\(\int \frac {x^4 (d+e x)^{3/2}}{a+b x+c x^2} \, dx\) [533]

Optimal result

Integrand size = 25, antiderivative size = 650 \[ \int \frac {x^4 (d+e x)^{3/2}}{a+b x+c x^2} \, dx=-\frac {2 \left (b^3 c d-2 a b c^2 d-b^4 e+3 a b^2 c e-a^2 c^2 e\right ) \sqrt {d+e x}}{c^5}-\frac {2 b \left (b^2-2 a c\right ) (d+e x)^{3/2}}{3 c^4}+\frac {2 \left (c^2 d^2+b^2 e^2+c e (b d-a e)\right ) (d+e x)^{5/2}}{5 c^3 e^3}-\frac {2 (2 c d+b e) (d+e x)^{7/2}}{7 c^2 e^3}+\frac {2 (d+e x)^{9/2}}{9 c e^3}+\frac {\sqrt {2} \left (\left (b c d-b^2 e+a c e\right ) \left (b^2 c d-2 a c^2 d-b^3 e+3 a b c e\right )+\frac {2 b^5 c d e-10 a b^3 c^2 d e+10 a^2 b c^3 d e-b^6 e^2+a b^2 c^2 \left (4 c d^2-9 a e^2\right )-b^4 c \left (c d^2-6 a e^2\right )-2 a^2 c^3 \left (c d^2-a e^2\right )}{\sqrt {b^2-4 a c}}\right ) \text {arctanh}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e}}\right )}{c^{11/2} \sqrt {2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e}}+\frac {\sqrt {2} \left (\left (b c d-b^2 e+a c e\right ) \left (b^2 c d-2 a c^2 d-b^3 e+3 a b c e\right )-\frac {2 b^5 c d e-10 a b^3 c^2 d e+10 a^2 b c^3 d e-b^6 e^2+a b^2 c^2 \left (4 c d^2-9 a e^2\right )-b^4 c \left (c d^2-6 a e^2\right )-2 a^2 c^3 \left (c d^2-a e^2\right )}{\sqrt {b^2-4 a c}}\right ) \text {arctanh}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e}}\right )}{c^{11/2} \sqrt {2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e}} \]

[Out]

-2/3*b*(-2*a*c+b^2)*(e*x+d)^(3/2)/c^4+2/5*(c^2*d^2+b^2*e^2+c*e*(-a*e+b*d))*(e*x+d)^(5/2)/c^3/e^3-2/7*(b*e+2*c*
d)*(e*x+d)^(7/2)/c^2/e^3+2/9*(e*x+d)^(9/2)/c/e^3-2*(-a^2*c^2*e+3*a*b^2*c*e-2*a*b*c^2*d-b^4*e+b^3*c*d)*(e*x+d)^
(1/2)/c^5+arctanh(2^(1/2)*c^(1/2)*(e*x+d)^(1/2)/(2*c*d-e*(b-(-4*a*c+b^2)^(1/2)))^(1/2))*2^(1/2)*((a*c*e-b^2*e+
b*c*d)*(3*a*b*c*e-2*a*c^2*d-b^3*e+b^2*c*d)+(2*b^5*c*d*e-10*a*b^3*c^2*d*e+10*a^2*b*c^3*d*e-b^6*e^2+a*b^2*c^2*(-
9*a*e^2+4*c*d^2)-b^4*c*(-6*a*e^2+c*d^2)-2*a^2*c^3*(-a*e^2+c*d^2))/(-4*a*c+b^2)^(1/2))/c^(11/2)/(2*c*d-e*(b-(-4
*a*c+b^2)^(1/2)))^(1/2)+arctanh(2^(1/2)*c^(1/2)*(e*x+d)^(1/2)/(2*c*d-e*(b+(-4*a*c+b^2)^(1/2)))^(1/2))*2^(1/2)*
((a*c*e-b^2*e+b*c*d)*(3*a*b*c*e-2*a*c^2*d-b^3*e+b^2*c*d)+(-2*b^5*c*d*e+10*a*b^3*c^2*d*e-10*a^2*b*c^3*d*e+b^6*e
^2-a*b^2*c^2*(-9*a*e^2+4*c*d^2)+b^4*c*(-6*a*e^2+c*d^2)+2*a^2*c^3*(-a*e^2+c*d^2))/(-4*a*c+b^2)^(1/2))/c^(11/2)/
(2*c*d-e*(b+(-4*a*c+b^2)^(1/2)))^(1/2)

Rubi [A] (verified)

Time = 1.71 (sec) , antiderivative size = 650, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.160, Rules used = {911, 1301, 1180, 214} \[ \int \frac {x^4 (d+e x)^{3/2}}{a+b x+c x^2} \, dx=\frac {\sqrt {2} \left (\frac {10 a^2 b c^3 d e-2 a^2 c^3 \left (c d^2-a e^2\right )-b^4 c \left (c d^2-6 a e^2\right )-10 a b^3 c^2 d e+a b^2 c^2 \left (4 c d^2-9 a e^2\right )+b^6 \left (-e^2\right )+2 b^5 c d e}{\sqrt {b^2-4 a c}}+\left (a c e+b^2 (-e)+b c d\right ) \left (3 a b c e-2 a c^2 d+b^3 (-e)+b^2 c d\right )\right ) \text {arctanh}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )}}\right )}{c^{11/2} \sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )}}+\frac {\sqrt {2} \left (\left (a c e+b^2 (-e)+b c d\right ) \left (3 a b c e-2 a c^2 d+b^3 (-e)+b^2 c d\right )-\frac {10 a^2 b c^3 d e-2 a^2 c^3 \left (c d^2-a e^2\right )-b^4 c \left (c d^2-6 a e^2\right )-10 a b^3 c^2 d e+a b^2 c^2 \left (4 c d^2-9 a e^2\right )+b^6 \left (-e^2\right )+2 b^5 c d e}{\sqrt {b^2-4 a c}}\right ) \text {arctanh}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}\right )}{c^{11/2} \sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}-\frac {2 \sqrt {d+e x} \left (-a^2 c^2 e+3 a b^2 c e-2 a b c^2 d+b^4 (-e)+b^3 c d\right )}{c^5}-\frac {2 b \left (b^2-2 a c\right ) (d+e x)^{3/2}}{3 c^4}+\frac {2 (d+e x)^{5/2} \left (c e (b d-a e)+b^2 e^2+c^2 d^2\right )}{5 c^3 e^3}-\frac {2 (d+e x)^{7/2} (b e+2 c d)}{7 c^2 e^3}+\frac {2 (d+e x)^{9/2}}{9 c e^3} \]

[In]

Int[(x^4*(d + e*x)^(3/2))/(a + b*x + c*x^2),x]

[Out]

(-2*(b^3*c*d - 2*a*b*c^2*d - b^4*e + 3*a*b^2*c*e - a^2*c^2*e)*Sqrt[d + e*x])/c^5 - (2*b*(b^2 - 2*a*c)*(d + e*x
)^(3/2))/(3*c^4) + (2*(c^2*d^2 + b^2*e^2 + c*e*(b*d - a*e))*(d + e*x)^(5/2))/(5*c^3*e^3) - (2*(2*c*d + b*e)*(d
+ e*x)^(7/2))/(7*c^2*e^3) + (2*(d + e*x)^(9/2))/(9*c*e^3) + (Sqrt[2]*((b*c*d - b^2*e + a*c*e)*(b^2*c*d - 2*a*
c^2*d - b^3*e + 3*a*b*c*e) + (2*b^5*c*d*e - 10*a*b^3*c^2*d*e + 10*a^2*b*c^3*d*e - b^6*e^2 + a*b^2*c^2*(4*c*d^2
- 9*a*e^2) - b^4*c*(c*d^2 - 6*a*e^2) - 2*a^2*c^3*(c*d^2 - a*e^2))/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]
*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(c^(11/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) +
(Sqrt[2]*((b*c*d - b^2*e + a*c*e)*(b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e) - (2*b^5*c*d*e - 10*a*b^3*c^2*d*e
+ 10*a^2*b*c^3*d*e - b^6*e^2 + a*b^2*c^2*(4*c*d^2 - 9*a*e^2) - b^4*c*(c*d^2 - 6*a*e^2) - 2*a^2*c^3*(c*d^2 - a
*e^2))/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(c
^(11/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])

