1,1,345,0,2.734613," ","integrate((e*x+d)**4*(a+b*atan(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{atan}{\left(c x \right)} + 2 b d^{3} e x^{2} \operatorname{atan}{\left(c x \right)} + 2 b d^{2} e^{2} x^{3} \operatorname{atan}{\left(c x \right)} + b d e^{3} x^{4} \operatorname{atan}{\left(c x \right)} + \frac{b e^{4} x^{5} \operatorname{atan}{\left(c x \right)}}{5} - \frac{b d^{4} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 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{atan}{\left(c x \right)}}{c^{2}} + \frac{b d^{2} e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \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{atan}{\left(c x \right)}}{c^{4}} - \frac{b e^{4} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{10 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*atan(c*x) + 2*b*d**3*e*x**2*atan(c*x) + 2*b*d**2*e**2*x**3*atan(c*x) + b*d*e**3*x**4*atan(c*x) + b*e**4*x**5*atan(c*x)/5 - b*d**4*log(x**2 + c**(-2))/(2*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*atan(c*x)/c**2 + b*d**2*e**2*log(x**2 + c**(-2))/c**3 + b*d*e**3*x/c**3 + b*e**4*x**2/(10*c**3) - b*d*e**3*atan(c*x)/c**4 - b*e**4*log(x**2 + c**(-2))/(10*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
2,1,262,0,1.845508," ","integrate((e*x+d)**3*(a+b*atan(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{atan}{\left(c x \right)} + \frac{3 b d^{2} e x^{2} \operatorname{atan}{\left(c x \right)}}{2} + b d e^{2} x^{3} \operatorname{atan}{\left(c x \right)} + \frac{b e^{3} x^{4} \operatorname{atan}{\left(c x \right)}}{4} - \frac{b d^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 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{atan}{\left(c x \right)}}{2 c^{2}} + \frac{b d e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c^{3}} + \frac{b e^{3} x}{4 c^{3}} - \frac{b e^{3} \operatorname{atan}{\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*atan(c*x) + 3*b*d**2*e*x**2*atan(c*x)/2 + b*d*e**2*x**3*atan(c*x) + b*e**3*x**4*atan(c*x)/4 - b*d**3*log(x**2 + c**(-2))/(2*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*atan(c*x)/(2*c**2) + b*d*e**2*log(x**2 + c**(-2))/(2*c**3) + b*e**3*x/(4*c**3) - b*e**3*atan(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
3,1,160,0,1.046397," ","integrate((e*x+d)**2*(a+b*atan(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{atan}{\left(c x \right)} + b d e x^{2} \operatorname{atan}{\left(c x \right)} + \frac{b e^{2} x^{3} \operatorname{atan}{\left(c x \right)}}{3} - \frac{b d^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c} - \frac{b d e x}{c} - \frac{b e^{2} x^{2}}{6 c} + \frac{b d e \operatorname{atan}{\left(c x \right)}}{c^{2}} + \frac{b e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{6 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*atan(c*x) + b*d*e*x**2*atan(c*x) + b*e**2*x**3*atan(c*x)/3 - b*d**2*log(x**2 + c**(-2))/(2*c) - b*d*e*x/c - b*e**2*x**2/(6*c) + b*d*e*atan(c*x)/c**2 + b*e**2*log(x**2 + c**(-2))/(6*c**3), Ne(c, 0)), (a*(d**2*x + d*e*x**2 + e**2*x**3/3), True))","A",0
4,1,87,0,0.590043," ","integrate((e*x+d)*(a+b*atan(c*x)),x)","\begin{cases} a d x + \frac{a e x^{2}}{2} + b d x \operatorname{atan}{\left(c x \right)} + \frac{b e x^{2} \operatorname{atan}{\left(c x \right)}}{2} - \frac{b d \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c} - \frac{b e x}{2 c} + \frac{b e \operatorname{atan}{\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*atan(c*x) + b*e*x**2*atan(c*x)/2 - b*d*log(x**2 + c**(-2))/(2*c) - b*e*x/(2*c) + b*e*atan(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*atan(c*x))/(e*x+d),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{d + e x}\, dx"," ",0,"Integral((a + b*atan(c*x))/(d + e*x), x)","F",0
6,1,695,0,4.255830," ","integrate((a+b*atan(c*x))/(e*x+d)**2,x)","\begin{cases} - \frac{a}{d e + e^{2} x} & \text{for}\: c = 0 \\\frac{a x + b x \operatorname{atan}{\left(c x \right)} - \frac{b \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c}}{d^{2}} & \text{for}\: e = 0 \\\frac{2 a d}{- 2 d^{2} e - 2 d e^{2} x} - \frac{i b d \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{- 2 d^{2} e - 2 d e^{2} x} - \frac{i b d}{- 2 d^{2} e - 2 d e^{2} x} + \frac{i b e x \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{- 2 d^{2} e - 2 d e^{2} x} & \text{for}\: c = - \frac{i e}{d} \\\frac{2 a d}{- 2 d^{2} e - 2 d e^{2} x} + \frac{i b d \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{- 2 d^{2} e - 2 d e^{2} x} + \frac{i b d}{- 2 d^{2} e - 2 d e^{2} x} - \frac{i b e x \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{- 2 d^{2} e - 2 d e^{2} x} & \text{for}\: c = \frac{i e}{d} \\\tilde{\infty} \left(a x + b x \operatorname{atan}{\left(c x \right)} - \frac{b \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c}\right) & \text{for}\: d = - e x \\- \frac{2 a c^{2} d^{2}}{2 c^{2} d^{3} e + 2 c^{2} d^{2} e^{2} x + 2 d e^{3} + 2 e^{4} x} - \frac{2 a e^{2}}{2 c^{2} d^{3} e + 2 c^{2} d^{2} e^{2} x + 2 d e^{3} + 2 e^{4} x} + \frac{2 b c^{2} d e x \operatorname{atan}{\left(c x \right)}}{2 c^{2} d^{3} e + 2 c^{2} d^{2} e^{2} x + 2 d e^{3} + 2 e^{4} x} - \frac{b c d e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c^{2} d^{3} e + 2 c^{2} d^{2} e^{2} x + 2 d e^{3} + 2 e^{4} x} + \frac{2 b c d e \log{\left(\frac{d}{e} + x \right)}}{2 c^{2} d^{3} e + 2 c^{2} d^{2} e^{2} x + 2 d e^{3} + 2 e^{4} x} - \frac{b c e^{2} x \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c^{2} d^{3} e + 2 c^{2} d^{2} e^{2} x + 2 d e^{3} + 2 e^{4} x} + \frac{2 b c e^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 c^{2} d^{3} e + 2 c^{2} d^{2} e^{2} x + 2 d e^{3} + 2 e^{4} x} - \frac{2 b e^{2} \operatorname{atan}{\left(c x \right)}}{2 c^{2} d^{3} e + 2 c^{2} d^{2} e^{2} x + 2 d e^{3} + 2 e^{4} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(d*e + e**2*x), Eq(c, 0)), ((a*x + b*x*atan(c*x) - b*log(x**2 + c**(-2))/(2*c))/d**2, Eq(e, 0)), (2*a*d/(-2*d**2*e - 2*d*e**2*x) - I*b*d*atanh(e*x/d)/(-2*d**2*e - 2*d*e**2*x) - I*b*d/(-2*d**2*e - 2*d*e**2*x) + I*b*e*x*atanh(e*x/d)/(-2*d**2*e - 2*d*e**2*x), Eq(c, -I*e/d)), (2*a*d/(-2*d**2*e - 2*d*e**2*x) + I*b*d*atanh(e*x/d)/(-2*d**2*e - 2*d*e**2*x) + I*b*d/(-2*d**2*e - 2*d*e**2*x) - I*b*e*x*atanh(e*x/d)/(-2*d**2*e - 2*d*e**2*x), Eq(c, I*e/d)), (zoo*(a*x + b*x*atan(c*x) - b*log(x**2 + c**(-2))/(2*c)), Eq(d, -e*x)), (-2*a*c**2*d**2/(2*c**2*d**3*e + 2*c**2*d**2*e**2*x + 2*d*e**3 + 2*e**4*x) - 2*a*e**2/(2*c**2*d**3*e + 2*c**2*d**2*e**2*x + 2*d*e**3 + 2*e**4*x) + 2*b*c**2*d*e*x*atan(c*x)/(2*c**2*d**3*e + 2*c**2*d**2*e**2*x + 2*d*e**3 + 2*e**4*x) - b*c*d*e*log(x**2 + c**(-2))/(2*c**2*d**3*e + 2*c**2*d**2*e**2*x + 2*d*e**3 + 2*e**4*x) + 2*b*c*d*e*log(d/e + x)/(2*c**2*d**3*e + 2*c**2*d**2*e**2*x + 2*d*e**3 + 2*e**4*x) - b*c*e**2*x*log(x**2 + c**(-2))/(2*c**2*d**3*e + 2*c**2*d**2*e**2*x + 2*d*e**3 + 2*e**4*x) + 2*b*c*e**2*x*log(d/e + x)/(2*c**2*d**3*e + 2*c**2*d**2*e**2*x + 2*d*e**3 + 2*e**4*x) - 2*b*e**2*atan(c*x)/(2*c**2*d**3*e + 2*c**2*d**2*e**2*x + 2*d*e**3 + 2*e**4*x), True))","A",0
7,1,2887,0,9.645170," ","integrate((a+b*atan(c*x))/(e*x+d)**3,x)","\begin{cases} \frac{a x}{d^{3}} & \text{for}\: c = 0 \wedge e = 0 \\- \frac{a}{2 d^{2} e + 4 d e^{2} x + 2 e^{3} x^{2}} & \text{for}\: c = 0 \\\frac{a x + b x \operatorname{atan}{\left(c x \right)} - \frac{b \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c}}{d^{3}} & \text{for}\: 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 i 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 i b d^{2}}{- 8 d^{4} e - 16 d^{3} e^{2} x - 8 d^{2} e^{3} x^{2}} + \frac{2 i 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{i b d e x}{- 8 d^{4} e - 16 d^{3} e^{2} x - 8 d^{2} e^{3} x^{2}} + \frac{i 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{i 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 i 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 i b d^{2}}{- 8 d^{4} e - 16 d^{3} e^{2} x - 8 d^{2} e^{3} x^{2}} - \frac{2 i 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{i b d e x}{- 8 d^{4} e - 16 d^{3} e^{2} x - 8 d^{2} e^{3} x^{2}} - \frac{i 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{i e}{d} \\- \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{atan}{\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{atan}{\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 \log{\left(x^{2} + \frac{1}{c^{2}} \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{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{2 b c^{3} d^{2} e^{2} x \log{\left(x^{2} + \frac{1}{c^{2}} \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{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{b c^{3} d e^{3} x^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \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{3 b c^{2} d^{2} e^{2} \operatorname{atan}{\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{atan}{\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{atan}{\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{atan}{\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)), (-a/(2*d**2*e + 4*d*e**2*x + 2*e**3*x**2), Eq(c, 0)), ((a*x + b*x*atan(c*x) - b*log(x**2 + c**(-2))/(2*c))/d**3, 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*I*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*I*b*d**2/(-8*d**4*e - 16*d**3*e**2*x - 8*d**2*e**3*x**2) + 2*I*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) - I*b*d*e*x/(-8*d**4*e - 16*d**3*e**2*x - 8*d**2*e**3*x**2) + I*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, -I*e/d)), (4*a*d**2/(-8*d**4*e - 16*d**3*e**2*x - 8*d**2*e**3*x**2) + 3*I*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*I*b*d**2/(-8*d**4*e - 16*d**3*e**2*x - 8*d**2*e**3*x**2) - 2*I*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) + I*b*d*e*x/(-8*d**4*e - 16*d**3*e**2*x - 8*d**2*e**3*x**2) - I*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, I*e/d)), (-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*atan(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*atan(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*log(x**2 + c**(-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) + 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) - 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) - 2*b*c**3*d**2*e**2*x*log(x**2 + c**(-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) + 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) - 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) - b*c**3*d*e**3*x**2*log(x**2 + c**(-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) + 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) - 3*b*c**2*d**2*e**2*atan(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*atan(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*atan(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*atan(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
