1,1,381,0,2.960929," ","integrate((e*x+d)**4*(a+b*atanh(c*x)),x)","\begin{cases} a d^{4} x + 2 a d^{3} e x^{2} + 2 a d^{2} e^{2} x^{3} + a d e^{3} x^{4} + \frac{a e^{4} x^{5}}{5} + b d^{4} x \operatorname{atanh}{\left(c x \right)} + 2 b d^{3} e x^{2} \operatorname{atanh}{\left(c x \right)} + 2 b d^{2} e^{2} x^{3} \operatorname{atanh}{\left(c x \right)} + b d e^{3} x^{4} \operatorname{atanh}{\left(c x \right)} + \frac{b e^{4} x^{5} \operatorname{atanh}{\left(c x \right)}}{5} + \frac{b d^{4} \log{\left(x - \frac{1}{c} \right)}}{c} + \frac{b d^{4} \operatorname{atanh}{\left(c x \right)}}{c} + \frac{2 b d^{3} e x}{c} + \frac{b d^{2} e^{2} x^{2}}{c} + \frac{b d e^{3} x^{3}}{3 c} + \frac{b e^{4} x^{4}}{20 c} - \frac{2 b d^{3} e \operatorname{atanh}{\left(c x \right)}}{c^{2}} + \frac{2 b d^{2} e^{2} \log{\left(x - \frac{1}{c} \right)}}{c^{3}} + \frac{2 b d^{2} e^{2} \operatorname{atanh}{\left(c x \right)}}{c^{3}} + \frac{b d e^{3} x}{c^{3}} + \frac{b e^{4} x^{2}}{10 c^{3}} - \frac{b d e^{3} \operatorname{atanh}{\left(c x \right)}}{c^{4}} + \frac{b e^{4} \log{\left(x - \frac{1}{c} \right)}}{5 c^{5}} + \frac{b e^{4} \operatorname{atanh}{\left(c x \right)}}{5 c^{5}} & \text{for}\: c \neq 0 \\a \left(d^{4} x + 2 d^{3} e x^{2} + 2 d^{2} e^{2} x^{3} + d e^{3} x^{4} + \frac{e^{4} x^{5}}{5}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**4*x + 2*a*d**3*e*x**2 + 2*a*d**2*e**2*x**3 + a*d*e**3*x**4 + a*e**4*x**5/5 + b*d**4*x*atanh(c*x) + 2*b*d**3*e*x**2*atanh(c*x) + 2*b*d**2*e**2*x**3*atanh(c*x) + b*d*e**3*x**4*atanh(c*x) + b*e**4*x**5*atanh(c*x)/5 + b*d**4*log(x - 1/c)/c + b*d**4*atanh(c*x)/c + 2*b*d**3*e*x/c + b*d**2*e**2*x**2/c + b*d*e**3*x**3/(3*c) + b*e**4*x**4/(20*c) - 2*b*d**3*e*atanh(c*x)/c**2 + 2*b*d**2*e**2*log(x - 1/c)/c**3 + 2*b*d**2*e**2*atanh(c*x)/c**3 + b*d*e**3*x/c**3 + b*e**4*x**2/(10*c**3) - b*d*e**3*atanh(c*x)/c**4 + b*e**4*log(x - 1/c)/(5*c**5) + b*e**4*atanh(c*x)/(5*c**5), Ne(c, 0)), (a*(d**4*x + 2*d**3*e*x**2 + 2*d**2*e**2*x**3 + d*e**3*x**4 + e**4*x**5/5), True))","A",0
2,1,279,0,1.982017," ","integrate((e*x+d)**3*(a+b*atanh(c*x)),x)","\begin{cases} a d^{3} x + \frac{3 a d^{2} e x^{2}}{2} + a d e^{2} x^{3} + \frac{a e^{3} x^{4}}{4} + b d^{3} x \operatorname{atanh}{\left(c x \right)} + \frac{3 b d^{2} e x^{2} \operatorname{atanh}{\left(c x \right)}}{2} + b d e^{2} x^{3} \operatorname{atanh}{\left(c x \right)} + \frac{b e^{3} x^{4} \operatorname{atanh}{\left(c x \right)}}{4} + \frac{b d^{3} \log{\left(x - \frac{1}{c} \right)}}{c} + \frac{b d^{3} \operatorname{atanh}{\left(c x \right)}}{c} + \frac{3 b d^{2} e x}{2 c} + \frac{b d e^{2} x^{2}}{2 c} + \frac{b e^{3} x^{3}}{12 c} - \frac{3 b d^{2} e \operatorname{atanh}{\left(c x \right)}}{2 c^{2}} + \frac{b d e^{2} \log{\left(x - \frac{1}{c} \right)}}{c^{3}} + \frac{b d e^{2} \operatorname{atanh}{\left(c x \right)}}{c^{3}} + \frac{b e^{3} x}{4 c^{3}} - \frac{b e^{3} \operatorname{atanh}{\left(c x \right)}}{4 c^{4}} & \text{for}\: c \neq 0 \\a \left(d^{3} x + \frac{3 d^{2} e x^{2}}{2} + d e^{2} x^{3} + \frac{e^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*x + 3*a*d**2*e*x**2/2 + a*d*e**2*x**3 + a*e**3*x**4/4 + b*d**3*x*atanh(c*x) + 3*b*d**2*e*x**2*atanh(c*x)/2 + b*d*e**2*x**3*atanh(c*x) + b*e**3*x**4*atanh(c*x)/4 + b*d**3*log(x - 1/c)/c + b*d**3*atanh(c*x)/c + 3*b*d**2*e*x/(2*c) + b*d*e**2*x**2/(2*c) + b*e**3*x**3/(12*c) - 3*b*d**2*e*atanh(c*x)/(2*c**2) + b*d*e**2*log(x - 1/c)/c**3 + b*d*e**2*atanh(c*x)/c**3 + b*e**3*x/(4*c**3) - b*e**3*atanh(c*x)/(4*c**4), Ne(c, 0)), (a*(d**3*x + 3*d**2*e*x**2/2 + d*e**2*x**3 + e**3*x**4/4), True))","A",0
3,1,178,0,1.263706," ","integrate((e*x+d)**2*(a+b*atanh(c*x)),x)","\begin{cases} a d^{2} x + a d e x^{2} + \frac{a e^{2} x^{3}}{3} + b d^{2} x \operatorname{atanh}{\left(c x \right)} + b d e x^{2} \operatorname{atanh}{\left(c x \right)} + \frac{b e^{2} x^{3} \operatorname{atanh}{\left(c x \right)}}{3} + \frac{b d^{2} \log{\left(x - \frac{1}{c} \right)}}{c} + \frac{b d^{2} \operatorname{atanh}{\left(c x \right)}}{c} + \frac{b d e x}{c} + \frac{b e^{2} x^{2}}{6 c} - \frac{b d e \operatorname{atanh}{\left(c x \right)}}{c^{2}} + \frac{b e^{2} \log{\left(x - \frac{1}{c} \right)}}{3 c^{3}} + \frac{b e^{2} \operatorname{atanh}{\left(c x \right)}}{3 c^{3}} & \text{for}\: c \neq 0 \\a \left(d^{2} x + d e x^{2} + \frac{e^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*x + a*d*e*x**2 + a*e**2*x**3/3 + b*d**2*x*atanh(c*x) + b*d*e*x**2*atanh(c*x) + b*e**2*x**3*atanh(c*x)/3 + b*d**2*log(x - 1/c)/c + b*d**2*atanh(c*x)/c + b*d*e*x/c + b*e**2*x**2/(6*c) - b*d*e*atanh(c*x)/c**2 + b*e**2*log(x - 1/c)/(3*c**3) + b*e**2*atanh(c*x)/(3*c**3), Ne(c, 0)), (a*(d**2*x + d*e*x**2 + e**2*x**3/3), True))","A",0
4,1,92,0,0.673501," ","integrate((e*x+d)*(a+b*atanh(c*x)),x)","\begin{cases} a d x + \frac{a e x^{2}}{2} + b d x \operatorname{atanh}{\left(c x \right)} + \frac{b e x^{2} \operatorname{atanh}{\left(c x \right)}}{2} + \frac{b d \log{\left(x - \frac{1}{c} \right)}}{c} + \frac{b d \operatorname{atanh}{\left(c x \right)}}{c} + \frac{b e x}{2 c} - \frac{b e \operatorname{atanh}{\left(c x \right)}}{2 c^{2}} & \text{for}\: c \neq 0 \\a \left(d x + \frac{e x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x + a*e*x**2/2 + b*d*x*atanh(c*x) + b*e*x**2*atanh(c*x)/2 + b*d*log(x - 1/c)/c + b*d*atanh(c*x)/c + b*e*x/(2*c) - b*e*atanh(c*x)/(2*c**2), Ne(c, 0)), (a*(d*x + e*x**2/2), True))","A",0
5,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/(e*x+d),x)","\int \frac{a + b \operatorname{atanh}{\left(c x \right)}}{d + e x}\, dx"," ",0,"Integral((a + b*atanh(c*x))/(d + e*x), x)","F",0
