1,1,200,79,0.280000," ","int(x^3*coth(b*x+a),x)","-\frac{x^{4}}{4}-\frac{3 a^{4}}{2 b^{4}}+\frac{6 \polylog \left(4, -{\mathrm e}^{b x +a}\right)}{b^{4}}-\frac{a^{3} \ln \left({\mathrm e}^{b x +a}-1\right)}{b^{4}}+\frac{3 \polylog \left(2, -{\mathrm e}^{b x +a}\right) x^{2}}{b^{2}}-\frac{6 \polylog \left(3, -{\mathrm e}^{b x +a}\right) x}{b^{3}}+\frac{\ln \left(1-{\mathrm e}^{b x +a}\right) x^{3}}{b}+\frac{3 \polylog \left(2, {\mathrm e}^{b x +a}\right) x^{2}}{b^{2}}-\frac{6 \polylog \left(3, {\mathrm e}^{b x +a}\right) x}{b^{3}}+\frac{\ln \left(1+{\mathrm e}^{b x +a}\right) x^{3}}{b}+\frac{6 \polylog \left(4, {\mathrm e}^{b x +a}\right)}{b^{4}}-\frac{2 a^{3} x}{b^{3}}+\frac{2 a^{3} \ln \left({\mathrm e}^{b x +a}\right)}{b^{4}}+\frac{\ln \left(1-{\mathrm e}^{b x +a}\right) a^{3}}{b^{4}}"," ",0,"-1/4*x^4-3/2/b^4*a^4+6/b^4*polylog(4,-exp(b*x+a))-1/b^4*a^3*ln(exp(b*x+a)-1)+3/b^2*polylog(2,-exp(b*x+a))*x^2-6/b^3*polylog(3,-exp(b*x+a))*x+1/b*ln(1-exp(b*x+a))*x^3+3/b^2*polylog(2,exp(b*x+a))*x^2-6/b^3*polylog(3,exp(b*x+a))*x+1/b*ln(1+exp(b*x+a))*x^3+6/b^4*polylog(4,exp(b*x+a))-2/b^3*a^3*x+2/b^4*a^3*ln(exp(b*x+a))+1/b^4*ln(1-exp(b*x+a))*a^3","B"
2,1,166,59,0.273000," ","int(x^2*coth(b*x+a),x)","-\frac{x^{3}}{3}+\frac{a^{2} \ln \left({\mathrm e}^{b x +a}-1\right)}{b^{3}}-\frac{2 a^{2} \ln \left({\mathrm e}^{b x +a}\right)}{b^{3}}+\frac{2 a^{2} x}{b^{2}}+\frac{4 a^{3}}{3 b^{3}}+\frac{\ln \left(1-{\mathrm e}^{b x +a}\right) x^{2}}{b}-\frac{\ln \left(1-{\mathrm e}^{b x +a}\right) a^{2}}{b^{3}}+\frac{2 \polylog \left(2, {\mathrm e}^{b x +a}\right) x}{b^{2}}-\frac{2 \polylog \left(3, {\mathrm e}^{b x +a}\right)}{b^{3}}+\frac{\ln \left(1+{\mathrm e}^{b x +a}\right) x^{2}}{b}+\frac{2 \polylog \left(2, -{\mathrm e}^{b x +a}\right) x}{b^{2}}-\frac{2 \polylog \left(3, -{\mathrm e}^{b x +a}\right)}{b^{3}}"," ",0,"-1/3*x^3+1/b^3*a^2*ln(exp(b*x+a)-1)-2/b^3*a^2*ln(exp(b*x+a))+2/b^2*a^2*x+4/3/b^3*a^3+1/b*ln(1-exp(b*x+a))*x^2-1/b^3*ln(1-exp(b*x+a))*a^2+2/b^2*polylog(2,exp(b*x+a))*x-2/b^3*polylog(3,exp(b*x+a))+1/b*ln(1+exp(b*x+a))*x^2+2/b^2*polylog(2,-exp(b*x+a))*x-2/b^3*polylog(3,-exp(b*x+a))","B"
3,1,122,41,0.266000," ","int(x*coth(b*x+a),x)","-\frac{x^{2}}{2}-\frac{2 a x}{b}-\frac{a^{2}}{b^{2}}+\frac{\ln \left(1-{\mathrm e}^{b x +a}\right) x}{b}+\frac{\ln \left(1-{\mathrm e}^{b x +a}\right) a}{b^{2}}+\frac{\polylog \left(2, {\mathrm e}^{b x +a}\right)}{b^{2}}+\frac{\ln \left(1+{\mathrm e}^{b x +a}\right) x}{b}+\frac{\polylog \left(2, -{\mathrm e}^{b x +a}\right)}{b^{2}}+\frac{2 a \ln \left({\mathrm e}^{b x +a}\right)}{b^{2}}-\frac{a \ln \left({\mathrm e}^{b x +a}-1\right)}{b^{2}}"," ",0,"-1/2*x^2-2/b*a*x-a^2/b^2+1/b*ln(1-exp(b*x+a))*x+1/b^2*ln(1-exp(b*x+a))*a+1/b^2*polylog(2,exp(b*x+a))+1/b*ln(1+exp(b*x+a))*x+1/b^2*polylog(2,-exp(b*x+a))+2/b^2*a*ln(exp(b*x+a))-1/b^2*a*ln(exp(b*x+a)-1)","B"
4,0,0,12,0.316000," ","int(coth(b*x+a)/x,x)","\int \frac{\coth \left(b x +a \right)}{x}\, dx"," ",0,"int(coth(b*x+a)/x,x)","F"
5,0,0,12,0.293000," ","int(coth(b*x+a)/x^2,x)","\int \frac{\coth \left(b x +a \right)}{x^{2}}\, dx"," ",0,"int(coth(b*x+a)/x^2,x)","F"
6,1,198,83,0.180000," ","int(x^3*coth(b*x+a)^2,x)","\frac{x^{4}}{4}-\frac{2 x^{3}}{b \left({\mathrm e}^{2 b x +2 a}-1\right)}+\frac{3 a^{2} \ln \left({\mathrm e}^{b x +a}-1\right)}{b^{4}}-\frac{6 a^{2} \ln \left({\mathrm e}^{b x +a}\right)}{b^{4}}-\frac{2 x^{3}}{b}+\frac{6 a^{2} x}{b^{3}}+\frac{4 a^{3}}{b^{4}}+\frac{3 \ln \left(1-{\mathrm e}^{b x +a}\right) x^{2}}{b^{2}}-\frac{3 \ln \left(1-{\mathrm e}^{b x +a}\right) a^{2}}{b^{4}}+\frac{6 \polylog \left(2, {\mathrm e}^{b x +a}\right) x}{b^{3}}-\frac{6 \polylog \left(3, {\mathrm e}^{b x +a}\right)}{b^{4}}+\frac{3 \ln \left(1+{\mathrm e}^{b x +a}\right) x^{2}}{b^{2}}+\frac{6 \polylog \left(2, -{\mathrm e}^{b x +a}\right) x}{b^{3}}-\frac{6 \polylog \left(3, -{\mathrm e}^{b x +a}\right)}{b^{4}}"," ",0,"1/4*x^4-2*x^3/b/(exp(2*b*x+2*a)-1)+3/b^4*a^2*ln(exp(b*x+a)-1)-6/b^4*a^2*ln(exp(b*x+a))-2*x^3/b+6/b^3*a^2*x+4/b^4*a^3+3/b^2*ln(1-exp(b*x+a))*x^2-3/b^4*ln(1-exp(b*x+a))*a^2+6/b^3*polylog(2,exp(b*x+a))*x-6/b^4*polylog(3,exp(b*x+a))+3/b^2*ln(1+exp(b*x+a))*x^2+6/b^3*polylog(2,-exp(b*x+a))*x-6/b^4*polylog(3,-exp(b*x+a))","B"
7,1,156,63,0.174000," ","int(x^2*coth(b*x+a)^2,x)","\frac{x^{3}}{3}-\frac{2 x^{2}}{b \left({\mathrm e}^{2 b x +2 a}-1\right)}-\frac{2 x^{2}}{b}-\frac{4 a x}{b^{2}}-\frac{2 a^{2}}{b^{3}}+\frac{2 \ln \left(1-{\mathrm e}^{b x +a}\right) x}{b^{2}}+\frac{2 \ln \left(1-{\mathrm e}^{b x +a}\right) a}{b^{3}}+\frac{2 \polylog \left(2, {\mathrm e}^{b x +a}\right)}{b^{3}}+\frac{2 \ln \left(1+{\mathrm e}^{b x +a}\right) x}{b^{2}}+\frac{2 \polylog \left(2, -{\mathrm e}^{b x +a}\right)}{b^{3}}+\frac{4 a \ln \left({\mathrm e}^{b x +a}\right)}{b^{3}}-\frac{2 a \ln \left({\mathrm e}^{b x +a}-1\right)}{b^{3}}"," ",0,"1/3*x^3-2*x^2/b/(exp(2*b*x+2*a)-1)-2*x^2/b-4*a*x/b^2-2/b^3*a^2+2/b^2*ln(1-exp(b*x+a))*x+2/b^3*ln(1-exp(b*x+a))*a+2/b^3*polylog(2,exp(b*x+a))+2/b^2*ln(1+exp(b*x+a))*x+2/b^3*polylog(2,-exp(b*x+a))+4/b^3*a*ln(exp(b*x+a))-2/b^3*a*ln(exp(b*x+a)-1)","B"
8,1,54,29,0.127000," ","int(x*coth(b*x+a)^2,x)","\frac{x^{2}}{2}-\frac{2 x}{b}-\frac{2 a}{b^{2}}-\frac{2 x}{b \left({\mathrm e}^{2 b x +2 a}-1\right)}+\frac{\ln \left({\mathrm e}^{2 b x +2 a}-1\right)}{b^{2}}"," ",0,"1/2*x^2-2*x/b-2/b^2*a-2*x/b/(exp(2*b*x+2*a)-1)+1/b^2*ln(exp(2*b*x+2*a)-1)","A"
9,0,0,14,0.266000," ","int(coth(b*x+a)^2/x,x)","\int \frac{\coth^{2}\left(b x +a \right)}{x}\, dx"," ",0,"int(coth(b*x+a)^2/x,x)","F"
10,0,0,14,0.275000," ","int(coth(b*x+a)^2/x^2,x)","\int \frac{\coth^{2}\left(b x +a \right)}{x^{2}}\, dx"," ",0,"int(coth(b*x+a)^2/x^2,x)","F"
11,1,375,161,0.329000," ","int(x^3*coth(b*x+a)^3,x)","-\frac{x^{2} \left(2 b x \,{\mathrm e}^{2 b x +2 a}+3 \,{\mathrm e}^{2 b x +2 a}-3\right)}{b^{2} \left({\mathrm e}^{2 b x +2 a}-1\right)^{2}}-\frac{x^{4}}{4}-\frac{3 x^{2}}{b^{2}}-\frac{3 a^{2}}{b^{4}}+\frac{3 \ln \left(1-{\mathrm e}^{b x +a}\right) x}{b^{3}}+\frac{3 \ln \left(1+{\mathrm e}^{b x +a}\right) x}{b^{3}}+\frac{6 a \ln \left({\mathrm e}^{b x +a}\right)}{b^{4}}-\frac{3 a \ln \left({\mathrm e}^{b x +a}-1\right)}{b^{4}}+\frac{3 \polylog \left(2, -{\mathrm e}^{b x +a}\right) x^{2}}{b^{2}}-\frac{6 \polylog \left(3, -{\mathrm e}^{b x +a}\right) x}{b^{3}}+\frac{3 \polylog \left(2, {\mathrm e}^{b x +a}\right) x^{2}}{b^{2}}-\frac{6 \polylog \left(3, {\mathrm e}^{b x +a}\right) x}{b^{3}}+\frac{\ln \left(1-{\mathrm e}^{b x +a}\right) x^{3}}{b}+\frac{\ln \left(1+{\mathrm e}^{b x +a}\right) x^{3}}{b}+\frac{2 a^{3} \ln \left({\mathrm e}^{b x +a}\right)}{b^{4}}+\frac{\ln \left(1-{\mathrm e}^{b x +a}\right) a^{3}}{b^{4}}-\frac{2 a^{3} x}{b^{3}}-\frac{a^{3} \ln \left({\mathrm e}^{b x +a}-1\right)}{b^{4}}-\frac{6 a x}{b^{3}}+\frac{3 a \ln \left(1-{\mathrm e}^{b x +a}\right)}{b^{4}}+\frac{6 \polylog \left(4, {\mathrm e}^{b x +a}\right)}{b^{4}}-\frac{3 a^{4}}{2 b^{4}}+\frac{3 \polylog \left(2, {\mathrm e}^{b x +a}\right)}{b^{4}}+\frac{3 \polylog \left(2, -{\mathrm e}^{b x +a}\right)}{b^{4}}+\frac{6 \polylog \left(4, -{\mathrm e}^{b x +a}\right)}{b^{4}}"," ",0,"-x^2*(2*b*x*exp(2*b*x+2*a)+3*exp(2*b*x+2*a)-3)/b^2/(exp(2*b*x+2*a)-1)^2-1/4*x^4-3*x^2/b^2+3/b^4*polylog(2,exp(b*x+a))+3/b^4*polylog(2,-exp(b*x+a))-3/b^4*a^2+3/b^3*ln(1-exp(b*x+a))*x+3/b^3*ln(1+exp(b*x+a))*x+6/b^4*a*ln(exp(b*x+a))-3/b^4*a*ln(exp(b*x+a)-1)-6/b^3*polylog(3,-exp(b*x+a))*x+1/b*ln(1-exp(b*x+a))*x^3+3/b^2*polylog(2,exp(b*x+a))*x^2-6/b^3*polylog(3,exp(b*x+a))*x+1/b*ln(1+exp(b*x+a))*x^3+2/b^4*a^3*ln(exp(b*x+a))+1/b^4*ln(1-exp(b*x+a))*a^3-2/b^3*a^3*x-1/b^4*a^3*ln(exp(b*x+a)-1)+3/b^2*polylog(2,-exp(b*x+a))*x^2-6*a*x/b^3+3/b^4*a*ln(1-exp(b*x+a))-3/2/b^4*a^4+6/b^4*polylog(4,-exp(b*x+a))+6/b^4*polylog(4,exp(b*x+a))","B"
12,1,246,106,0.311000," ","int(x^2*coth(b*x+a)^3,x)","-\frac{x^{3}}{3}-\frac{2 x \left(b x \,{\mathrm e}^{2 b x +2 a}+{\mathrm e}^{2 b x +2 a}-1\right)}{b^{2} \left({\mathrm e}^{2 b x +2 a}-1\right)^{2}}+\frac{4 a^{3}}{3 b^{3}}+\frac{2 a^{2} x}{b^{2}}-\frac{2 \ln \left({\mathrm e}^{b x +a}\right)}{b^{3}}+\frac{\ln \left({\mathrm e}^{b x +a}-1\right)}{b^{3}}+\frac{\ln \left(1-{\mathrm e}^{b x +a}\right) x^{2}}{b}+\frac{2 \polylog \left(2, {\mathrm e}^{b x +a}\right) x}{b^{2}}+\frac{\ln \left(1+{\mathrm e}^{b x +a}\right) x^{2}}{b}+\frac{2 \polylog \left(2, -{\mathrm e}^{b x +a}\right) x}{b^{2}}-\frac{2 \polylog \left(3, -{\mathrm e}^{b x +a}\right)}{b^{3}}-\frac{2 \polylog \left(3, {\mathrm e}^{b x +a}\right)}{b^{3}}+\frac{\ln \left(1+{\mathrm e}^{b x +a}\right)}{b^{3}}+\frac{a^{2} \ln \left({\mathrm e}^{b x +a}-1\right)}{b^{3}}-\frac{2 a^{2} \ln \left({\mathrm e}^{b x +a}\right)}{b^{3}}-\frac{\ln \left(1-{\mathrm e}^{b x +a}\right) a^{2}}{b^{3}}"," ",0,"-1/3*x^3-2*x*(b*x*exp(2*b*x+2*a)+exp(2*b*x+2*a)-1)/b^2/(exp(2*b*x+2*a)-1)^2+4/3/b^3*a^3+2/b^2*a^2*x-2/b^3*ln(exp(b*x+a))+1/b^3*ln(exp(b*x+a)-1)+1/b*ln(1-exp(b*x+a))*x^2+2/b^2*polylog(2,exp(b*x+a))*x+1/b*ln(1+exp(b*x+a))*x^2+2/b^2*polylog(2,-exp(b*x+a))*x-2/b^3*polylog(3,-exp(b*x+a))-2/b^3*polylog(3,exp(b*x+a))+1/b^3*ln(1+exp(b*x+a))+1/b^3*a^2*ln(exp(b*x+a)-1)-2/b^3*a^2*ln(exp(b*x+a))-1/b^3*ln(1-exp(b*x+a))*a^2","B"
13,1,164,72,0.258000," ","int(x*coth(b*x+a)^3,x)","-\frac{x^{2}}{2}-\frac{2 b x \,{\mathrm e}^{2 b x +2 a}+{\mathrm e}^{2 b x +2 a}-1}{b^{2} \left({\mathrm e}^{2 b x +2 a}-1\right)^{2}}-\frac{2 a x}{b}-\frac{a^{2}}{b^{2}}+\frac{\ln \left(1-{\mathrm e}^{b x +a}\right) x}{b}+\frac{\ln \left(1-{\mathrm e}^{b x +a}\right) a}{b^{2}}+\frac{\polylog \left(2, {\mathrm e}^{b x +a}\right)}{b^{2}}+\frac{\ln \left(1+{\mathrm e}^{b x +a}\right) x}{b}+\frac{\polylog \left(2, -{\mathrm e}^{b x +a}\right)}{b^{2}}+\frac{2 a \ln \left({\mathrm e}^{b x +a}\right)}{b^{2}}-\frac{a \ln \left({\mathrm e}^{b x +a}-1\right)}{b^{2}}"," ",0,"-1/2*x^2-(2*b*x*exp(2*b*x+2*a)+exp(2*b*x+2*a)-1)/b^2/(exp(2*b*x+2*a)-1)^2-2/b*a*x-a^2/b^2+1/b*ln(1-exp(b*x+a))*x+1/b^2*ln(1-exp(b*x+a))*a+1/b^2*polylog(2,exp(b*x+a))+1/b*ln(1+exp(b*x+a))*x+1/b^2*polylog(2,-exp(b*x+a))+2/b^2*a*ln(exp(b*x+a))-1/b^2*a*ln(exp(b*x+a)-1)","B"
14,0,0,14,0.813000," ","int(coth(b*x+a)^3/x,x)","\int \frac{\coth^{3}\left(b x +a \right)}{x}\, dx"," ",0,"int(coth(b*x+a)^3/x,x)","F"
15,0,0,14,0.826000," ","int(coth(b*x+a)^3/x^2,x)","\int \frac{\coth^{3}\left(b x +a \right)}{x^{2}}\, dx"," ",0,"int(coth(b*x+a)^3/x^2,x)","F"
16,1,959,153,0.432000," ","int((d*x+c)^3/(a+a*coth(f*x+e)),x)","\frac{-\frac{d^{3} \left(\frac{\left(f x +e \right)^{3} \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{4}}{8}-\frac{3 \left(f x +e \right)^{2} \left(\cosh^{2}\left(f x +e \right)\right)}{4}+\frac{3 \left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{4}+\frac{3 \left(f x +e \right)^{2}}{8}-\frac{3 \left(\cosh^{2}\left(f x +e \right)\right)}{8}\right)}{f^{3}}+\frac{d^{3} \left(\frac{\left(f x +e \right)^{3} \left(\cosh^{2}\left(f x +e \right)\right)}{2}-\frac{3 \left(f x +e \right)^{2} \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{4}-\frac{\left(f x +e \right)^{3}}{4}+\frac{3 \left(f x +e \right) \left(\cosh^{2}\left(f x +e \right)\right)}{4}-\frac{3 \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{8}-\frac{3 f x}{8}-\frac{3 e}{8}\right)}{f^{3}}+\frac{3 d^{3} e \left(\frac{\left(f x +e \right)^{2} \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{3}}{6}-\frac{\left(f x +e \right) \left(\cosh^{2}\left(f x +e \right)\right)}{2}+\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{4}+\frac{f x}{4}+\frac{e}{4}\right)}{f^{3}}-\frac{3 d^{3} e \left(\frac{\left(f x +e \right)^{2} \left(\cosh^{2}\left(f x +e \right)\right)}{2}-\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{2}}{4}+\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{4}\right)}{f^{3}}-\frac{3 d^{2} c \left(\frac{\left(f x +e \right)^{2} \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{3}}{6}-\frac{\left(f x +e \right) \left(\cosh^{2}\left(f x +e \right)\right)}{2}+\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{4}+\frac{f x}{4}+\frac{e}{4}\right)}{f^{2}}+\frac{3 d^{2} c \left(\frac{\left(f x +e \right)^{2} \left(\cosh^{2}\left(f x +e \right)\right)}{2}-\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{2}}{4}+\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{4}\right)}{f^{2}}-\frac{3 d^{3} e^{2} \left(\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{4}\right)}{f^{3}}+\frac{3 d^{3} e^{2} \left(\frac{\left(f x +e \right) \left(\cosh^{2}\left(f x +e \right)\right)}{2}-\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{4}-\frac{f x}{4}-\frac{e}{4}\right)}{f^{3}}+\frac{6 d^{2} e c \left(\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{4}\right)}{f^{2}}-\frac{6 d^{2} e c \left(\frac{\left(f x +e \right) \left(\cosh^{2}\left(f x +e \right)\right)}{2}-\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{4}-\frac{f x}{4}-\frac{e}{4}\right)}{f^{2}}-\frac{3 d \,c^{2} \left(\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{4}\right)}{f}+\frac{3 d \,c^{2} \left(\frac{\left(f x +e \right) \left(\cosh^{2}\left(f x +e \right)\right)}{2}-\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{4}-\frac{f x}{4}-\frac{e}{4}\right)}{f}+\frac{d^{3} e^{3} \left(\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{f x}{2}-\frac{e}{2}\right)}{f^{3}}-\frac{d^{3} e^{3} \left(\cosh^{2}\left(f x +e \right)\right)}{2 f^{3}}-\frac{3 d^{2} e^{2} c \left(\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{f x}{2}-\frac{e}{2}\right)}{f^{2}}+\frac{3 d^{2} e^{2} c \left(\cosh^{2}\left(f x +e \right)\right)}{2 f^{2}}+\frac{3 d e \,c^{2} \left(\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{f x}{2}-\frac{e}{2}\right)}{f}-\frac{3 d e \,c^{2} \left(\cosh^{2}\left(f x +e \right)\right)}{2 f}-c^{3} \left(\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{f x}{2}-\frac{e}{2}\right)+\frac{c^{3} \left(\cosh^{2}\left(f x +e \right)\right)}{2}}{a f}"," ",0,"1/a/f*(-1/f^3*d^3*(1/2*(f*x+e)^3*cosh(f*x+e)*sinh(f*x+e)-1/8*(f*x+e)^4-3/4*(f*x+e)^2*cosh(f*x+e)^2+3/4*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+3/8*(f*x+e)^2-3/8*cosh(f*x+e)^2)+1/f^3*d^3*(1/2*(f*x+e)^3*cosh(f*x+e)^2-3/4*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^3+3/4*(f*x+e)*cosh(f*x+e)^2-3/8*cosh(f*x+e)*sinh(f*x+e)-3/8*f*x-3/8*e)+3/f^3*d^3*e*(1/2*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)-1/6*(f*x+e)^3-1/2*(f*x+e)*cosh(f*x+e)^2+1/4*cosh(f*x+e)*sinh(f*x+e)+1/4*f*x+1/4*e)-3/f^3*d^3*e*(1/2*(f*x+e)^2*cosh(f*x+e)^2-1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2+1/4*cosh(f*x+e)^2)-3/f^2*d^2*c*(1/2*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)-1/6*(f*x+e)^3-1/2*(f*x+e)*cosh(f*x+e)^2+1/4*cosh(f*x+e)*sinh(f*x+e)+1/4*f*x+1/4*e)+3/f^2*d^2*c*(1/2*(f*x+e)^2*cosh(f*x+e)^2-1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2+1/4*cosh(f*x+e)^2)-3/f^3*d^3*e^2*(1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2-1/4*cosh(f*x+e)^2)+3/f^3*d^3*e^2*(1/2*(f*x+e)*cosh(f*x+e)^2-1/4*cosh(f*x+e)*sinh(f*x+e)-1/4*f*x-1/4*e)+6/f^2*d^2*e*c*(1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2-1/4*cosh(f*x+e)^2)-6/f^2*d^2*e*c*(1/2*(f*x+e)*cosh(f*x+e)^2-1/4*cosh(f*x+e)*sinh(f*x+e)-1/4*f*x-1/4*e)-3/f*d*c^2*(1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2-1/4*cosh(f*x+e)^2)+3/f*d*c^2*(1/2*(f*x+e)*cosh(f*x+e)^2-1/4*cosh(f*x+e)*sinh(f*x+e)-1/4*f*x-1/4*e)+d^3*e^3/f^3*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)-1/2*d^3*e^3/f^3*cosh(f*x+e)^2-3*d^2*e^2/f^2*c*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)+3/2*d^2*e^2/f^2*c*cosh(f*x+e)^2+3*d*e/f*c^2*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)-3/2*d*e/f*c^2*cosh(f*x+e)^2-c^3*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)+1/2*c^3*cosh(f*x+e)^2)","B"
