4} d^{2} f\right)} x^{2} + 2 \, {\left(a^{4} c d f - 2 \, a^{2} b^{2} c d f + b^{4} c d f\right)} x - {\left(a^{4} c^{2} f e^{\left(2 \, e\right)} + 2 \, a^{3} b c^{2} f e^{\left(2 \, e\right)} - 2 \, a b^{3} c^{2} f e^{\left(2 \, e\right)} - b^{4} c^{2} f e^{\left(2 \, e\right)} + {\left(a^{4} d^{2} f e^{\left(2 \, e\right)} + 2 \, a^{3} b d^{2} f e^{\left(2 \, e\right)} - 2 \, a b^{3} d^{2} f e^{\left(2 \, e\right)} - b^{4} d^{2} f e^{\left(2 \, e\right)}\right)} x^{2} + 2 \, {\left(a^{4} c d f e^{\left(2 \, e\right)} + 2 \, a^{3} b c d f e^{\left(2 \, e\right)} - 2 \, a b^{3} c d f e^{\left(2 \, e\right)} - b^{4} c d f e^{\left(2 \, e\right)}\right)} x\right)} e^{\left(2 \, f x\right)}}\,{d x}"," ",0,"2*b^2/(a^4*c*f - 2*a^2*b^2*c*f + b^4*c*f + (a^4*d*f - 2*a^2*b^2*d*f + b^4*d*f)*x - (a^4*c*f*e^(2*e) + 2*a^3*b*c*f*e^(2*e) - 2*a*b^3*c*f*e^(2*e) - b^4*c*f*e^(2*e) + (a^4*d*f*e^(2*e) + 2*a^3*b*d*f*e^(2*e) - 2*a*b^3*d*f*e^(2*e) - b^4*d*f*e^(2*e))*x)*e^(2*f*x)) + log(d*x + c)/(a^2*d + 2*a*b*d + b^2*d) - integrate(-2*(2*a*b*d*f*x + 2*a*b*c*f + b^2*d)/(a^4*c^2*f - 2*a^2*b^2*c^2*f + b^4*c^2*f + (a^4*d^2*f - 2*a^2*b^2*d^2*f + b^4*d^2*f)*x^2 + 2*(a^4*c*d*f - 2*a^2*b^2*c*d*f + b^4*c*d*f)*x - (a^4*c^2*f*e^(2*e) + 2*a^3*b*c^2*f*e^(2*e) - 2*a*b^3*c^2*f*e^(2*e) - b^4*c^2*f*e^(2*e) + (a^4*d^2*f*e^(2*e) + 2*a^3*b*d^2*f*e^(2*e) - 2*a*b^3*d^2*f*e^(2*e) - b^4*d^2*f*e^(2*e))*x^2 + 2*(a^4*c*d*f*e^(2*e) + 2*a^3*b*c*d*f*e^(2*e) - 2*a*b^3*c*d*f*e^(2*e) - b^4*c*d*f*e^(2*e))*x)*e^(2*f*x)), x)","F",0
61,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+b*coth(f*x+e))^2,x, algorithm=""maxima"")","-\frac{a^{2} c f - 2 \, a b c f + {\left(c f - 2 \, d\right)} b^{2} + {\left(a^{2} d f - 2 \, a b d f + b^{2} d f\right)} x - {\left(a^{2} c f e^{\left(2 \, e\right)} - b^{2} c f e^{\left(2 \, e\right)} + {\left(a^{2} d f e^{\left(2 \, e\right)} - b^{2} d f e^{\left(2 \, e\right)}\right)} x\right)} e^{\left(2 \, f x\right)}}{a^{4} c^{2} d f - 2 \, a^{2} b^{2} c^{2} d f + b^{4} c^{2} d f + {\left(a^{4} d^{3} f - 2 \, a^{2} b^{2} d^{3} f + b^{4} d^{3} f\right)} x^{2} + 2 \, {\left(a^{4} c d^{2} f - 2 \, a^{2} b^{2} c d^{2} f + b^{4} c d^{2} f\right)} x - {\left(a^{4} c^{2} d f e^{\left(2 \, e\right)} + 2 \, a^{3} b c^{2} d f e^{\left(2 \, e\right)} - 2 \, a b^{3} c^{2} d f e^{\left(2 \, e\right)} - b^{4} c^{2} d f e^{\left(2 \, e\right)} + {\left(a^{4} d^{3} f e^{\left(2 \, e\right)} + 2 \, a^{3} b d^{3} f e^{\left(2 \, e\right)} - 2 \, a b^{3} d^{3} f e^{\left(2 \, e\right)} - b^{4} d^{3} f e^{\left(2 \, e\right)}\right)} x^{2} + 2 \, {\left(a^{4} c d^{2} f e^{\left(2 \, e\right)} + 2 \, a^{3} b c d^{2} f e^{\left(2 \, e\right)} - 2 \, a b^{3} c d^{2} f e^{\left(2 \, e\right)} - b^{4} c d^{2} f e^{\left(2 \, e\right)}\right)} x\right)} e^{\left(2 \, f x\right)}} - \int -\frac{4 \, {\left(a b d f x + a b c f + b^{2} d\right)}}{a^{4} c^{3} f - 2 \, a^{2} b^{2} c^{3} f + b^{4} c^{3} f + {\left(a^{4} d^{3} f - 2 \, a^{2} b^{2} d^{3} f + b^{4} d^{3} f\right)} x^{3} + 3 \, {\left(a^{4} c d^{2} f - 2 \, a^{2} b^{2} c d^{2} f + b^{4} c d^{2} f\right)} x^{2} + 3 \, {\left(a^{4} c^{2} d f - 2 \, a^{2} b^{2} c^{2} d f + b^{4} c^{2} d f\right)} x - {\left(a^{4} c^{3} f e^{\left(2 \, e\right)} + 2 \, a^{3} b c^{3} f e^{\left(2 \, e\right)} - 2 \, a b^{3} c^{3} f e^{\left(2 \, e\right)} - b^{4} c^{3} f e^{\left(2 \, e\right)} + {\left(a^{4} d^{3} f e^{\left(2 \, e\right)} + 2 \, a^{3} b d^{3} f e^{\left(2 \, e\right)} - 2 \, a b^{3} d^{3} f e^{\left(2 \, e\right)} - b^{4} d^{3} f e^{\left(2 \, e\right)}\right)} x^{3} + 3 \, {\left(a^{4} c d^{2} f e^{\left(2 \, e\right)} + 2 \, a^{3} b c d^{2} f e^{\left(2 \, e\right)} - 2 \, a b^{3} c d^{2} f e^{\left(2 \, e\right)} - b^{4} c d^{2} f e^{\left(2 \, e\right)}\right)} x^{2} + 3 \, {\left(a^{4} c^{2} d f e^{\left(2 \, e\right)} + 2 \, a^{3} b c^{2} d f e^{\left(2 \, e\right)} - 2 \, a b^{3} c^{2} d f e^{\left(2 \, e\right)} - b^{4} c^{2} d f e^{\left(2 \, e\right)}\right)} x\right)} e^{\left(2 \, f x\right)}}\,{d x}"," ",0,"-(a^2*c*f - 2*a*b*c*f + (c*f - 2*d)*b^2 + (a^2*d*f - 2*a*b*d*f + b^2*d*f)*x - (a^2*c*f*e^(2*e) - b^2*c*f*e^(2*e) + (a^2*d*f*e^(2*e) - b^2*d*f*e^(2*e))*x)*e^(2*f*x))/(a^4*c^2*d*f - 2*a^2*b^2*c^2*d*f + b^4*c^2*d*f + (a^4*d^3*f - 2*a^2*b^2*d^3*f + b^4*d^3*f)*x^2 + 2*(a^4*c*d^2*f - 2*a^2*b^2*c*d^2*f + b^4*c*d^2*f)*x - (a^4*c^2*d*f*e^(2*e) + 2*a^3*b*c^2*d*f*e^(2*e) - 2*a*b^3*c^2*d*f*e^(2*e) - b^4*c^2*d*f*e^(2*e) + (a^4*d^3*f*e^(2*e) + 2*a^3*b*d^3*f*e^(2*e) - 2*a*b^3*d^3*f*e^(2*e) - b^4*d^3*f*e^(2*e))*x^2 + 2*(a^4*c*d^2*f*e^(2*e) + 2*a^3*b*c*d^2*f*e^(2*e) - 2*a*b^3*c*d^2*f*e^(2*e) - b^4*c*d^2*f*e^(2*e))*x)*e^(2*f*x)) - integrate(-4*(a*b*d*f*x + a*b*c*f + b^2*d)/(a^4*c^3*f - 2*a^2*b^2*c^3*f + b^4*c^3*f + (a^4*d^3*f - 2*a^2*b^2*d^3*f + b^4*d^3*f)*x^3 + 3*(a^4*c*d^2*f - 2*a^2*b^2*c*d^2*f + b^4*c*d^2*f)*x^2 + 3*(a^4*c^2*d*f - 2*a^2*b^2*c^2*d*f + b^4*c^2*d*f)*x - (a^4*c^3*f*e^(2*e) + 2*a^3*b*c^3*f*e^(2*e) - 2*a*b^3*c^3*f*e^(2*e) - b^4*c^3*f*e^(2*e) + (a^4*d^3*f*e^(2*e) + 2*a^3*b*d^3*f*e^(2*e) - 2*a*b^3*d^3*f*e^(2*e) - b^4*d^3*f*e^(2*e))*x^3 + 3*(a^4*c*d^2*f*e^(2*e) + 2*a^3*b*c*d^2*f*e^(2*e) - 2*a*b^3*c*d^2*f*e^(2*e) - b^4*c*d^2*f*e^(2*e))*x^2 + 3*(a^4*c^2*d*f*e^(2*e) + 2*a^3*b*c^2*d*f*e^(2*e) - 2*a*b^3*c^2*d*f*e^(2*e) - b^4*c^2*d*f*e^(2*e))*x)*e^(2*f*x)), x)","F",0