6,1,690,0,3.617903," ","integrate((a+b*atanh(c*x))/(e*x+d)**2,x)","\begin{cases} \frac{a x + b x \operatorname{atanh}{\left(c x \right)} + \frac{b \log{\left(x - \frac{1}{c} \right)}}{c} + \frac{b \operatorname{atanh}{\left(c x \right)}}{c}}{d^{2}} & \text{for}\: e = 0 \\- \frac{a}{d e + e^{2} x} & \text{for}\: c = 0 \\- \frac{2 a d}{2 d^{2} e + 2 d e^{2} x} + \frac{b d \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{2 d^{2} e + 2 d e^{2} x} + \frac{b d}{2 d^{2} e + 2 d e^{2} x} - \frac{b e x \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{2 d^{2} e + 2 d e^{2} x} & \text{for}\: c = - \frac{e}{d} \\- \frac{2 a d}{2 d^{2} e + 2 d e^{2} x} - \frac{b d \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{2 d^{2} e + 2 d e^{2} x} - \frac{b d}{2 d^{2} e + 2 d e^{2} x} + \frac{b e x \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{2 d^{2} e + 2 d e^{2} x} & \text{for}\: c = \frac{e}{d} \\\tilde{\infty} \left(a x + b x \operatorname{atanh}{\left(c x \right)} + \frac{b \log{\left(x - \frac{1}{c} \right)}}{c} + \frac{b \operatorname{atanh}{\left(c x \right)}}{c}\right) & \text{for}\: d = - e x \\- \frac{a c^{2} d^{2}}{c^{2} d^{3} e + c^{2} d^{2} e^{2} x - d e^{3} - e^{4} x} + \frac{a e^{2}}{c^{2} d^{3} e + c^{2} d^{2} e^{2} x - d e^{3} - e^{4} x} + \frac{b c^{2} d e x \operatorname{atanh}{\left(c x \right)}}{c^{2} d^{3} e + c^{2} d^{2} e^{2} x - d e^{3} - e^{4} x} + \frac{b c d e \log{\left(x - \frac{1}{c} \right)}}{c^{2} d^{3} e + c^{2} d^{2} e^{2} x - d e^{3} - e^{4} x} - \frac{b c d e \log{\left(\frac{d}{e} + x \right)}}{c^{2} d^{3} e + c^{2} d^{2} e^{2} x - d e^{3} - e^{4} x} + \frac{b c d e \operatorname{atanh}{\left(c x \right)}}{c^{2} d^{3} e + c^{2} d^{2} e^{2} x - d e^{3} - e^{4} x} + \frac{b c e^{2} x \log{\left(x - \frac{1}{c} \right)}}{c^{2} d^{3} e + c^{2} d^{2} e^{2} x - d e^{3} - e^{4} x} - \frac{b c e^{2} x \log{\left(\frac{d}{e} + x \right)}}{c^{2} d^{3} e + c^{2} d^{2} e^{2} x - d e^{3} - e^{4} x} + \frac{b c e^{2} x \operatorname{atanh}{\left(c x \right)}}{c^{2} d^{3} e + c^{2} d^{2} e^{2} x - d e^{3} - e^{4} x} + \frac{b e^{2} \operatorname{atanh}{\left(c x \right)}}{c^{2} d^{3} e + c^{2} d^{2} e^{2} x - d e^{3} - e^{4} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a*x + b*x*atanh(c*x) + b*log(x - 1/c)/c + b*atanh(c*x)/c)/d**2, Eq(e, 0)), (-a/(d*e + e**2*x), Eq(c, 0)), (-2*a*d/(2*d**2*e + 2*d*e**2*x) + b*d*atanh(e*x/d)/(2*d**2*e + 2*d*e**2*x) + b*d/(2*d**2*e + 2*d*e**2*x) - b*e*x*atanh(e*x/d)/(2*d**2*e + 2*d*e**2*x), Eq(c, -e/d)), (-2*a*d/(2*d**2*e + 2*d*e**2*x) - b*d*atanh(e*x/d)/(2*d**2*e + 2*d*e**2*x) - b*d/(2*d**2*e + 2*d*e**2*x) + b*e*x*atanh(e*x/d)/(2*d**2*e + 2*d*e**2*x), Eq(c, e/d)), (zoo*(a*x + b*x*atanh(c*x) + b*log(x - 1/c)/c + b*atanh(c*x)/c), Eq(d, -e*x)), (-a*c**2*d**2/(c**2*d**3*e + c**2*d**2*e**2*x - d*e**3 - e**4*x) + a*e**2/(c**2*d**3*e + c**2*d**2*e**2*x - d*e**3 - e**4*x) + b*c**2*d*e*x*atanh(c*x)/(c**2*d**3*e + c**2*d**2*e**2*x - d*e**3 - e**4*x) + b*c*d*e*log(x - 1/c)/(c**2*d**3*e + c**2*d**2*e**2*x - d*e**3 - e**4*x) - b*c*d*e*log(d/e + x)/(c**2*d**3*e + c**2*d**2*e**2*x - d*e**3 - e**4*x) + b*c*d*e*atanh(c*x)/(c**2*d**3*e + c**2*d**2*e**2*x - d*e**3 - e**4*x) + b*c*e**2*x*log(x - 1/c)/(c**2*d**3*e + c**2*d**2*e**2*x - d*e**3 - e**4*x) - b*c*e**2*x*log(d/e + x)/(c**2*d**3*e + c**2*d**2*e**2*x - d*e**3 - e**4*x) + b*c*e**2*x*atanh(c*x)/(c**2*d**3*e + c**2*d**2*e**2*x - d*e**3 - e**4*x) + b*e**2*atanh(c*x)/(c**2*d**3*e + c**2*d**2*e**2*x - d*e**3 - e**4*x), True))","A",0
7,1,3216,0,7.125596," ","integrate((a+b*atanh(c*x))/(e*x+d)**3,x)","\begin{cases} \frac{a x}{d^{3}} & \text{for}\: c = 0 \wedge e = 0 \\- \frac{4 a d^{2}}{8 d^{4} e + 16 d^{3} e^{2} x + 8 d^{2} e^{3} x^{2}} + \frac{3 b d^{2} \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{8 d^{4} e + 16 d^{3} e^{2} x + 8 d^{2} e^{3} x^{2}} + \frac{2 b d^{2}}{8 d^{4} e + 16 d^{3} e^{2} x + 8 d^{2} e^{3} x^{2}} - \frac{2 b d e x \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{8 d^{4} e + 16 d^{3} e^{2} x + 8 d^{2} e^{3} x^{2}} + \frac{b d e x}{8 d^{4} e + 16 d^{3} e^{2} x + 8 d^{2} e^{3} x^{2}} - \frac{b e^{2} x^{2} \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{8 d^{4} e + 16 d^{3} e^{2} x + 8 d^{2} e^{3} x^{2}} & \text{for}\: c = - \frac{e}{d} \\- \frac{4 a d^{2}}{8 d^{4} e + 16 d^{3} e^{2} x + 8 d^{2} e^{3} x^{2}} - \frac{3 b d^{2} \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{8 d^{4} e + 16 d^{3} e^{2} x + 8 d^{2} e^{3} x^{2}} - \frac{2 b d^{2}}{8 d^{4} e + 16 d^{3} e^{2} x + 8 d^{2} e^{3} x^{2}} + \frac{2 b d e x \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{8 d^{4} e + 16 d^{3} e^{2} x + 8 d^{2} e^{3} x^{2}} - \frac{b d e x}{8 d^{4} e + 16 d^{3} e^{2} x + 8 d^{2} e^{3} x^{2}} + \frac{b e^{2} x^{2} \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{8 d^{4} e + 16 d^{3} e^{2} x + 8 d^{2} e^{3} x^{2}} & \text{for}\: c = \frac{e}{d} \\\frac{a x + b x \operatorname{atanh}{\left(c x \right)} + \frac{b \log{\left(x - \frac{1}{c} \right)}}{c} + \frac{b \operatorname{atanh}{\left(c x \right)}}{c}}{d^{3}} & \text{for}\: e = 0 \\- \frac{a}{2 d^{2} e + 4 d e^{2} x + 2 e^{3} x^{2}} & \text{for}\: c = 0 \\- \frac{a c^{4} d^{4}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{2 a c^{2} d^{2} e^{2}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{a e^{4}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{2 b c^{4} d^{3} e x \operatorname{atanh}{\left(c x \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{b c^{4} d^{2} e^{2} x^{2} \operatorname{atanh}{\left(c x \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{2 b c^{3} d^{3} e \log{\left(x - \frac{1}{c} \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{2 b c^{3} d^{3} e \log{\left(\frac{d}{e} + x \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{2 b c^{3} d^{3} e \operatorname{atanh}{\left(c x \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{b c^{3} d^{3} e}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 b c^{3} d^{2} e^{2} x \log{\left(x - \frac{1}{c} \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{4 b c^{3} d^{2} e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 b c^{3} d^{2} e^{2} x \operatorname{atanh}{\left(c x \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{b c^{3} d^{2} e^{2} x}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{2 b c^{3} d e^{3} x^{2} \log{\left(x - \frac{1}{c} \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{2 b c^{3} d