17,1,469,110,0.392000," ","int((d*x+c)^2/(a+a*coth(f*x+e)),x)","\frac{-\frac{d^{2} \left(\frac{\left(f x +e \right)^{2} \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{3}}{6}-\frac{\left(f x +e \right) \left(\cosh^{2}\left(f x +e \right)\right)}{2}+\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{4}+\frac{f x}{4}+\frac{e}{4}\right)}{f^{2}}+\frac{d^{2} \left(\frac{\left(f x +e \right)^{2} \left(\cosh^{2}\left(f x +e \right)\right)}{2}-\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{2}}{4}+\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{4}\right)}{f^{2}}+\frac{2 d^{2} e \left(\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{4}\right)}{f^{2}}-\frac{2 d^{2} e \left(\frac{\left(f x +e \right) \left(\cosh^{2}\left(f x +e \right)\right)}{2}-\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{4}-\frac{f x}{4}-\frac{e}{4}\right)}{f^{2}}-\frac{2 d c \left(\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{4}\right)}{f}+\frac{2 d c \left(\frac{\left(f x +e \right) \left(\cosh^{2}\left(f x +e \right)\right)}{2}-\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{4}-\frac{f x}{4}-\frac{e}{4}\right)}{f}-\frac{d^{2} e^{2} \left(\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{f x}{2}-\frac{e}{2}\right)}{f^{2}}+\frac{d^{2} e^{2} \left(\cosh^{2}\left(f x +e \right)\right)}{2 f^{2}}+\frac{2 d e c \left(\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{f x}{2}-\frac{e}{2}\right)}{f}-\frac{d e c \left(\cosh^{2}\left(f x +e \right)\right)}{f}-c^{2} \left(\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{f x}{2}-\frac{e}{2}\right)+\frac{c^{2} \left(\cosh^{2}\left(f x +e \right)\right)}{2}}{a f}"," ",0,"1/a/f*(-1/f^2*d^2*(1/2*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)-1/6*(f*x+e)^3-1/2*(f*x+e)*cosh(f*x+e)^2+1/4*cosh(f*x+e)*sinh(f*x+e)+1/4*f*x+1/4*e)+1/f^2*d^2*(1/2*(f*x+e)^2*cosh(f*x+e)^2-1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2+1/4*cosh(f*x+e)^2)+2/f^2*d^2*e*(1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2-1/4*cosh(f*x+e)^2)-2/f^2*d^2*e*(1/2*(f*x+e)*cosh(f*x+e)^2-1/4*cosh(f*x+e)*sinh(f*x+e)-1/4*f*x-1/4*e)-2/f*d*c*(1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2-1/4*cosh(f*x+e)^2)+2/f*d*c*(1/2*(f*x+e)*cosh(f*x+e)^2-1/4*cosh(f*x+e)*sinh(f*x+e)-1/4*f*x-1/4*e)-d^2*e^2/f^2*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)+1/2*d^2*e^2/f^2*cosh(f*x+e)^2+2*d*e/f*c*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)-d*e/f*c*cosh(f*x+e)^2-c^2*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)+1/2*c^2*cosh(f*x+e)^2)","B"
18,1,175,69,0.375000," ","int((d*x+c)/(a+a*coth(f*x+e)),x)","\frac{-\frac{d \left(\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{4}\right)}{f}+\frac{d \left(\frac{\left(f x +e \right) \left(\cosh^{2}\left(f x +e \right)\right)}{2}-\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{4}-\frac{f x}{4}-\frac{e}{4}\right)}{f}+\frac{d e \left(\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{f x}{2}-\frac{e}{2}\right)}{f}-\frac{d e \left(\cosh^{2}\left(f x +e \right)\right)}{2 f}-c \left(\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{f x}{2}-\frac{e}{2}\right)+\frac{c \left(\cosh^{2}\left(f x +e \right)\right)}{2}}{a f}"," ",0,"1/a/f*(-1/f*d*(1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2-1/4*cosh(f*x+e)^2)+1/f*d*(1/2*(f*x+e)*cosh(f*x+e)^2-1/4*cosh(f*x+e)*sinh(f*x+e)-1/4*f*x-1/4*e)+d*e/f*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)-1/2*d*e/f*cosh(f*x+e)^2-c*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)+1/2*c*cosh(f*x+e)^2)","B"
19,1,61,147,1.025000," ","int(1/(d*x+c)/(a+a*coth(f*x+e)),x)","\frac{\ln \left(d x +c \right)}{2 d a}+\frac{{\mathrm e}^{\frac{2 c f -2 d e}{d}} \Ei \left(1, 2 f x +2 e +\frac{2 c f -2 d e}{d}\right)}{2 a d}"," ",0,"1/2*ln(d*x+c)/d/a+1/2/a/d*exp(2*(c*f-d*e)/d)*Ei(1,2*f*x+2*e+2*(c*f-d*e)/d)","A"
20,1,91,159,1.050000," ","int(1/(d*x+c)^2/(a+a*coth(f*x+e)),x)","-\frac{1}{2 d a \left(d x +c \right)}+\frac{f \,{\mathrm e}^{-2 f x -2 e}}{2 a d \left(d f x +c f \right)}-\frac{f \,{\mathrm e}^{\frac{2 c f -2 d e}{d}} \Ei \left(1, 2 f x +2 e +\frac{2 c f -2 d e}{d}\right)}{a \,d^{2}}"," ",0,"-1/2/d/a/(d*x+c)+1/2*f/a*exp(-2*f*x-2*e)/d/(d*f*x+c*f)-f/a/d^2*exp(2*(c*f-d*e)/d)*Ei(1,2*f*x+2*e+2*(c*f-d*e)/d)","A"
21,1,210,207,1.063000," ","int(1/(d*x+c)^3/(a+a*coth(f*x+e)),x)","-\frac{1}{4 d a \left(d x +c \right)^{2}}-\frac{f^{3} {\mathrm e}^{-2 f x -2 e} x}{2 a d \left(d^{2} f^{2} x^{2}+2 c d \,f^{2} x +c^{2} f^{2}\right)}-\frac{f^{3} {\mathrm e}^{-2 f x -2 e} c}{2 a \,d^{2} \left(d^{2} f^{2} x^{2}+2 c d \,f^{2} x +c^{2} f^{2}\right)}+\frac{f^{2} {\mathrm e}^{-2 f x -2 e}}{4 a d \left(d^{2} f^{2} x^{2}+2 c d \,f^{2} x +c^{2} f^{2}\right)}+\frac{f^{2} {\mathrm e}^{\frac{2 c f -2 d e}{d}} \Ei \left(1, 2 f x +2 e +\frac{2 c f -2 d e}{d}\right)}{a \,d^{3}}"," ",0,"-1/4/d/a/(d*x+c)^2-1/2*f^3/a*exp(-2*f*x-2*e)/d/(d^2*f^2*x^2+2*c*d*f^2*x+c^2*f^2)*x-1/2*f^3/a*exp(-2*f*x-2*e)/d^2/(d^2*f^2*x^2+2*c*d*f^2*x+c^2*f^2)*c+1/4*f^2/a*exp(-2*f*x-2*e)/d/(d^2*f^2*x^2+2*c*d*f^2*x+c^2*f^2)+f^2/a/d^3*exp(2*(c*f-d*e)/d)*Ei(1,2*f*x+2*e+2*(c*f-d*e)/d)","A"
22,1,1979,204,0.596000," ","int((d*x+c)^3/(a+a*coth(f*x+e))^2,x)","\text{Expression too large to display}"," ",0,"1/a^2/f*(-1/2*c^3*sinh(f*x+e)^4+2*c^3*(1/4*cosh(f*x+e)^3*sinh(f*x+e)-1/8*cosh(f*x+e)*sinh(f*x+e)-1/8*f*x-1/8*e)+3/f^3*d^3*e*(1/2*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)-1/6*(f*x+e)^3-1/2*(f*x+e)*cosh(f*x+e)^2+1/4*cosh(f*x+e)*sinh(f*x+e)+1/4*f*x+1/4*e)-3/f^2*d^2*c*(1/2*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)-1/6*(f*x+e)^3-1/2*(f*x+e)*cosh(f*x+e)^2+1/4*cosh(f*x+e)*sinh(f*x+e)+1/4*f*x+1/4*e)-3/f^3*d^3*e^2*(1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2-1/4*cosh(f*x+e)^2)-1/f^3*d^3*(1/2*(f*x+e)^3*cosh(f*x+e)*sinh(f*x+e)-1/8*(f*x+e)^4-3/4*(f*x+e)^2*cosh(f*x+e)^2+3/4*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+3/8*(f*x+e)^2-3/8*cosh(f*x+e)^2)-3/f*d*c^2*(1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2-1/4*cosh(f*x+e)^2)+d^3*e^3/f^3*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)-2/f^3*d^3*(1/4*(f*x+e)^3*sinh(f*x+e)^4-3/16*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)^3+9/32*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)-3/32*(f*x+e)^3+3/32*(f*x+e)*sinh(f*x+e)^4-3/128*sinh(f*x+e)^3*cosh(f*x+e)+45/256*cosh(f*x+e)*sinh(f*x+e)+27/256*f*x+27/256*e-9/32*(f*x+e)*cosh(f*x+e)^2)+2/f^3*d^3*(1/4*(f*x+e)^3*sinh(f*x+e)*cosh(f*x+e)^3-1/8*(f*x+e)^3*cosh(f*x+e)*sinh(f*x+e)-1/32*(f*x+e)^4-3/16*(f*x+e)^2*cosh(f*x+e)^4+3/32*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3-3/64*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-3/128*(f*x+e)^2-3/128*cosh(f*x+e)^4+3/128*cosh(f*x+e)^2+3/16*(f*x+e)^2*cosh(f*x+e)^2)-c^3*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)+6/f^2*d^2*e*c*(1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2-1/4*cosh(f*x+e)^2)-3*d^2*e^2/f^2*c*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)+3*d*e/f*c^2*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)+1/2/f^3*d^3*e^3*sinh(f*x+e)^4+6/f^3*d^3*e^2*(1/4*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3-1/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/16*(f*x+e)^2-1/16*cosh(f*x+e)^4+1/16*cosh(f*x+e)^2)+6/f^2*c*d^2*(1/4*(f*x+e)^2*sinh(f*x+e)*cosh(f*x+e)^3-1/8*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)-1/24*(f*x+e)^3-1/8*(f*x+e)*cosh(f*x+e)^4+1/32*cosh(f*x+e)^3*sinh(f*x+e)-1/64*cosh(f*x+e)*sinh(f*x+e)-1/64*f*x-1/64*e+1/8*(f*x+e)*cosh(f*x+e)^2)+6/f*c^2*d*(1/4*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3-1/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/16*(f*x+e)^2-1/16*cosh(f*x+e)^4+1/16*cosh(f*x+e)^2)+6/f^3*d^3*e*(1/4*(f*x+e)^2*sinh(f*x+e)^4-1/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)^3+3/16*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-3/32*(f*x+e)^2+1/32*sinh(f*x+e)^4-3/32*cosh(f*x+e)^2)-6/f^3*d^3*e^2*(1/4*(f*x+e)*sinh(f*x+e)^4-1/16*sinh(f*x+e)^3*cosh(f*x+e)+3/32*cosh(f*x+e)*sinh(f*x+e)-3/32*f*x-3/32*e)-6/f^2*c*d^2*(1/4*(f*x+e)^2*sinh(f*x+e)^4-1/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)^3+3/16*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-3/32*(f*x+e)^2+1/32*sinh(f*x+e)^4-3/32*cosh(f*x+e)^2)-6/f*c^2*d*(1/4*(f*x+e)*sinh(f*x+e)^4-1/16*sinh(f*x+e)^3*cosh(f*x+e)+3/32*cosh(f*x+e)*sinh(f*x+e)-3/32*f*x-3/32*e)-6/f^3*d^3*e*(1/4*(f*x+e)^2*sinh(f*x+e)*cosh(f*x+e)^3-1/8*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)-1/24*(f*x+e)^3-1/8*(f*x+e)*cosh(f*x+e)^4+1/32*cosh(f*x+e)^3*sinh(f*x+e)-1/64*cosh(f*x+e)*sinh(f*x+e)-1/64*f*x-1/64*e+1/8*(f*x+e)*cosh(f*x+e)^2)-2/f^3*d^3*e^3*(1/4*cosh(f*x+e)^3*sinh(f*x+e)-1/8*cosh(f*x+e)*sinh(f*x+e)-1/8*f*x-1/8*e)+6/f^2*c*d^2*e^2*(1/4*cosh(f*x+e)^3*sinh(f*x+e)-1/8*cosh(f*x+e)*sinh(f*x+e)-1/8*f*x-1/8*e)-6/f*c^2*d*e*(1/4*cosh(f*x+e)^3*sinh(f*x+e)-1/8*cosh(f*x+e)*sinh(f*x+e)-1/8*f*x-1/8*e)-3/2/f^2*c*d^2*e^2*sinh(f*x+e)^4+3/2/f*c^2*d*e*sinh(f*x+e)^4+12/f^2*c*d^2*e*(1/4*(f*x+e)*sinh(f*x+e)^4-1/16*sinh(f*x+e)^3*cosh(f*x+e)+3/32*cosh(f*x+e)*sinh(f*x+e)-3/32*f*x-3/32*e)-12/f^2*c*d^2*e*(1/4*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3-1/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/16*(f*x+e)^2-1/16*cosh(f*x+e)^4+1/16*cosh(f*x+e)^2))","B"
23,1,955,150,0.579000," ","int((d*x+c)^2/(a+a*coth(f*x+e))^2,x)","\frac{\frac{2 d^{2} \left(\frac{\left(f x +e \right)^{2} \sinh \left(f x +e \right) \left(\cosh^{3}\left(f x +e \right)\right)}{4}-\frac{\left(f x +e \right)^{2} \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{8}-\frac{\left(f x +e \right)^{3}}{24}-\frac{\left(f x +e \right) \left(\cosh^{4}\left(f x +e \right)\right)}{8}+\frac{\left(\cosh^{3}\left(f x +e \right)\right) \sinh \left(f x +e \right)}{32}-\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{64}-\frac{f x}{64}-\frac{e}{64}+\frac{\left(f x +e \right) \left(\cosh^{2}\left(f x +e \right)\right)}{8}\right)}{f^{2}}-\frac{2 d^{2} \left(\frac{\left(f x +e \right)^{2} \left(\sinh^{4}\left(f x +e \right)\right)}{4}-\frac{\left(f x +e \right) \cosh \left(f x +e \right) \left(\sinh^{3}\left(f x +e \right)\right)}{8}+\frac{3 \left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{16}-\frac{3 \left(f x +e \right)^{2}}{32}+\frac{\left(\sinh^{4}\left(f x +e \right)\right)}{32}-\frac{3 \left(\cosh^{2}\left(f x +e \right)\right)}{32}\right)}{f^{2}}-\frac{d^{2} \left(\frac{\left(f x +e \right)^{2} \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{3}}{6}-\frac{\left(f x +e \right) \left(\cosh^{2}\left(f x +e \right)\right)}{2}+\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{4}+\frac{f x}{4}+\frac{e}{4}\right)}{f^{2}}-\frac{4 d^{2} e \left(\frac{\left(f x +e \right) \sinh \left(f x +e \right) \left(\cosh^{3}\left(f x +e \right)\right)}{4}-\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{8}-\frac{\left(f x +e \right)^{2}}{16}-\frac{\left(\cosh^{4}\left(f x +e \right)\right)}{16}+\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{16}\right)}{f^{2}}+\frac{4 d^{2} e \left(\frac{\left(f x +e \right) \left(\sinh^{4}\left(f x +e \right)\right)}{4}-\frac{\left(\sinh^{3}\left(f x +e \right)\right) \cosh \left(f x +e \right)}{16}+\frac{3 \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{32}-\frac{3 f x}{32}-\frac{3 e}{32}\right)}{f^{2}}+\frac{2 d^{2} e \left(\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{4}\right)}{f^{2}}+\frac{4 d c \left(\frac{\left(f x +e \right) \sinh \left(f x +e \right) \left(\cosh^{3}\left(f x +e \right)\right)}{4}-\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{8}-\frac{\left(f x +e \right)^{2}}{16}-\frac{\left(\cosh^{4}\left(f x +e \right)\right)}{16}+\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{16}\right)}{f}-\frac{4 d c \left(\frac{\left(f x +e \right) \left(\sinh^{4}\left(f x +e \right)\right)}{4}-\frac{\left(\sinh^{3}\left(f x +e \right)\right) \cosh \left(f x +e \right)}{16}+\frac{3 \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{32}-\frac{3 f x}{32}-\frac{3 e}{32}\right)}{f}-\frac{2 d c \left(\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{4}\right)}{f}+\frac{2 d^{2} e^{2} \left(\frac{\left(\cosh^{3}\left(f x +e \right)\right) \sinh \left(f x +e \right)}{4}-\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{8}-\frac{f x}{8}-\frac{e}{8}\right)}{f^{2}}-\frac{d^{2} e^{2} \left(\sinh^{4}\left(f x +e \right)\right)}{2 f^{2}}-\frac{d^{2} e^{2} \left(\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{f x}{2}-\frac{e}{2}\right)}{f^{2}}-\frac{4 d e c \left(\frac{\left(\cosh^{3}\left(f x +e \right)\right) \sinh \left(f x +e \right)}{4}-\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{8}-\frac{f x}{8}-\frac{e}{8}\right)}{f}+\frac{d e c \left(\sinh^{4}\left(f x +e \right)\right)}{f}+\frac{2 d e c \left(\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{f x}{2}-\frac{e}{2}\right)}{f}+2 c^{2} \left(\frac{\left(\cosh^{3}\left(f x +e \right)\right) \sinh \left(f x +e \right)}{4}-\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{8}-\frac{f x}{8}-\frac{e}{8}\right)-\frac{c^{2} \left(\sinh^{4}\left(f x +e \right)\right)}{2}-c^{2} \left(\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{f x}{2}-\frac{e}{2}\right)}{a^{2} f}"," ",0,"1/a^2/f*(2/f^2*d^2*(1/4*(f*x+e)^2*sinh(f*x+e)*cosh(f*x+e)^3-1/8*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)-1/24*(f*x+e)^3-1/8*(f*x+e)*cosh(f*x+e)^4+1/32*cosh(f*x+e)^3*sinh(f*x+e)-1/64*cosh(f*x+e)*sinh(f*x+e)-1/64*f*x-1/64*e+1/8*(f*x+e)*cosh(f*x+e)^2)-2/f^2*d^2*(1/4*(f*x+e)^2*sinh(f*x+e)^4-1/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)^3+3/16*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-3/32*(f*x+e)^2+1/32*sinh(f*x+e)^4-3/32*cosh(f*x+e)^2)-1/f^2*d^2*(1/2*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)-1/6*(f*x+e)^3-1/2*(f*x+e)*cosh(f*x+e)^2+1/4*cosh(f*x+e)*sinh(f*x+e)+1/4*f*x+1/4*e)-4/f^2*d^2*e*(1/4*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3-1/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/16*(f*x+e)^2-1/16*cosh(f*x+e)^4+1/16*cosh(f*x+e)^2)+4/f^2*d^2*e*(1/4*(f*x+e)*sinh(f*x+e)^4-1/16*sinh(f*x+e)^3*cosh(f*x+e)+3/32*cosh(f*x+e)*sinh(f*x+e)-3/32*f*x-3/32*e)+2/f^2*d^2*e*(1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2-1/4*cosh(f*x+e)^2)+4/f*d*c*(1/4*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3-1/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/16*(f*x+e)^2-1/16*cosh(f*x+e)^4+1/16*cosh(f*x+e)^2)-4/f*d*c*(1/4*(f*x+e)*sinh(f*x+e)^4-1/16*sinh(f*x+e)^3*cosh(f*x+e)+3/32*cosh(f*x+e)*sinh(f*x+e)-3/32*f*x-3/32*e)-2/f*d*c*(1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2-1/4*cosh(f*x+e)^2)+2*d^2*e^2/f^2*(1/4*cosh(f*x+e)^3*sinh(f*x+e)-1/8*cosh(f*x+e)*sinh(f*x+e)-1/8*f*x-1/8*e)-1/2*d^2*e^2/f^2*sinh(f*x+e)^4-d^2*e^2/f^2*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)-4*d*e/f*c*(1/4*cosh(f*x+e)^3*sinh(f*x+e)-1/8*cosh(f*x+e)*sinh(f*x+e)-1/8*f*x-1/8*e)+d*e/f*c*sinh(f*x+e)^4+2*d*e/f*c*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)+2*c^2*(1/4*cosh(f*x+e)^3*sinh(f*x+e)-1/8*cosh(f*x+e)*sinh(f*x+e)-1/8*f*x-1/8*e)-1/2*c^2*sinh(f*x+e)^4-c^2*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e))","B"