8,1,9229,0,20.035885," ","integrate((a+b*atan(c*x))/(e*x+d)**4,x)","\begin{cases} \frac{a x}{d^{4}} & \text{for}\: c = 0 \wedge 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{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 i 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 i 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 i 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 i 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 i 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 i 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 i 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{i 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 i 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 i 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 i 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 i 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 i 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 i 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 i 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{i e}{d} \\\frac{a x + b x \operatorname{atan}{\left(c x \right)} - \frac{b \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c}}{d^{4}} & \text{for}\: e = 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{atan}{\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{atan}{\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{atan}{\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{3 b c^{5} d^{5} e \log{\left(x^{2} + \frac{1}{c^{2}} \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{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{9 b c^{5} d^{4} e^{2} x \log{\left(x^{2} + \frac{1}{c^{2}} \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{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{9 b c^{5} d^{3} e^{3} x^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \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{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{3 b c^{5} d^{2} e^{4} x^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \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{12 b c^{4} d^{4} e^{2} \operatorname{atan}{\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{atan}{\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{atan}{\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{atan}{\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^{3} d^{3} e^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \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{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{3 b c^{3} d^{2} e^{4} x \log{\left(x^{2} + \frac{1}{c^{2}} \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{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{3 b c^{3} d e^{5} x^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \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{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{b c^{3} e^{6} x^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \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{6 b c^{2} d^{2} e^{4} \operatorname{atan}{\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{atan}{\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)), (-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)), (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*I*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*I*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*I*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*I*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*I*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*I*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*I*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, -I*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*I*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*I*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*I*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*I*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*I*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*I*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*I*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, I*e/d)), ((a*x + b*x*atan(c*x) - b*log(x**2 + c**(-2))/(2*c))/d**4, Eq(e, 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*atan(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*atan(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*atan(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) - 3*b*c**5*d**5*e*log(x**2 + c**(-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**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) - 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) - 9*b*c**5*d**4*e**2*x*log(x**2 + c**(-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) + 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) - 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) - 9*b*c**5*d**3*e**3*x**2*log(x**2 + c**(-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) + 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) - 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) - 