e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{2 b c^{3} d e^{3} x^{2} \operatorname{atanh}{\left(c x \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{3 b c^{2} d^{2} e^{2} \operatorname{atanh}{\left(c x \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{2 b c^{2} d e^{3} x \operatorname{atanh}{\left(c x \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{b c^{2} e^{4} x^{2} \operatorname{atanh}{\left(c x \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{b c d e^{3}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{b c e^{4} x}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{b e^{4} \operatorname{atanh}{\left(c x \right)}}{2 c^{4} d^{6} e + 4 c^{4} d^{5} e^{2} x + 2 c^{4} d^{4} e^{3} x^{2} - 4 c^{2} d^{4} e^{3} - 8 c^{2} d^{3} e^{4} x - 4 c^{2} d^{2} e^{5} x^{2} + 2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x/d**3, Eq(c, 0) & Eq(e, 0)), (-4*a*d**2/(8*d**4*e + 16*d**3*e**2*x + 8*d**2*e**3*x**2) + 3*b*d**2*atanh(e*x/d)/(8*d**4*e + 16*d**3*e**2*x + 8*d**2*e**3*x**2) + 2*b*d**2/(8*d**4*e + 16*d**3*e**2*x + 8*d**2*e**3*x**2) - 2*b*d*e*x*atanh(e*x/d)/(8*d**4*e + 16*d**3*e**2*x + 8*d**2*e**3*x**2) + b*d*e*x/(8*d**4*e + 16*d**3*e**2*x + 8*d**2*e**3*x**2) - b*e**2*x**2*atanh(e*x/d)/(8*d**4*e + 16*d**3*e**2*x + 8*d**2*e**3*x**2), Eq(c, -e/d)), (-4*a*d**2/(8*d**4*e + 16*d**3*e**2*x + 8*d**2*e**3*x**2) - 3*b*d**2*atanh(e*x/d)/(8*d**4*e + 16*d**3*e**2*x + 8*d**2*e**3*x**2) - 2*b*d**2/(8*d**4*e + 16*d**3*e**2*x + 8*d**2*e**3*x**2) + 2*b*d*e*x*atanh(e*x/d)/(8*d**4*e + 16*d**3*e**2*x + 8*d**2*e**3*x**2) - b*d*e*x/(8*d**4*e + 16*d**3*e**2*x + 8*d**2*e**3*x**2) + b*e**2*x**2*atanh(e*x/d)/(8*d**4*e + 16*d**3*e**2*x + 8*d**2*e**3*x**2), Eq(c, e/d)), ((a*x + b*x*atanh(c*x) + b*log(x - 1/c)/c + b*atanh(c*x)/c)/d**3, Eq(e, 0)), (-a/(2*d**2*e + 4*d*e**2*x + 2*e**3*x**2), Eq(c, 0)), (-a*c**4*d**4/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 2*a*c**2*d**2*e**2/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - a*e**4/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 2*b*c**4*d**3*e*x*atanh(c*x)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + b*c**4*d**2*e**2*x**2*atanh(c*x)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 2*b*c**3*d**3*e*log(x - 1/c)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 2*b*c**3*d**3*e*log(d/e + x)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 2*b*c**3*d**3*e*atanh(c*x)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + b*c**3*d**3*e/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*b*c**3*d**2*e**2*x*log(x - 1/c)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 4*b*c**3*d**2*e**2*x*log(d/e + x)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*b*c**3*d**2*e**2*x*atanh(c*x)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + b*c**3*d**2*e**2*x/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 2*b*c**3*d*e**3*x**2*log(x - 1/c)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 2*b*c**3*d*e**3*x**2*log(d/e + x)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 2*b*c**3*d*e**3*x**2*atanh(c*x)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 3*b*c**2*d**2*e**2*atanh(c*x)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 2*b*c**2*d*e**3*x*atanh(c*x)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + b*c**2*e**4*x**2*atanh(c*x)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - b*c*d*e**3/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - b*c*e**4*x/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - b*e**4*atanh(c*x)/(2*c**4*d**6*e + 4*c**4*d**5*e**2*x + 2*c**4*d**4*e**3*x**2 - 4*c**2*d**4*e**3 - 8*c**2*d**3*e**4*x - 4*c**2*d**2*e**5*x**2 + 2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2), True))","A",0
8,1,10946,0,12.913545," ","integrate((a+b*atanh(c*x))/(e*x+d)**4,x)","\begin{cases} \frac{a x}{d^{4}} & \text{for}\: c = 0 \wedge e = 0 \\- \frac{24 a d^{3}}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} + \frac{21 b d^{3} \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} + \frac{10 b d^{3}}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} - \frac{9 b d^{2} e x \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} + \frac{9 b d^{2} e x}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} - \frac{9 b d e^{2} x^{2} \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} + \frac{3 b d e^{2} x^{2}}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} - \frac{3 b e^{3} x^{3} \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} & \text{for}\: c = - \frac{e}{d} \\- \frac{24 a d^{3}}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} - \frac{21 b d^{3} \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} - \frac{10 b d^{3}}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} + \frac{9 b d^{2} e x \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} - \frac{9 b d^{2} e x}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} + \frac{9 b d e^{2} x^{2} \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} - \frac{3 b d e^{2} x^{2}}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} + \frac{3 b e^{3} x^{3} \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{72 d^{6} e + 216 d^{5} e^{2} x + 216 d^{4} e^{3} x^{2} + 72 d^{3} e^{4} x^{3}} & \text{for}\: c = \frac{e}{d} \\\frac{a x + b x \operatorname{atanh}{\left(c x \right)} + \frac{b \log{\left(x - \frac{1}{c} \right)}}{c} + \frac{b \operatorname{atanh}{\left(c x \right)}}{c}}{d^{4}} & \text{for}\: e = 0 \\- \frac{a}{3 d^{3} e + 9 d^{2} e^{2} x + 9 d e^{3} x^{2} + 3 e^{4} x^{3}} & \text{for}\: c = 0 \\- \frac{2 a c^{6} d^{6}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{6 a c^{4} d^{4} e^{2}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} - \frac{6 a c^{2} d^{2} e^{4}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{2 a e^{6}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{6 b c^{6} d^{5} e x \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{6 b c^{6} d^{4} e^{2} x^{2} \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{2 b c^{6} d^{3} e^{3} x^{3} \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{6 