24,1,354,125,0.510000," ","int((d*x+c)/(a+a*coth(f*x+e))^2,x)","\frac{\frac{2 d \left(\frac{\left(f x +e \right) \sinh \left(f x +e \right) \left(\cosh^{3}\left(f x +e \right)\right)}{4}-\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{8}-\frac{\left(f x +e \right)^{2}}{16}-\frac{\left(\cosh^{4}\left(f x +e \right)\right)}{16}+\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{16}\right)}{f}-\frac{2 d \left(\frac{\left(f x +e \right) \left(\sinh^{4}\left(f x +e \right)\right)}{4}-\frac{\left(\sinh^{3}\left(f x +e \right)\right) \cosh \left(f x +e \right)}{16}+\frac{3 \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{32}-\frac{3 f x}{32}-\frac{3 e}{32}\right)}{f}-\frac{d \left(\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{4}\right)}{f}-\frac{2 d e \left(\frac{\left(\cosh^{3}\left(f x +e \right)\right) \sinh \left(f x +e \right)}{4}-\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{8}-\frac{f x}{8}-\frac{e}{8}\right)}{f}+\frac{d e \left(\sinh^{4}\left(f x +e \right)\right)}{2 f}+\frac{d e \left(\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{f x}{2}-\frac{e}{2}\right)}{f}+2 c \left(\frac{\left(\cosh^{3}\left(f x +e \right)\right) \sinh \left(f x +e \right)}{4}-\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{8}-\frac{f x}{8}-\frac{e}{8}\right)-\frac{c \left(\sinh^{4}\left(f x +e \right)\right)}{2}-c \left(\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{2}-\frac{f x}{2}-\frac{e}{2}\right)}{a^{2} f}"," ",0,"1/a^2/f*(2/f*d*(1/4*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3-1/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/16*(f*x+e)^2-1/16*cosh(f*x+e)^4+1/16*cosh(f*x+e)^2)-2/f*d*(1/4*(f*x+e)*sinh(f*x+e)^4-1/16*sinh(f*x+e)^3*cosh(f*x+e)+3/32*cosh(f*x+e)*sinh(f*x+e)-3/32*f*x-3/32*e)-1/f*d*(1/2*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-1/4*(f*x+e)^2-1/4*cosh(f*x+e)^2)-2*d*e/f*(1/4*cosh(f*x+e)^3*sinh(f*x+e)-1/8*cosh(f*x+e)*sinh(f*x+e)-1/8*f*x-1/8*e)+1/2*d*e/f*sinh(f*x+e)^4+d*e/f*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e)+2*c*(1/4*cosh(f*x+e)^3*sinh(f*x+e)-1/8*cosh(f*x+e)*sinh(f*x+e)-1/8*f*x-1/8*e)-1/2*c*sinh(f*x+e)^4-c*(1/2*cosh(f*x+e)*sinh(f*x+e)-1/2*f*x-1/2*e))","B"
25,1,106,279,1.109000," ","int(1/(d*x+c)/(a+a*coth(f*x+e))^2,x)","\frac{\ln \left(d x +c \right)}{4 d \,a^{2}}-\frac{{\mathrm e}^{\frac{4 c f -4 d e}{d}} \Ei \left(1, 4 f x +4 e +\frac{4 c f -4 d e}{d}\right)}{4 a^{2} d}+\frac{{\mathrm e}^{\frac{2 c f -2 d e}{d}} \Ei \left(1, 2 f x +2 e +\frac{2 c f -2 d e}{d}\right)}{2 a^{2} d}"," ",0,"1/4*ln(d*x+c)/d/a^2-1/4/a^2/d*exp(4*(c*f-d*e)/d)*Ei(1,4*f*x+4*e+4*(c*f-d*e)/d)+1/2/a^2/d*exp(2*(c*f-d*e)/d)*Ei(1,2*f*x+2*e+2*(c*f-d*e)/d)","A"
26,1,164,408,1.174000," ","int(1/(d*x+c)^2/(a+a*coth(f*x+e))^2,x)","-\frac{1}{4 a^{2} d \left(d x +c \right)}-\frac{f \,{\mathrm e}^{-4 f x -4 e}}{4 a^{2} d \left(d f x +c f \right)}+\frac{f \,{\mathrm e}^{\frac{4 c f -4 d e}{d}} \Ei \left(1, 4 f x +4 e +\frac{4 c f -4 d e}{d}\right)}{a^{2} d^{2}}+\frac{f \,{\mathrm e}^{-2 f x -2 e}}{2 a^{2} d \left(d f x +c f \right)}-\frac{f \,{\mathrm e}^{\frac{2 c f -2 d e}{d}} \Ei \left(1, 2 f x +2 e +\frac{2 c f -2 d e}{d}\right)}{a^{2} d^{2}}"," ",0,"-1/4/a^2/d/(d*x+c)-1/4*f/a^2*exp(-4*f*x-4*e)/d/(d*f*x+c*f)+f/a^2/d^2*exp(4*(c*f-d*e)/d)*Ei(1,4*f*x+4*e+4*(c*f-d*e)/d)+1/2*f/a^2*exp(-2*f*x-2*e)/d/(d*f*x+c*f)-f/a^2/d^2*exp(2*(c*f-d*e)/d)*Ei(1,2*f*x+2*e+2*(c*f-d*e)/d)","A"
27,1,3691,298,0.710000," ","int((d*x+c)^3/(a+a*coth(f*x+e))^3,x)","\text{output too large to display}"," ",0,"1/a^3/f*(1/f^3*d^3*(1/4*(f*x+e)^3*cosh(f*x+e)*sinh(f*x+e)^3-3/8*(f*x+e)^3*cosh(f*x+e)*sinh(f*x+e)+3/32*(f*x+e)^4-3/16*(f*x+e)^2*sinh(f*x+e)^4+3/32*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)^3-45/64*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-27/128*(f*x+e)^2-3/128*sinh(f*x+e)^4+45/128*cosh(f*x+e)^2+9/16*(f*x+e)^2*cosh(f*x+e)^2)+4/f^3*d^3*(1/6*(f*x+e)^3*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*(f*x+e)^3*cosh(f*x+e)^4-1/12*(f*x+e)^2*sinh(f*x+e)*cosh(f*x+e)^5+1/12*(f*x+e)^2*sinh(f*x+e)*cosh(f*x+e)^3+1/8*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)+1/24*(f*x+e)^3+1/36*(f*x+e)*cosh(f*x+e)^6-1/216*cosh(f*x+e)^5*sinh(f*x+e)+1/216*cosh(f*x+e)^3*sinh(f*x+e)+5/72*cosh(f*x+e)*sinh(f*x+e)+5/72*f*x+5/72*e-1/24*(f*x+e)*cosh(f*x+e)^4-1/8*(f*x+e)*cosh(f*x+e)^2)-4/f^3*d^3*(1/6*(f*x+e)^3*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*(f*x+e)^3*sinh(f*x+e)*cosh(f*x+e)^3+1/16*(f*x+e)^3*cosh(f*x+e)*sinh(f*x+e)+1/64*(f*x+e)^4-1/12*(f*x+e)^2*sinh(f*x+e)^2*cosh(f*x+e)^4+13/96*(f*x+e)^2*cosh(f*x+e)^4+1/36*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^5-43/576*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3-7/384*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-7/768*(f*x+e)^2-1/216*cosh(f*x+e)^6+43/2304*cosh(f*x+e)^4+7/768*cosh(f*x+e)^2-3/32*(f*x+e)^2*cosh(f*x+e)^2)+4*c^3*(1/6*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*cosh(f*x+e)^4)-4*c^3*(1/6*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*cosh(f*x+e)^3*sinh(f*x+e)+1/16*cosh(f*x+e)*sinh(f*x+e)+1/16*f*x+1/16*e)+c^3*((1/4*sinh(f*x+e)^3-3/8*sinh(f*x+e))*cosh(f*x+e)+3/8*f*x+3/8*e)-3/4*c^3*sinh(f*x+e)^4-3/f^3*d^3*(1/4*(f*x+e)^3*sinh(f*x+e)^4-3/16*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)^3+9/32*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)-3/32*(f*x+e)^3+3/32*(f*x+e)*sinh(f*x+e)^4-3/128*sinh(f*x+e)^3*cosh(f*x+e)+45/256*cosh(f*x+e)*sinh(f*x+e)+27/256*f*x+27/256*e-9/32*(f*x+e)*cosh(f*x+e)^2)+24/f^2*d^2*c*e*(1/6*(f*x+e)*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3+1/16*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+1/32*(f*x+e)^2-1/36*sinh(f*x+e)^2*cosh(f*x+e)^4+13/288*cosh(f*x+e)^4-1/32*cosh(f*x+e)^2)+3*d^2*e^2/f^2*c*((1/4*sinh(f*x+e)^3-3/8*sinh(f*x+e))*cosh(f*x+e)+3/8*f*x+3/8*e)-3*d*e/f*c^2*((1/4*sinh(f*x+e)^3-3/8*sinh(f*x+e))*cosh(f*x+e)+3/8*f*x+3/8*e)-24/f^2*d^2*c*e*(1/6*(f*x+e)*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*(f*x+e)*cosh(f*x+e)^4-1/36*cosh(f*x+e)^5*sinh(f*x+e)+1/36*cosh(f*x+e)^3*sinh(f*x+e)+1/24*cosh(f*x+e)*sinh(f*x+e)+1/24*f*x+1/24*e)+12*d^2*e^2/f^2*c*(1/6*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*cosh(f*x+e)^4)-12*d*e/f*c^2*(1/6*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*cosh(f*x+e)^4)-6/f^2*d^2*c*e*(1/4*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)^3-3/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+3/16*(f*x+e)^2-1/16*sinh(f*x+e)^4+3/16*cosh(f*x+e)^2)-12*d^2*e^2/f^2*c*(1/6*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*cosh(f*x+e)^3*sinh(f*x+e)+1/16*cosh(f*x+e)*sinh(f*x+e)+1/16*f*x+1/16*e)+12*d*e/f*c^2*(1/6*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*cosh(f*x+e)^3*sinh(f*x+e)+1/16*cosh(f*x+e)*sinh(f*x+e)+1/16*f*x+1/16*e)+3/4/f^3*d^3*e^3*sinh(f*x+e)^4+9/f^3*d^3*e*(1/4*(f*x+e)^2*sinh(f*x+e)^4-1/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)^3+3/16*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-3/32*(f*x+e)^2+1/32*sinh(f*x+e)^4-3/32*cosh(f*x+e)^2)-9/f^3*d^3*e^2*(1/4*(f*x+e)*sinh(f*x+e)^4-1/16*sinh(f*x+e)^3*cosh(f*x+e)+3/32*cosh(f*x+e)*sinh(f*x+e)-3/32*f*x-3/32*e)-9/f^2*c*d^2*(1/4*(f*x+e)^2*sinh(f*x+e)^4-1/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)^3+3/16*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-3/32*(f*x+e)^2+1/32*sinh(f*x+e)^4-3/32*cosh(f*x+e)^2)-9/f*c^2*d*(1/4*(f*x+e)*sinh(f*x+e)^4-1/16*sinh(f*x+e)^3*cosh(f*x+e)+3/32*cosh(f*x+e)*sinh(f*x+e)-3/32*f*x-3/32*e)-9/4/f^2*c*d^2*e^2*sinh(f*x+e)^4+9/4/f*c^2*d*e*sinh(f*x+e)^4+18/f^2*c*d^2*e*(1/4*(f*x+e)*sinh(f*x+e)^4-1/16*sinh(f*x+e)^3*cosh(f*x+e)+3/32*cosh(f*x+e)*sinh(f*x+e)-3/32*f*x-3/32*e)-4*d^3*e^3/f^3*(1/6*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*cosh(f*x+e)^4)+3/f^3*d^3*e^2*(1/4*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)^3-3/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+3/16*(f*x+e)^2-1/16*sinh(f*x+e)^4+3/16*cosh(f*x+e)^2)+3/f^2*d^2*c*(1/4*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)^3-3/8*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)+1/8*(f*x+e)^3-1/8*(f*x+e)*sinh(f*x+e)^4+1/32*sinh(f*x+e)^3*cosh(f*x+e)-15/64*cosh(f*x+e)*sinh(f*x+e)-9/64*f*x-9/64*e+3/8*(f*x+e)*cosh(f*x+e)^2)-d^3*e^3/f^3*((1/4*sinh(f*x+e)^3-3/8*sinh(f*x+e))*cosh(f*x+e)+3/8*f*x+3/8*e)+12/f*d*c^2*(1/6*(f*x+e)*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*(f*x+e)*cosh(f*x+e)^4-1/36*cosh(f*x+e)^5*sinh(f*x+e)+1/36*cosh(f*x+e)^3*sinh(f*x+e)+1/24*cosh(f*x+e)*sinh(f*x+e)+1/24*f*x+1/24*e)-12/f^3*d^3*e*(1/6*(f*x+e)^2*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*(f*x+e)^2*cosh(f*x+e)^4-1/18*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^5+1/18*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3+1/12*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+1/24*(f*x+e)^2+1/108*cosh(f*x+e)^6-1/72*cosh(f*x+e)^4-1/24*cosh(f*x+e)^2)-12/f*d*c^2*(1/6*(f*x+e)*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3+1/16*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+1/32*(f*x+e)^2-1/36*sinh(f*x+e)^2*cosh(f*x+e)^4+13/288*cosh(f*x+e)^4-1/32*cosh(f*x+e)^2)+4*d^3*e^3/f^3*(1/6*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*cosh(f*x+e)^3*sinh(f*x+e)+1/16*cosh(f*x+e)*sinh(f*x+e)+1/16*f*x+1/16*e)-3/f^3*d^3*e*(1/4*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)^3-3/8*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)+1/8*(f*x+e)^3-1/8*(f*x+e)*sinh(f*x+e)^4+1/32*sinh(f*x+e)^3*cosh(f*x+e)-15/64*cosh(f*x+e)*sinh(f*x+e)-9/64*f*x-9/64*e+3/8*(f*x+e)*cosh(f*x+e)^2)+3/f*d*c^2*(1/4*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)^3-3/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+3/16*(f*x+e)^2-1/16*sinh(f*x+e)^4+3/16*cosh(f*x+e)^2)+12/f^3*d^3*e*(1/6*(f*x+e)^2*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*(f*x+e)^2*sinh(f*x+e)*cosh(f*x+e)^3+1/16*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)+1/48*(f*x+e)^3-1/18*(f*x+e)*sinh(f*x+e)^2*cosh(f*x+e)^4+13/144*(f*x+e)*cosh(f*x+e)^4+1/108*cosh(f*x+e)^5*sinh(f*x+e)-43/1728*cosh(f*x+e)^3*sinh(f*x+e)-7/1152*cosh(f*x+e)*sinh(f*x+e)-7/1152*f*x-7/1152*e-1/16*(f*x+e)*cosh(f*x+e)^2)-12/f^3*d^3*e^2*(1/6*(f*x+e)*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3+1/16*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+1/32*(f*x+e)^2-1/36*sinh(f*x+e)^2*cosh(f*x+e)^4+13/288*cosh(f*x+e)^4-1/32*cosh(f*x+e)^2)-12/f^2*d^2*c*(1/6*(f*x+e)^2*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*(f*x+e)^2*sinh(f*x+e)*cosh(f*x+e)^3+1/16*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)+1/48*(f*x+e)^3-1/18*(f*x+e)*sinh(f*x+e)^2*cosh(f*x+e)^4+13/144*(f*x+e)*cosh(f*x+e)^4+1/108*cosh(f*x+e)^5*sinh(f*x+e)-43/1728*cosh(f*x+e)^3*sinh(f*x+e)-7/1152*cosh(f*x+e)*sinh(f*x+e)-7/1152*f*x-7/1152*e-1/16*(f*x+e)*cosh(f*x+e)^2)+12/f^3*d^3*e^2*(1/6*(f*x+e)*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*(f*x+e)*cosh(f*x+e)^4-1/36*cosh(f*x+e)^5*sinh(f*x+e)+1/36*cosh(f*x+e)^3*sinh(f*x+e)+1/24*cosh(f*x+e)*sinh(f*x+e)+1/24*f*x+1/24*e)+12/f^2*d^2*c*(1/6*(f*x+e)^2*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*(f*x+e)^2*cosh(f*x+e)^4-1/18*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^5+1/18*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3+1/12*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+1/24*(f*x+e)^2+1/108*cosh(f*x+e)^6-1/72*cosh(f*x+e)^4-1/24*cosh(f*x+e)^2))","B"
28,1,1767,217,0.618000," ","int((d*x+c)^2/(a+a*coth(f*x+e))^3,x)","\text{Expression too large to display}"," ",0,"1/a^3/f*(-4/f^2*d^2*(1/6*(f*x+e)^2*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*(f*x+e)^2*sinh(f*x+e)*cosh(f*x+e)^3+1/16*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)+1/48*(f*x+e)^3-1/18*(f*x+e)*sinh(f*x+e)^2*cosh(f*x+e)^4+13/144*(f*x+e)*cosh(f*x+e)^4+1/108*cosh(f*x+e)^5*sinh(f*x+e)-43/1728*cosh(f*x+e)^3*sinh(f*x+e)-7/1152*cosh(f*x+e)*sinh(f*x+e)-7/1152*f*x-7/1152*e-1/16*(f*x+e)*cosh(f*x+e)^2)+4/f^2*d^2*(1/6*(f*x+e)^2*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*(f*x+e)^2*cosh(f*x+e)^4-1/18*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^5+1/18*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3+1/12*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+1/24*(f*x+e)^2+1/108*cosh(f*x+e)^6-1/72*cosh(f*x+e)^4-1/24*cosh(f*x+e)^2)+1/f^2*d^2*(1/4*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)^3-3/8*(f*x+e)^2*cosh(f*x+e)*sinh(f*x+e)+1/8*(f*x+e)^3-1/8*(f*x+e)*sinh(f*x+e)^4+1/32*sinh(f*x+e)^3*cosh(f*x+e)-15/64*cosh(f*x+e)*sinh(f*x+e)-9/64*f*x-9/64*e+3/8*(f*x+e)*cosh(f*x+e)^2)-3/f^2*d^2*(1/4*(f*x+e)^2*sinh(f*x+e)^4-1/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)^3+3/16*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)-3/32*(f*x+e)^2+1/32*sinh(f*x+e)^4-3/32*cosh(f*x+e)^2)+8/f^2*d^2*e*(1/6*(f*x+e)*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3+1/16*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+1/32*(f*x+e)^2-1/36*sinh(f*x+e)^2*cosh(f*x+e)^4+13/288*cosh(f*x+e)^4-1/32*cosh(f*x+e)^2)-8/f^2*d^2*e*(1/6*(f*x+e)*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*(f*x+e)*cosh(f*x+e)^4-1/36*cosh(f*x+e)^5*sinh(f*x+e)+1/36*cosh(f*x+e)^3*sinh(f*x+e)+1/24*cosh(f*x+e)*sinh(f*x+e)+1/24*f*x+1/24*e)-2/f^2*d^2*e*(1/4*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)^3-3/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+3/16*(f*x+e)^2-1/16*sinh(f*x+e)^4+3/16*cosh(f*x+e)^2)+6/f^2*d^2*e*(1/4*(f*x+e)*sinh(f*x+e)^4-1/16*sinh(f*x+e)^3*cosh(f*x+e)+3/32*cosh(f*x+e)*sinh(f*x+e)-3/32*f*x-3/32*e)-4/f^2*d^2*e^2*(1/6*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*cosh(f*x+e)^3*sinh(f*x+e)+1/16*cosh(f*x+e)*sinh(f*x+e)+1/16*f*x+1/16*e)+4/f^2*d^2*e^2*(1/6*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*cosh(f*x+e)^4)+1/f^2*d^2*e^2*((1/4*sinh(f*x+e)^3-3/8*sinh(f*x+e))*cosh(f*x+e)+3/8*f*x+3/8*e)-3/4*d^2*e^2/f^2*sinh(f*x+e)^4-8/f*c*d*(1/6*(f*x+e)*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3+1/16*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+1/32*(f*x+e)^2-1/36*sinh(f*x+e)^2*cosh(f*x+e)^4+13/288*cosh(f*x+e)^4-1/32*cosh(f*x+e)^2)+8/f*c*d*(1/6*(f*x+e)*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*(f*x+e)*cosh(f*x+e)^4-1/36*cosh(f*x+e)^5*sinh(f*x+e)+1/36*cosh(f*x+e)^3*sinh(f*x+e)+1/24*cosh(f*x+e)*sinh(f*x+e)+1/24*f*x+1/24*e)+2/f*c*d*(1/4*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)^3-3/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+3/16*(f*x+e)^2-1/16*sinh(f*x+e)^4+3/16*cosh(f*x+e)^2)-6/f*d*c*(1/4*(f*x+e)*sinh(f*x+e)^4-1/16*sinh(f*x+e)^3*cosh(f*x+e)+3/32*cosh(f*x+e)*sinh(f*x+e)-3/32*f*x-3/32*e)+8/f*c*d*e*(1/6*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*cosh(f*x+e)^3*sinh(f*x+e)+1/16*cosh(f*x+e)*sinh(f*x+e)+1/16*f*x+1/16*e)-8/f*c*d*e*(1/6*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*cosh(f*x+e)^4)-2/f*c*d*e*((1/4*sinh(f*x+e)^3-3/8*sinh(f*x+e))*cosh(f*x+e)+3/8*f*x+3/8*e)+3/2*d*e/f*c*sinh(f*x+e)^4-4*c^2*(1/6*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*cosh(f*x+e)^3*sinh(f*x+e)+1/16*cosh(f*x+e)*sinh(f*x+e)+1/16*f*x+1/16*e)+4*c^2*(1/6*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*cosh(f*x+e)^4)+c^2*((1/4*sinh(f*x+e)^3-3/8*sinh(f*x+e))*cosh(f*x+e)+3/8*f*x+3/8*e)-3/4*c^2*sinh(f*x+e)^4)","B"