Rule 214

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(Rt[-a/b, 2]/a)*ArcTanh[x/Rt[-a/b, 2]], x] /; FreeQ[{a, b},
x] && NegQ[a/b]

Rule 911

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))^(n_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :
> With[{q = Denominator[m]}, Dist[q/e, Subst[Int[x^(q*(m + 1) - 1)*((e*f - d*g)/e + g*(x^q/e))^n*((c*d^2 - b*d
*e + a*e^2)/e^2 - (2*c*d - b*e)*(x^q/e^2) + c*(x^(2*q)/e^2))^p, x], x, (d + e*x)^(1/q)], x]] /; FreeQ[{a, b, c
, d, e, f, g}, x] && NeQ[e*f - d*g, 0] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && IntegersQ[n,
p] && FractionQ[m]

Rule 1180

Int[((d_) + (e_.)*(x_)^2)/((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4), x_Symbol] :> With[{q = Rt[b^2 - 4*a*c, 2]}, Di
st[e/2 + (2*c*d - b*e)/(2*q), Int[1/(b/2 - q/2 + c*x^2), x], x] + Dist[e/2 - (2*c*d - b*e)/(2*q), Int[1/(b/2 +
q/2 + c*x^2), x], x]] /; FreeQ[{a, b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - a*e^2, 0] && PosQ[b^
2 - 4*a*c]

Rule 1301

Int[(((f_.)*(x_))^(m_.)*((d_) + (e_.)*(x_)^2)^(q_.))/((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4), x_Symbol] :> Int[Ex
pandIntegrand[(f*x)^m*((d + e*x^2)^q/(a + b*x^2 + c*x^4)), x], x] /; FreeQ[{a, b, c, d, e, f, m}, x] && NeQ[b^
2 - 4*a*c, 0] && IntegerQ[q] && IntegerQ[m]

Rubi steps \begin{align*} \text {integral}& = \frac {2 \text {Subst}\left (\int \frac {x^4 \left (-\frac {d}{e}+\frac {x^2}{e}\right )^4}{\frac {c d^2-b d e+a e^2}{e^2}-\frac {(2 c d-b e) x^2}{e^2}+\frac {c x^4}{e^2}} \, dx,x,\sqrt {d+e x}\right )}{e} \\ & = \frac {2 \text {Subst}\left (\int \left (-\frac {e \left (b^3 c d-2 a b c^2 d-b^4 e+3 a b^2 c e-a^2 c^2 e\right )}{c^5}-\frac {b \left (b^2-2 a c\right ) e x^2}{c^4}+\frac {\left (c^2 d^2+b^2 e^2+c e (b d-a e)\right ) x^4}{c^3 e^2}-\frac {(2 c d+b e) x^6}{c^2 e^2}+\frac {x^8}{c e^2}+\frac {\left (b^3 c d-2 a b c^2 d-b^4 e+3 a b^2 c e-a^2 c^2 e\right ) \left (c d^2-b d e+a e^2\right )-\left (b c d-b^2 e+a c e\right ) \left (b^2 c d-2 a c^2 d-b^3 e+3 a b c e\right ) x^2}{c^5 e \left (\frac {c d^2-b d e+a e^2}{e^2}-\frac {(2 c d-b e) x^2}{e^2}+\frac {c x^4}{e^2}\right )}\right ) \, dx,x,\sqrt {d+e x}\right )}{e} \\ & = -\frac {2 \left (b^3 c d-2 a b c^2 d-b^4 e+3 a b^2 c e-a^2 c^2 e\right ) \sqrt {d+e x}}{c^5}-\frac {2 b \left (b^2-2 a c\right ) (d+e x)^{3/2}}{3 c^4}+\frac {2 \left (c^2 d^2+b^2 e^2+c e (b d-a e)\right ) (d+e x)^{5/2}}{5 c^3 e^3}-\frac {2 (2 c d+b e) (d+e x)^{7/2}}{7 c^2 e^3}+\frac {2 (d+e x)^{9/2}}{9 c e^3}+\frac {2 \text {Subst}\left (\int \frac {\left (b^3 c d-2 a b c^2 d-b^4 e+3 a b^2 c e-a^2 c^2 e\right ) \left (c d^2-b d e+a e^2\right )-\left (b c d-b^2 e+a c e\right ) \left (b^2 c d-2 a c^2 d-b^3 e+3 a b c e\right ) x^2}{\frac {c d^2-b d e+a e^2}{e^2}-\frac {(2 c d-b e) x^2}{e^2}+\frac {c x^4}{e^2}} \, dx,x,\sqrt {d+e x}\right )}{c^5 e^2} \\ & = -\frac {2 \left (b^3 c d-2 a b c^2 d-b^4 e+3 a b^2 c e-a^2 c^2 e\right ) \sqrt {d+e x}}{c^5}-\frac {2 b \left (b^2-2 a c\right ) (d+e x)^{3/2}}{3 c^4}+\frac {2 \left (c^2 d^2+b^2 e^2+c e (b d-a e)\right ) (d+e x)^{5/2}}{5 c^3 e^3}-\frac {2 (2 c d+b e) (d+e x)^{7/2}}{7 c^2 e^3}+\frac {2 (d+e x)^{9/2}}{9 c e^3}-\frac {\left (\left (b c d-b^2 e+a c e\right ) \left (b^2 c d-2 a c^2 d-b^3 e+3 a b c e\right )-\frac {2 b^5 c d e-10 a b^3 c^2 d e+10 a^2 b c^3 d e-b^6 e^2+a b^2 c^2 \left (4 c d^2-9 a e^2\right )-b^4 c \left (c d^2-6 a e^2\right )-2 a^2 c^3 \left (c d^2-a e^2\right )}{\sqrt {b^2-4 a c}}\right ) \text {Subst}\left (\int \frac {1}{\frac {\sqrt {b^2-4 a c}}{2 e}-\frac {2 c d-b e}{2 e^2}+\frac {c x^2}{e^2}} \, dx,x,\sqrt {d+e x}\right )}{c^5 e^2}-\frac {\left (\left (b c d-b^2 e+a c e\right ) \left (b^2 c d-2 a c^2 d-b^3 e+3 a b c e\right )+\frac {2 b^5 c d e-10 a b^3 c^2 d e+10 a^2 b c^3 d e-b^6 e^2+a b^2 c^2 \left (4 c d^2-9 a e^2\right )-b^4 c \left (c d^2-6 a e^2\right )-2 a^2 c^3 \left (c d^2-a e^2\right )}{\sqrt {b^2-4 a c}}\right ) \text {Subst}\left (\int \frac {1}{-\frac {\sqrt {b^2-4 a c}}{2 e}-\frac {2 c d-b e}{2 e^2}+\frac {c x^2}{e^2}} \, dx,x,\sqrt {d+e x}\right )}{c^5 e^2} \\ & = -\frac {2 \left (b^3 c d-2 a b c^2 d-b^4 e+3 a b^2 c e-a^2 c^2 e\right ) \sqrt {d+e x}}{c^5}-\frac {2 b \left (b^2-2 a c\right ) (d+e x)^{3/2}}{3 c^4}+\frac {2 \left (c^2 d^2+b^2 e^2+c e (b d-a e)\right ) (d+e x)^{5/2}}{5 c^3 e^3}-\frac {2 (2 c d+b e) (d+e x)^{7/2}}{7 c^2 e^3}+\frac {2 (d+e x)^{9/2}}{9 c e^3}+\frac {\sqrt {2} \left (\left (b c d-b^2 e+a c e\right ) \left (b^2 c d-2 a c^2 d-b^3 e+3 a b c e\right )+\frac {2 b^5 c d e-10 a b^3 c^2 d e+10 a^2 b c^3 d e-b^6 e^2+a b^2 c^2 \left (4 c d^2-9 a e^2\right )-b^4 c \left (c d^2-6 a e^2\right )-2 a^2 c^3 \left (c d^2-a e^2\right )}{\sqrt {b^2-4 a c}}\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e}}\right )}{c^{11/2} \sqrt {2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e}}+\frac {\sqrt {2} \left (\left (b c d-b^2 e+a c e\right ) \left (b^2 c d-2 a c^2 d-b^3 e+3 a b c e\right )-\frac {2 b^5 c d e-10 a b^3 c^2 d e+10 a^2 b c^3 d e-b^6 e^2+a b^2 c^2 \left (4 c d^2-9 a e^2\right )-b^4 c \left (c d^2-6 a e^2\right )-2 a^2 c^3 \left (c d^2-a e^2\right )}{\sqrt {b^2-4 a c}}\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e}}\right )}{c^{11/2} \sqrt {2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e}} \\ \end{align*}