b c^{5} d^{5} e \log{\left(x - \frac{1}{c} \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} - \frac{6 b c^{5} d^{5} e \log{\left(\frac{d}{e} + x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{6 b c^{5} d^{5} e \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{5 b c^{5} d^{5} e}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{18 b c^{5} d^{4} e^{2} x \log{\left(x - \frac{1}{c} \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} - \frac{18 b c^{5} d^{4} e^{2} x \log{\left(\frac{d}{e} + x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{18 b c^{5} d^{4} e^{2} x \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{9 b c^{5} d^{4} e^{2} x}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{18 b c^{5} d^{3} e^{3} x^{2} \log{\left(x - \frac{1}{c} \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} - \frac{18 b c^{5} d^{3} e^{3} x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{18 b c^{5} d^{3} e^{3} x^{2} \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{4 b c^{5} d^{3} e^{3} x^{2}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{6 b c^{5} d^{2} e^{4} x^{3} \log{\left(x - \frac{1}{c} \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} - \frac{6 b c^{5} d^{2} e^{4} x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{6 b c^{5} d^{2} e^{4} x^{3} \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{12 b c^{4} d^{4} e^{2} \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{18 b c^{4} d^{3} e^{3} x \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{18 b c^{4} d^{2} e^{4} x^{2} \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{6 b c^{4} d e^{5} x^{3} \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{2 b c^{3} d^{3} e^{3} \log{\left(x - \frac{1}{c} \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} - \frac{2 b c^{3} d^{3} e^{3} \log{\left(\frac{d}{e} + x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{2 b c^{3} d^{3} e^{3} \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} - \frac{6 b c^{3} d^{3} e^{3}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{6 b c^{3} d^{2} e^{4} x \log{\left(x - \frac{1}{c} \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} - \frac{6 b c^{3} d^{2} e^{4} x \log{\left(\frac{d}{e} + x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{6 b c^{3} d^{2} e^{4} x \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} - \frac{10 b c^{3} d^{2} e^{4} x}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{6 b c^{3} d e^{5} x^{2} \log{\left(x - \frac{1}{c} \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} - \frac{6 b c^{3} d e^{5} x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{6 b c^{3} d e^{5} x^{2} \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} - \frac{4 b c^{3} d e^{5} x^{2}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{2 b c^{3} e^{6} x^{3} \log{\left(x - \frac{1}{c} \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} - \frac{2 b c^{3} e^{6} x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{2 b c^{3} e^{6} x^{3} \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} - \frac{6 b c^{2} d^{2} e^{4} \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{b c d e^{5}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{b c e^{6} x}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} + \frac{2 b e^{6} \operatorname{atanh}{\left(c x \right)}}{6 c^{6} d^{9} e + 18 c^{6} d^{8} e^{2} x + 18 c^{6} d^{7} e^{3} x^{2} + 6 c^{6} d^{6} e^{4} x^{3} - 18 c^{4} d^{7} e^{3} - 54 c^{4} d^{6} e^{4} x - 54 c^{4} d^{5} e^{5} x^{2} - 18 c^{4} d^{4} e^{6} x^{3} + 18 c^{2} d^{5} e^{5} + 54 c^{2} d^{4} e^{6} x + 54 c^{2} d^{3} e^{7} x^{2} + 18 c^{2} d^{2} e^{8} x^{3} - 6 d^{3} e^{7} - 18 d^{2} e^{8} x - 18 d e^{9} x^{2} - 6 e^{10} x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x/d**4, Eq(c, 0) & Eq(e, 0)), (-24*a*d**3/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3) + 21*b*d**3*atanh(e*x/d)/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3) + 10*b*d**3/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3) - 9*b*d**2*e*x*atanh(e*x/d)/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3) + 9*b*d**2*e*x/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3) - 9*b*d*e**2*x**2*atanh(e*x/d)/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3) + 3*b*d*e**2*x**2/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3) - 3*b*e**3*x**3*atanh(e*x/d)/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3), Eq(c, -e/d)), (-24*a*d**3/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3) - 21*b*d**3*atanh(e*x/d)/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3) - 10*b*d**3/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3) + 9*b*d**2*e*x*atanh(e*x/d)/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3) - 9*b*d**2*e*x/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3) + 9*b*d*e**2*x**2*atanh(e*x/d)/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3) - 3*b*d*e**2*x**2/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3) + 3*b*e**3*x**3*atanh(e*x/d)/(72*d**6*e + 216*d**5*e**2*x + 216*d**4*e**3*x**2 + 72*d**3*e**4*x**3), Eq(c, e/d)), ((a*x + b*x*atanh(c*x) + b*log(x - 1/c)/c + b*atanh(c*x)/c)/d**4, Eq(e, 0)), (-a/(3*d**3*e + 9*d**2*e**2*x + 9*d*e**3*x**2 + 3*e**4*x**3), Eq(c, 0)), (-2*a*c**6*d**6/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 6*a*c**4*d**4*e**2/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) - 6*a*c**2*d**2*e**4/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 2*a*e**6/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 6*b*c**6*d**5*e*x*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 6*b*c**6*d**4*e**2*x**2*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 2*b*c**6*d**3*e**3*x**3*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 6*b*c**5*d**5*e*log(x - 1/c)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) - 6*b*c**5*d**5*e*log(d/e + x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 6*b*c**5*d**5*e*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 