29,1,651,174,0.632000," ","int((d*x+c)/(a+a*coth(f*x+e))^3,x)","\frac{-\frac{4 d \left(\frac{\left(f x +e \right) \left(\sinh^{3}\left(f x +e \right)\right) \left(\cosh^{3}\left(f x +e \right)\right)}{6}-\frac{\left(f x +e \right) \sinh \left(f x +e \right) \left(\cosh^{3}\left(f x +e \right)\right)}{8}+\frac{\left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{16}+\frac{\left(f x +e \right)^{2}}{32}-\frac{\left(\sinh^{2}\left(f x +e \right)\right) \left(\cosh^{4}\left(f x +e \right)\right)}{36}+\frac{13 \left(\cosh^{4}\left(f x +e \right)\right)}{288}-\frac{\left(\cosh^{2}\left(f x +e \right)\right)}{32}\right)}{f}+\frac{4 d \left(\frac{\left(f x +e \right) \left(\sinh^{2}\left(f x +e \right)\right) \left(\cosh^{4}\left(f x +e \right)\right)}{6}-\frac{\left(f x +e \right) \left(\cosh^{4}\left(f x +e \right)\right)}{12}-\frac{\left(\cosh^{5}\left(f x +e \right)\right) \sinh \left(f x +e \right)}{36}+\frac{\left(\cosh^{3}\left(f x +e \right)\right) \sinh \left(f x +e \right)}{36}+\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{24}+\frac{f x}{24}+\frac{e}{24}\right)}{f}+\frac{d \left(\frac{\left(f x +e \right) \cosh \left(f x +e \right) \left(\sinh^{3}\left(f x +e \right)\right)}{4}-\frac{3 \left(f x +e \right) \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{8}+\frac{3 \left(f x +e \right)^{2}}{16}-\frac{\left(\sinh^{4}\left(f x +e \right)\right)}{16}+\frac{3 \left(\cosh^{2}\left(f x +e \right)\right)}{16}\right)}{f}-\frac{3 d \left(\frac{\left(f x +e \right) \left(\sinh^{4}\left(f x +e \right)\right)}{4}-\frac{\left(\sinh^{3}\left(f x +e \right)\right) \cosh \left(f x +e \right)}{16}+\frac{3 \cosh \left(f x +e \right) \sinh \left(f x +e \right)}{32}-\frac{3 f x}{32}-\frac{3 e}{32}\right)}{f}+\frac{4 d e \left(\frac{\left(\sinh^{3}\left(f x +e \right)\right) \left(\cosh^{3}\left(f x +e \right)\right)}{6}-\frac{\left(\cosh^{3}\left(f x +e \right)\right) \sinh \left(f x +e \right)}{8}+\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{16}+\frac{f x}{16}+\frac{e}{16}\right)}{f}-\frac{4 d e \left(\frac{\left(\sinh^{2}\left(f x +e \right)\right) \left(\cosh^{4}\left(f x +e \right)\right)}{6}-\frac{\left(\cosh^{4}\left(f x +e \right)\right)}{12}\right)}{f}-\frac{d e \left(\left(\frac{\left(\sinh^{3}\left(f x +e \right)\right)}{4}-\frac{3 \sinh \left(f x +e \right)}{8}\right) \cosh \left(f x +e \right)+\frac{3 f x}{8}+\frac{3 e}{8}\right)}{f}+\frac{3 d e \left(\sinh^{4}\left(f x +e \right)\right)}{4 f}-4 c \left(\frac{\left(\sinh^{3}\left(f x +e \right)\right) \left(\cosh^{3}\left(f x +e \right)\right)}{6}-\frac{\left(\cosh^{3}\left(f x +e \right)\right) \sinh \left(f x +e \right)}{8}+\frac{\cosh \left(f x +e \right) \sinh \left(f x +e \right)}{16}+\frac{f x}{16}+\frac{e}{16}\right)+4 c \left(\frac{\left(\sinh^{2}\left(f x +e \right)\right) \left(\cosh^{4}\left(f x +e \right)\right)}{6}-\frac{\left(\cosh^{4}\left(f x +e \right)\right)}{12}\right)+c \left(\left(\frac{\left(\sinh^{3}\left(f x +e \right)\right)}{4}-\frac{3 \sinh \left(f x +e \right)}{8}\right) \cosh \left(f x +e \right)+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{3 c \left(\sinh^{4}\left(f x +e \right)\right)}{4}}{a^{3} f}"," ",0,"1/a^3/f*(-4/f*d*(1/6*(f*x+e)*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*(f*x+e)*sinh(f*x+e)*cosh(f*x+e)^3+1/16*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+1/32*(f*x+e)^2-1/36*sinh(f*x+e)^2*cosh(f*x+e)^4+13/288*cosh(f*x+e)^4-1/32*cosh(f*x+e)^2)+4/f*d*(1/6*(f*x+e)*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*(f*x+e)*cosh(f*x+e)^4-1/36*cosh(f*x+e)^5*sinh(f*x+e)+1/36*cosh(f*x+e)^3*sinh(f*x+e)+1/24*cosh(f*x+e)*sinh(f*x+e)+1/24*f*x+1/24*e)+1/f*d*(1/4*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)^3-3/8*(f*x+e)*cosh(f*x+e)*sinh(f*x+e)+3/16*(f*x+e)^2-1/16*sinh(f*x+e)^4+3/16*cosh(f*x+e)^2)-3/f*d*(1/4*(f*x+e)*sinh(f*x+e)^4-1/16*sinh(f*x+e)^3*cosh(f*x+e)+3/32*cosh(f*x+e)*sinh(f*x+e)-3/32*f*x-3/32*e)+4*d*e/f*(1/6*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*cosh(f*x+e)^3*sinh(f*x+e)+1/16*cosh(f*x+e)*sinh(f*x+e)+1/16*f*x+1/16*e)-4*d*e/f*(1/6*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*cosh(f*x+e)^4)-d*e/f*((1/4*sinh(f*x+e)^3-3/8*sinh(f*x+e))*cosh(f*x+e)+3/8*f*x+3/8*e)+3/4*d*e/f*sinh(f*x+e)^4-4*c*(1/6*sinh(f*x+e)^3*cosh(f*x+e)^3-1/8*cosh(f*x+e)^3*sinh(f*x+e)+1/16*cosh(f*x+e)*sinh(f*x+e)+1/16*f*x+1/16*e)+4*c*(1/6*sinh(f*x+e)^2*cosh(f*x+e)^4-1/12*cosh(f*x+e)^4)+c*((1/4*sinh(f*x+e)^3-3/8*sinh(f*x+e))*cosh(f*x+e)+3/8*f*x+3/8*e)-3/4*c*sinh(f*x+e)^4)","B"
30,1,151,411,1.637000," ","int(1/(d*x+c)/(a+a*coth(f*x+e))^3,x)","\frac{\ln \left(d x +c \right)}{8 a^{3} d}+\frac{{\mathrm e}^{\frac{6 c f -6 d e}{d}} \Ei \left(1, 6 f x +6 e +\frac{6 c f -6 d e}{d}\right)}{8 a^{3} d}-\frac{3 \,{\mathrm e}^{\frac{4 c f -4 d e}{d}} \Ei \left(1, 4 f x +4 e +\frac{4 c f -4 d e}{d}\right)}{8 a^{3} d}+\frac{3 \,{\mathrm e}^{\frac{2 c f -2 d e}{d}} \Ei \left(1, 2 f x +2 e +\frac{2 c f -2 d e}{d}\right)}{8 a^{3} d}"," ",0,"1/8*ln(d*x+c)/a^3/d+1/8/a^3/d*exp(6*(c*f-d*e)/d)*Ei(1,6*f*x+6*e+6*(c*f-d*e)/d)-3/8/a^3/d*exp(4*(c*f-d*e)/d)*Ei(1,4*f*x+4*e+4*(c*f-d*e)/d)+3/8/a^3/d*exp(2*(c*f-d*e)/d)*Ei(1,2*f*x+2*e+2*(c*f-d*e)/d)","A"
31,1,239,648,4.387000," ","int(1/(d*x+c)^2/(a+a*coth(f*x+e))^3,x)","-\frac{1}{8 a^{3} d \left(d x +c \right)}+\frac{f \,{\mathrm e}^{-6 f x -6 e}}{8 a^{3} d \left(d f x +c f \right)}-\frac{3 f \,{\mathrm e}^{\frac{6 c f -6 d e}{d}} \Ei \left(1, 6 f x +6 e +\frac{6 c f -6 d e}{d}\right)}{4 a^{3} d^{2}}-\frac{3 f \,{\mathrm e}^{-4 f x -4 e}}{8 a^{3} d \left(d f x +c f \right)}+\frac{3 f \,{\mathrm e}^{\frac{4 c f -4 d e}{d}} \Ei \left(1, 4 f x +4 e +\frac{4 c f -4 d e}{d}\right)}{2 a^{3} d^{2}}+\frac{3 f \,{\mathrm e}^{-2 f x -2 e}}{8 a^{3} d \left(d f x +c f \right)}-\frac{3 f \,{\mathrm e}^{\frac{2 c f -2 d e}{d}} \Ei \left(1, 2 f x +2 e +\frac{2 c f -2 d e}{d}\right)}{4 a^{3} d^{2}}"," ",0,"-1/8/a^3/d/(d*x+c)+1/8*f/a^3*exp(-6*f*x-6*e)/d/(d*f*x+c*f)-3/4*f/a^3/d^2*exp(6*(c*f-d*e)/d)*Ei(1,6*f*x+6*e+6*(c*f-d*e)/d)-3/8*f/a^3*exp(-4*f*x-4*e)/d/(d*f*x+c*f)+3/2*f/a^3/d^2*exp(4*(c*f-d*e)/d)*Ei(1,4*f*x+4*e+4*(c*f-d*e)/d)+3/8*f/a^3*exp(-2*f*x-2*e)/d/(d*f*x+c*f)-3/4*f/a^3/d^2*exp(2*(c*f-d*e)/d)*Ei(1,2*f*x+2*e+2*(c*f-d*e)/d)","A"
32,0,0,22,0.301000," ","int((d*x+c)^m*(a+a*coth(f*x+e))^2,x)","\int \left(d x +c \right)^{m} \left(a +a \coth \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*x+c)^m*(a+a*coth(f*x+e))^2,x)","F"
33,0,0,20,0.376000," ","int((d*x+c)^m*(a+a*coth(f*x+e)),x)","\int \left(d x +c \right)^{m} \left(a +a \coth \left(f x +e \right)\right)\, dx"," ",0,"int((d*x+c)^m*(a+a*coth(f*x+e)),x)","F"
34,0,0,85,0.580000," ","int((d*x+c)^m/(a+a*coth(f*x+e)),x)","\int \frac{\left(d x +c \right)^{m}}{a +a \coth \left(f x +e \right)}\, dx"," ",0,"int((d*x+c)^m/(a+a*coth(f*x+e)),x)","F"
35,0,0,148,0.467000," ","int((d*x+c)^m/(a+a*coth(f*x+e))^2,x)","\int \frac{\left(d x +c \right)^{m}}{\left(a +a \coth \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*x+c)^m/(a+a*coth(f*x+e))^2,x)","F"
36,0,0,218,0.549000," ","int((d*x+c)^m/(a+a*coth(f*x+e))^3,x)","\int \frac{\left(d x +c \right)^{m}}{\left(a +a \coth \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((d*x+c)^m/(a+a*coth(f*x+e))^3,x)","F"
37,1,748,123,0.446000," ","int((d*x+c)^3*(a+b*coth(f*x+e)),x)","a c \,d^{2} x^{3}-b c \,d^{2} x^{3}-\frac{3 b \,e^{4} d^{3}}{2 f^{4}}+\frac{b \,c^{3} \ln \left({\mathrm e}^{f x +e}+1\right)}{f}+\frac{b \,c^{3} \ln \left({\mathrm e}^{f x +e}-1\right)}{f}-\frac{2 b \,c^{3} \ln \left({\mathrm e}^{f x +e}\right)}{f}+\frac{6 b \,d^{3} \polylog \left(4, -{\mathrm e}^{f x +e}\right)}{f^{4}}+\frac{6 b \,d^{3} \polylog \left(4, {\mathrm e}^{f x +e}\right)}{f^{4}}+\frac{3 a \,c^{2} d \,x^{2}}{2}-\frac{3 b \,c^{2} d \,x^{2}}{2}+\frac{a \,d^{3} x^{4}}{4}-\frac{b \,d^{3} x^{4}}{4}+c^{3} a x +b \,c^{3} x -\frac{6 b \,c^{2} d e x}{f}+\frac{6 b c \,d^{2} e^{2} x}{f^{2}}-\frac{3 b c \,d^{2} e^{2} \ln \left(1-{\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{3 b \,d^{3} \polylog \left(2, -{\mathrm e}^{f x +e}\right) x^{2}}{f^{2}}-\frac{6 b \,d^{3} \polylog \left(3, -{\mathrm e}^{f x +e}\right) x}{f^{3}}+\frac{3 b \,d^{3} \polylog \left(2, {\mathrm e}^{f x +e}\right) x^{2}}{f^{2}}-\frac{6 b \,d^{3} \polylog \left(3, {\mathrm e}^{f x +e}\right) x}{f^{3}}+\frac{3 b \,c^{2} d \polylog \left(2, {\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{6 b c \,d^{2} \polylog \left(3, {\mathrm e}^{f x +e}\right)}{f^{3}}-\frac{2 b \,e^{3} d^{3} x}{f^{3}}-\frac{3 b \,c^{2} d \,e^{2}}{f^{2}}+\frac{4 b c \,d^{2} e^{3}}{f^{3}}-\frac{b \,d^{3} e^{3} \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{4}}+\frac{2 b \,d^{3} e^{3} \ln \left({\mathrm e}^{f x +e}\right)}{f^{4}}+\frac{b \,d^{3} \ln \left({\mathrm e}^{f x +e}+1\right) x^{3}}{f}+\frac{b \,d^{3} \ln \left(1-{\mathrm e}^{f x +e}\right) x^{3}}{f}+\frac{b \,d^{3} \ln \left(1-{\mathrm e}^{f x +e}\right) e^{3}}{f^{4}}-\frac{6 b c \,d^{2} \polylog \left(3, -{\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{3 b \,c^{2} d \polylog \left(2, -{\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{6 b c \,d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{6 b \,c^{2} d e \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{3 b c \,d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{3}}-\frac{3 b \,c^{2} d e \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}+\frac{3 b c \,d^{2} \ln \left(1-{\mathrm e}^{f x +e}\right) x^{2}}{f}+\frac{3 b \,c^{2} d \ln \left({\mathrm e}^{f x +e}+1\right) x}{f}+\frac{3 b \,c^{2} d \ln \left(1-{\mathrm e}^{f x +e}\right) x}{f}+\frac{3 b \,c^{2} d \ln \left(1-{\mathrm e}^{f x +e}\right) e}{f^{2}}+\frac{3 b c \,d^{2} \ln \left({\mathrm e}^{f x +e}+1\right) x^{2}}{f}+\frac{6 b c \,d^{2} \polylog \left(2, -{\mathrm e}^{f x +e}\right) x}{f^{2}}+\frac{6 b c \,d^{2} \polylog \left(2, {\mathrm e}^{f x +e}\right) x}{f^{2}}"," ",0,"a*c*d^2*x^3-b*c*d^2*x^3-3/2/f^4*b*e^4*d^3+1/f*b*c^3*ln(exp(f*x+e)+1)+1/f*b*c^3*ln(exp(f*x+e)-1)-2/f*b*c^3*ln(exp(f*x+e))+6/f^4*b*d^3*polylog(4,-exp(f*x+e))+6/f^4*b*d^3*polylog(4,exp(f*x+e))+3/2*a*c^2*d*x^2-3/2*b*c^2*d*x^2+1/4*a*d^3*x^4-1/4*b*d^3*x^4+c^3*a*x+b*c^3*x-6/f*b*c^2*d*e*x+6/f^2*b*c*d^2*e^2*x-3/f^3*b*c*d^2*e^2*ln(1-exp(f*x+e))-2/f^3*b*e^3*d^3*x-3/f^2*b*c^2*d*e^2+4/f^3*b*c*d^2*e^3-6/f^3*b*c*d^2*polylog(3,-exp(f*x+e))-1/f^4*b*d^3*e^3*ln(exp(f*x+e)-1)+2/f^4*b*d^3*e^3*ln(exp(f*x+e))+3/f^2*b*c^2*d*polylog(2,-exp(f*x+e))+1/f*b*d^3*ln(exp(f*x+e)+1)*x^3+3/f^2*b*d^3*polylog(2,-exp(f*x+e))*x^2-6/f^3*b*d^3*polylog(3,-exp(f*x+e))*x+1/f*b*d^3*ln(1-exp(f*x+e))*x^3+1/f^4*b*d^3*ln(1-exp(f*x+e))*e^3+3/f^2*b*d^3*polylog(2,exp(f*x+e))*x^2-6/f^3*b*d^3*polylog(3,exp(f*x+e))*x+3/f^2*b*c^2*d*polylog(2,exp(f*x+e))-6/f^3*b*c*d^2*polylog(3,exp(f*x+e))+6/f^2*b*c*d^2*polylog(2,-exp(f*x+e))*x-6/f^3*b*c*d^2*e^2*ln(exp(f*x+e))+6/f^2*b*c^2*d*e*ln(exp(f*x+e))+3/f^3*b*c*d^2*e^2*ln(exp(f*x+e)-1)-3/f^2*b*c^2*d*e*ln(exp(f*x+e)-1)+3/f*b*c*d^2*ln(1-exp(f*x+e))*x^2+6/f^2*b*c*d^2*polylog(2,exp(f*x+e))*x+3/f*b*c^2*d*ln(exp(f*x+e)+1)*x+3/f*b*c^2*d*ln(1-exp(f*x+e))*x+3/f^2*b*c^2*d*ln(1-exp(f*x+e))*e+3/f*b*c*d^2*ln(exp(f*x+e)+1)*x^2","B"
38,1,447,95,0.349000," ","int((d*x+c)^2*(a+b*coth(f*x+e)),x)","\frac{2 b c d \ln \left({\mathrm e}^{f x +e}+1\right) x}{f}+\frac{2 b c d \ln \left(1-{\mathrm e}^{f x +e}\right) x}{f}+\frac{4 b \,e^{3} d^{2}}{3 f^{3}}+\frac{b \,c^{2} \ln \left({\mathrm e}^{f x +e}-1\right)}{f}-\frac{2 b \,c^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f}+\frac{b \,c^{2} \ln \left({\mathrm e}^{f x +e}+1\right)}{f}-\frac{2 b \,d^{2} \polylog \left(3, {\mathrm e}^{f x +e}\right)}{f^{3}}-\frac{2 b \,d^{2} \polylog \left(3, -{\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{2 b \,e^{2} d^{2} x}{f^{2}}+\frac{b \,d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{3}}-\frac{2 b \,d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{b \,d^{2} \ln \left({\mathrm e}^{f x +e}+1\right) x^{2}}{f}-b c d \,x^{2}+a c d \,x^{2}-\frac{4 b d c e x}{f}+\frac{2 b c d \ln \left(1-{\mathrm e}^{f x +e}\right) e}{f^{2}}+\frac{4 b c d e \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{2 b c d e \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}+\frac{a \,d^{2} x^{3}}{3}-\frac{b \,d^{2} x^{3}}{3}+c^{2} a x +b \,c^{2} x -\frac{2 b d c \,e^{2}}{f^{2}}+\frac{2 b c d \polylog \left(2, {\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{2 b \,d^{2} \polylog \left(2, -{\mathrm e}^{f x +e}\right) x}{f^{2}}+\frac{2 b \,d^{2} \polylog \left(2, {\mathrm e}^{f x +e}\right) x}{f^{2}}+\frac{b \,d^{2} \ln \left(1-{\mathrm e}^{f x +e}\right) x^{2}}{f}-\frac{b \,d^{2} \ln \left(1-{\mathrm e}^{f x +e}\right) e^{2}}{f^{3}}+\frac{2 b c d \polylog \left(2, -{\mathrm e}^{f x +e}\right)}{f^{2}}"," ",0,"2/f*b*c*d*ln(exp(f*x+e)+1)*x+2/f*b*c*d*ln(1-exp(f*x+e))*x+4/3/f^3*b*e^3*d^2+1/f*b*c^2*ln(exp(f*x+e)-1)-2/f*b*c^2*ln(exp(f*x+e))+1/f*b*c^2*ln(exp(f*x+e)+1)-2/f^3*b*d^2*polylog(3,exp(f*x+e))-2/f^3*b*d^2*polylog(3,-exp(f*x+e))+2/f^2*b*e^2*d^2*x+1/f^3*b*d^2*e^2*ln(exp(f*x+e)-1)+2/f^2*b*c*d*polylog(2,-exp(f*x+e))+2/f^2*b*c*d*polylog(2,exp(f*x+e))-2/f^3*b*d^2*e^2*ln(exp(f*x+e))+1/f*b*d^2*ln(exp(f*x+e)+1)*x^2+2/f^2*b*d^2*polylog(2,-exp(f*x+e))*x-b*c*d*x^2+a*c*d*x^2-4/f*b*d*c*e*x+2/f^2*b*c*d*ln(1-exp(f*x+e))*e+4/f^2*b*c*d*e*ln(exp(f*x+e))-2/f^2*b*c*d*e*ln(exp(f*x+e)-1)+1/3*a*d^2*x^3-1/3*b*d^2*x^3+c^2*a*x+b*c^2*x-2/f^2*b*d*c*e^2+1/f*b*d^2*ln(1-exp(f*x+e))*x^2-1/f^3*b*d^2*ln(1-exp(f*x+e))*e^2+2/f^2*b*d^2*polylog(2,exp(f*x+e))*x","B"