Mathematica [C] (verified)

Result contains complex when optimal does not.

Time = 3.09 (sec) , antiderivative size = 901, normalized size of antiderivative = 1.39 \[ \int \frac {x^4 (d+e x)^{3/2}}{a+b x+c x^2} \, dx=\frac {2 \sqrt {d+e x} \left (315 b^4 e^4-105 b^2 c e^3 (4 b d+9 a e+b e x)-9 c^3 e (d+e x)^2 (-2 b d+7 a e+5 b e x)+c^4 (d+e x)^2 \left (8 d^2-20 d e x+35 e^2 x^2\right )+21 c^2 e^2 \left (15 a^2 e^2+3 b^2 (d+e x)^2+10 a b e (4 d+e x)\right )\right )}{315 c^5 e^3}-\frac {\left (i b^6 e^2+b^5 e \left (-2 i c d+\sqrt {-b^2+4 a c} e\right )+i b^4 c \left (c d^2+2 i \sqrt {-b^2+4 a c} d e-6 a e^2\right )+a b^2 c^2 \left (-4 i c d^2+6 \sqrt {-b^2+4 a c} d e+9 i a e^2\right )+a b c^2 \left (3 a \sqrt {-b^2+4 a c} e^2-2 c d \left (\sqrt {-b^2+4 a c} d+5 i a e\right )\right )+b^3 c \left (-4 a \sqrt {-b^2+4 a c} e^2+c d \left (\sqrt {-b^2+4 a c} d+10 i a e\right )\right )-2 i a^2 c^3 \left (-c d^2+e \left (-i \sqrt {-b^2+4 a c} d+a e\right )\right )\right ) \arctan \left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {-2 c d+b e-i \sqrt {-b^2+4 a c} e}}\right )}{c^{11/2} \sqrt {-\frac {b^2}{2}+2 a c} \sqrt {-2 c d+\left (b-i \sqrt {-b^2+4 a c}\right ) e}}-\frac {\left (-i b^6 e^2+b^5 e \left (2 i c d+\sqrt {-b^2+4 a c} e\right )+b^4 c \left (-i c d^2-2 \sqrt {-b^2+4 a c} d e+6 i a e^2\right )+a b^2 c^2 \left (4 i c d^2+6 \sqrt {-b^2+4 a c} d e-9 i a e^2\right )+a b c^2 \left (3 a \sqrt {-b^2+4 a c} e^2-2 c d \left (\sqrt {-b^2+4 a c} d-5 i a e\right )\right )+b^3 c \left (-4 a \sqrt {-b^2+4 a c} e^2+c d \left (\sqrt {-b^2+4 a c} d-10 i a e\right )\right )+2 i a^2 c^3 \left (-c d^2+e \left (i \sqrt {-b^2+4 a c} d+a e\right )\right )\right ) \arctan \left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {-2 c d+b e+i \sqrt {-b^2+4 a c} e}}\right )}{c^{11/2} \sqrt {-\frac {b^2}{2}+2 a c} \sqrt {-2 c d+\left (b+i \sqrt {-b^2+4 a c}\right ) e}} \]

[In]

Integrate[(x^4*(d + e*x)^(3/2))/(a + b*x + c*x^2),x]

[Out]

(2*Sqrt[d + e*x]*(315*b^4*e^4 - 105*b^2*c*e^3*(4*b*d + 9*a*e + b*e*x) - 9*c^3*e*(d + e*x)^2*(-2*b*d + 7*a*e +
5*b*e*x) + c^4*(d + e*x)^2*(8*d^2 - 20*d*e*x + 35*e^2*x^2) + 21*c^2*e^2*(15*a^2*e^2 + 3*b^2*(d + e*x)^2 + 10*a
*b*e*(4*d + e*x))))/(315*c^5*e^3) - ((I*b^6*e^2 + b^5*e*((-2*I)*c*d + Sqrt[-b^2 + 4*a*c]*e) + I*b^4*c*(c*d^2 +
(2*I)*Sqrt[-b^2 + 4*a*c]*d*e - 6*a*e^2) + a*b^2*c^2*((-4*I)*c*d^2 + 6*Sqrt[-b^2 + 4*a*c]*d*e + (9*I)*a*e^2) +
a*b*c^2*(3*a*Sqrt[-b^2 + 4*a*c]*e^2 - 2*c*d*(Sqrt[-b^2 + 4*a*c]*d + (5*I)*a*e)) + b^3*c*(-4*a*Sqrt[-b^2 + 4*a
*c]*e^2 + c*d*(Sqrt[-b^2 + 4*a*c]*d + (10*I)*a*e)) - (2*I)*a^2*c^3*(-(c*d^2) + e*((-I)*Sqrt[-b^2 + 4*a*c]*d +
a*e)))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[-2*c*d + b*e - I*Sqrt[-b^2 + 4*a*c]*e]])/(c^(11/2)*Sqrt[-1/
2*b^2 + 2*a*c]*Sqrt[-2*c*d + (b - I*Sqrt[-b^2 + 4*a*c])*e]) - (((-I)*b^6*e^2 + b^5*e*((2*I)*c*d + Sqrt[-b^2 +
4*a*c]*e) + b^4*c*((-I)*c*d^2 - 2*Sqrt[-b^2 + 4*a*c]*d*e + (6*I)*a*e^2) + a*b^2*c^2*((4*I)*c*d^2 + 6*Sqrt[-b^2
+ 4*a*c]*d*e - (9*I)*a*e^2) + a*b*c^2*(3*a*Sqrt[-b^2 + 4*a*c]*e^2 - 2*c*d*(Sqrt[-b^2 + 4*a*c]*d - (5*I)*a*e))
+ b^3*c*(-4*a*Sqrt[-b^2 + 4*a*c]*e^2 + c*d*(Sqrt[-b^2 + 4*a*c]*d - (10*I)*a*e)) + (2*I)*a^2*c^3*(-(c*d^2) + e
*(I*Sqrt[-b^2 + 4*a*c]*d + a*e)))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[-2*c*d + b*e + I*Sqrt[-b^2 + 4*a
*c]*e]])/(c^(11/2)*Sqrt[-1/2*b^2 + 2*a*c]*Sqrt[-2*c*d + (b + I*Sqrt[-b^2 + 4*a*c])*e])