3*b*c**5*d**2*e**4*x**3*log(x**2 + c**(-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(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) - 12*b*c**4*d**4*e**2*atan(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*atan(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*atan(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*atan(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**3*d**3*e**3*log(x**2 + c**(-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*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) - 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) + 3*b*c**3*d**2*e**4*x*log(x**2 + c**(-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**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) - 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) + 3*b*c**3*d*e**5*x**2*log(x**2 + c**(-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**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) - 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) + b*c**3*e**6*x**3*log(x**2 + c**(-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(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**2*d**2*e**4*atan(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*atan(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*atan(c*x))**2,x)","\int \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2} \left(d + e x\right)^{3}\, dx"," ",0,"Integral((a + b*atan(c*x))**2*(d + e*x)**3, x)","F",0
10,0,0,0,0.000000," ","integrate((e*x+d)**2*(a+b*atan(c*x))**2,x)","\int \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2} \left(d + e x\right)^{2}\, dx"," ",0,"Integral((a + b*atan(c*x))**2*(d + e*x)**2, x)","F",0
11,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*atan(c*x))**2,x)","\int \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2} \left(d + e x\right)\, dx"," ",0,"Integral((a + b*atan(c*x))**2*(d + e*x), x)","F",0
12,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/(e*x+d),x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral((a + b*atan(c*x))**2/(d + e*x), x)","F",0
13,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/(e*x+d)**2,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*atan(c*x))**2/(d + e*x)**2, x)","F",0
14,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,0,0,0,0.000000," ","integrate((e*x+d)**3*(a+b*atan(c*x))**3,x)","\int \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3} \left(d + e x\right)^{3}\, dx"," ",0,"Integral((a + b*atan(c*x))**3*(d + e*x)**3, x)","F",0
16,0,0,0,0.000000," ","integrate((e*x+d)**2*(a+b*atan(c*x))**3,x)","\int \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3} \left(d + e x\right)^{2}\, dx"," ",0,"Integral((a + b*atan(c*x))**3*(d + e*x)**2, x)","F",0
17,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*atan(c*x))**3,x)","\int \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3} \left(d + e x\right)\, dx"," ",0,"Integral((a + b*atan(c*x))**3*(d + e*x), x)","F",0
18,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/(e*x+d),x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3}}{d + e x}\, dx"," ",0,"Integral((a + b*atan(c*x))**3/(d + e*x), x)","F",0
19,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/(e*x+d)**2,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*atan(c*x))**3/(d + e*x)**2, x)","F",0
20,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
21,1,464,0,25.999179," ","integrate((e*x+d)**2*(a+b*atan(c*x**2)),x)","\begin{cases} a d^{2} x + a d e x^{2} + \frac{a e^{2} x^{3}}{3} + b d^{2} x \operatorname{atan}{\left(c x^{2} \right)} + b d e x^{2} \operatorname{atan}{\left(c x^{2} \right)} + \frac{b e^{2} x^{3} \operatorname{atan}{\left(c x^{2} \right)}}{3} + \frac{\left(-1\right)^{\frac{3}{4}} b d^{2} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{c^{2}}} \right)}}{c \sqrt[4]{\frac{1}{c^{2}}}} - \frac{\left(-1\right)^{\frac{3}{4}} b d^{2} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{2 c \sqrt[4]{\frac{1}{c^{2}}}} - \frac{\left(-1\right)^{\frac{3}{4}} b d^{2} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{c^{2}}}} \right)}}{c \sqrt[4]{\frac{1}{c^{2}}}} - \frac{b d e \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{c} - \frac{2 b e^{2} x}{3 c} + \frac{\sqrt[4]{-1} b d^{2} \operatorname{atan}{\left(c x^{2} \right)}}{c^{2} \left(\frac{1}{c^{2}}\right)^{\frac{3}{4}}} - \frac{i b d e \operatorname{atan}{\left(c x^{2} \right)}}{c^{2} \sqrt{\frac{1}{c^{2}}}} + \frac{\left(-1\right)^{\frac{3}{4}} b e^{2} \operatorname{atan}{\left(c x^{2} \right)}}{3 c^{2} \sqrt[4]{\frac{1}{c^{2}}}} - \frac{\sqrt[4]{-1} b e^{2} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{c^{2}}} \right)}}{3 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{3}{4}}} + \frac{\sqrt[4]{-1} b e^{2} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{6 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{3}{4}}} - \frac{\sqrt[4]{-1} b e^{2} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{c^{2}}}} \right)}}{3 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{3}{4}}} & \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*atan(c*x**2) + b*d*e*x**2*atan(c*x**2) + b*e**2*x**3*atan(c*x**2)/3 + (-1)**(3/4)*b*d**2*log(x - (-1)**(1/4)*(c**(-2))**(1/4))/(c*(c**(-2))**(1/4)) - (-1)**(3/4)*b*d**2*log(x**2 + I*sqrt(c**(-2)))/(2*c*(c**(-2))**(1/4)) - (-1)**(3/4)*b*d**2*atan((-1)**(3/4)*x/(c**(-2))**(1/4))/(c*(c**(-2))**(1/4)) - b*d*e*log(x**2 + I*sqrt(c**(-2)))/c - 2*b*e**2*x/(3*c) + (-1)**(1/4)*b*d**2*atan(c*x**2)/(c**2*(c**(-2))**(3/4)) - I*b*d*e*atan(c*x**2)/(c**2*sqrt(c**(-2))) + (-1)**(3/4)*b*e**2*atan(c*x**2)/(3*c**2*(c**(-2))**(1/4)) - (-1)**(1/4)*b*e**2*log(x - (-1)**(1/4)*(c**(-2))**(1/4))/(3*c**3*(c**(-2))**(3/4)) + (-1)**(1/4)*b*e**2*log(x**2 + I*sqrt(c**(-2)))/(6*c**3*(c**(-2))**(3/4)) - (-1)**(1/4)*b*e**2*atan((-1)**(3/4)*x/(c**(-2))**(1/4))/(3*c**3*(c**(-2))**(3/4)), Ne(c, 0)), (a*(d**2*x + d*e*x**2 + e**2*x**3/3), True))","A",0