39,1,201,69,0.310000," ","int((d*x+c)*(a+b*coth(f*x+e)),x)","\frac{a d \,x^{2}}{2}-\frac{b d \,x^{2}}{2}+a c x +b c x -\frac{2 b c \ln \left({\mathrm e}^{f x +e}\right)}{f}+\frac{b c \ln \left({\mathrm e}^{f x +e}-1\right)}{f}+\frac{b c \ln \left({\mathrm e}^{f x +e}+1\right)}{f}-\frac{2 b d e x}{f}-\frac{b d \,e^{2}}{f^{2}}+\frac{b d \ln \left({\mathrm e}^{f x +e}+1\right) x}{f}+\frac{b d \polylog \left(2, -{\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{b d \ln \left(1-{\mathrm e}^{f x +e}\right) x}{f}+\frac{b d \ln \left(1-{\mathrm e}^{f x +e}\right) e}{f^{2}}+\frac{b d \polylog \left(2, {\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{2 b d e \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{b d e \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}"," ",0,"1/2*a*d*x^2-1/2*b*d*x^2+a*c*x+b*c*x-2/f*b*c*ln(exp(f*x+e))+1/f*b*c*ln(exp(f*x+e)-1)+1/f*b*c*ln(exp(f*x+e)+1)-2/f*b*d*e*x-1/f^2*b*d*e^2+1/f*b*d*ln(exp(f*x+e)+1)*x+1/f^2*b*d*polylog(2,-exp(f*x+e))+1/f*b*d*ln(1-exp(f*x+e))*x+1/f^2*b*d*ln(1-exp(f*x+e))*e+1/f^2*b*d*polylog(2,exp(f*x+e))+2/f^2*b*d*e*ln(exp(f*x+e))-1/f^2*b*d*e*ln(exp(f*x+e)-1)","B"
40,0,0,20,0.580000," ","int((a+b*coth(f*x+e))/(d*x+c),x)","\int \frac{a +b \coth \left(f x +e \right)}{d x +c}\, dx"," ",0,"int((a+b*coth(f*x+e))/(d*x+c),x)","F"
41,0,0,20,0.633000," ","int((a+b*coth(f*x+e))/(d*x+c)^2,x)","\int \frac{a +b \coth \left(f x +e \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int((a+b*coth(f*x+e))/(d*x+c)^2,x)","F"
42,1,1393,261,0.677000," ","int((d*x+c)^3*(a+b*coth(f*x+e))^2,x)","b^{2} c^{3} x +\frac{6 b^{2} d^{3} e^{2} x}{f^{3}}-\frac{6 b^{2} d^{2} c \,x^{2}}{f}-\frac{6 b^{2} d^{2} c \,e^{2}}{f^{3}}+\frac{a^{2} d^{3} x^{4}}{4}+b^{2} c \,d^{2} x^{3}+a^{2} c \,d^{2} x^{3}+\frac{6 b a c \,d^{2} \ln \left(1-{\mathrm e}^{f x +e}\right) x^{2}}{f}+\frac{12 b a \,c^{2} d e \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{12 b a c \,d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{12 b a c \,d^{2} \polylog \left(2, {\mathrm e}^{f x +e}\right) x}{f^{2}}+\frac{12 b a c \,d^{2} \polylog \left(2, -{\mathrm e}^{f x +e}\right) x}{f^{2}}+\frac{12 b a c \,d^{2} e^{2} x}{f^{2}}-\frac{12 b a \,c^{2} d e x}{f}+\frac{6 b a c \,d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{3}}-\frac{6 b a \,c^{2} d e \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}+\frac{6 b \ln \left(1-{\mathrm e}^{f x +e}\right) a \,c^{2} d e}{f^{2}}+\frac{6 b \ln \left(1-{\mathrm e}^{f x +e}\right) a \,c^{2} d x}{f}+\frac{6 b \ln \left({\mathrm e}^{f x +e}+1\right) a \,c^{2} d x}{f}+\frac{6 b a c \,d^{2} \ln \left({\mathrm e}^{f x +e}+1\right) x^{2}}{f}-\frac{6 b a c \,d^{2} e^{2} \ln \left(1-{\mathrm e}^{f x +e}\right)}{f^{3}}-\frac{6 b a \,c^{2} d \,e^{2}}{f^{2}}+\frac{6 b^{2} c \,d^{2} \ln \left(1-{\mathrm e}^{f x +e}\right) e}{f^{3}}+\frac{6 b^{2} c \,d^{2} \ln \left({\mathrm e}^{f x +e}+1\right) x}{f^{2}}+\frac{2 b a \,d^{3} \ln \left(1-{\mathrm e}^{f x +e}\right) x^{3}}{f}+\frac{2 b a \,d^{3} \ln \left(1-{\mathrm e}^{f x +e}\right) e^{3}}{f^{4}}+\frac{2 b a \,d^{3} \ln \left({\mathrm e}^{f x +e}+1\right) x^{3}}{f}+\frac{12 b^{2} c \,d^{2} e \ln \left({\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{4 b a \,d^{3} e^{3} \ln \left({\mathrm e}^{f x +e}\right)}{f^{4}}-\frac{2 b a \,d^{3} e^{3} \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{4}}-\frac{6 b^{2} c \,d^{2} e \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{3}}+\frac{6 b^{2} c \,d^{2} \ln \left(1-{\mathrm e}^{f x +e}\right) x}{f^{2}}+\frac{6 b a \,d^{3} \polylog \left(2, {\mathrm e}^{f x +e}\right) x^{2}}{f^{2}}-\frac{12 b a \,d^{3} \polylog \left(3, {\mathrm e}^{f x +e}\right) x}{f^{3}}+\frac{6 b a \,d^{3} \polylog \left(2, -{\mathrm e}^{f x +e}\right) x^{2}}{f^{2}}-\frac{12 b a \,d^{3} \polylog \left(3, -{\mathrm e}^{f x +e}\right) x}{f^{3}}-\frac{12 b a c \,d^{2} \polylog \left(3, {\mathrm e}^{f x +e}\right)}{f^{3}}-\frac{12 b a c \,d^{2} \polylog \left(3, -{\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{6 b a \,c^{2} d \polylog \left(2, -{\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{6 b a \,c^{2} d \polylog \left(2, {\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{a b \,d^{3} x^{4}}{2}+\frac{3 a^{2} c^{2} d \,x^{2}}{2}+\frac{3 b^{2} c^{2} d \,x^{2}}{2}+2 c^{3} a b x -2 a b c \,d^{2} x^{3}-3 a b \,c^{2} d \,x^{2}-\frac{3 b \,e^{4} a \,d^{3}}{f^{4}}-\frac{6 b^{2} d^{3} e^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f^{4}}+\frac{3 b^{2} d^{3} e^{2} \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{4}}+\frac{3 b^{2} d^{3} \ln \left(1-{\mathrm e}^{f x +e}\right) x^{2}}{f^{2}}-\frac{3 b^{2} d^{3} \ln \left(1-{\mathrm e}^{f x +e}\right) e^{2}}{f^{4}}+\frac{3 b^{2} d^{3} \ln \left({\mathrm e}^{f x +e}+1\right) x^{2}}{f^{2}}+\frac{2 b a \,c^{3} \ln \left({\mathrm e}^{f x +e}+1\right)}{f}+\frac{2 b a \,c^{3} \ln \left({\mathrm e}^{f x +e}-1\right)}{f}+\frac{3 b^{2} c^{2} d \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}+\frac{3 b^{2} c^{2} d \ln \left({\mathrm e}^{f x +e}+1\right)}{f^{2}}-\frac{4 b a \,c^{3} \ln \left({\mathrm e}^{f x +e}\right)}{f}-\frac{6 b^{2} c^{2} d \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{6 b^{2} c \,d^{2} \polylog \left(2, {\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{6 b^{2} c \,d^{2} \polylog \left(2, -{\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{6 b^{2} d^{3} \polylog \left(2, {\mathrm e}^{f x +e}\right) x}{f^{3}}+\frac{6 b^{2} d^{3} \polylog \left(2, -{\mathrm e}^{f x +e}\right) x}{f^{3}}+\frac{12 b a \,d^{3} \polylog \left(4, {\mathrm e}^{f x +e}\right)}{f^{4}}+\frac{12 b a \,d^{3} \polylog \left(4, -{\mathrm e}^{f x +e}\right)}{f^{4}}+\frac{b^{2} d^{3} x^{4}}{4}-\frac{2 b^{2} \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right)}{f \left({\mathrm e}^{2 f x +2 e}-1\right)}+c^{3} a^{2} x -\frac{6 b^{2} d^{3} \polylog \left(3, {\mathrm e}^{f x +e}\right)}{f^{4}}-\frac{6 b^{2} d^{3} \polylog \left(3, -{\mathrm e}^{f x +e}\right)}{f^{4}}+\frac{8 b a c \,d^{2} e^{3}}{f^{3}}-\frac{4 b \,e^{3} a \,d^{3} x}{f^{3}}-\frac{12 b^{2} d^{2} c e x}{f^{2}}+\frac{4 b^{2} d^{3} e^{3}}{f^{4}}-\frac{2 b^{2} d^{3} x^{3}}{f}"," ",0,"b^2*c^3*x+6/f^3*b^2*d^3*e^2*x-6/f*b^2*d^2*c*x^2-6/f^3*b^2*d^2*c*e^2+1/4*a^2*d^3*x^4+b^2*c*d^2*x^3+a^2*c*d^2*x^3+6/f*b*a*c*d^2*ln(1-exp(f*x+e))*x^2+12/f^2*b*a*c^2*d*e*ln(exp(f*x+e))-12/f^3*b*a*c*d^2*e^2*ln(exp(f*x+e))+12/f^2*b*a*c*d^2*e^2*x-12/f*b*a*c^2*d*e*x+6/f^3*b*a*c*d^2*e^2*ln(exp(f*x+e)-1)-6/f^2*b*a*c^2*d*e*ln(exp(f*x+e)-1)+6/f^2*b*ln(1-exp(f*x+e))*a*c^2*d*e+6/f*b*ln(1-exp(f*x+e))*a*c^2*d*x+6/f*b*ln(exp(f*x+e)+1)*a*c^2*d*x+12/f^2*b*a*c*d^2*polylog(2,exp(f*x+e))*x+6/f*b*a*c*d^2*ln(exp(f*x+e)+1)*x^2+12/f^2*b*a*c*d^2*polylog(2,-exp(f*x+e))*x-6/f^3*b*a*c*d^2*e^2*ln(1-exp(f*x+e))-6/f^2*b*a*c^2*d*e^2+6/f^3*b^2*c*d^2*ln(1-exp(f*x+e))*e+6/f^2*b^2*c*d^2*ln(exp(f*x+e)+1)*x+2/f*b*a*d^3*ln(1-exp(f*x+e))*x^3+2/f^4*b*a*d^3*ln(1-exp(f*x+e))*e^3+6/f^2*b*a*d^3*polylog(2,exp(f*x+e))*x^2-12/f^3*b*a*d^3*polylog(3,exp(f*x+e))*x+2/f*b*a*d^3*ln(exp(f*x+e)+1)*x^3+6/f^2*b*a*d^3*polylog(2,-exp(f*x+e))*x^2-12/f^3*b*a*d^3*polylog(3,-exp(f*x+e))*x+12/f^3*b^2*c*d^2*e*ln(exp(f*x+e))+4/f^4*b*a*d^3*e^3*ln(exp(f*x+e))-2/f^4*b*a*d^3*e^3*ln(exp(f*x+e)-1)-12/f^3*b*a*c*d^2*polylog(3,exp(f*x+e))-12/f^3*b*a*c*d^2*polylog(3,-exp(f*x+e))+6/f^2*b*a*c^2*d*polylog(2,-exp(f*x+e))+6/f^2*b*a*c^2*d*polylog(2,exp(f*x+e))-6/f^3*b^2*c*d^2*e*ln(exp(f*x+e)-1)+6/f^2*b^2*c*d^2*ln(1-exp(f*x+e))*x-1/2*a*b*d^3*x^4+3/2*a^2*c^2*d*x^2+3/2*b^2*c^2*d*x^2+2*c^3*a*b*x-2*a*b*c*d^2*x^3-3*a*b*c^2*d*x^2-3/f^4*b*e^4*a*d^3-6/f^4*b^2*d^3*e^2*ln(exp(f*x+e))+3/f^4*b^2*d^3*e^2*ln(exp(f*x+e)-1)+6/f^3*b^2*c*d^2*polylog(2,exp(f*x+e))+6/f^3*b^2*c*d^2*polylog(2,-exp(f*x+e))+3/f^2*b^2*d^3*ln(1-exp(f*x+e))*x^2-3/f^4*b^2*d^3*ln(1-exp(f*x+e))*e^2+6/f^3*b^2*d^3*polylog(2,exp(f*x+e))*x+3/f^2*b^2*d^3*ln(exp(f*x+e)+1)*x^2+6/f^3*b^2*d^3*polylog(2,-exp(f*x+e))*x+12/f^4*b*a*d^3*polylog(4,exp(f*x+e))+12/f^4*b*a*d^3*polylog(4,-exp(f*x+e))+2/f*b*a*c^3*ln(exp(f*x+e)+1)+2/f*b*a*c^3*ln(exp(f*x+e)-1)+3/f^2*b^2*c^2*d*ln(exp(f*x+e)-1)+3/f^2*b^2*c^2*d*ln(exp(f*x+e)+1)-4/f*b*a*c^3*ln(exp(f*x+e))-6/f^2*b^2*c^2*d*ln(exp(f*x+e))+1/4*b^2*d^3*x^4-2/f*b^2*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/(exp(2*f*x+2*e)-1)+c^3*a^2*x+8/f^3*b*a*c*d^2*e^3-4/f^3*b*e^3*a*d^3*x-12/f^2*b^2*d^2*c*e*x+4/f^4*b^2*d^3*e^3-2/f*b^2*d^3*x^3-6/f^4*b^2*d^3*polylog(3,exp(f*x+e))-6/f^4*b^2*d^3*polylog(3,-exp(f*x+e))","B"
43,1,793,203,0.591000," ","int((d*x+c)^2*(a+b*coth(f*x+e))^2,x)","-\frac{8 b a c d e x}{f}+b^{2} c d \,x^{2}+a^{2} c d \,x^{2}+\frac{2 b a \,c^{2} \ln \left({\mathrm e}^{f x +e}-1\right)}{f}+\frac{2 b a \,c^{2} \ln \left({\mathrm e}^{f x +e}+1\right)}{f}+\frac{2 b^{2} c d \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}+\frac{2 b^{2} c d \ln \left({\mathrm e}^{f x +e}+1\right)}{f^{2}}+\frac{2 b^{2} d^{2} \ln \left(1-{\mathrm e}^{f x +e}\right) x}{f^{2}}+\frac{2 b^{2} d^{2} \ln \left(1-{\mathrm e}^{f x +e}\right) e}{f^{3}}+\frac{2 b^{2} d^{2} \ln \left({\mathrm e}^{f x +e}+1\right) x}{f^{2}}-\frac{2 b^{2} d^{2} e \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{3}}+\frac{4 b^{2} d^{2} e \ln \left({\mathrm e}^{f x +e}\right)}{f^{3}}-\frac{4 b a \,c^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f}-\frac{4 b^{2} c d \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{4 b a \,d^{2} \polylog \left(3, {\mathrm e}^{f x +e}\right)}{f^{3}}-\frac{4 b a \,d^{2} \polylog \left(3, -{\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{4 b \ln \left(1-{\mathrm e}^{f x +e}\right) a c d e}{f^{2}}-\frac{4 b a c d e \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}+\frac{4 b \ln \left(1-{\mathrm e}^{f x +e}\right) a c d x}{f}+\frac{4 b \ln \left({\mathrm e}^{f x +e}+1\right) a c d x}{f}+\frac{8 b a c d e \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{2 b^{2} \left(d^{2} x^{2}+2 c d x +c^{2}\right)}{f \left({\mathrm e}^{2 f x +2 e}-1\right)}+\frac{a^{2} d^{2} x^{3}}{3}+\frac{b^{2} d^{2} x^{3}}{3}+c^{2} a^{2} x +c^{2} b^{2} x -\frac{2 b^{2} d^{2} x^{2}}{f}-\frac{2 b^{2} d^{2} e^{2}}{f^{3}}+\frac{2 b^{2} d^{2} \polylog \left(2, {\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{2 b^{2} d^{2} \polylog \left(2, -{\mathrm e}^{f x +e}\right)}{f^{3}}-\frac{2 a b \,d^{2} x^{3}}{3}+2 c^{2} a b x -2 a b c d \,x^{2}-\frac{4 b^{2} d^{2} e x}{f^{2}}+\frac{8 b a \,d^{2} e^{3}}{3 f^{3}}+\frac{4 b a \,d^{2} e^{2} x}{f^{2}}-\frac{4 b a c d \,e^{2}}{f^{2}}-\frac{2 b a \,d^{2} e^{2} \ln \left(1-{\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{2 b a \,d^{2} \ln \left(1-{\mathrm e}^{f x +e}\right) x^{2}}{f}+\frac{2 b a \,d^{2} \ln \left({\mathrm e}^{f x +e}+1\right) x^{2}}{f}+\frac{2 b a \,d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{3}}-\frac{4 b a \,d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{4 b a c d \polylog \left(2, {\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{4 b a c d \polylog \left(2, -{\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{4 b a \,d^{2} \polylog \left(2, {\mathrm e}^{f x +e}\right) x}{f^{2}}+\frac{4 b a \,d^{2} \polylog \left(2, -{\mathrm e}^{f x +e}\right) x}{f^{2}}"," ",0,"-8/f*b*a*c*d*e*x+b^2*c*d*x^2+a^2*c*d*x^2+2/f*b*a*c^2*ln(exp(f*x+e)-1)+2/f*b*a*c^2*ln(exp(f*x+e)+1)+2/f^2*b^2*c*d*ln(exp(f*x+e)-1)+2/f^2*b^2*c*d*ln(exp(f*x+e)+1)-4/f^3*b*a*d^2*polylog(3,exp(f*x+e))-4/f^3*b*a*d^2*polylog(3,-exp(f*x+e))+2/f^2*b^2*d^2*ln(1-exp(f*x+e))*x+2/f^3*b^2*d^2*ln(1-exp(f*x+e))*e+2/f^2*b^2*d^2*ln(exp(f*x+e)+1)*x-2/f^3*b^2*d^2*e*ln(exp(f*x+e)-1)+4/f^3*b^2*d^2*e*ln(exp(f*x+e))-4/f*b*a*c^2*ln(exp(f*x+e))-4/f^2*b^2*c*d*ln(exp(f*x+e))+4/f^2*b*ln(1-exp(f*x+e))*a*c*d*e-4/f^2*b*a*c*d*e*ln(exp(f*x+e)-1)+4/f*b*ln(1-exp(f*x+e))*a*c*d*x+4/f*b*ln(exp(f*x+e)+1)*a*c*d*x+8/f^2*b*a*c*d*e*ln(exp(f*x+e))-2/f*b^2*(d^2*x^2+2*c*d*x+c^2)/(exp(2*f*x+2*e)-1)+1/3*a^2*d^2*x^3+1/3*b^2*d^2*x^3+c^2*a^2*x+c^2*b^2*x-2/f*b^2*d^2*x^2-2/f^3*b^2*d^2*e^2+2/f^3*b^2*d^2*polylog(2,exp(f*x+e))+2/f^3*b^2*d^2*polylog(2,-exp(f*x+e))-2/3*a*b*d^2*x^3+2*c^2*a*b*x-2*a*b*c*d*x^2-4/f^2*b^2*d^2*e*x+8/3/f^3*b*a*d^2*e^3+4/f^2*b*a*d^2*e^2*x-4/f^2*b*a*c*d*e^2+4/f^2*b*a*c*d*polylog(2,exp(f*x+e))+4/f^2*b*a*c*d*polylog(2,-exp(f*x+e))-2/f^3*b*a*d^2*e^2*ln(1-exp(f*x+e))+2/f*b*a*d^2*ln(1-exp(f*x+e))*x^2+4/f^2*b*a*d^2*polylog(2,exp(f*x+e))*x+2/f*b*a*d^2*ln(exp(f*x+e)+1)*x^2+4/f^2*b*a*d^2*polylog(2,-exp(f*x+e))*x+2/f^3*b*a*d^2*e^2*ln(exp(f*x+e)-1)-4/f^3*b*a*d^2*e^2*ln(exp(f*x+e))","B"
44,1,318,123,0.519000," ","int((d*x+c)*(a+b*coth(f*x+e))^2,x)","\frac{a^{2} d \,x^{2}}{2}-a b d \,x^{2}+\frac{b^{2} d \,x^{2}}{2}+a^{2} c x +2 c a b x +b^{2} c x -\frac{2 b^{2} \left(d x +c \right)}{f \left({\mathrm e}^{2 f x +2 e}-1\right)}-\frac{2 b^{2} d \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{b^{2} d \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}+\frac{b^{2} d \ln \left({\mathrm e}^{f x +e}+1\right)}{f^{2}}+\frac{2 b a c \ln \left({\mathrm e}^{f x +e}+1\right)}{f}-\frac{4 b a c \ln \left({\mathrm e}^{f x +e}\right)}{f}+\frac{2 b a c \ln \left({\mathrm e}^{f x +e}-1\right)}{f}+\frac{4 b d a e \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{2 b d a e \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}+\frac{2 b \ln \left(1-{\mathrm e}^{f x +e}\right) a d x}{f}+\frac{2 b \ln \left(1-{\mathrm e}^{f x +e}\right) a d e}{f^{2}}+\frac{2 b \ln \left({\mathrm e}^{f x +e}+1\right) a d x}{f}-\frac{4 b a d e x}{f}-\frac{2 b a d \,e^{2}}{f^{2}}+\frac{2 b d a \polylog \left(2, -{\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{2 b d a \polylog \left(2, {\mathrm e}^{f x +e}\right)}{f^{2}}"," ",0,"1/2*a^2*d*x^2-a*b*d*x^2+1/2*b^2*d*x^2+a^2*c*x+2*c*a*b*x+b^2*c*x-2/f*b^2*(d*x+c)/(exp(2*f*x+2*e)-1)-2/f^2*b^2*d*ln(exp(f*x+e))+1/f^2*b^2*d*ln(exp(f*x+e)-1)+1/f^2*b^2*d*ln(exp(f*x+e)+1)+2/f*b*a*c*ln(exp(f*x+e)+1)-4/f*b*a*c*ln(exp(f*x+e))+2/f*b*a*c*ln(exp(f*x+e)-1)+4/f^2*b*d*a*e*ln(exp(f*x+e))-2/f^2*b*d*a*e*ln(exp(f*x+e)-1)+2/f*b*ln(1-exp(f*x+e))*a*d*x+2/f^2*b*ln(1-exp(f*x+e))*a*d*e+2/f*b*ln(exp(f*x+e)+1)*a*d*x-4/f*b*a*d*e*x-2/f^2*b*a*d*e^2+2/f^2*b*d*a*polylog(2,-exp(f*x+e))+2/f^2*b*d*a*polylog(2,exp(f*x+e))","B"