Maple [A] (verified)

Time = 0.90 (sec) , antiderivative size = 762, normalized size of antiderivative = 1.17

method	result	size
pseudoelliptic	\(\frac {2 \left (\frac {3 \left (\left (a c -b^{2}\right ) e +b c d \right ) \left (\left (a b c -\frac {1}{3} b^{3}\right ) e -\frac {2 d \left (a c -\frac {b^{2}}{2}\right ) c}{3}\right ) \sqrt {-4 e^{2} \left (a c -\frac {b^{2}}{4}\right )}}{2}+e \left (\left (-\frac {9}{2} a^{2} b^{2} c^{2}+3 a \,b^{4} c +a^{3} c^{3}-\frac {1}{2} b^{6}\right ) e^{2}+5 d b \left (a^{2} c^{2}-a \,b^{2} c +\frac {1}{5} b^{4}\right ) c e -d^{2} \left (a^{2} c^{2}-2 a \,b^{2} c +\frac {1}{2} b^{4}\right ) c^{2}\right )\right ) \sqrt {2}\, \sqrt {\left (b e -2 c d +\sqrt {-4 e^{2} \left (a c -\frac {b^{2}}{4}\right )}\right ) c}\, e^{3} \operatorname {arctanh}\left (\frac {c \sqrt {e x +d}\, \sqrt {2}}{\sqrt {\left (-b e +2 c d +\sqrt {-4 e^{2} \left (a c -\frac {b^{2}}{4}\right )}\right ) c}}\right )+2 \left (\sqrt {2}\, e^{3} \left (-\frac {3 \left (\left (a c -b^{2}\right ) e +b c d \right ) \left (\left (a b c -\frac {1}{3} b^{3}\right ) e -\frac {2 d \left (a c -\frac {b^{2}}{2}\right ) c}{3}\right ) \sqrt {-4 e^{2} \left (a c -\frac {b^{2}}{4}\right )}}{2}+e \left (\left (-\frac {9}{2} a^{2} b^{2} c^{2}+3 a \,b^{4} c +a^{3} c^{3}-\frac {1}{2} b^{6}\right ) e^{2}+5 d b \left (a^{2} c^{2}-a \,b^{2} c +\frac {1}{5} b^{4}\right ) c e -d^{2} \left (a^{2} c^{2}-2 a \,b^{2} c +\frac {1}{2} b^{4}\right ) c^{2}\right )\right ) \arctan \left (\frac {c \sqrt {e x +d}\, \sqrt {2}}{\sqrt {\left (b e -2 c d +\sqrt {-4 e^{2} \left (a c -\frac {b^{2}}{4}\right )}\right ) c}}\right )+\sqrt {-4 e^{2} \left (a c -\frac {b^{2}}{4}\right )}\, \sqrt {\left (b e -2 c d +\sqrt {-4 e^{2} \left (a c -\frac {b^{2}}{4}\right )}\right ) c}\, \left (\left (\frac {c^{4} x^{4}}{9}-\frac {\left (\frac {5 b x}{7}+a \right ) x^{2} c^{3}}{5}+\left (\frac {2}{3} a b x +\frac {1}{5} b^{2} x^{2}+a^{2}\right ) c^{2}+\left (-\frac {1}{3} b^{3} x -3 b^{2} a \right ) c +b^{4}\right ) e^{4}+\frac {8 d \left (\frac {5 c^{3} x^{3}}{84}-\frac {3 \left (\frac {4 b x}{7}+a \right ) x \,c^{2}}{20}+b \left (\frac {3 b x}{20}+a \right ) c -\frac {b^{3}}{2}\right ) c \,e^{3}}{3}-\frac {d^{2} \left (-\frac {c^{2} x^{2}}{21}+\left (\frac {b x}{7}+a \right ) c -b^{2}\right ) c^{2} e^{2}}{5}+\frac {2 d^{3} \left (-\frac {2 c x}{9}+b \right ) c^{3} e}{35}+\frac {8 c^{4} d^{4}}{315}\right ) \sqrt {e x +d}\right ) \sqrt {\left (-b e +2 c d +\sqrt {-4 e^{2} \left (a c -\frac {b^{2}}{4}\right )}\right ) c}}{\sqrt {-4 e^{2} \left (a c -\frac {b^{2}}{4}\right )}\, \sqrt {\left (b e -2 c d +\sqrt {-4 e^{2} \left (a c -\frac {b^{2}}{4}\right )}\right ) c}\, \sqrt {\left (-b e +2 c d +\sqrt {-4 e^{2} \left (a c -\frac {b^{2}}{4}\right )}\right ) c}\, e^{3} c^{5}}\)	\(762\)
derivativedivides	\(\text {Expression too large to display}\)	\(1094\)
default	\(\text {Expression too large to display}\)	\(1094\)
risch	\(\text {Expression too large to display}\)	\(1128\)

[In]

int(x^4*(e*x+d)^(3/2)/(c*x^2+b*x+a),x,method=_RETURNVERBOSE)

[Out]

2*((3/2*((a*c-b^2)*e+b*c*d)*((a*b*c-1/3*b^3)*e-2/3*d*(a*c-1/2*b^2)*c)*(-4*e^2*(a*c-1/4*b^2))^(1/2)+e*((-9/2*a^
2*b^2*c^2+3*a*b^4*c+a^3*c^3-1/2*b^6)*e^2+5*d*b*(a^2*c^2-a*b^2*c+1/5*b^4)*c*e-d^2*(a^2*c^2-2*a*b^2*c+1/2*b^4)*c
^2))*2^(1/2)*((b*e-2*c*d+(-4*e^2*(a*c-1/4*b^2))^(1/2))*c)^(1/2)*e^3*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c
*d+(-4*e^2*(a*c-1/4*b^2))^(1/2))*c)^(1/2))+(2^(1/2)*e^3*(-3/2*((a*c-b^2)*e+b*c*d)*((a*b*c-1/3*b^3)*e-2/3*d*(a*
c-1/2*b^2)*c)*(-4*e^2*(a*c-1/4*b^2))^(1/2)+e*((-9/2*a^2*b^2*c^2+3*a*b^4*c+a^3*c^3-1/2*b^6)*e^2+5*d*b*(a^2*c^2-
a*b^2*c+1/5*b^4)*c*e-d^2*(a^2*c^2-2*a*b^2*c+1/2*b^4)*c^2))*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-4*e^2*
(a*c-1/4*b^2))^(1/2))*c)^(1/2))+(-4*e^2*(a*c-1/4*b^2))^(1/2)*((b*e-2*c*d+(-4*e^2*(a*c-1/4*b^2))^(1/2))*c)^(1/2
)*((1/9*c^4*x^4-1/5*(5/7*b*x+a)*x^2*c^3+(2/3*a*b*x+1/5*b^2*x^2+a^2)*c^2+(-1/3*b^3*x-3*b^2*a)*c+b^4)*e^4+8/3*d*
(5/84*c^3*x^3-3/20*(4/7*b*x+a)*x*c^2+b*(3/20*b*x+a)*c-1/2*b^3)*c*e^3-1/5*d^2*(-1/21*c^2*x^2+(1/7*b*x+a)*c-b^2)
*c^2*e^2+2/35*d^3*(-2/9*c*x+b)*c^3*e+8/315*c^4*d^4)*(e*x+d)^(1/2))*((-b*e+2*c*d+(-4*e^2*(a*c-1/4*b^2))^(1/2))*
c)^(1/2))/(-4*e^2*(a*c-1/4*b^2))^(1/2)/((b*e-2*c*d+(-4*e^2*(a*c-1/4*b^2))^(1/2))*c)^(1/2)/((-b*e+2*c*d+(-4*e^2
*(a*c-1/4*b^2))^(1/2))*c)^(1/2)/e^3/c^5

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 14340 vs. \(2 (592) = 1184\).