5*b*c**5*d**5*e/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 18*b*c**5*d**4*e**2*x*log(x - 1/c)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) - 18*b*c**5*d**4*e**2*x*log(d/e + x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 18*b*c**5*d**4*e**2*x*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 9*b*c**5*d**4*e**2*x/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 18*b*c**5*d**3*e**3*x**2*log(x - 1/c)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) - 18*b*c**5*d**3*e**3*x**2*log(d/e + x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 18*b*c**5*d**3*e**3*x**2*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 4*b*c**5*d**3*e**3*x**2/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 6*b*c**5*d**2*e**4*x**3*log(x - 1/c)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) - 6*b*c**5*d**2*e**4*x**3*log(d/e + x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 6*b*c**5*d**2*e**4*x**3*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 12*b*c**4*d**4*e**2*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 18*b*c**4*d**3*e**3*x*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 18*b*c**4*d**2*e**4*x**2*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 6*b*c**4*d*e**5*x**3*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 2*b*c**3*d**3*e**3*log(x - 1/c)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) - 2*b*c**3*d**3*e**3*log(d/e + x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 2*b*c**3*d**3*e**3*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) - 6*b*c**3*d**3*e**3/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 6*b*c**3*d**2*e**4*x*log(x - 1/c)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) - 6*b*c**3*d**2*e**4*x*log(d/e + x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 6*b*c**3*d**2*e**4*x*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) - 10*b*c**3*d**2*e**4*x/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 6*b*c**3*d*e**5*x**2*log(x - 1/c)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) - 6*b*c**3*d*e**5*x**2*log(d/e + x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 6*b*c**3*d*e**5*x**2*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) - 4*b*c**3*d*e**5*x**2/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 2*b*c**3*e**6*x**3*log(x - 1/c)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) - 2*b*c**3*e**6*x**3*log(d/e + x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 2*b*c**3*e**6*x**3*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) - 6*b*c**2*d**2*e**4*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + b*c*d*e**5/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + b*c*e**6*x/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3) + 2*b*e**6*atanh(c*x)/(6*c**6*d**9*e + 18*c**6*d**8*e**2*x + 18*c**6*d**7*e**3*x**2 + 6*c**6*d**6*e**4*x**3 - 18*c**4*d**7*e**3 - 54*c**4*d**6*e**4*x - 54*c**4*d**5*e**5*x**2 - 18*c**4*d**4*e**6*x**3 + 18*c**2*d**5*e**5 + 54*c**2*d**4*e**6*x + 54*c**2*d**3*e**7*x**2 + 18*c**2*d**2*e**8*x**3 - 6*d**3*e**7 - 18*d**2*e**8*x - 18*d*e**9*x**2 - 6*e**10*x**3), True))","A",0
9,0,0,0,0.000000," ","integrate((e*x+d)**3*(a+b*atanh(c*x))**2,x)","\int \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2} \left(d + e x\right)^{3}\, dx"," ",0,"Integral((a + b*atanh(c*x))**2*(d + e*x)**3, x)","F",0
10,0,0,0,0.000000," ","integrate((e*x+d)**2*(a+b*atanh(c*x))**2,x)","\int \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2} \left(d + e x\right)^{2}\, dx"," ",0,"Integral((a + b*atanh(c*x))**2*(d + e*x)**2, x)","F",0
11,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*atanh(c*x))**2,x)","\int \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2} \left(d + e x\right)\, dx"," ",0,"Integral((a + b*atanh(c*x))**2*(d + e*x), x)","F",0
12,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/(e*x+d),x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral((a + b*atanh(c*x))**2/(d + e*x), x)","F",0
13,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/(e*x+d)**2,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*atanh(c*x))**2/(d + e*x)**2, x)","F",0
14,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/(e*x+d)**3,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*atanh(c*x))**2/(d + e*x)**3, x)","F",0
15,0,0,0,0.000000," ","integrate((e*x+d)**3*(a+b*atanh(c*x))**3,x)","\int \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3} \left(d + e x\right)^{3}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3*(d + e*x)**3, x)","F",0
16,0,0,0,0.000000," ","integrate((e*x+d)**2*(a+b*atanh(c*x))**3,x)","\int \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3} \left(d + e x\right)^{2}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3*(d + e*x)**2, x)","F",0
17,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*atanh(c*x))**3,x)","\int \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3} \left(d + e x\right)\, dx"," ",0,"Integral((a + b*atanh(c*x))**3*(d + e*x), x)","F",0
18,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**3/(e*x+d),x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}}{d + e x}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3/(d + e*x), x)","F",0
19,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**3/(e*x+d)**2,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3/(d + e*x)**2, x)","F",0
20,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**3/(e*x+d)**3,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3/(d + e*x)**3, x)","F",0
21,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/(2*c*x+1),x)","\int \frac{a + b \operatorname{atanh}{\left(c x \right)}}{2 c x + 1}\, dx"," ",0,"Integral((a + b*atanh(c*x))/(2*c*x + 1), x)","F",0
22,0,0,0,0.000000," ","integrate(atanh(x)/(1-x*2**(1/2)),x)","- \int \frac{\operatorname{atanh}{\left(x \right)}}{\sqrt{2} x - 1}\, dx"," ",0,"-Integral(atanh(x)/(sqrt(2)*x - 1), x)","F",0