45,0,0,22,1.062000," ","int((a+b*coth(f*x+e))^2/(d*x+c),x)","\int \frac{\left(a +b \coth \left(f x +e \right)\right)^{2}}{d x +c}\, dx"," ",0,"int((a+b*coth(f*x+e))^2/(d*x+c),x)","F"
46,0,0,22,1.292000," ","int((a+b*coth(f*x+e))^2/(d*x+c)^2,x)","\int \frac{\left(a +b \coth \left(f x +e \right)\right)^{2}}{\left(d x +c \right)^{2}}\, dx"," ",0,"int((a+b*coth(f*x+e))^2/(d*x+c)^2,x)","F"
47,1,2777,524,0.877000," ","int((d*x+c)^3*(a+b*coth(f*x+e))^3,x)","\text{Expression too large to display}"," ",0,"1/4*a^3*d^3*x^4-1/4*b^3*d^3*x^4+c^3*a^3*x+c^3*b^3*x+a^3*c*d^2*x^3-b^3*c*d^2*x^3-3*a^2*b*c*d^2*x^3+3*a*b^2*c*d^2*x^3-9/2*a^2*b*c^2*d*x^2+9/2*a*b^2*c^2*d*x^2+1/f*b^3*d^3*ln(exp(f*x+e)+1)*x^3+3/f^2*b^3*d^3*polylog(2,-exp(f*x+e))*x^2-6/f^3*b^3*d^3*polylog(3,-exp(f*x+e))*x+1/f*b^3*d^3*ln(1-exp(f*x+e))*x^3+1/f^4*b^3*d^3*ln(1-exp(f*x+e))*e^3+3/f^2*b^3*d^3*polylog(2,exp(f*x+e))*x^2-6/f^3*b^3*d^3*polylog(3,exp(f*x+e))*x-3/f^4*b^3*d^3*e*ln(exp(f*x+e)-1)-18/f^4*b^2*a*d^3*polylog(3,-exp(f*x+e))-18/f^4*b^2*a*d^3*polylog(3,exp(f*x+e))+18/f^4*b*a^2*d^3*polylog(4,exp(f*x+e))-6/f^3*b^3*c*d^2*polylog(3,-exp(f*x+e))-6/f^3*b^3*c*d^2*polylog(3,exp(f*x+e))+3/f*b*a^2*c^3*ln(exp(f*x+e)+1)+3/f*b*a^2*c^3*ln(exp(f*x+e)-1)-3/4*a^2*b*d^3*x^4+3/4*a*b^2*d^3*x^4+3/2*a^3*c^2*d*x^2-3/2*b^3*c^2*d*x^2+3*c^3*a^2*b*x+3*c^3*a*b^2*x-9/2/f^4*b*e^4*a^2*d^3+4/f^3*b^3*c*d^2*e^3-3/f^2*b^3*c^2*d*e^2-6/f*b^2*a*d^3*x^3+12/f^4*b^2*a*d^3*e^3-2/f^3*b^3*e^3*d^3*x+3/f^3*b^3*c*d^2*ln(exp(f*x+e)+1)+3/f^3*b^3*c*d^2*ln(exp(f*x+e)-1)+18/f^4*b*a^2*d^3*polylog(4,-exp(f*x+e))-6/f*b*a^2*c^3*ln(exp(f*x+e))-6/f^3*b^3*c*d^2*ln(exp(f*x+e))+3/f^2*b^3*c^2*d*polylog(2,-exp(f*x+e))+3/f^2*b^3*c^2*d*polylog(2,exp(f*x+e))-1/f^4*b^3*d^3*e^3*ln(exp(f*x+e)-1)+6/f^4*b^3*d^3*e*ln(exp(f*x+e))+2/f^4*b^3*d^3*e^3*ln(exp(f*x+e))+3/f^3*b^3*d^3*ln(exp(f*x+e)+1)*x+3/f^3*b^3*d^3*ln(1-exp(f*x+e))*x+3/f^4*b^3*d^3*ln(1-exp(f*x+e))*e-3/f^4*b^3*e^2*d^3-3/2/f^4*b^3*e^4*d^3-3/f^2*b^3*d^3*x^2+6/f^4*b^3*d^3*polylog(4,-exp(f*x+e))+6/f^4*b^3*d^3*polylog(4,exp(f*x+e))+1/f*b^3*c^3*ln(exp(f*x+e)+1)+1/f*b^3*c^3*ln(exp(f*x+e)-1)+3/f^4*b^3*d^3*polylog(2,-exp(f*x+e))+3/f^4*b^3*d^3*polylog(2,exp(f*x+e))-2/f*b^3*c^3*ln(exp(f*x+e))-b^2*(6*a*d^3*f*x^3*exp(2*f*x+2*e)+2*b*d^3*f*x^3*exp(2*f*x+2*e)+18*a*c*d^2*f*x^2*exp(2*f*x+2*e)+6*b*c*d^2*f*x^2*exp(2*f*x+2*e)+18*a*c^2*d*f*x*exp(2*f*x+2*e)-6*a*d^3*f*x^3+6*b*c^2*d*f*x*exp(2*f*x+2*e)+3*b*d^3*x^2*exp(2*f*x+2*e)+6*a*c^3*f*exp(2*f*x+2*e)-18*a*c*d^2*f*x^2+2*b*c^3*f*exp(2*f*x+2*e)+6*b*c*d^2*x*exp(2*f*x+2*e)-18*a*c^2*d*f*x+3*b*c^2*d*exp(2*f*x+2*e)-3*b*d^3*x^2-6*a*c^3*f-6*b*c*d^2*x-3*b*c^2*d)/f^2/(exp(2*f*x+2*e)-1)^2-36/f^2*b^2*a*c*d^2*e*x-18/f*b*a^2*c^2*d*e*x+18/f^2*b*a^2*c*d^2*e^2*x-18/f^3*b*a^2*c*d^2*e^2*ln(exp(f*x+e))+9/f^3*b*a^2*c*d^2*e^2*ln(exp(f*x+e)-1)+18/f^2*b^2*ln(1-exp(f*x+e))*a*c*d^2*x+18/f^2*b^2*ln(exp(f*x+e)+1)*a*c*d^2*x-9/f^3*b*ln(1-exp(f*x+e))*a^2*c*d^2*e^2+18/f^2*b*a^2*c^2*d*e*ln(exp(f*x+e))+36/f^3*b^2*a*c*d^2*e*ln(exp(f*x+e))-9/f^2*b*a^2*c^2*d*e*ln(exp(f*x+e)-1)-18/f^3*b^2*a*c*d^2*e*ln(exp(f*x+e)-1)+18/f^3*b^2*ln(1-exp(f*x+e))*a*c*d^2*e+9/f*b*ln(1-exp(f*x+e))*a^2*c^2*d*x+9/f^2*b*ln(1-exp(f*x+e))*a^2*c^2*d*e+9/f*b*ln(exp(f*x+e)+1)*a^2*c*d^2*x^2+18/f^2*b*polylog(2,-exp(f*x+e))*a^2*c*d^2*x+9/f*b*ln(1-exp(f*x+e))*a^2*c*d^2*x^2+18/f^2*b*polylog(2,exp(f*x+e))*a^2*c*d^2*x+9/f*b*ln(exp(f*x+e)+1)*a^2*c^2*d*x-6/f^3*b^3*d^3*e*x+12/f^3*b*a^2*c*d^2*e^3-18/f^3*b^2*a*c*d^2*e^2-6/f^3*b*e^3*a^2*d^3*x+18/f^3*b^2*a*d^3*e^2*x-9/f^2*b*a^2*c^2*d*e^2-6/f*b^3*c^2*d*e*x+6/f^2*b^3*c*d^2*e^2*x-18/f*b^2*a*c*d^2*x^2+18/f^3*b^2*a*c*d^2*polylog(2,-exp(f*x+e))+18/f^3*b^2*a*c*d^2*polylog(2,exp(f*x+e))+9/f^4*b^2*a*d^3*e^2*ln(exp(f*x+e)-1)-18/f^3*b*a^2*c*d^2*polylog(3,-exp(f*x+e))-18/f^3*b*a^2*c*d^2*polylog(3,exp(f*x+e))+9/f^2*b*a^2*c^2*d*polylog(2,exp(f*x+e))-3/f^4*b*a^2*d^3*e^3*ln(exp(f*x+e)-1)-6/f^3*b^3*c*d^2*e^2*ln(exp(f*x+e))+3/f^3*b^3*c*d^2*e^2*ln(exp(f*x+e)-1)+6/f^4*b*a^2*d^3*e^3*ln(exp(f*x+e))+9/f^2*b*a^2*c^2*d*polylog(2,-exp(f*x+e))+3/f*b*a^2*d^3*ln(exp(f*x+e)+1)*x^3+9/f^2*b*a^2*d^3*polylog(2,-exp(f*x+e))*x^2-18/f^3*b*a^2*d^3*polylog(3,-exp(f*x+e))*x+3/f*b*a^2*d^3*ln(1-exp(f*x+e))*x^3+9/f^2*b*a^2*d^3*polylog(2,exp(f*x+e))*x^2-18/f^3*b*a^2*d^3*polylog(3,exp(f*x+e))*x-3/f^3*b^3*ln(1-exp(f*x+e))*c*d^2*e^2-18/f^2*b^2*a*c^2*d*ln(exp(f*x+e))+6/f^2*b^3*c^2*d*e*ln(exp(f*x+e))-18/f^4*b^2*a*d^3*e^2*ln(exp(f*x+e))+9/f^2*b^2*a*c^2*d*ln(exp(f*x+e)+1)+9/f^2*b^2*a*c^2*d*ln(exp(f*x+e)-1)-3/f^2*b^3*c^2*d*e*ln(exp(f*x+e)-1)+3/f^4*b*a^2*d^3*e^3*ln(1-exp(f*x+e))+3/f*b^3*ln(exp(f*x+e)+1)*c^2*d*x+3/f*b^3*ln(1-exp(f*x+e))*c^2*d*x+3/f^2*b^3*ln(1-exp(f*x+e))*c^2*d*e+3/f*b^3*ln(exp(f*x+e)+1)*c*d^2*x^2+6/f^2*b^3*polylog(2,-exp(f*x+e))*c*d^2*x+3/f*b^3*ln(1-exp(f*x+e))*c*d^2*x^2+6/f^2*b^3*polylog(2,exp(f*x+e))*c*d^2*x-9/f^4*b^2*a*d^3*e^2*ln(1-exp(f*x+e))+9/f^2*b^2*a*d^3*ln(exp(f*x+e)+1)*x^2+18/f^3*b^2*a*d^3*polylog(2,-exp(f*x+e))*x+9/f^2*b^2*a*d^3*ln(1-exp(f*x+e))*x^2+18/f^3*b^2*a*d^3*polylog(2,exp(f*x+e))*x","B"
48,1,1542,389,0.753000," ","int((d*x+c)^2*(a+b*coth(f*x+e))^3,x)","\frac{3 b \ln \left(1-{\mathrm e}^{f x +e}\right) a^{2} d^{2} x^{2}}{f}+\frac{6 b^{2} \ln \left(1-{\mathrm e}^{f x +e}\right) a \,d^{2} e}{f^{3}}+\frac{2 b^{3} \ln \left({\mathrm e}^{f x +e}+1\right) c d x}{f}+\frac{2 b^{3} \ln \left(1-{\mathrm e}^{f x +e}\right) c d x}{f}+\frac{2 b^{3} \ln \left(1-{\mathrm e}^{f x +e}\right) c d e}{f^{2}}+\frac{6 b^{2} \ln \left({\mathrm e}^{f x +e}+1\right) a \,d^{2} x}{f^{2}}+\frac{6 b^{2} \ln \left(1-{\mathrm e}^{f x +e}\right) a \,d^{2} x}{f^{2}}+\frac{12 b^{2} a \,d^{2} e \ln \left({\mathrm e}^{f x +e}\right)}{f^{3}}-\frac{3 b \ln \left(1-{\mathrm e}^{f x +e}\right) a^{2} d^{2} e^{2}}{f^{3}}-\frac{2 b^{3} c d e \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}+\frac{6 b^{2} a c d \ln \left({\mathrm e}^{f x +e}+1\right)}{f^{2}}+\frac{6 b^{2} a c d \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}+\frac{4 b^{3} c d e \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}-3 a^{2} b c d \,x^{2}+3 a \,b^{2} c d \,x^{2}-\frac{12 b \,a^{2} c d e x}{f}-\frac{6 b \,a^{2} c d e \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}+\frac{12 b \,a^{2} c d e \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{6 b \ln \left(1-{\mathrm e}^{f x +e}\right) a^{2} c d x}{f}+\frac{6 b \ln \left(1-{\mathrm e}^{f x +e}\right) a^{2} c d e}{f^{2}}+\frac{6 b \ln \left({\mathrm e}^{f x +e}+1\right) a^{2} c d x}{f}-\frac{2 b^{2} \left(3 a \,d^{2} f \,x^{2} {\mathrm e}^{2 f x +2 e}+b \,d^{2} f \,x^{2} {\mathrm e}^{2 f x +2 e}+6 a c d f x \,{\mathrm e}^{2 f x +2 e}+2 b c d f x \,{\mathrm e}^{2 f x +2 e}+3 a \,c^{2} f \,{\mathrm e}^{2 f x +2 e}-3 a \,d^{2} f \,x^{2}+b \,c^{2} f \,{\mathrm e}^{2 f x +2 e}+b \,d^{2} x \,{\mathrm e}^{2 f x +2 e}-6 a c d f x +b c d \,{\mathrm e}^{2 f x +2 e}-3 a \,c^{2} f -b \,d^{2} x -c b d \right)}{f^{2} \left({\mathrm e}^{2 f x +2 e}-1\right)^{2}}-a^{2} b \,d^{2} x^{3}+a \,b^{2} d^{2} x^{3}+a^{3} c d \,x^{2}-b^{3} c d \,x^{2}+\frac{a^{3} d^{2} x^{3}}{3}-\frac{b^{3} d^{2} x^{3}}{3}+c^{2} a^{3} x +b^{3} c^{2} x +\frac{4 b \,a^{2} d^{2} e^{3}}{f^{3}}-\frac{2 b^{3} c d \,e^{2}}{f^{2}}-\frac{6 b^{2} a \,d^{2} x^{2}}{f}-\frac{6 b^{2} a \,d^{2} e^{2}}{f^{3}}+\frac{2 b^{3} d^{2} e^{2} x}{f^{2}}-\frac{b^{3} \ln \left(1-{\mathrm e}^{f x +e}\right) d^{2} e^{2}}{f^{3}}-\frac{2 b^{3} d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f^{3}}-\frac{2 b^{3} d^{2} \polylog \left(3, -{\mathrm e}^{f x +e}\right)}{f^{3}}-\frac{2 b^{3} d^{2} \polylog \left(3, {\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{4 b^{3} d^{2} e^{3}}{3 f^{3}}+\frac{b^{3} d^{2} \ln \left({\mathrm e}^{f x +e}+1\right)}{f^{3}}+\frac{b^{3} d^{2} \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{3}}-\frac{2 b^{3} d^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f^{3}}-\frac{2 b^{3} c^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f}+\frac{b^{3} c^{2} \ln \left({\mathrm e}^{f x +e}+1\right)}{f}+\frac{b^{3} c^{2} \ln \left({\mathrm e}^{f x +e}-1\right)}{f}+3 c^{2} a^{2} b x +3 c^{2} a \,b^{2} x -\frac{6 b \,a^{2} c^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f}+\frac{3 b \,a^{2} c^{2} \ln \left({\mathrm e}^{f x +e}+1\right)}{f}+\frac{3 b \,a^{2} c^{2} \ln \left({\mathrm e}^{f x +e}-1\right)}{f}+\frac{b^{3} d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{3}}+\frac{b^{3} \ln \left({\mathrm e}^{f x +e}+1\right) d^{2} x^{2}}{f}+\frac{b^{3} \ln \left(1-{\mathrm e}^{f x +e}\right) d^{2} x^{2}}{f}-\frac{6 b \,a^{2} d^{2} \polylog \left(3, {\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{6 b^{2} a \,d^{2} \polylog \left(2, -{\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{6 b^{2} a \,d^{2} \polylog \left(2, {\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{2 b^{3} c d \polylog \left(2, -{\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{2 b^{3} c d \polylog \left(2, {\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{2 b^{3} \polylog \left(2, -{\mathrm e}^{f x +e}\right) d^{2} x}{f^{2}}+\frac{2 b^{3} \polylog \left(2, {\mathrm e}^{f x +e}\right) d^{2} x}{f^{2}}-\frac{6 b \,a^{2} d^{2} \polylog \left(3, -{\mathrm e}^{f x +e}\right)}{f^{3}}-\frac{12 b^{2} a c d \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{6 b \,a^{2} d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f^{3}}+\frac{3 b \,a^{2} d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{3}}-\frac{6 b^{2} a \,d^{2} e \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{3}}+\frac{3 b \ln \left({\mathrm e}^{f x +e}+1\right) a^{2} d^{2} x^{2}}{f}+\frac{6 b \polylog \left(2, -{\mathrm e}^{f x +e}\right) a^{2} d^{2} x}{f^{2}}+\frac{6 b \polylog \left(2, {\mathrm e}^{f x +e}\right) a^{2} d^{2} x}{f^{2}}+\frac{6 b \,a^{2} c d \polylog \left(2, -{\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{6 b \,a^{2} c d \polylog \left(2, {\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{4 b^{3} c d e x}{f}-\frac{12 b^{2} a \,d^{2} e x}{f^{2}}+\frac{6 b \,a^{2} d^{2} e^{2} x}{f^{2}}-\frac{6 b \,a^{2} c d \,e^{2}}{f^{2}}"," ",0,"6/f^2*b*polylog(2,-exp(f*x+e))*a^2*d^2*x+3/f*b*ln(1-exp(f*x+e))*a^2*d^2*x^2+6/f^2*b*polylog(2,exp(f*x+e))*a^2*d^2*x+6/f^3*b^2*ln(1-exp(f*x+e))*a*d^2*e+2/f*b^3*ln(exp(f*x+e)+1)*c*d*x+2/f*b^3*ln(1-exp(f*x+e))*c*d*x+2/f^2*b^3*ln(1-exp(f*x+e))*c*d*e+6/f^2*b^2*ln(exp(f*x+e)+1)*a*d^2*x+6/f^2*b^2*ln(1-exp(f*x+e))*a*d^2*x+12/f^3*b^2*a*d^2*e*ln(exp(f*x+e))-3/f^3*b*ln(1-exp(f*x+e))*a^2*d^2*e^2-2/f^2*b^3*c*d*e*ln(exp(f*x+e)-1)+6/f^2*b^2*a*c*d*ln(exp(f*x+e)+1)+6/f^2*b^2*a*c*d*ln(exp(f*x+e)-1)+4/f^2*b^3*c*d*e*ln(exp(f*x+e))-3*a^2*b*c*d*x^2+3*a*b^2*c*d*x^2-12/f*b*a^2*c*d*e*x-6/f^2*b*a^2*c*d*e*ln(exp(f*x+e)-1)+12/f^2*b*a^2*c*d*e*ln(exp(f*x+e))+6/f*b*ln(1-exp(f*x+e))*a^2*c*d*x+6/f^2*b*ln(1-exp(f*x+e))*a^2*c*d*e+6/f*b*ln(exp(f*x+e)+1)*a^2*c*d*x-2*b^2*(3*a*d^2*f*x^2*exp(2*f*x+2*e)+b*d^2*f*x^2*exp(2*f*x+2*e)+6*a*c*d*f*x*exp(2*f*x+2*e)+2*b*c*d*f*x*exp(2*f*x+2*e)+3*a*c^2*f*exp(2*f*x+2*e)-3*a*d^2*f*x^2+b*c^2*f*exp(2*f*x+2*e)+b*d^2*x*exp(2*f*x+2*e)-6*a*c*d*f*x+b*c*d*exp(2*f*x+2*e)-3*a*c^2*f-b*d^2*x-c*b*d)/f^2/(exp(2*f*x+2*e)-1)^2-a^2*b*d^2*x^3+a*b^2*d^2*x^3+a^3*c*d*x^2-b^3*c*d*x^2+1/3*a^3*d^2*x^3-1/3*b^3*d^2*x^3+c^2*a^3*x+b^3*c^2*x+4/f^3*b*a^2*d^2*e^3-2/f^2*b^3*c*d*e^2-6/f*b^2*a*d^2*x^2-6/f^3*b^2*a*d^2*e^2+2/f^2*b^3*d^2*e^2*x-6/f^3*b*a^2*d^2*polylog(3,exp(f*x+e))-1/f^3*b^3*ln(1-exp(f*x+e))*d^2*e^2-2/f^3*b^3*d^2*e^2*ln(exp(f*x+e))+4/3/f^3*b^3*d^2*e^3-2/f^3*b^3*d^2*polylog(3,-exp(f*x+e))-2/f^3*b^3*d^2*polylog(3,exp(f*x+e))+1/f^3*b^3*d^2*ln(exp(f*x+e)+1)+1/f^3*b^3*d^2*ln(exp(f*x+e)-1)-2/f^3*b^3*d^2*ln(exp(f*x+e))-2/f*b^3*c^2*ln(exp(f*x+e))+1/f*b^3*c^2*ln(exp(f*x+e)+1)+1/f*b^3*c^2*ln(exp(f*x+e)-1)+3*c^2*a^2*b*x+3*c^2*a*b^2*x-6/f*b*a^2*c^2*ln(exp(f*x+e))+6/f^3*b^2*a*d^2*polylog(2,-exp(f*x+e))+6/f^3*b^2*a*d^2*polylog(2,exp(f*x+e))+3/f*b*a^2*c^2*ln(exp(f*x+e)+1)+3/f*b*a^2*c^2*ln(exp(f*x+e)-1)+1/f^3*b^3*d^2*e^2*ln(exp(f*x+e)-1)+2/f^2*b^3*c*d*polylog(2,-exp(f*x+e))+2/f^2*b^3*c*d*polylog(2,exp(f*x+e))+1/f*b^3*ln(exp(f*x+e)+1)*d^2*x^2+2/f^2*b^3*polylog(2,-exp(f*x+e))*d^2*x+1/f*b^3*ln(1-exp(f*x+e))*d^2*x^2+2/f^2*b^3*polylog(2,exp(f*x+e))*d^2*x-6/f^3*b*a^2*d^2*polylog(3,-exp(f*x+e))-12/f^2*b^2*a*c*d*ln(exp(f*x+e))-6/f^3*b*a^2*d^2*e^2*ln(exp(f*x+e))+3/f^3*b*a^2*d^2*e^2*ln(exp(f*x+e)-1)+6/f^2*b*a^2*c*d*polylog(2,-exp(f*x+e))+6/f^2*b*a^2*c*d*polylog(2,exp(f*x+e))-6/f^3*b^2*a*d^2*e*ln(exp(f*x+e)-1)+3/f*b*ln(exp(f*x+e)+1)*a^2*d^2*x^2-4/f*b^3*c*d*e*x-12/f^2*b^2*a*d^2*e*x+6/f^2*b*a^2*d^2*e^2*x-6/f^2*b*a^2*c*d*e^2","B"
49,1,651,243,0.645000," ","int((d*x+c)*(a+b*coth(f*x+e))^3,x)","-\frac{6 b \,a^{2} d e x}{f}+\frac{3 b \ln \left({\mathrm e}^{f x +e}+1\right) a^{2} d x}{f}+\frac{3 b \ln \left(1-{\mathrm e}^{f x +e}\right) a^{2} d x}{f}+\frac{3 b \ln \left(1-{\mathrm e}^{f x +e}\right) a^{2} d e}{f^{2}}+\frac{6 b d \,a^{2} e \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{3 b \,a^{2} d e \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}-\frac{3 a^{2} b d \,x^{2}}{2}+3 c \,a^{2} b x +\frac{a^{3} d \,x^{2}}{2}-\frac{b^{3} d \,x^{2}}{2}+c \,a^{3} x +b^{3} c x +\frac{3 b^{2} d a \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}+\frac{3 b^{2} d a \ln \left({\mathrm e}^{f x +e}+1\right)}{f^{2}}+\frac{3 b \,a^{2} c \ln \left({\mathrm e}^{f x +e}+1\right)}{f}-\frac{6 b \,a^{2} c \ln \left({\mathrm e}^{f x +e}\right)}{f}-\frac{6 b^{2} d a \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{3 b \,a^{2} c \ln \left({\mathrm e}^{f x +e}-1\right)}{f}+\frac{b^{3} \ln \left({\mathrm e}^{f x +e}+1\right) d x}{f}+\frac{b^{3} \ln \left(1-{\mathrm e}^{f x +e}\right) d x}{f}+\frac{b^{3} \ln \left(1-{\mathrm e}^{f x +e}\right) d e}{f^{2}}+\frac{2 b^{3} d e \ln \left({\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{b^{3} d e \ln \left({\mathrm e}^{f x +e}-1\right)}{f^{2}}-\frac{b^{2} \left(6 a d f x \,{\mathrm e}^{2 f x +2 e}+2 b d f x \,{\mathrm e}^{2 f x +2 e}+6 a c f \,{\mathrm e}^{2 f x +2 e}+2 b c f \,{\mathrm e}^{2 f x +2 e}-6 a d f x +b d \,{\mathrm e}^{2 f x +2 e}-6 a c f -b d \right)}{f^{2} \left({\mathrm e}^{2 f x +2 e}-1\right)^{2}}+3 a \,b^{2} c x +\frac{3 a \,b^{2} d \,x^{2}}{2}+\frac{3 b \,a^{2} d \polylog \left(2, -{\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{3 b \,a^{2} d \polylog \left(2, {\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{b^{3} d \,e^{2}}{f^{2}}+\frac{b^{3} c \ln \left({\mathrm e}^{f x +e}-1\right)}{f}+\frac{b^{3} c \ln \left({\mathrm e}^{f x +e}+1\right)}{f}-\frac{2 b^{3} c \ln \left({\mathrm e}^{f x +e}\right)}{f}+\frac{b^{3} d \polylog \left(2, -{\mathrm e}^{f x +e}\right)}{f^{2}}+\frac{b^{3} d \polylog \left(2, {\mathrm e}^{f x +e}\right)}{f^{2}}-\frac{3 b \,a^{2} d \,e^{2}}{f^{2}}-\frac{2 b^{3} d e x}{f}"," ",0,"-6/f*b*a^2*d*e*x+3/f*b*ln(exp(f*x+e)+1)*a^2*d*x+3/f*b*ln(1-exp(f*x+e))*a^2*d*x+3/f^2*b*ln(1-exp(f*x+e))*a^2*d*e+6/f^2*b*d*a^2*e*ln(exp(f*x+e))-3/f^2*b*a^2*d*e*ln(exp(f*x+e)-1)-3/2*a^2*b*d*x^2+3*c*a^2*b*x+1/2*a^3*d*x^2-1/2*b^3*d*x^2+c*a^3*x+b^3*c*x+3/f^2*b^2*d*a*ln(exp(f*x+e)-1)+3/f^2*b^2*d*a*ln(exp(f*x+e)+1)+3/f*b*a^2*c*ln(exp(f*x+e)+1)-6/f*b*a^2*c*ln(exp(f*x+e))-6/f^2*b^2*d*a*ln(exp(f*x+e))+3/f*b*a^2*c*ln(exp(f*x+e)-1)+1/f*b^3*ln(exp(f*x+e)+1)*d*x+1/f*b^3*ln(1-exp(f*x+e))*d*x+3/f^2*b*a^2*d*polylog(2,-exp(f*x+e))+3/f^2*b*a^2*d*polylog(2,exp(f*x+e))+1/f^2*b^3*ln(1-exp(f*x+e))*d*e+2/f^2*b^3*d*e*ln(exp(f*x+e))-1/f^2*b^3*d*e*ln(exp(f*x+e)-1)-b^2*(6*a*d*f*x*exp(2*f*x+2*e)+2*b*d*f*x*exp(2*f*x+2*e)+6*a*c*f*exp(2*f*x+2*e)+2*b*c*f*exp(2*f*x+2*e)-6*a*d*f*x+b*d*exp(2*f*x+2*e)-6*a*c*f-b*d)/f^2/(exp(2*f*x+2*e)-1)^2+3*a*b^2*c*x+3/2*a*b^2*d*x^2-1/f^2*b^3*d*e^2+1/f^2*b^3*d*polylog(2,-exp(f*x+e))+1/f^2*b^3*d*polylog(2,exp(f*x+e))+1/f*b^3*c*ln(exp(f*x+e)-1)+1/f*b^3*c*ln(exp(f*x+e)+1)-2/f*b^3*c*ln(exp(f*x+e))-3/f^2*b*a^2*d*e^2-2/f*b^3*d*e*x","B"