Time = 17.37 (sec) , antiderivative size = 14340, normalized size of antiderivative = 22.06 \[ \int \frac {x^4 (d+e x)^{3/2}}{a+b x+c x^2} \, dx=\text {Too large to display} \]

[In]

integrate(x^4*(e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm="fricas")

[Out]

Too large to include

Sympy [F(-1)]

Timed out. \[ \int \frac {x^4 (d+e x)^{3/2}}{a+b x+c x^2} \, dx=\text {Timed out} \]

[In]

integrate(x**4*(e*x+d)**(3/2)/(c*x**2+b*x+a),x)

[Out]

Timed out

Maxima [F]

\[ \int \frac {x^4 (d+e x)^{3/2}}{a+b x+c x^2} \, dx=\int { \frac {{\left (e x + d\right )}^{\frac {3}{2}} x^{4}}{c x^{2} + b x + a} \,d x } \]

[In]

integrate(x^4*(e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm="maxima")

[Out]

integrate((e*x + d)^(3/2)*x^4/(c*x^2 + b*x + a), x)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1612 vs. \(2 (592) = 1184\).

Time = 0.40 (sec) , antiderivative size = 1612, normalized size of antiderivative = 2.48 \[ \int \frac {x^4 (d+e x)^{3/2}}{a+b x+c x^2} \, dx=\text {Too large to display} \]

[In]

integrate(x^4*(e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm="giac")

[Out]

-1/4*(sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*((b^5*c^2 - 6*a*b^3*c^3 + 8*a^2*b*c^4)*d^2 - 2*(b^6*c -
7*a*b^4*c^2 + 13*a^2*b^2*c^3 - 4*a^3*c^4)*d*e + (b^7 - 8*a*b^5*c + 19*a^2*b^3*c^2 - 12*a^3*b*c^3)*e^2)*c^2*e^
2 - 2*((b^3*c^4 - 2*a*b*c^5)*sqrt(b^2 - 4*a*c)*d^3 - (2*b^4*c^3 - 5*a*b^2*c^4 + a^2*c^5)*sqrt(b^2 - 4*a*c)*d^2
*e + (b^5*c^2 - 2*a*b^3*c^3 - a^2*b*c^4)*sqrt(b^2 - 4*a*c)*d*e^2 - (a*b^4*c^2 - 3*a^2*b^2*c^3 + a^3*c^4)*sqrt(
b^2 - 4*a*c)*e^3)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(c)*abs(e) + (2*(b^4*c^5 - 4*a*b^2*c^6 +
2*a^2*c^7)*d^3*e - (5*b^5*c^4 - 24*a*b^3*c^5 + 22*a^2*b*c^6)*d^2*e^2 + 2*(2*b^6*c^3 - 11*a*b^4*c^4 + 14*a^2*b
^2*c^5 - 2*a^3*c^6)*d*e^3 - (b^7*c^2 - 6*a*b^5*c^3 + 9*a^2*b^3*c^4 - 2*a^3*b*c^5)*e^4)*sqrt(-4*c^2*d + 2*(b*c
- sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(e*x + d)/sqrt(-(2*c^10*d*e^30 - b*c^9*e^31 + sqrt(-4*(c^10*
d^2*e^30 - b*c^9*d*e^31 + a*c^9*e^32)*c^10*e^30 + (2*c^10*d*e^30 - b*c^9*e^31)^2))/(c^10*e^30)))/((sqrt(b^2 -
4*a*c)*c^8*d^2 - sqrt(b^2 - 4*a*c)*b*c^7*d*e + sqrt(b^2 - 4*a*c)*a*c^7*e^2)*c^2*abs(e)) + 1/4*(sqrt(-4*c^2*d +
2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*((b^5*c^2 - 6*a*b^3*c^3 + 8*a^2*b*c^4)*d^2 - 2*(b^6*c - 7*a*b^4*c^2 + 13*a^2
*b^2*c^3 - 4*a^3*c^4)*d*e + (b^7 - 8*a*b^5*c + 19*a^2*b^3*c^2 - 12*a^3*b*c^3)*e^2)*c^2*e^2 + 2*((b^3*c^4 - 2*a
*b*c^5)*sqrt(b^2 - 4*a*c)*d^3 - (2*b^4*c^3 - 5*a*b^2*c^4 + a^2*c^5)*sqrt(b^2 - 4*a*c)*d^2*e + (b^5*c^2 - 2*a*b
^3*c^3 - a^2*b*c^4)*sqrt(b^2 - 4*a*c)*d*e^2 - (a*b^4*c^2 - 3*a^2*b^2*c^3 + a^3*c^4)*sqrt(b^2 - 4*a*c)*e^3)*sqr
t(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(c)*abs(e) + (2*(b^4*c^5 - 4*a*b^2*c^6 + 2*a^2*c^7)*d^3*e - (
5*b^5*c^4 - 24*a*b^3*c^5 + 22*a^2*b*c^6)*d^2*e^2 + 2*(2*b^6*c^3 - 11*a*b^4*c^4 + 14*a^2*b^2*c^5 - 2*a^3*c^6)*d
*e^3 - (b^7*c^2 - 6*a*b^5*c^3 + 9*a^2*b^3*c^4 - 2*a^3*b*c^5)*e^4)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c
)*e))*arctan(2*sqrt(1/2)*sqrt(e*x + d)/sqrt(-(2*c^10*d*e^30 - b*c^9*e^31 - sqrt(-4*(c^10*d^2*e^30 - b*c^9*d*e^
31 + a*c^9*e^32)*c^10*e^30 + (2*c^10*d*e^30 - b*c^9*e^31)^2))/(c^10*e^30)))/((sqrt(b^2 - 4*a*c)*c^8*d^2 - sqrt
(b^2 - 4*a*c)*b*c^7*d*e + sqrt(b^2 - 4*a*c)*a*c^7*e^2)*c^2*abs(e)) + 2/315*(35*(e*x + d)^(9/2)*c^8*e^24 - 90*(
e*x + d)^(7/2)*c^8*d*e^24 + 63*(e*x + d)^(5/2)*c^8*d^2*e^24 - 45*(e*x + d)^(7/2)*b*c^7*e^25 + 63*(e*x + d)^(5/
2)*b*c^7*d*e^25 + 63*(e*x + d)^(5/2)*b^2*c^6*e^26 - 63*(e*x + d)^(5/2)*a*c^7*e^26 - 105*(e*x + d)^(3/2)*b^3*c^
5*e^27 + 210*(e*x + d)^(3/2)*a*b*c^6*e^27 - 315*sqrt(e*x + d)*b^3*c^5*d*e^27 + 630*sqrt(e*x + d)*a*b*c^6*d*e^2
7 + 315*sqrt(e*x + d)*b^4*c^4*e^28 - 945*sqrt(e*x + d)*a*b^2*c^5*e^28 + 315*sqrt(e*x + d)*a^2*c^6*e^28)/(c^9*e
^27)

Mupad [B] (verification not implemented)

Time = 16.93 (sec) , antiderivative size = 31485, normalized size of antiderivative = 48.44 \[ \int \frac {x^4 (d+e x)^{3/2}}{a+b x+c x^2} \, dx=\text {Too large to display} \]