22,1,1734,0,18.145772," ","integrate((e*x+d)*(a+b*atan(c*x**2)),x)","\begin{cases} \left(a - b \operatorname{atan}{\left(\frac{1}{\left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)^{2}} \right)}\right) \left(d x + \frac{e x^{2}}{2}\right) & \text{for}\: c = - \frac{1}{x^{2} \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)^{2}} \\\left(a - b \operatorname{atan}{\left(\frac{1}{\left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)^{2}} \right)}\right) \left(d x + \frac{e x^{2}}{2}\right) & \text{for}\: c = - \frac{1}{x^{2} \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)^{2}} \\\left(a - b \operatorname{atan}{\left(\frac{1}{\left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)^{2}} \right)}\right) \left(d x + \frac{e x^{2}}{2}\right) & \text{for}\: c = - \frac{1}{x^{2} \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)^{2}} \\\left(a - b \operatorname{atan}{\left(\frac{1}{\left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)^{2}} \right)}\right) \left(d x + \frac{e x^{2}}{2}\right) & \text{for}\: c = - \frac{1}{x^{2} \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)^{2}} \\a \left(d x + \frac{e x^{2}}{2}\right) & \text{for}\: c = 0 \\\frac{2 \left(-1\right)^{\frac{3}{4}} a c^{5} d x^{5} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} + \frac{\left(-1\right)^{\frac{3}{4}} a c^{5} e x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} + \frac{2 \left(-1\right)^{\frac{3}{4}} a c^{3} d x \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} + \frac{\left(-1\right)^{\frac{3}{4}} a c^{3} e x^{2} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} + \frac{2 \left(-1\right)^{\frac{3}{4}} b c^{5} d x^{5} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} \operatorname{atan}{\left(c x^{2} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} + \frac{\left(-1\right)^{\frac{3}{4}} b c^{5} e x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} \operatorname{atan}{\left(c x^{2} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} - \frac{2 i b c^{4} d x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{5}{2}} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{c^{2}}} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} + \frac{i b c^{4} d x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{5}{2}} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} + \frac{2 i b c^{4} d x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{5}{2}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{c^{2}}}} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} - \frac{\left(-1\right)^{\frac{3}{4}} b c^{4} e x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} + \frac{2 \left(-1\right)^{\frac{3}{4}} b c^{3} d x \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} \operatorname{atan}{\left(c x^{2} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} + \frac{\left(-1\right)^{\frac{3}{4}} b c^{3} e x^{2} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} \operatorname{atan}{\left(c x^{2} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} - \frac{2 i b c^{2} d \left(\frac{1}{c^{2}}\right)^{\frac{5}{2}} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{c^{2}}} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} + \frac{i b c^{2} d \left(\frac{1}{c^{2}}\right)^{\frac{5}{2}} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} + \frac{2 i b c^{2} d \left(\frac{1}{c^{2}}\right)^{\frac{5}{2}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{c^{2}}}} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} - \frac{\left(-1\right)^{\frac{3}{4}} b c^{2} e \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} - \frac{2 b d x^{4} \operatorname{atan}{\left(c x^{2} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{6} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} - \frac{2 b d \operatorname{atan}{\left(c x^{2} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{8} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{6} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} + \frac{\sqrt[4]{-1} b e x^{4} \sqrt[4]{\frac{1}{c^{2}}} \operatorname{atan}{\left(c x^{2} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{6} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} + \frac{\sqrt[4]{-1} b e \sqrt[4]{\frac{1}{c^{2}}} \operatorname{atan}{\left(c x^{2} \right)}}{2 \left(-1\right)^{\frac{3}{4}} c^{8} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}} + 2 \left(-1\right)^{\frac{3}{4}} c^{6} \left(\frac{1}{c^{2}}\right)^{\frac{11}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a - b*atan((-sqrt(2)/2 - sqrt(2)*I/2)**(-2)))*(d*x + e*x**2/2), Eq(c, -1/(x**2*(-sqrt(2)/2 - sqrt(2)*I/2)**2))), ((a - b*atan((-sqrt(2)/2 + sqrt(2)*I/2)**(-2)))*(d*x + e*x**2/2), Eq(c, -1/(x**2*(-sqrt(2)/2 + sqrt(2)*I/2)**2))), ((a - b*atan((sqrt(2)/2 - sqrt(2)*I/2)**(-2)))*(d*x + e*x**2/2), Eq(c, -1/(x**2*(sqrt(2)/2 - sqrt(2)*I/2)**2))), ((a - b*atan((sqrt(2)/2 + sqrt(2)*I/2)**(-2)))*(d*x + e*x**2/2), Eq(c, -1/(x**2*(sqrt(2)/2 + sqrt(2)*I/2)**2))), (a*(d*x + e*x**2/2), Eq(c, 0)), (2*(-1)**(3/4)*a*c**5*d*x**5*(c**(-2))**(11/4)/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) + (-1)**(3/4)*a*c**5*e*x**6*(c**(-2))**(11/4)/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) + 2*(-1)**(3/4)*a*c**3*d*x*(c**(-2))**(11/4)/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) + (-1)**(3/4)*a*c**3*e*x**2*(c**(-2))**(11/4)/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) + 2*(-1)**(3/4)*b*c**5*d*x**5*(c**(-2))**(11/4)*atan(c*x**2)/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) + (-1)**(3/4)*b*c**5*e*x**6*(c**(-2))**(11/4)*atan(c*x**2)/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) - 2*I*b*c**4*d*x**4*(c**(-2))**(5/2)*log(x - (-1)**(1/4)*(c**(-2))**(1/4))/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) + I*b*c**4*d*x**4*(c**(-2))**(5/2)*log(x**2 + I*sqrt(c**(-2)))/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) + 2*I*b*c**4*d*x**4*(c**(-2))**(5/2)*atan((-1)**(3/4)*x/(c**(-2))**(1/4))/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) - (-1)**(3/4)*b*c**4*e*x**4*(c**(-2))**(11/4)*log(x**2 + I*sqrt(c**(-2)))/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) + 2*(-1)**(3/4)*b*c**3*d*x*(c**(-2))**(11/4)*atan(c*x**2)/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) + (-1)**(3/4)*b*c**3*e*x**2*(c**(-2))**(11/4)*atan(c*x**2)/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) - 2*I*b*c**2*d*(c**(-2))**(5/2)*log(x - (-1)**(1/4)*(c**(-2))**(1/4))/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) + I*b*c**2*d*(c**(-2))**(5/2)*log(x**2 + I*sqrt(c**(-2)))/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) + 2*I*b*c**2*d*(c**(-2))**(5/2)*atan((-1)**(3/4)*x/(c**(-2))**(1/4))/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) - (-1)**(3/4)*b*c**2*e*(c**(-2))**(11/4)*log(x**2 + I*sqrt(c**(-2)))/(2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**3*(c**(-2))**(11/4)) - 2*b*d*x**4*atan(c*x**2)/(2*(-1)**(3/4)*c**6*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**4*(c**(-2))**(11/4)) - 2*b*d*atan(c*x**2)/(2*(-1)**(3/4)*c**8*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**6*(c**(-2))**(11/4)) + (-1)**(1/4)*b*e*x**4*(c**(-2))**(1/4)*atan(c*x**2)/(2*(-1)**(3/4)*c**6*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**4*(c**(-2))**(11/4)) + (-1)**(1/4)*b*e*(c**(-2))**(1/4)*atan(c*x**2)/(2*(-1)**(3/4)*c**8*x**4*(c**(-2))**(11/4) + 2*(-1)**(3/4)*c**6*(c**(-2))**(11/4)), True))","A",0
23,-1,0,0,0.000000," ","integrate((a+b*atan(c*x**2))/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,-1,0,0,0.000000," ","integrate((a+b*atan(c*x**2))/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*atan(c*x**2))**2,x)","\int \left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{2} \left(d + e x\right)\, dx"," ",0,"Integral((a + b*atan(c*x**2))**2*(d + e*x), x)","F",0
26,-1,0,0,0.000000," ","integrate((a+b*atan(c*x**2))**2/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,-1,0,0,0.000000," ","integrate((a+b*atan(c*x**2))**2/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,1,151,0,50.144211," ","integrate((e*x+d)**2*(a+b*atan(c*x**3)),x)","a d^{2} x + a d e x^{2} + \frac{a e^{2} x^{3}}{3} - 3 b c d^{2} \operatorname{RootSum} {\left(216 t^{3} c^{4} + 1, \left( t \mapsto t \log{\left(36 t^{2} c^{2} + x^{2} \right)} \right)\right)} - 3 b c d e \operatorname{RootSum} {\left(46656 t^{6} c^{10} + 1, \left( t \mapsto t \log{\left(7776 t^{5} c^{8} + x \right)} \right)\right)} + b d^{2} x \operatorname{atan}{\left(c x^{3} \right)} + b d e x^{2} \operatorname{atan}{\left(c x^{3} \right)} + b e^{2} \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{x^{3} \operatorname{atan}{\left(c x^{3} \right)}}{3} - \frac{\log{\left(c^{2} x^{6} + 1 \right)}}{6 c} & \text{otherwise} \end{cases}\right)"," ",0,"a*d**2*x + a*d*e*x**2 + a*e**2*x**3/3 - 3*b*c*d**2*RootSum(216*_t**3*c**4 + 1, Lambda(_t, _t*log(36*_t**2*c**2 + x**2))) - 3*b*c*d*e*RootSum(46656*_t**6*c**10 + 1, Lambda(_t, _t*log(7776*_t**5*c**8 + x))) + b*d**2*x*atan(c*x**3) + b*d*e*x**2*atan(c*x**3) + b*e**2*Piecewise((0, Eq(c, 0)), (x**3*atan(c*x**3)/3 - log(c**2*x**6 + 1)/(6*c), True))","A",0
29,1,3068,0,46.473573," ","integrate((e*x+d)*(a+b*atan(c*x**3)),x)","\begin{cases} a \left(d x + \frac{e x^{2}}{2}\right) & \text{for}\: c = 0 \\\left(a - \infty i b\right) \left(d x + \frac{e x^{2}}{2}\right) & \text{for}\: c = - \frac{i}{x^{3}} \\\left(a + \infty i b\right) \left(d x + \frac{e x^{2}}{2}\right) & \text{for}\: c = \frac{i}{x^{3}} \\\left(a - b \operatorname{atan}{\left(\frac{1}{\left(- \frac{\sqrt{3}}{2} - \frac{i}{2}\right)^{3}} \right)}\right) \left(d x + \frac{e x^{2}}{2}\right) & \text{for}\: c = - \frac{1}{x^{3} \left(- \frac{\sqrt{3}}{2} - \frac{i}{2}\right)^{3}} \\\left(a - b \operatorname{atan}{\left(\frac{1}{\left(- \frac{\sqrt{3}}{2} + \frac{i}{2}\right)^{3}} \right)}\right) \left(d x + \frac{e x^{2}}{2}\right) & \text{for}\: c = - \frac{1}{x^{3} \left(- \frac{\sqrt{3}}{2} + \frac{i}{2}\right)^{3}} \\\left(a - b \operatorname{atan}{\left(\frac{1}{\left(\frac{\sqrt{3}}{2} - \frac{i}{2}\right)^{3}} \right)}\right) \left(d x + \frac{e x^{2}}{2}\right) & \text{for}\: c = - \frac{1}{x^{3} \left(\frac{\sqrt{3}}{2} - \frac{i}{2}\right)^{3}} \\\left(a - b \operatorname{atan}{\left(\frac{1}{\left(\frac{\sqrt{3}}{2} + \frac{i}{2}\right)^{3}} \right)}\right) \left(d x + \frac{e x^{2}}{2}\right) & \text{for}\: c = - \frac{1}{x^{3} \left(\frac{\sqrt{3}}{2} + \frac{i}{2}\right)^{3}} \\\frac{8 \sqrt[6]{-1} a c^{6} d x^{7} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{4 \sqrt[6]{-1} a c^{6} e x^{8} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{8 \sqrt[6]{-1} a c^{4} d x \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{4 \sqrt[6]{-1} a c^{4} e x^{2} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{8 \sqrt[6]{-1} b c^{6} d x^{7} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} \operatorname{atan}{\left(c x^{3} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{8 \sqrt[3]{-1} b c^{6} d x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{7}{3}} \operatorname{atan}{\left(c x^{3} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{4 \sqrt[6]{-1} b c^{6} e x^{8} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} \operatorname{atan}{\left(c x^{3} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{8 \left(-1\right)^{\frac{5}{6}} b c^{5} d x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{11}{6}} \log{\left(x - \sqrt[6]{-1} \sqrt[6]{\frac{1}{c^{2}}} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} - \frac{6 \left(-1\right)^{\frac{5}{6}} b c^{5} d x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{11}{6}} \log{\left(4 x^{2} - 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{2 \left(-1\right)^{\frac{5}{6}} b c^{5} d x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{11}{6}} \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{4 \left(-1\right)^{\frac{5}{6}} \sqrt{3} b c^{5} d x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{11}{6}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt{3}}{3} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} - \frac{4 \left(-1\right)^{\frac{5}{6}} \sqrt{3} b c^{5} d x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{11}{6}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt{3}}{3} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{8 \left(-1\right)^{\frac{5}{6}} b c^{5} d x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{11}{6}} \log{\left(2 \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{8 \sqrt[6]{-1} b c^{4} d x \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} \operatorname{atan}{\left(c x^{3} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{8 \sqrt[3]{-1} b c^{4} d \left(\frac{1}{c^{2}}\right)^{\frac{7}{3}} \operatorname{atan}{\left(c x^{3} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} - \frac{4 i b c^{4} e x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{3}{2}} \operatorname{atan}{\left(c x^{3} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{4 \sqrt[6]{-1} b c^{4} e x^{2} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} \operatorname{atan}{\left(c x^{3} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{8 \left(-1\right)^{\frac{5}{6}} b c^{3} d \left(\frac{1}{c^{2}}\right)^{\frac{11}{6}} \log{\left(x - \sqrt[6]{-1} \sqrt[6]{\frac{1}{c^{2}}} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} - \frac{6 \left(-1\right)^{\frac{5}{6}} b c^{3} d \left(\frac{1}{c^{2}}\right)^{\frac{11}{6}} \log{\left(4 x^{2} - 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{2 \left(-1\right)^{\frac{5}{6}} b c^{3} d \left(\frac{1}{c^{2}}\right)^{\frac{11}{6}} \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{4 \left(-1\right)^{\frac{5}{6}} \sqrt{3} b c^{3} d \left(\frac{1}{c^{2}}\right)^{\frac{11}{6}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt{3}}{3} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} - \frac{4 \left(-1\right)^{\frac{5}{6}} \sqrt{3} b c^{3} d \left(\frac{1}{c^{2}}\right)^{\frac{11}{6}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt{3}}{3} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{8 \left(-1\right)^{\frac{5}{6}} b c^{3} d \left(\frac{1}{c^{2}}\right)^{\frac{11}{6}} \log{\left(2 \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} - \frac{4 i b c^{2} e \left(\frac{1}{c^{2}}\right)^{\frac{3}{2}} \operatorname{atan}{\left(c x^{3} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} - \frac{3 b c e x^{6} \log{\left(4 x^{2} - 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{3 b c e x^{6} \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{2 \sqrt{3} b c e x^{6} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt{3}}{3} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{2 \sqrt{3} b c e x^{6} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt{3}}{3} \right)}}{8 \sqrt[6]{-1} c^{6} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} - \frac{3 b e \log{\left(4 x^{2} - 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{8 \sqrt[6]{-1} c^{7} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{5} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{3 b e \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{8 \sqrt[6]{-1} c^{7} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{5} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{2 \sqrt{3} b e \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt{3}}{3} \right)}}{8 \sqrt[6]{-1} c^{7} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{5} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} + \frac{2 \sqrt{3} b e \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt{3}}{3} \right)}}{8 \sqrt[6]{-1} c^{7} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}} + 8 \sqrt[6]{-1} c^{5} \left(\frac{1}{c^{2}}\right)^{\frac{13}{6}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*(d*x + e*x**2/2), Eq(c, 0)), ((a - oo*I*b)*(d*x + e*x**2/2), Eq(c, -I/x**3)), ((a + oo*I*b)*(d*x + e*x**2/2), Eq(c, I/x**3)), ((a - b*atan((-sqrt(3)/2 - I/2)**(-3)))*(d*x + e*x**2/2), Eq(c, -1/(x**3*(-sqrt(3)/2 - I/2)**3))), ((a - b*atan((-sqrt(3)/2 + I/2)**(-3)))*(d*x + e*x**2/2), Eq(c, -1/(x**3*(-sqrt(3)/2 + I/2)**3))), ((a - b*atan((sqrt(3)/2 - I/2)**(-3)))*(d*x + e*x**2/2), Eq(c, -1/(x**3*(sqrt(3)/2 - I/2)**3))), ((a - b*atan((sqrt(3)/2 + I/2)**(-3)))*(d*x + e*x**2/2), Eq(c, -1/(x**3*(sqrt(3)/2 + I/2)**3))), (8*(-1)**(1/6)*a*c**6*d*x**7*(c**(-2))**(13/6)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 4*(-1)**(1/6)*a*c**6*e*x**8*(c**(-2))**(13/6)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 8*(-1)**(1/6)*a*c**4*d*x*(c**(-2))**(13/6)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 4*(-1)**(1/6)*a*c**4*e*x**2*(c**(-2))**(13/6)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 8*(-1)**(1/6)*b*c**6*d*x**7*(c**(-2))**(13/6)*atan(c*x**3)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 8*(-1)**(1/3)*b*c**6*d*x**6*(c**(-2))**(7/3)*atan(c*x**3)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 4*(-1)**(1/6)*b*c**6*e*x**8*(c**(-2))**(13/6)*atan(c*x**3)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 8*(-1)**(5/6)*b*c**5*d*x**6*(c**(-2))**(11/6)*log(x - (-1)**(1/6)*(c**(-2))**(1/6))/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) - 6*(-1)**(5/6)*b*c**5*d*x**6*(c**(-2))**(11/6)*log(4*x**2 - 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 2*(-1)**(5/6)*b*c**5*d*x**6*(c**(-2))**(11/6)*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 4*(-1)**(5/6)*sqrt(3)*b*c**5*d*x**6*(c**(-2))**(11/6)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) - sqrt(3)/3)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) - 4*(-1)**(5/6)*sqrt(3)*b*c**5*d*x**6*(c**(-2))**(11/6)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) + sqrt(3)/3)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 8*(-1)**(5/6)*b*c**5*d*x**6*(c**(-2))**(11/6)*log(2)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 8*(-1)**(1/6)*b*c**4*d*x*(c**(-2))**(13/6)*atan(c*x**3)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 8*(-1)**(1/3)*b*c**4*d*(c**(-2))**(7/3)*atan(c*x**3)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) - 4*I*b*c**4*e*x**6*(c**(-2))**(3/2)*atan(c*x**3)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 4*(-1)**(1/6)*b*c**4*e*x**2*(c**(-2))**(13/6)*atan(c*x**3)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 8*(-1)**(5/6)*b*c**3*d*(c**(-2))**(11/6)*log(x - (-1)**(1/6)*(c**(-2))**(1/6))/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) - 6*(-1)**(5/6)*b*c**3*d*(c**(-2))**(11/6)*log(4*x**2 - 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 2*(-1)**(5/6)*b*c**3*d*(c**(-2))**(11/6)*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 4*(-1)**(5/6)*sqrt(3)*b*c**3*d*(c**(-2))**(11/6)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) - sqrt(3)/3)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) - 4*(-1)**(5/6)*sqrt(3)*b*c**3*d*(c**(-2))**(11/6)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) + sqrt(3)/3)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 8*(-1)**(5/6)*b*c**3*d*(c**(-2))**(11/6)*log(2)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) - 4*I*b*c**2*e*(c**(-2))**(3/2)*atan(c*x**3)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) - 3*b*c*e*x**6*log(4*x**2 - 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 3*b*c*e*x**6*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 2*sqrt(3)*b*c*e*x**6*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) - sqrt(3)/3)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) + 2*sqrt(3)*b*c*e*x**6*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) + sqrt(3)/3)/(8*(-1)**(1/6)*c**6*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**4*(c**(-2))**(13/6)) - 3*b*e*log(4*x**2 - 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(8*(-1)**(1/6)*c**7*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**5*(c**(-2))**(13/6)) + 3*b*e*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(8*(-1)**(1/6)*c**7*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**5*(c**(-2))**(13/6)) + 2*sqrt(3)*b*e*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) - sqrt(3)/3)/(8*(-1)**(1/6)*c**7*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**5*(c**(-2))**(13/6)) + 2*sqrt(3)*b*e*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) + sqrt(3)/3)/(8*(-1)**(1/6)*c**7*x**6*(c**(-2))**(13/6) + 8*(-1)**(1/6)*c**5*(c**(-2))**(13/6)), True))","A",0
30,-1,0,0,0.000000," ","integrate((a+b*atan(c*x**3))/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,-1,0,0,0.000000," ","integrate((a+b*atan(c*x**3))/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