50,0,0,22,1.396000," ","int((a+b*coth(f*x+e))^3/(d*x+c),x)","\int \frac{\left(a +b \coth \left(f x +e \right)\right)^{3}}{d x +c}\, dx"," ",0,"int((a+b*coth(f*x+e))^3/(d*x+c),x)","F"
51,0,0,22,1.777000," ","int((a+b*coth(f*x+e))^3/(d*x+c)^2,x)","\int \frac{\left(a +b \coth \left(f x +e \right)\right)^{3}}{\left(d x +c \right)^{2}}\, dx"," ",0,"int((a+b*coth(f*x+e))^3/(d*x+c)^2,x)","F"
52,1,1145,209,0.839000," ","int((d*x+c)^3/(a+b*coth(f*x+e)),x)","-\frac{b \,d^{3} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x^{3}}{f \left(a +b \right) \left(a -b \right)}-\frac{b \,d^{3} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) e^{3}}{f^{4} \left(a +b \right) \left(a -b \right)}-\frac{2 b \,d^{3} e^{3} \ln \left({\mathrm e}^{f x +e}\right)}{f^{4} \left(a +b \right) \left(a -b \right)}+\frac{b \,d^{3} e^{3} \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{f^{4} \left(a +b \right) \left(a -b \right)}-\frac{3 b \,d^{3} \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x^{2}}{2 f^{2} \left(a +b \right) \left(a -b \right)}+\frac{3 b \,d^{3} \polylog \left(3, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{2 f^{3} \left(a +b \right) \left(a -b \right)}-\frac{3 b \,c^{2} d \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{2 f^{2} \left(a +b \right) \left(a -b \right)}+\frac{3 b c \,d^{2} \polylog \left(3, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{2 f^{3} \left(a +b \right) \left(a -b \right)}+\frac{c \,d^{2} x^{3}}{a +b}+\frac{3 c^{2} d \,x^{2}}{2 \left(a +b \right)}-\frac{3 b c \,d^{2} e^{2} \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{f^{3} \left(a +b \right) \left(a -b \right)}+\frac{3 b c \,d^{2} e^{2} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{f^{3} \left(a +b \right) \left(a -b \right)}-\frac{3 b \,c^{2} d \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{f \left(a +b \right) \left(a -b \right)}-\frac{3 b \,c^{2} d \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) e}{f^{2} \left(a +b \right) \left(a -b \right)}-\frac{3 b c \,d^{2} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x^{2}}{f \left(a +b \right) \left(a -b \right)}-\frac{3 b c \,d^{2} \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{f^{2} \left(a +b \right) \left(a -b \right)}-\frac{6 b \,e^{2} c \,d^{2} x}{f^{2} \left(a +b \right) \left(a -b \right)}+\frac{6 b \,c^{2} d e x}{f \left(a +b \right) \left(a -b \right)}-\frac{6 b \,c^{2} d e \ln \left({\mathrm e}^{f x +e}\right)}{f^{2} \left(a +b \right) \left(a -b \right)}+\frac{6 b c \,d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f^{3} \left(a +b \right) \left(a -b \right)}+\frac{3 b \,c^{2} d e \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{f^{2} \left(a +b \right) \left(a -b \right)}+\frac{b \,d^{3} x^{4}}{2 \left(a +b \right) \left(a -b \right)}+\frac{3 b \,d^{3} e^{4}}{2 f^{4} \left(a +b \right) \left(a -b \right)}-\frac{b \,c^{3} \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{f \left(a +b \right) \left(a -b \right)}+\frac{2 b \,c^{3} \ln \left({\mathrm e}^{f x +e}\right)}{f \left(a +b \right) \left(a -b \right)}-\frac{3 b \,d^{3} \polylog \left(4, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{4 f^{4} \left(a +b \right) \left(a -b \right)}+\frac{c^{3} x}{a +b}-\frac{4 b \,e^{3} c \,d^{2}}{f^{3} \left(a +b \right) \left(a -b \right)}+\frac{2 b \,d^{3} e^{3} x}{f^{3} \left(a +b \right) \left(a -b \right)}+\frac{2 b c \,d^{2} x^{3}}{\left(a +b \right) \left(a -b \right)}+\frac{3 b \,c^{2} d \,x^{2}}{\left(a +b \right) \left(a -b \right)}+\frac{3 b \,c^{2} d \,e^{2}}{f^{2} \left(a +b \right) \left(a -b \right)}+\frac{d^{3} x^{4}}{4 a +4 b}"," ",0,"-1/f*b/(a+b)*d^3/(a-b)*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x^3-1/f^4*b/(a+b)*d^3/(a-b)*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*e^3-3/2/f^2*b/(a+b)*d^3/(a-b)*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))*x^2+3/2/f^3*b/(a+b)*d^3/(a-b)*polylog(3,(a+b)*exp(2*f*x+2*e)/(a-b))*x-3/2/f^2*b/(a+b)*c^2*d/(a-b)*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))-2/f^4*b/(a+b)*d^3*e^3/(a-b)*ln(exp(f*x+e))+1/f^4*b/(a+b)*d^3*e^3/(a-b)*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)+3/2/f^3*b/(a+b)*c*d^2/(a-b)*polylog(3,(a+b)*exp(2*f*x+2*e)/(a-b))+1/(a+b)*c*d^2*x^3+3/2/(a+b)*c^2*d*x^2-3/f^3*b/(a+b)*c*d^2*e^2/(a-b)*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)+3/f^3*b/(a+b)*c*d^2*e^2/(a-b)*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))-3/f*b/(a+b)*c^2*d/(a-b)*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x-3/f^2*b/(a+b)*c^2*d/(a-b)*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*e-3/f*b/(a+b)*c*d^2/(a-b)*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x^2-3/f^2*b/(a+b)*c*d^2/(a-b)*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))*x-6/f^2*b/(a+b)/(a-b)*e^2*c*d^2*x+6/f*b/(a+b)/(a-b)*c^2*d*e*x-6/f^2*b/(a+b)*c^2*d*e/(a-b)*ln(exp(f*x+e))+6/f^3*b/(a+b)*c*d^2*e^2/(a-b)*ln(exp(f*x+e))+3/f^2*b/(a+b)*c^2*d*e/(a-b)*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)+1/2*b/(a+b)/(a-b)*d^3*x^4+3/2/f^4*b/(a+b)/(a-b)*d^3*e^4-1/f*b/(a+b)*c^3/(a-b)*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)+2/f*b/(a+b)*c^3/(a-b)*ln(exp(f*x+e))-3/4/f^4*b/(a+b)*d^3/(a-b)*polylog(4,(a+b)*exp(2*f*x+2*e)/(a-b))+1/4/(a+b)*d^3*x^4+1/(a+b)*c^3*x-4/f^3*b/(a+b)/(a-b)*e^3*c*d^2+2/f^3*b/(a+b)/(a-b)*d^3*e^3*x+2*b/(a+b)/(a-b)*c*d^2*x^3+3*b/(a+b)/(a-b)*c^2*d*x^2+3/f^2*b/(a+b)/(a-b)*c^2*d*e^2","B"
53,1,722,157,0.854000," ","int((d*x+c)^2/(a+b*coth(f*x+e)),x)","\frac{d^{2} x^{3}}{3 a +3 b}+\frac{c d \,x^{2}}{a +b}+\frac{c^{2} x}{a +b}+\frac{2 b \,c^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f \left(a +b \right) \left(a -b \right)}-\frac{b \,c^{2} \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{f \left(a +b \right) \left(a -b \right)}+\frac{2 b \,d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}\right)}{f^{3} \left(a +b \right) \left(a -b \right)}-\frac{b \,d^{2} e^{2} \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{f^{3} \left(a +b \right) \left(a -b \right)}+\frac{2 b \,d^{2} x^{3}}{3 \left(a +b \right) \left(a -b \right)}-\frac{2 b \,d^{2} e^{2} x}{f^{2} \left(a +b \right) \left(a -b \right)}-\frac{4 b \,d^{2} e^{3}}{3 f^{3} \left(a +b \right) \left(a -b \right)}-\frac{b \,d^{2} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x^{2}}{f \left(a +b \right) \left(a -b \right)}+\frac{b \,d^{2} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) e^{2}}{f^{3} \left(a +b \right) \left(a -b \right)}-\frac{b \,d^{2} \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{f^{2} \left(a +b \right) \left(a -b \right)}+\frac{b \,d^{2} \polylog \left(3, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{2 f^{3} \left(a +b \right) \left(a -b \right)}-\frac{4 b c d e \ln \left({\mathrm e}^{f x +e}\right)}{f^{2} \left(a +b \right) \left(a -b \right)}+\frac{2 b c d e \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{f^{2} \left(a +b \right) \left(a -b \right)}-\frac{2 b c d \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{f \left(a +b \right) \left(a -b \right)}-\frac{2 b c d \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) e}{f^{2} \left(a +b \right) \left(a -b \right)}+\frac{2 b d c \,x^{2}}{\left(a +b \right) \left(a -b \right)}+\frac{4 b d c e x}{f \left(a +b \right) \left(a -b \right)}+\frac{2 b d c \,e^{2}}{f^{2} \left(a +b \right) \left(a -b \right)}-\frac{b c d \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{f^{2} \left(a +b \right) \left(a -b \right)}"," ",0,"1/3/(a+b)*d^2*x^3+1/(a+b)*c*d*x^2+1/(a+b)*c^2*x+2/f*b/(a+b)*c^2/(a-b)*ln(exp(f*x+e))-1/f*b/(a+b)*c^2/(a-b)*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)+2/f^3*b/(a+b)*d^2*e^2/(a-b)*ln(exp(f*x+e))-1/f^3*b/(a+b)*d^2*e^2/(a-b)*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)+2/3*b/(a+b)/(a-b)*d^2*x^3-2/f^2*b/(a+b)/(a-b)*d^2*e^2*x-4/3/f^3*b/(a+b)/(a-b)*d^2*e^3-1/f*b/(a+b)*d^2/(a-b)*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x^2+1/f^3*b/(a+b)*d^2/(a-b)*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*e^2-1/f^2*b/(a+b)*d^2/(a-b)*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))*x+1/2/f^3*b/(a+b)*d^2/(a-b)*polylog(3,(a+b)*exp(2*f*x+2*e)/(a-b))-4/f^2*b/(a+b)*c*d*e/(a-b)*ln(exp(f*x+e))+2/f^2*b/(a+b)*c*d*e/(a-b)*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)-2/f*b/(a+b)*c*d/(a-b)*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x-2/f^2*b/(a+b)*c*d/(a-b)*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*e+2*b/(a+b)/(a-b)*d*c*x^2+4/f*b/(a+b)/(a-b)*d*c*e*x+2/f^2*b/(a+b)/(a-b)*d*c*e^2-1/f^2*b/(a+b)*c*d/(a-b)*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))","B"
54,1,357,107,0.751000," ","int((d*x+c)/(a+b*coth(f*x+e)),x)","\frac{d \,x^{2}}{2 b +2 a}+\frac{c x}{a +b}+\frac{2 b c \ln \left({\mathrm e}^{f x +e}\right)}{f \left(a +b \right) \left(a -b \right)}-\frac{b c \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{f \left(a +b \right) \left(a -b \right)}-\frac{b d \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{f \left(a +b \right) \left(a -b \right)}-\frac{b d \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) e}{f^{2} \left(a +b \right) \left(a -b \right)}+\frac{b d \,x^{2}}{\left(a +b \right) \left(a -b \right)}+\frac{2 b d e x}{f \left(a +b \right) \left(a -b \right)}+\frac{b d \,e^{2}}{f^{2} \left(a +b \right) \left(a -b \right)}-\frac{b d \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{2 f^{2} \left(a +b \right) \left(a -b \right)}-\frac{2 b d e \ln \left({\mathrm e}^{f x +e}\right)}{f^{2} \left(a +b \right) \left(a -b \right)}+\frac{b d e \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{f^{2} \left(a +b \right) \left(a -b \right)}"," ",0,"1/2/(a+b)*d*x^2+1/(a+b)*c*x+2/f*b/(a+b)*c/(a-b)*ln(exp(f*x+e))-1/f*b/(a+b)*c/(a-b)*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)-1/f*b/(a+b)*d/(a-b)*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x-1/f^2*b/(a+b)*d/(a-b)*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*e+b/(a+b)/(a-b)*d*x^2+2/f*b/(a+b)/(a-b)*d*e*x+1/f^2*b/(a+b)/(a-b)*d*e^2-1/2/f^2*b/(a+b)*d/(a-b)*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))-2/f^2*b/(a+b)*d*e/(a-b)*ln(exp(f*x+e))+1/f^2*b/(a+b)*d*e/(a-b)*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)","B"
55,0,0,22,0.686000," ","int(1/(d*x+c)/(a+b*coth(f*x+e)),x)","\int \frac{1}{\left(d x +c \right) \left(a +b \coth \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)/(a+b*coth(f*x+e)),x)","F"
56,0,0,22,0.690000," ","int(1/(d*x+c)^2/(a+b*coth(f*x+e)),x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a +b \coth \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)^2/(a+b*coth(f*x+e)),x)","F"
57,1,2423,618,1.066000," ","int((d*x+c)^3/(a+b*coth(f*x+e))^2,x)","\frac{12 b a c \,d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{6 b a c \,d^{2} e^{2} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}-\frac{6 b a \,c^{2} d \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{\left(a^{2}+2 a b +b^{2}\right) f \left(a -b \right)^{2}}-\frac{6 b a c \,d^{2} e^{2} \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{6 b a \,c^{2} d e \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}-\frac{6 b a \,c^{2} d \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) e}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}-\frac{12 b a \,c^{2} d e \ln \left({\mathrm e}^{f x +e}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}-\frac{6 b a c \,d^{2} \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}-\frac{2 b^{2} d^{3} x^{3}}{\left(a^{2}+2 a b +b^{2}\right) f \left(a -b \right)^{2}}+\frac{4 b^{2} e^{3} d^{3}}{\left(a^{2}+2 a b +b^{2}\right) f^{4} \left(a -b \right)^{2}}-\frac{3 b^{2} d^{3} \polylog \left(3, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{2 \left(a^{2}+2 a b +b^{2}\right) f^{4} \left(a -b \right)^{2}}+\frac{2 b a \,d^{3} e^{3} \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{\left(a^{2}+2 a b +b^{2}\right) f^{4} \left(a -b \right)^{2}}-\frac{4 b a \,d^{3} e^{3} \ln \left({\mathrm e}^{f x +e}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{4} \left(a -b \right)^{2}}-\frac{6 b^{2} c \,d^{2} e \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}-\frac{2 b a \,d^{3} e^{3} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{4} \left(a -b \right)^{2}}+\frac{12 b^{2} c \,d^{2} e \ln \left({\mathrm e}^{f x +e}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}-\frac{3 b a \,c^{2} d \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}-\frac{3 b a \,d^{3} \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x^{2}}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}+\frac{3 b a \,d^{3} \polylog \left(3, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{3 b a c \,d^{2} \polylog \left(3, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{6 b a \,c^{2} d \,x^{2}}{\left(a^{2}+2 a b +b^{2}\right) \left(a -b \right)^{2}}+\frac{4 b \,e^{3} a \,d^{3} x}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{4 b a c \,d^{2} x^{3}}{\left(a^{2}+2 a b +b^{2}\right) \left(a -b \right)^{2}}-\frac{8 b a c \,d^{2} e^{3}}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}-\frac{2 b a \,d^{3} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x^{3}}{\left(a^{2}+2 a b +b^{2}\right) f \left(a -b \right)^{2}}+\frac{6 b^{2} c \,d^{2} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}+\frac{6 b^{2} c \,d^{2} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) e}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{6 b a \,c^{2} d \,e^{2}}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}-\frac{12 b^{2} d^{2} c e