[In]

int((x^4*(d + e*x)^(3/2))/(a + b*x + c*x^2),x)

[Out]

(d + e*x)^(1/2)*((2*d^4)/(c*e^3) - ((a*e^5 + c*d^2*e^3 - b*d*e^4)*((12*d^2)/(c*e^3) - (2*(a*e^5 + c*d^2*e^3 -
b*d*e^4))/(c^2*e^6) + (((8*d)/(c*e^3) + (2*(b*e^4 - 2*c*d*e^3))/(c^2*e^6))*(b*e^4 - 2*c*d*e^3))/(c*e^3)))/(c*e
^3) + ((b*e^4 - 2*c*d*e^3)*((8*d^3)/(c*e^3) - (((8*d)/(c*e^3) + (2*(b*e^4 - 2*c*d*e^3))/(c^2*e^6))*(a*e^5 + c*
d^2*e^3 - b*d*e^4))/(c*e^3) + ((b*e^4 - 2*c*d*e^3)*((12*d^2)/(c*e^3) - (2*(a*e^5 + c*d^2*e^3 - b*d*e^4))/(c^2*
e^6) + (((8*d)/(c*e^3) + (2*(b*e^4 - 2*c*d*e^3))/(c^2*e^6))*(b*e^4 - 2*c*d*e^3))/(c*e^3)))/(c*e^3)))/(c*e^3))
- atan(((((8*(4*a^4*c^9*e^5 - a*b^6*c^6*e^5 + b^7*c^6*d*e^4 + 7*a^2*b^4*c^7*e^5 - 13*a^3*b^2*c^8*e^5 + 4*a^3*c
^10*d^2*e^3 + b^5*c^8*d^3*e^2 - 2*b^6*c^7*d^2*e^3 - 21*a^2*b^2*c^9*d^2*e^3 - 6*a*b^5*c^7*d*e^4 + 4*a^3*b*c^9*d
*e^4 - 6*a*b^3*c^9*d^3*e^2 + 13*a*b^4*c^8*d^2*e^3 + 8*a^2*b*c^10*d^3*e^2 + 7*a^2*b^3*c^8*d*e^4))/c^9 - (8*(d +
e*x)^(1/2)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 - b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3
+ 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^
2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 + a^5*c^5*e^3
*(-(4*a*c - b^2)^3)^(1/2) + b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 + 10*a^2*b
^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) - 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 35*a^3*b^4*c^3*e^3*(-(4*a*
c - b^2)^3)^(1/2) - 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) + 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*
a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e + 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^5
*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) - 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2
*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2
+ 306*a^5*b^2*c^6*d*e^2 - 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2)
+ 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b*c^5*d*
e^2*(-(4*a*c - b^2)^3)^(1/2) - 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 63*a^2*b^5*c^3*d*e^2*(-(4*a*c -
b^2)^3)^(1/2) + 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2)
)/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2)*(b^3*c^11*e^3 - 2*b^2*c^12*d*e^2 - 4*a*b*c^12*e^3 + 8*a*c
^13*d*e^2))/c^9)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 - b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4
*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a
^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 + a^5*c^
5*e^3*(-(4*a*c - b^2)^3)^(1/2) + b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 + 10*
a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) - 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 35*a^3*b^4*c^3*e^3*(-
(4*a*c - b^2)^3)^(1/2) - 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) + 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2)
- 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e + 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 6*
a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) - 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 22
5*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*
d*e^2 + 306*a^5*b^2*c^6*d*e^2 - 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^
(1/2) + 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b*c
^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 63*a^2*b^5*c^3*d*e^2*(-(4*
a*c - b^2)^3)^(1/2) + 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^
(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2) - (8*(d + e*x)^(1/2)*(b^12*e^6 + 2*a^6*c^6*e^6 + 54*
a^2*b^8*c^2*e^6 - 112*a^3*b^6*c^3*e^6 + 105*a^4*b^4*c^4*e^6 - 36*a^5*b^2*c^5*e^6 + 2*a^4*c^8*d^4*e^2 - 12*a^5*
c^7*d^2*e^4 + b^8*c^4*d^4*e^2 - 4*b^9*c^3*d^3*e^3 + 6*b^10*c^2*d^2*e^4 - 12*a*b^10*c*e^6 - 4*b^11*c*d*e^5 + 20
*a^2*b^4*c^6*d^4*e^2 - 108*a^2*b^5*c^5*d^3*e^3 + 210*a^2*b^6*c^4*d^2*e^4 - 16*a^3*b^2*c^7*d^4*e^2 + 120*a^3*b^
3*c^6*d^3*e^3 - 300*a^3*b^4*c^5*d^2*e^4 + 150*a^4*b^2*c^6*d^2*e^4 + 44*a*b^9*c^2*d*e^5 + 44*a^5*b*c^6*d*e^5 -
8*a*b^6*c^5*d^4*e^2 + 36*a*b^7*c^4*d^3*e^3 - 60*a*b^8*c^3*d^2*e^4 - 176*a^2*b^7*c^3*d*e^5 + 308*a^3*b^5*c^4*d*
e^5 - 36*a^4*b*c^7*d^3*e^3 - 220*a^4*b^3*c^5*d*e^5))/c^9)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 - b^10*e^
3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^
2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b
^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 + a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2)
- 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 + 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) - 28*a^2*b^6*c^2*e^3*(-(4*a*
c - b^2)^3)^(1/2) + 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2)
+ 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e + 3*
b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) - 4*a^3*b*c^6*d^3*(-(4*a*c - b
^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 +
387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 - 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1
/2) - 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 24*a*b^7*c^2*d*
e^2*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b
^2)^3)^(1/2) + 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) -
60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2)*1i - (((8*(
4*a^4*c^9*e^5 - a*b^6*c^6*e^5 + b^7*c^6*d*e^4 + 7*a^2*b^4*c^7*e^5 - 13*a^3*b^2*c^8*e^5 + 4*a^3*c^10*d^2*e^3 +
b^5*c^8*d^3*e^2 - 2*b^6*c^7*d^2*e^3 - 21*a^2*b^2*c^9*d^2*e^3 - 6*a*b^5*c^7*d*e^4 + 4*a^3*b*c^9*d*e^4 - 6*a*b^3
*c^9*d^3*e^2 + 13*a*b^4*c^8*d^2*e^3 + 8*a^2*b*c^10*d^3*e^2 + 7*a^2*b^3*c^8*d*e^4))/c^9 + (8*(d + e*x)^(1/2)*(-
(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 - b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6
*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88
*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 + a^5*c^5*e^3*(-(4*a*c - b^
2)^3)^(1/2) + b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 + 10*a^2*b^3*c^5*d^3*(-(
4*a*c - b^2)^3)^(1/2) - 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1
/2) - 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) + 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*
e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e + 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^5*c^4*d^3*(-(4*
a*c - b^2)^3)^(1/2) - 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2
- 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2
*c^6*d*e^2 - 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 21*a*b^6*c^
3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b*c^5*d*e^2*(-(4*a*c -
b^2)^3)^(1/2) - 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2)
+ 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c
^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2)*(b^3*c^11*e^3 - 2*b^2*c^12*d*e^2 - 4*a*b*c^12*e^3 + 8*a*c^13*d*e^2))/c^
9)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 - b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*
b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3
+ 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 + a^5*c^5*e^3*(-(4*a*c
- b^2)^3)^(1/2) + b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 + 10*a^2*b^3*c^5*d^
3*(-(4*a*c - b^2)^3)^(1/2) - 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^
3)^(1/2) - 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) + 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3
*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e + 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^5*c^4*d^3*
(-(4*a*c - b^2)^3)^(1/2) - 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*
d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^
5*b^2*c^6*d*e^2 - 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 21*a*b
^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b*c^5*d*e^2*(-(4*