23,1,622,0,18.879573," ","integrate((e*x+d)**3*(a+b*atanh(c*x**2)),x)","\begin{cases} a d^{3} x + \frac{3 a d^{2} e x^{2}}{2} + a d e^{2} x^{3} + \frac{a e^{3} x^{4}}{4} + \frac{b c d^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{4} - \frac{i b c d^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{4} + b d^{3} x \operatorname{atanh}{\left(c x^{2} \right)} - \frac{b d^{3} \sqrt{\frac{1}{c}} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{2} - \frac{i b d^{3} \sqrt{\frac{1}{c}} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{2} - \frac{3 b d^{3} \sqrt{\frac{1}{c}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{4} + \frac{3 i b d^{3} \sqrt{\frac{1}{c}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{4} + b d^{3} \sqrt{\frac{1}{c}} \log{\left(x - \sqrt{\frac{1}{c}} \right)} + b d^{3} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)} + \frac{3 b d^{2} e x^{2} \operatorname{atanh}{\left(c x^{2} \right)}}{2} + b d e^{2} x^{3} \operatorname{atanh}{\left(c x^{2} \right)} + \frac{b e^{3} x^{4} \operatorname{atanh}{\left(c x^{2} \right)}}{4} + \frac{3 b d^{2} e \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{2 c} + \frac{3 b d^{2} e \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{2 c} - \frac{3 b d^{2} e \operatorname{atanh}{\left(c x^{2} \right)}}{2 c} + \frac{2 b d e^{2} x}{c} - \frac{b d e^{2} \sqrt{\frac{1}{c}} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{2 c} + \frac{i b d e^{2} \sqrt{\frac{1}{c}} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{2 c} - \frac{b d e^{2} \sqrt{\frac{1}{c}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{2 c} - \frac{i b d e^{2} \sqrt{\frac{1}{c}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{2 c} + \frac{b d e^{2} \sqrt{\frac{1}{c}} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{c} + \frac{b d e^{2} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{c} + \frac{b e^{3} x^{2}}{4 c} - \frac{b e^{3} \operatorname{atanh}{\left(c x^{2} \right)}}{4 c^{2}} & \text{for}\: c \neq 0 \\a \left(d^{3} x + \frac{3 d^{2} e x^{2}}{2} + d e^{2} x^{3} + \frac{e^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*x + 3*a*d**2*e*x**2/2 + a*d*e**2*x**3 + a*e**3*x**4/4 + b*c*d**3*(1/c)**(3/2)*log(x + I*sqrt(1/c))/4 - I*b*c*d**3*(1/c)**(3/2)*log(x + I*sqrt(1/c))/4 + b*d**3*x*atanh(c*x**2) - b*d**3*sqrt(1/c)*log(x - I*sqrt(1/c))/2 - I*b*d**3*sqrt(1/c)*log(x - I*sqrt(1/c))/2 - 3*b*d**3*sqrt(1/c)*log(x + I*sqrt(1/c))/4 + 3*I*b*d**3*sqrt(1/c)*log(x + I*sqrt(1/c))/4 + b*d**3*sqrt(1/c)*log(x - sqrt(1/c)) + b*d**3*sqrt(1/c)*atanh(c*x**2) + 3*b*d**2*e*x**2*atanh(c*x**2)/2 + b*d*e**2*x**3*atanh(c*x**2) + b*e**3*x**4*atanh(c*x**2)/4 + 3*b*d**2*e*log(x - I*sqrt(1/c))/(2*c) + 3*b*d**2*e*log(x + I*sqrt(1/c))/(2*c) - 3*b*d**2*e*atanh(c*x**2)/(2*c) + 2*b*d*e**2*x/c - b*d*e**2*sqrt(1/c)*log(x - I*sqrt(1/c))/(2*c) + I*b*d*e**2*sqrt(1/c)*log(x - I*sqrt(1/c))/(2*c) - b*d*e**2*sqrt(1/c)*log(x + I*sqrt(1/c))/(2*c) - I*b*d*e**2*sqrt(1/c)*log(x + I*sqrt(1/c))/(2*c) + b*d*e**2*sqrt(1/c)*log(x - sqrt(1/c))/c + b*d*e**2*sqrt(1/c)*atanh(c*x**2)/c + b*e**3*x**2/(4*c) - b*e**3*atanh(c*x**2)/(4*c**2), Ne(c, 0)), (a*(d**3*x + 3*d**2*e*x**2/2 + d*e**2*x**3 + e**3*x**4/4), True))","A",0
24,1,2907,0,15.808406," ","integrate((e*x+d)**2*(a+b*atanh(c*x**2)),x)","\begin{cases} \frac{12 a c^{2} d^{2} x \sqrt{\frac{1}{c}}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{12 i a c^{2} d^{2} x \sqrt{\frac{1}{c}}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{12 a c^{2} d e x^{2} \sqrt{\frac{1}{c}}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{12 i a c^{2} d e x^{2} \sqrt{\frac{1}{c}}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{4 a c^{2} e^{2} x^{3} \sqrt{\frac{1}{c}}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{4 i a c^{2} e^{2} x^{3} \sqrt{\frac{1}{c}}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{6 i b c^{3} d^{2} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{- 12 c^{5} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{5} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{4} \sqrt{\frac{1}{c}} + 24 i c^{4} \sqrt{\frac{1}{c}}} - \frac{6 i b c^{3} d^{2} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{- 12 c^{5} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{5} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{4} \sqrt{\frac{1}{c}} + 24 i c^{4} \sqrt{\frac{1}{c}}} + \frac{12 b c^{2} d^{2} x \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{12 i b c^{2} d^{2} x \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} - \frac{18 i b c^{2} d^{2} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{- 12 c^{4} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{4} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{3} \sqrt{\frac{1}{c}} + 24 i c^{3} \sqrt{\frac{1}{c}}} + \frac{18 i b c^{2} d^{2} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{- 12 c^{4} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{4} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{3} \sqrt{\frac{1}{c}} + 24 i c^{3} \sqrt{\frac{1}{c}}} + \frac{12 i b c^{2} d^{2} \operatorname{atanh}{\left(c x^{2} \right)}}{- 12 c^{4} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{4} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{3} \sqrt{\frac{1}{c}} + 24 i c^{3} \sqrt{\frac{1}{c}}} + \frac{12 b c^{2} d e x^{2} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{12 i b c^{2} d e x^{2} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} - \frac{3 b c^{2} d e \left(\frac{1}{c}\right)^{\frac{3}{2}} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} - \frac{3 i b c^{2} d e \left(\frac{1}{c}\right)^{\frac{3}{2}} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} - \frac{12 b c^{2} d e \left(\frac{1}{c}\right)^{\frac{3}{2}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} - \frac{12 i b c^{2} d e \left(\frac{1}{c}\right)^{\frac{3}{2}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{4 b c^{2} e^{2} x^{3} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{4 i b c^{2} e^{2} x^{3} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} - \frac{2 i b c^{2} e^{2} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{- 12 