x}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}+\frac{c^{3} x}{a^{2}+2 a b +b^{2}}-\frac{12 b a c \,d^{2} e^{2} x}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}+\frac{12 b a \,c^{2} d e x}{\left(a^{2}+2 a b +b^{2}\right) f \left(a -b \right)^{2}}-\frac{6 b a c \,d^{2} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x^{2}}{\left(a^{2}+2 a b +b^{2}\right) f \left(a -b \right)^{2}}+\frac{d^{3} x^{4}}{4 a^{2}+8 a b +4 b^{2}}+\frac{c \,d^{2} x^{3}}{a^{2}+2 a b +b^{2}}+\frac{3 c^{2} d \,x^{2}}{2 \left(a^{2}+2 a b +b^{2}\right)}+\frac{b a \,d^{3} x^{4}}{\left(a^{2}+2 a b +b^{2}\right) \left(a -b \right)^{2}}+\frac{3 b \,e^{4} a \,d^{3}}{\left(a^{2}+2 a b +b^{2}\right) f^{4} \left(a -b \right)^{2}}-\frac{6 b^{2} d^{2} c \,x^{2}}{\left(a^{2}+2 a b +b^{2}\right) f \left(a -b \right)^{2}}-\frac{6 b^{2} d^{2} c \,e^{2}}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{6 b^{2} e^{2} d^{3} x}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{3 b^{2} d^{3} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x^{2}}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}+\frac{3 b^{2} d^{3} e^{2} \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{\left(a^{2}+2 a b +b^{2}\right) f^{4} \left(a -b \right)^{2}}-\frac{6 b^{2} d^{3} e^{2} \ln \left({\mathrm e}^{f x +e}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{4} \left(a -b \right)^{2}}-\frac{2 b a \,c^{3} \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{\left(a^{2}+2 a b +b^{2}\right) f \left(a -b \right)^{2}}+\frac{3 b^{2} c^{2} d \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}+\frac{4 b a \,c^{3} \ln \left({\mathrm e}^{f x +e}\right)}{\left(a^{2}+2 a b +b^{2}\right) f \left(a -b \right)^{2}}-\frac{6 b^{2} c^{2} d \ln \left({\mathrm e}^{f x +e}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}-\frac{3 b^{2} d^{3} e^{2} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{4} \left(a -b \right)^{2}}+\frac{3 b^{2} d^{3} \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{3 b^{2} c \,d^{2} \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}-\frac{3 b a \,d^{3} \polylog \left(4, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{2 \left(a^{2}+2 a b +b^{2}\right) f^{4} \left(a -b \right)^{2}}-\frac{2 \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right) b^{2}}{\left(a -b \right) f \left(a^{2}+2 a b +b^{2}\right) \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}"," ",0,"12/(a^2+2*a*b+b^2)/f^3*b/(a-b)^2*a*c*d^2*e^2*ln(exp(f*x+e))+6/(a^2+2*a*b+b^2)/f^3*b/(a-b)^2*a*c*d^2*e^2*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))-6/(a^2+2*a*b+b^2)/f*b/(a-b)^2*a*c^2*d*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x-6/(a^2+2*a*b+b^2)/f^3*b/(a-b)^2*a*c*d^2*e^2*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)+6/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*c^2*d*e*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)-6/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*c^2*d*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*e-6/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*c*d^2*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))*x-12/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*c^2*d*e*ln(exp(f*x+e))-2/(a^2+2*a*b+b^2)/f*b^2/(a-b)^2*d^3*x^3+4/(a^2+2*a*b+b^2)/f^4*b^2/(a-b)^2*e^3*d^3-3/2/(a^2+2*a*b+b^2)/f^4*b^2/(a-b)^2*d^3*polylog(3,(a+b)*exp(2*f*x+2*e)/(a-b))+2/(a^2+2*a*b+b^2)/f^4*b/(a-b)^2*a*d^3*e^3*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)-4/(a^2+2*a*b+b^2)/f^4*b/(a-b)^2*a*d^3*e^3*ln(exp(f*x+e))-3/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*c^2*d*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))-6/(a^2+2*a*b+b^2)/f^3*b^2/(a-b)^2*c*d^2*e*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)-2/(a^2+2*a*b+b^2)/f^4*b/(a-b)^2*a*d^3*e^3*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))-3/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*d^3*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))*x^2+3/(a^2+2*a*b+b^2)/f^3*b/(a-b)^2*a*d^3*polylog(3,(a+b)*exp(2*f*x+2*e)/(a-b))*x+12/(a^2+2*a*b+b^2)/f^3*b^2/(a-b)^2*c*d^2*e*ln(exp(f*x+e))+6/(a^2+2*a*b+b^2)*b/(a-b)^2*a*c^2*d*x^2+4/(a^2+2*a*b+b^2)/f^3*b/(a-b)^2*e^3*a*d^3*x+4/(a^2+2*a*b+b^2)*b/(a-b)^2*a*c*d^2*x^3-8/(a^2+2*a*b+b^2)/f^3*b/(a-b)^2*a*c*d^2*e^3-2/(a^2+2*a*b+b^2)/f*b/(a-b)^2*a*d^3*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x^3+6/(a^2+2*a*b+b^2)/f^2*b^2/(a-b)^2*c*d^2*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x+6/(a^2+2*a*b+b^2)/f^3*b^2/(a-b)^2*c*d^2*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*e+3/(a^2+2*a*b+b^2)/f^3*b/(a-b)^2*a*c*d^2*polylog(3,(a+b)*exp(2*f*x+2*e)/(a-b))+6/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*c^2*d*e^2-12/(a^2+2*a*b+b^2)/f^2*b^2/(a-b)^2*d^2*c*e*x+1/4/(a^2+2*a*b+b^2)*d^3*x^4+1/(a^2+2*a*b+b^2)*c^3*x-12/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*c*d^2*e^2*x+12/(a^2+2*a*b+b^2)/f*b/(a-b)^2*a*c^2*d*e*x-6/(a^2+2*a*b+b^2)/f*b/(a-b)^2*a*c*d^2*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x^2+1/(a^2+2*a*b+b^2)*c*d^2*x^3+3/2/(a^2+2*a*b+b^2)*c^2*d*x^2+1/(a^2+2*a*b+b^2)*b/(a-b)^2*a*d^3*x^4+3/(a^2+2*a*b+b^2)/f^4*b/(a-b)^2*e^4*a*d^3-6/(a^2+2*a*b+b^2)/f*b^2/(a-b)^2*d^2*c*x^2-6/(a^2+2*a*b+b^2)/f^3*b^2/(a-b)^2*d^2*c*e^2+6/(a^2+2*a*b+b^2)/f^3*b^2/(a-b)^2*e^2*d^3*x+3/(a^2+2*a*b+b^2)/f^2*b^2/(a-b)^2*d^3*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x^2+3/(a^2+2*a*b+b^2)/f^3*b^2/(a-b)^2*d^3*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))*x+3/(a^2+2*a*b+b^2)/f^3*b^2/(a-b)^2*c*d^2*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))+3/(a^2+2*a*b+b^2)/f^4*b^2/(a-b)^2*d^3*e^2*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)-6/(a^2+2*a*b+b^2)/f^4*b^2/(a-b)^2*d^3*e^2*ln(exp(f*x+e))-2/(a^2+2*a*b+b^2)/f*b/(a-b)^2*a*c^3*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)+3/(a^2+2*a*b+b^2)/f^2*b^2/(a-b)^2*c^2*d*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)-3/2/(a^2+2*a*b+b^2)/f^4*b/(a-b)^2*a*d^3*polylog(4,(a+b)*exp(2*f*x+2*e)/(a-b))+4/(a^2+2*a*b+b^2)/f*b/(a-b)^2*a*c^3*ln(exp(f*x+e))-6/(a^2+2*a*b+b^2)/f^2*b^2/(a-b)^2*c^2*d*ln(exp(f*x+e))-3/(a^2+2*a*b+b^2)/f^4*b^2/(a-b)^2*d^3*e^2*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))-2/(a-b)/f/(a^2+2*a*b+b^2)*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)*b^2/(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)","B"
58,1,1449,464,1.007000," ","int((d*x+c)^2/(a+b*coth(f*x+e))^2,x)","\frac{c^{2} x}{a^{2}+2 a b +b^{2}}+\frac{d^{2} x^{3}}{3 a^{2}+6 a b +3 b^{2}}+\frac{4 b a c d \,x^{2}}{\left(a^{2}+2 a b +b^{2}\right) \left(a -b \right)^{2}}-\frac{4 b a \,d^{2} e^{2} x}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}+\frac{4 b a c d \,e^{2}}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}-\frac{2 b a \,d^{2} e^{2} \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{4 b a \,d^{2} e^{2} \ln \left({\mathrm e}^{f x +e}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{2 b a \,d^{2} e^{2} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}-\frac{2 b a \,d^{2} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x^{2}}{\left(a^{2}+2 a b +b^{2}\right) f \left(a -b \right)^{2}}-\frac{2 b a \,d^{2} \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}-\frac{2 b a c d \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}+\frac{c d \,x^{2}}{a^{2}+2 a b +b^{2}}-\frac{2 b^{2} d^{2} x^{2}}{\left(a^{2}+2 a b +b^{2}\right) f \left(a -b \right)^{2}}-\frac{2 b^{2} d^{2} e^{2}}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{b^{2} d^{2} \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{2 b^{2} c d \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}-\frac{4 b^{2} c d \ln \left({\mathrm e}^{f x +e}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}+\frac{b a \,d^{2} \polylog \left(3, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{4 b a \,d^{2} x^{3}}{3 \left(a^{2}+2 a b +b^{2}\right) \left(a -b \right)^{2}}-\frac{8 b a \,d^{2} e^{3}}{3 \left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}-\frac{2 b^{2} d^{2} e \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{4 b^{2} d^{2} e \ln \left({\mathrm e}^{f x +e}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}+\frac{2 b^{2} d^{2} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}+\frac{2 b^{2} d^{2} \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) e}{\left(a^{2}+2 a b +b^{2}\right) f^{3} \left(a -b \right)^{2}}-\frac{2 b a \,c^{2} \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{\left(a^{2}+2 a b +b^{2}\right) f \left(a -b \right)^{2}}+\frac{4 b a \,c^{2} \ln \left({\mathrm e}^{f x +e}\right)}{\left(a^{2}+2 a b +b^{2}\right) f \left(a -b \right)^{2}}-\frac{4 b^{2} d^{2} e x}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}+\frac{8 b a c d e x}{\left(a^{2}+2 a b +b^{2}\right) f \left(a -b \right)^{2}}+\frac{4 b a c d e \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}-\frac{8 b a c d e \ln \left({\mathrm e}^{f x +e}\right)}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}-\frac{4 b a c d \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) e}{\left(a^{2}+2 a b +b^{2}\right) f^{2} \left(a -b \right)^{2}}-\frac{4 b a c d \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{\left(a^{2}+2 a b +b^{2}\right) f \left(a -b \right)^{2}}-\frac{2 \left(d^{2} x^{2}+2 c d x +c^{2}\right) b^{2}}{\left(a -b \right) f \left(a^{2}+2 a b +b^{2}\right) \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}"," ",0,"1/3/(a^2+2*a*b+b^2)*d^2*x^3+1/(a^2+2*a*b+b^2)*c^2*x+4/(a^2+2*a*b+b^2)*b/(a-b)^2*a*c*d*x^2-4/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*d^2*e^2*x+4/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*c*d*e^2-2/(a^2+2*a*b+b^2)/f^3*b/(a-b)^2*a*d^2*e^2*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)+4/(a^2+2*a*b+b^2)/f^3*b/(a-b)^2*a*d^2*e^2*ln(exp(f*x+e))+2/(a^2+2*a*b+b^2)/f^3*b/(a-b)^2*a*d^2*e^2*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))-2/(a^2+2*a*b+b^2)/f*b/(a-b)^2*a*d^2*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x^2-2/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*d^2*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))*x-2/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*c*d*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))+1/(a^2+2*a*b+b^2)*c*d*x^2-2/(a^2+2*a*b+b^2)/f*b^2/(a-b)^2*d^2*x^2-2/(a^2+2*a*b+b^2)/f^3*b^2/(a-b)^2*d^2*e^2+1/(a^2+2*a*b+b^2)/f^3*b^2/(a-b)^2*d^2*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))+2/(a^2+2*a*b+b^2)/f^2*b^2/(a-b)^2*c*d*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)-4/(a^2+2*a*b+b^2)/f^2*b^2/(a-b)^2*c*d*ln(exp(f*x+e))+4/3/(a^2+2*a*b+b^2)*b/(a-b)^2*a*d^2*x^3-8/3/(a^2+2*a*b+b^2)/f^3*b/(a-b)^2*a*d^2*e^3-2/(a^2+2*a*b+b^2)/f^3*b^2/(a-b)^2*d^2*e*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)+4/(a^2+2*a*b+b^2)/f^3*b^2/(a-b)^2*d^2*e*ln(exp(f*x+e))+2/(a^2+2*a*b+b^2)/f^2*b^2/(a-b)^2*d^2*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x+2/(a^2+2*a*b+b^2)/f^3*b^2/(a-b)^2*d^2*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*e-2/(a^2+2*a*b+b^2)/f*b/(a-b)^2*a*c^2*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)+4/(a^2+2*a*b+b^2)/f*b/(a-b)^2*a*c^2*ln(exp(f*x+e))+1/(a^2+2*a*b+b^2)/f^3*b/(a-b)^2*a*d^2*polylog(3,(a+b)*exp(2*f*x+2*e)/(a-b))-4/(a^2+2*a*b+b^2)/f^2*b^2/(a-b)^2*d^2*e*x+8/(a^2+2*a*b+b^2)/f*b/(a-b)^2*a*c*d*e*x+4/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*c*d*e*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)-8/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*c*d*e*ln(exp(f*x+e))-4/(a^2+2*a*b+b^2)/f^2*b/(a-b)^2*a*c*d*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*e-4/(a^2+2*a*b+b^2)/f*b/(a-b)^2*a*c*d*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x-2/(a-b)/f/(a^2+2*a*b+b^2)*(d^2*x^2+2*c*d*x+c^2)*b^2/(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)","B"
59,1,524,195,0.951000," ","int((d*x+c)/(a+b*coth(f*x+e))^2,x)","\frac{d \,x^{2}}{2 a^{2}+4 a b +2 b^{2}}+\frac{c x}{a^{2}+2 a b +b^{2}}-\frac{2 b^{2} \left(d x +c \right)}{\left(a -b \right) f \left(a^{2}+2 a b +b^{2}\right) \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}+\frac{b^{2} d \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{f^{2} \left(a -b \right)^{2} \left(a +b \right)^{2}}-\frac{2 b^{2} d \ln \left({\mathrm e}^{f x +e}\right)}{f^{2} \left(a -b \right)^{2} \left(a +b \right)^{2}}-\frac{2 b a c \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{f \left(a -b \right)^{2} \left(a +b \right)^{2}}+\frac{4 b a c \ln \left({\mathrm e}^{f x +e}\right)}{f \left(a -b \right)^{2} \left(a +b \right)^{2}}+\frac{2 b d a e \ln \left(a \,{\mathrm e}^{2 f x +2 e}+b \,{\mathrm e}^{2 f x +2 e}-a +b \right)}{f^{2} \left(a -b \right)^{2} \left(a +b \right)^{2}}-\frac{4 b d a e \ln \left({\mathrm e}^{f x +e}\right)}{f^{2} \left(a -b \right)^{2} \left(a +b \right)^{2}}-\frac{2 b d a \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) x}{f \left(a -b \right)^{2} \left(a +b \right)^{2}}-\frac{2 b d a \ln \left(1-\frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right) e}{f^{2} \left(a -b \right)^{2} \left(a +b \right)^{2}}+\frac{2 b d a \,x^{2}}{\left(a -b \right)^{2} \left(a +b \right)^{2}}+\frac{4 b d a e x}{f \left(a -b \right)^{2} \left(a +b \right)^{2}}+\frac{2 b d a \,e^{2}}{f^{2} \left(a -b \right)^{2} \left(a +b \right)^{2}}-\frac{b d a \polylog \left(2, \frac{\left(a +b \right) {\mathrm e}^{2 f x +2 e}}{a -b}\right)}{f^{2} \left(a -b \right)^{2} \left(a +b \right)^{2}}"," ",0,"1/2/(a^2+2*a*b+b^2)*d*x^2+1/(a^2+2*a*b+b^2)*c*x-2/(a-b)/f/(a^2+2*a*b+b^2)*b^2*(d*x+c)/(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)+1/f^2/(a-b)^2*b^2/(a+b)^2*d*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)-2/f^2/(a-b)^2*b^2/(a+b)^2*d*ln(exp(f*x+e))-2/f/(a-b)^2*b/(a+b)^2*a*c*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)+4/f/(a-b)^2*b/(a+b)^2*a*c*ln(exp(f*x+e))+2/f^2/(a-b)^2*b/(a+b)^2*d*a*e*ln(a*exp(2*f*x+2*e)+b*exp(2*f*x+2*e)-a+b)-4/f^2/(a-b)^2*b/(a+b)^2*d*a*e*ln(exp(f*x+e))-2/f/(a-b)^2*b/(a+b)^2*d*a*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*x-2/f^2/(a-b)^2*b/(a+b)^2*d*a*ln(1-(a+b)*exp(2*f*x+2*e)/(a-b))*e+2/(a-b)^2*b/(a+b)^2*d*a*x^2+4/f/(a-b)^2*b/(a+b)^2*d*a*e*x+2/f^2/(a-b)^2*b/(a+b)^2*d*a*e^2-1/f^2/(a-b)^2*b/(a+b)^2*d*a*polylog(2,(a+b)*exp(2*f*x+2*e)/(a-b))","B"
60,0,0,22,1.833000," ","int(1/(d*x+c)/(a+b*coth(f*x+e))^2,x)","\int \frac{1}{\left(d x +c \right) \left(a +b \coth \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*x+c)/(a+b*coth(f*x+e))^2,x)","F"
61,0,0,22,1.760000," ","int(1/(d*x+c)^2/(a+b*coth(f*x+e))^2,x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a +b \coth \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*x+c)^2/(a+b*coth(f*x+e))^2,x)","F"