a*c - b^2)^3)^(1/2) - 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^
(1/2) + 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*
a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2) + (8*(d + e*x)^(1/2)*(b^12*e^6 + 2*a^6*c^6*e^6 + 54*a^2*b^8*c^2*e^
6 - 112*a^3*b^6*c^3*e^6 + 105*a^4*b^4*c^4*e^6 - 36*a^5*b^2*c^5*e^6 + 2*a^4*c^8*d^4*e^2 - 12*a^5*c^7*d^2*e^4 +
b^8*c^4*d^4*e^2 - 4*b^9*c^3*d^3*e^3 + 6*b^10*c^2*d^2*e^4 - 12*a*b^10*c*e^6 - 4*b^11*c*d*e^5 + 20*a^2*b^4*c^6*d
^4*e^2 - 108*a^2*b^5*c^5*d^3*e^3 + 210*a^2*b^6*c^4*d^2*e^4 - 16*a^3*b^2*c^7*d^4*e^2 + 120*a^3*b^3*c^6*d^3*e^3
- 300*a^3*b^4*c^5*d^2*e^4 + 150*a^4*b^2*c^6*d^2*e^4 + 44*a*b^9*c^2*d*e^5 + 44*a^5*b*c^6*d*e^5 - 8*a*b^6*c^5*d^
4*e^2 + 36*a*b^7*c^4*d^3*e^3 - 60*a*b^8*c^3*d^2*e^4 - 176*a^2*b^7*c^3*d*e^5 + 308*a^3*b^5*c^4*d*e^5 - 36*a^4*b
*c^7*d^3*e^3 - 220*a^4*b^3*c^5*d*e^5))/c^9)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 - b^10*e^3*(-(4*a*c - b
^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3
+ 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 2
31*a^5*b^3*c^5*e^3 + a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c
*e^3 - 3*b^12*c*d*e^2 + 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) - 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1
/2) + 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) + 9*a*b^8*c*e^
3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e + 3*b^9*c*d*e^2*(-
(4*a*c - b^2)^3)^(1/2) - 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) - 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) +
189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c
^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 - 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 3*b^8*c^
2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 24*a*b^7*c^2*d*e^2*(-(4*a*c -
b^2)^3)^(1/2) + 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) +
63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 60*a^3*b^3*c^
4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2)*1i)/((16*(a^6*b^5*e^8 - 4
*a^7*b^3*c*e^8 + 3*a^8*b*c^2*e^8 - 2*a^5*b^6*d*e^7 - 2*a^8*c^3*d*e^7 + a^4*b^7*d^2*e^6 - 2*a^6*c^5*d^5*e^3 - 4
*a^7*c^4*d^3*e^5 + a^4*b^3*c^4*d^6*e^2 - 4*a^4*b^4*c^3*d^5*e^3 + 6*a^4*b^5*c^2*d^4*e^4 + 10*a^5*b^2*c^4*d^5*e^
3 - 16*a^5*b^3*c^3*d^4*e^4 + 8*a^5*b^4*c^2*d^3*e^5 + 8*a^6*b^2*c^3*d^3*e^5 - 16*a^6*b^3*c^2*d^2*e^6 + 6*a^6*b^
4*c*d*e^7 - 4*a^4*b^6*c*d^3*e^5 - 2*a^5*b*c^5*d^6*e^2 + 2*a^5*b^5*c*d^2*e^6 + 3*a^6*b*c^4*d^4*e^4 + 8*a^7*b*c^
3*d^2*e^6))/c^9 + (((8*(4*a^4*c^9*e^5 - a*b^6*c^6*e^5 + b^7*c^6*d*e^4 + 7*a^2*b^4*c^7*e^5 - 13*a^3*b^2*c^8*e^5
+ 4*a^3*c^10*d^2*e^3 + b^5*c^8*d^3*e^2 - 2*b^6*c^7*d^2*e^3 - 21*a^2*b^2*c^9*d^2*e^3 - 6*a*b^5*c^7*d*e^4 + 4*a
^3*b*c^9*d*e^4 - 6*a*b^3*c^9*d^3*e^2 + 13*a*b^4*c^8*d^2*e^3 + 8*a^2*b*c^10*d^3*e^2 + 7*a^2*b^3*c^8*d*e^4))/c^9
- (8*(d + e*x)^(1/2)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 - b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^
8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 -
66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 + a
^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2
+ 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) - 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 35*a^3*b^4*c^3*e
^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) + 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(
1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e + 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2)
- 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) - 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e
- 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4
*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 - 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 3*b^8*c^2*d^2*e*(-(4*a*c - b^2
)^3)^(1/2) + 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 15*a^
4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 63*a^2*b^5*c^3*d*e^2*
(-(4*a*c - b^2)^3)^(1/2) + 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2
)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2)*(b^3*c^11*e^3 - 2*b^2*c^12*d*e^2 - 4*a*b*c^12*e
^3 + 8*a*c^13*d*e^2))/c^9)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 - b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12
*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*
d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^
3 + a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d
*e^2 + 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) - 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 35*a^3*b^4*
c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) + 9*a*b^8*c*e^3*(-(4*a*c - b^2)
^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e + 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^
(1/2) - 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) - 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*
d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^
4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 - 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 3*b^8*c^2*d^2*e*(-(4*a*c
- b^2)^3)^(1/2) + 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) +
15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 63*a^2*b^5*c^3*d
*e^2*(-(4*a*c - b^2)^3)^(1/2) + 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 60*a^3*b^3*c^4*d*e^2*(-(4*a*c
- b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2) - (8*(d + e*x)^(1/2)*(b^12*e^6 + 2*a^6*c^6
*e^6 + 54*a^2*b^8*c^2*e^6 - 112*a^3*b^6*c^3*e^6 + 105*a^4*b^4*c^4*e^6 - 36*a^5*b^2*c^5*e^6 + 2*a^4*c^8*d^4*e^2
- 12*a^5*c^7*d^2*e^4 + b^8*c^4*d^4*e^2 - 4*b^9*c^3*d^3*e^3 + 6*b^10*c^2*d^2*e^4 - 12*a*b^10*c*e^6 - 4*b^11*c*
d*e^5 + 20*a^2*b^4*c^6*d^4*e^2 - 108*a^2*b^5*c^5*d^3*e^3 + 210*a^2*b^6*c^4*d^2*e^4 - 16*a^3*b^2*c^7*d^4*e^2 +
120*a^3*b^3*c^6*d^3*e^3 - 300*a^3*b^4*c^5*d^2*e^4 + 150*a^4*b^2*c^6*d^2*e^4 + 44*a*b^9*c^2*d*e^5 + 44*a^5*b*c^
6*d*e^5 - 8*a*b^6*c^5*d^4*e^2 + 36*a*b^7*c^4*d^3*e^3 - 60*a*b^8*c^3*d^2*e^4 - 176*a^2*b^7*c^3*d*e^5 + 308*a^3*
b^5*c^4*d*e^5 - 36*a^4*b*c^7*d^3*e^3 - 220*a^4*b^3*c^5*d*e^5))/c^9)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3
- b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2
*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 +
363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 + a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + b^7*c^3*d^3*(-(4*a*c - b^2
)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 + 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) - 28*a^2*b^6*c^2*e
^3*(-(4*a*c - b^2)^3)^(1/2) + 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)
^3)^(1/2) + 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*
d^2*e + 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) - 4*a^3*b*c^6*d^3*(-
(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c
^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 - 3*a^4*c^6*d^2*e*(-(4*a*c -
b^2)^3)^(1/2) - 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 24*a*
b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 45*a^2*b^4*c^4*d^2*e*(-
(4*a*c - b^2)^3)^(1/2) + 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^
3)^(1/2) - 60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2) +
(((8*(4*a^4*c^9*e^5 - a*b^6*c^6*e^5 + b^7*c^6*d*e^4 + 7*a^2*b^4*c^7*e^5 - 13*a^3*b^2*c^8*e^5 + 4*a^3*c^10*d^2
*e^3 + b^5*c^8*d^3*e^2 - 2*b^6*c^7*d^2*e^3 - 21*a^2*b^2*c^9*d^2*e^3 - 6*a*b^5*c^7*d*e^4 + 4*a^3*b*c^9*d*e^4 -
6*a*b^3*c^9*d^3*e^2 + 13*a*b^4*c^8*d^2*e^3 + 8*a^2*b*c^10*d^3*e^2 + 7*a^2*b^3*c^8*d*e^4))/c^9 + (8*(d + e*x)^(
1/2)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 - b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^
6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d
^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 + a^5*c^5*e^3*(-(4*a
*c - b^2)^3)^(1/2) + b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 + 10*a^2*b^3*c^5*