c^{5} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{5} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{4} \sqrt{\frac{1}{c}} + 24 i c^{4} \sqrt{\frac{1}{c}}} - \frac{12 b c d^{2} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{12 b c d^{2} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{12 b c d^{2} \operatorname{atanh}{\left(c x^{2} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{15 b c d e \sqrt{\frac{1}{c}} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{15 i b c d e \sqrt{\frac{1}{c}} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{24 b c d e \sqrt{\frac{1}{c}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{24 i b c d e \sqrt{\frac{1}{c}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} - \frac{12 b c d e \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} - \frac{12 i b c d e \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{8 b c e^{2} x \sqrt{\frac{1}{c}}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{8 i b c e^{2} x \sqrt{\frac{1}{c}}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} - \frac{4 i b c e^{2} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{- 12 c^{4} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{4} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{3} \sqrt{\frac{1}{c}} + 24 i c^{3} \sqrt{\frac{1}{c}}} + \frac{6 i b c e^{2} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{- 12 c^{4} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{4} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{3} \sqrt{\frac{1}{c}} + 24 i c^{3} \sqrt{\frac{1}{c}}} + \frac{4 i b c e^{2} \operatorname{atanh}{\left(c x^{2} \right)}}{- 12 c^{4} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{4} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{3} \sqrt{\frac{1}{c}} + 24 i c^{3} \sqrt{\frac{1}{c}}} - \frac{4 b e^{2} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{4 b e^{2} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} + \frac{4 b e^{2} \operatorname{atanh}{\left(c x^{2} \right)}}{- 12 c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} - 12 i c^{3} \left(\frac{1}{c}\right)^{\frac{3}{2}} + 24 c^{2} \sqrt{\frac{1}{c}} + 24 i c^{2} \sqrt{\frac{1}{c}}} & \text{for}\: c \neq 0 \\a \left(d^{2} x + d e x^{2} + \frac{e^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((12*a*c**2*d**2*x*sqrt(1/c)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 12*I*a*c**2*d**2*x*sqrt(1/c)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 12*a*c**2*d*e*x**2*sqrt(1/c)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 12*I*a*c**2*d*e*x**2*sqrt(1/c)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 4*a*c**2*e**2*x**3*sqrt(1/c)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 4*I*a*c**2*e**2*x**3*sqrt(1/c)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 6*I*b*c**3*d**2*log(x - I*sqrt(1/c))/(-12*c**5*(1/c)**(3/2) - 12*I*c**5*(1/c)**(3/2) + 24*c**4*sqrt(1/c) + 24*I*c**4*sqrt(1/c)) - 6*I*b*c**3*d**2*log(x - sqrt(1/c))/(-12*c**5*(1/c)**(3/2) - 12*I*c**5*(1/c)**(3/2) + 24*c**4*sqrt(1/c) + 24*I*c**4*sqrt(1/c)) + 12*b*c**2*d**2*x*sqrt(1/c)*atanh(c*x**2)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 12*I*b*c**2*d**2*x*sqrt(1/c)*atanh(c*x**2)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) - 18*I*b*c**2*d**2*log(x - I*sqrt(1/c))/(-12*c**4*(1/c)**(3/2) - 12*I*c**4*(1/c)**(3/2) + 24*c**3*sqrt(1/c) + 24*I*c**3*sqrt(1/c)) + 18*I*b*c**2*d**2*log(x - sqrt(1/c))/(-12*c**4*(1/c)**(3/2) - 12*I*c**4*(1/c)**(3/2) + 24*c**3*sqrt(1/c) + 24*I*c**3*sqrt(1/c)) + 12*I*b*c**2*d**2*atanh(c*x**2)/(-12*c**4*(1/c)**(3/2) - 12*I*c**4*(1/c)**(3/2) + 24*c**3*sqrt(1/c) + 24*I*c**3*sqrt(1/c)) + 12*b*c**2*d*e*x**2*sqrt(1/c)*atanh(c*x**2)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 12*I*b*c**2*d*e*x**2*sqrt(1/c)*atanh(c*x**2)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) - 3*b*c**2*d*e*(1/c)**(3/2)*log(x - I*sqrt(1/c))/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) - 3*I*b*c**2*d*e*(1/c)**(3/2)*log(x - I*sqrt(1/c))/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) - 12*b*c**2*d*e*(1/c)**(3/2)*log(x + I*sqrt(1/c))/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) - 12*I*b*c**2*d*e*(1/c)**(3/2)*log(x + I*sqrt(1/c))/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 4*b*c**2*e**2*x**3*sqrt(1/c)*atanh(c*x**2)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 4*I*b*c**2*e**2*x**3*sqrt(1/c)*atanh(c*x**2)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) - 2*I*b*c**2*e**2*log(x - sqrt(1/c))/(-12*c**5*(1/c)**(3/2) - 12*I*c**5*(1/c)**(3/2) + 24*c**4*sqrt(1/c) + 24*I*c**4*sqrt(1/c)) - 12*b*c*d**2*log(x + I*sqrt(1/c))/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 12*b*c*d**2*log(x - sqrt(1/c))/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 12*b*c*d**2*atanh(c*x**2)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 15*b*c*d*e*sqrt(1/c)*log(x - I*sqrt(1/c))/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 15*I*b*c*d*e*sqrt(1/c)*log(x - I*sqrt(1/c))/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 24*b*c*d*e*sqrt(1/c)*log(x + I*sqrt(1/c))/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 24*I*b*c*d*e*sqrt(1/c)*log(x + I*sqrt(1/c))/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) - 12*b*c*d*e*sqrt(1/c)*atanh(c*x**2)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) - 12*I*b*c*d*e*sqrt(1/c)*atanh(c*x**2)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 8*b*c*e**2*x*sqrt(1/c)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 8*I*b*c*e**2*x*sqrt(1/c)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) - 4*I*b*c*e**2*log(x + I*sqrt(1/c))/(-12*c**4*(1/c)**(3/2) - 12*I*c**4*(1/c)**(3/2) + 24*c**3*sqrt(1/c) + 24*I*c**3*sqrt(1/c)) + 6*I*b*c*e**2*log(x - sqrt(1/c))/(-12*c**4*(1/c)**(3/2) - 12*I*c**4*(1/c)**(3/2) + 24*c**3*sqrt(1/c) + 24*I*c**3*sqrt(1/c)) + 4*I*b*c*e**2*atanh(c*x**2)/(-12*c**4*(1/c)**(3/2) - 12*I*c**4*(1/c)**(3/2) + 24*c**3*sqrt(1/c) + 24*I*c**3*sqrt(1/c)) - 4*b*e**2*log(x - I*sqrt(1/c))/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 4*b*e**2*log(x - sqrt(1/c))/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)) + 4*b*e**2*atanh(c*x**2)/(-12*c**3*(1/c)**(3/2) - 12*I*c**3*(1/c)**(3/2) + 24*c**2*sqrt(1/c) + 24*I*c**2*sqrt(1/c)), Ne(c, 0)), (a*(d**2*x + d*e*x**2 + e**2*x**3/3), True))","A",0
25,1,294,0,10.478337," ","integrate((e*x+d)*(a+b*atanh(c*x**2)),x)","\begin{cases} a d x + \frac{a e x^{2}}{2} + \frac{b c d \left(\frac{1}{c}\right)^{\frac{3}{2}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{4} - \frac{i b c d \left(\frac{1}{c}\right)^{\frac{3}{2}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{4} + b d x \operatorname{atanh}{\left(c x^{2} \right)} - \frac{b d \sqrt{\frac{1}{c}} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{2} - \frac{i b d \sqrt{\frac{1}{c}} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{2} - \frac{3 b d \sqrt{\frac{1}{c}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{4} + \frac{3 i b d \sqrt{\frac{1}{c}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{4} + b d \sqrt{\frac{1}{c}} \log{\left(x - \sqrt{\frac{1}{c}} \right)} + b d \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)} + \frac{b e x^{2} \operatorname{atanh}{\left(c x^{2} \right)}}{2} + \frac{b e \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{2 c} + \frac{b e \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{2 c} - \frac{b e \operatorname{atanh}{\left(c x^{2} \right)}}{2 c} & \text{for}\: c \neq 0 \\a \left(d x + \frac{e x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x + a*e*x**2/2 + b*c*d*(1/c)**(3/2)*log(x + I*sqrt(1/c))/4 - I*b*c*d*(1/c)**(3/2)*log(x + I*sqrt(1/c))/4 + b*d*x*atanh(c*x**2) - b*d*sqrt(1/c)*log(x - I*sqrt(1/c))/2 - I*b*d*sqrt(1/c)*log(x - I*sqrt(1/c))/2 - 3*b*d*sqrt(1/c)*log(x + I*sqrt(1/c))/4 + 3*I*b*d*sqrt(1/c)*log(x + I*sqrt(1/c))/4 + b*d*sqrt(1/c)*log(x - sqrt(1/c)) + b*d*sqrt(1/c)*atanh(c*x**2) + b*e*x**2*atanh(c*x**2)/2 + b*e*log(x - I*sqrt(1/c))/(2*c) + b*e*log(x + I*sqrt(1/c))/(2*c) - b*e*atanh(c*x**2)/(2*c), Ne(c, 0)), (a*(d*x + e*x**2/2), True))","A",0
26,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
29,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*atanh(c*x**2))**2,x)","\int \left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2} \left(d + e x\right)\, dx"," ",0,"Integral((a + b*atanh(c*x**2))**2*(d + e*x), x)","F",0
30,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))**2/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))**2/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,-1,0,0,0.000000," ","integrate((e*x+d)**2*(a+b*atanh(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,-1,0,0,0.000000," ","integrate((e*x+d)*(a+b*atanh(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
35,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
36,0,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x**(1/2)))/(-c**2*x+1),x)","- \int \frac{a x^{3}}{c^{2} x - 1}\, dx - \int \frac{b x^{3} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x - 1}\, dx"," ",0,"-Integral(a*x**3/(c**2*x - 1), x) - Integral(b*x**3*atanh(c*sqrt(x))/(c**2*x - 1), x)","F",0
37,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x**(1/2)))/(-c**2*x+1),x)","- \int \frac{a x^{2}}{c^{2} x - 1}\, dx - \int \frac{b x^{2} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x - 1}\, dx"," ",0,"-Integral(a*x**2/(c**2*x - 1), x) - Integral(b*x**2*atanh(c*sqrt(x))/(c**2*x - 1), x)","F",0
38,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x**(1/2)))/(-c**2*x+1),x)","- \int \frac{a x}{c^{2} x - 1}\, dx - \int \frac{b x \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x - 1}\, dx"," ",0,"-Integral(a*x/(c**2*x - 1), x) - Integral(b*x*atanh(c*sqrt(x))/(c**2*x - 1), x)","F",0
39,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))/(-c**2*x+1),x)","- \int \frac{a}{c^{2} x - 1}\, dx - \int \frac{b \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x - 1}\, dx"," ",0,"-Integral(a/(c**2*x - 1), x) - Integral(b*atanh(c*sqrt(x))/(c**2*x - 1), x)","F",0
40,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))/x/(-c**2*x+1),x)","- \int \frac{a}{c^{2} x^{2} - x}\, dx - \int \frac{b \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x^{2} - x}\, dx"," ",0,"-Integral(a/(c**2*x**2 - x), x) - Integral(b*atanh(c*sqrt(x))/(c**2*x**2 - x), x)","F",0
41,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))/x**2/(-c**2*x+1),x)","- \int \frac{a}{c^{2} x^{3} - x^{2}}\, dx - \int \frac{b \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x^{3} - x^{2}}\, dx"," ",0,"-Integral(a/(c**2*x**3 - x**2), x) - Integral(b*atanh(c*sqrt(x))/(c**2*x**3 - x**2), x)","F",0
42,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))/x**3/(-c**2*x+1),x)","- \int \frac{a}{c^{2} x^{4} - x^{3}}\, dx - \int \frac{b \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x^{4} - x^{3}}\, dx"," ",0,"-Integral(a/(c**2*x**4 - x**3), x) - Integral(b*atanh(c*sqrt(x))/(c**2*x**4 - x**3), x)","F",0
43,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))/x**4/(-c**2*x+1),x)","- \int \frac{a}{c^{2} x^{5} - x^{4}}\, dx - \int \frac{b \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x^{5} - x^{4}}\, dx"," ",0,"-Integral(a/(c**2*x**5 - x**4), x) - Integral(b*atanh(c*sqrt(x))/(c**2*x**5 - x**4), x)","F",0
44,-1,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x**(1/2)))/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
45,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x**(1/2)))/(e*x+d),x)","\int \frac{x \left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)}{d + e x}\, dx"," ",0,"Integral(x*(a + b*atanh(c*sqrt(x)))/(d + e*x), x)","F",0
46,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))/(e*x+d),x)","\int \frac{a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}}{d + e x}\, dx"," ",0,"Integral((a + b*atanh(c*sqrt(x)))/(d + e*x), x)","F",0
47,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))/x/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))/x**2/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))/x**3/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