d^3*(-(4*a*c - b^2)^3)^(1/2) - 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2
)^3)^(1/2) - 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) + 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c
^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e + 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^5*c^4*d^
3*(-(4*a*c - b^2)^3)^(1/2) - 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^
3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*
a^5*b^2*c^6*d*e^2 - 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 21*a
*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b*c^5*d*e^2*(-(
4*a*c - b^2)^3)^(1/2) - 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3
)^(1/2) + 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(1
6*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2)*(b^3*c^11*e^3 - 2*b^2*c^12*d*e^2 - 4*a*b*c^12*e^3 + 8*a*c^13*d*e
^2))/c^9)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 - b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 +
44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*
c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 + a^5*c^5*e^3*(
-(4*a*c - b^2)^3)^(1/2) + b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 + 10*a^2*b^3
*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) - 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 35*a^3*b^4*c^3*e^3*(-(4*a*c
- b^2)^3)^(1/2) - 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) + 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*
b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e + 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^5*c
^4*d^3*(-(4*a*c - b^2)^3)^(1/2) - 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2*b
^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 +
306*a^5*b^2*c^6*d*e^2 - 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) +
21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b*c^5*d*e^
2*(-(4*a*c - b^2)^3)^(1/2) - 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b
^2)^3)^(1/2) + 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/
(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2) + (8*(d + e*x)^(1/2)*(b^12*e^6 + 2*a^6*c^6*e^6 + 54*a^2*b^8
*c^2*e^6 - 112*a^3*b^6*c^3*e^6 + 105*a^4*b^4*c^4*e^6 - 36*a^5*b^2*c^5*e^6 + 2*a^4*c^8*d^4*e^2 - 12*a^5*c^7*d^2
*e^4 + b^8*c^4*d^4*e^2 - 4*b^9*c^3*d^3*e^3 + 6*b^10*c^2*d^2*e^4 - 12*a*b^10*c*e^6 - 4*b^11*c*d*e^5 + 20*a^2*b^
4*c^6*d^4*e^2 - 108*a^2*b^5*c^5*d^3*e^3 + 210*a^2*b^6*c^4*d^2*e^4 - 16*a^3*b^2*c^7*d^4*e^2 + 120*a^3*b^3*c^6*d
^3*e^3 - 300*a^3*b^4*c^5*d^2*e^4 + 150*a^4*b^2*c^6*d^2*e^4 + 44*a*b^9*c^2*d*e^5 + 44*a^5*b*c^6*d*e^5 - 8*a*b^6
*c^5*d^4*e^2 + 36*a*b^7*c^4*d^3*e^3 - 60*a*b^8*c^3*d^2*e^4 - 176*a^2*b^7*c^3*d*e^5 + 308*a^3*b^5*c^4*d*e^5 - 3
6*a^4*b*c^7*d^3*e^3 - 220*a^4*b^3*c^5*d*e^5))/c^9)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 - b^10*e^3*(-(4*
a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c
^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*
e^3 - 231*a^5*b^3*c^5*e^3 + a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a
*b^11*c*e^3 - 3*b^12*c*d*e^2 + 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) - 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2
)^3)^(1/2) + 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) + 9*a*b
^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e + 3*b^9*c*d
*e^2*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) - 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^
(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^
4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 - 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 3
*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 24*a*b^7*c^2*d*e^2*(-(
4*a*c - b^2)^3)^(1/2) + 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^
(1/2) + 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 60*a^3
*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2)))*(-(b^13*e^3 + 8*
a^5*c^8*d^3 - b^10*c^3*d^3 - b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*
c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e
^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 + a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) +
b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 + 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3
)^(1/2) - 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a^4*b
^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) + 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*
c^2*d*e^2 - 108*a^5*b*c^7*d^2*e + 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^
(1/2) - 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5
*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 - 3
*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 21*a*b^6*c^3*d^2*e*(-(4*a
*c - b^2)^3)^(1/2) - 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2)
- 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 30*a^3*b^2*
c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11
- 8*a*b^2*c^12)))^(1/2)*2i - atan(((((8*(4*a^4*c^9*e^5 - a*b^6*c^6*e^5 + b^7*c^6*d*e^4 + 7*a^2*b^4*c^7*e^5 -
13*a^3*b^2*c^8*e^5 + 4*a^3*c^10*d^2*e^3 + b^5*c^8*d^3*e^2 - 2*b^6*c^7*d^2*e^3 - 21*a^2*b^2*c^9*d^2*e^3 - 6*a*b
^5*c^7*d*e^4 + 4*a^3*b*c^9*d*e^4 - 6*a*b^3*c^9*d^3*e^2 + 13*a*b^4*c^8*d^2*e^3 + 8*a^2*b*c^10*d^3*e^2 + 7*a^2*b
^3*c^8*d*e^4))/c^9 - (8*(d + e*x)^(1/2)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 + b^10*e^3*(-(4*a*c - b^2)^
3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96
*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a
^5*b^3*c^5*e^3 - a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) - b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3
- 3*b^12*c*d*e^2 - 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2)
- 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^8*c*e^3*(-
(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e - 3*b^9*c*d*e^2*(-(4*a
*c - b^2)^3)^(1/2) + 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) + 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189
*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d
^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 + 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 3*b^8*c^2*d^
2*e*(-(4*a*c - b^2)^3)^(1/2) - 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2
)^3)^(1/2) - 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 63*
a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 60*a^3*b^3*c^4*d*
e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2)*(b^3*c^11*e^3 - 2*b^2*c^12*d*
e^2 - 4*a*b*c^12*e^3 + 8*a*c^13*d*e^2))/c^9)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 + b^10*e^3*(-(4*a*c -
b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3
+ 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 -
231*a^5*b^3*c^5*e^3 - a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) - b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*
c*e^3 - 3*b^12*c*d*e^2 - 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(
1/2) - 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^8*c*e
^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e - 3*b^9*c*d*e^2*(
-(4*a*c - b^2)^3)^(1/2) + 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) + 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2)
+ 189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*
c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 + 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 3*b^8*c
^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 24*a*b^7*c^2*d*e^2*(-(4*a*c
- b^2)^3)^(1/2) - 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2)
- 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 60*a^3*b^3*c
^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2) - (8*(d + e*x)^(1/2)*(b^
12*e^6 + 2*a^6*c^6*e^6 + 54*a^2*b^8*c^2*e^6 - 112*a^3*b^6*c^3*e^6 + 105*a^4*b^4*c^4*e^6 - 36*a^5*b^2*c^5*e^6 +
2*a^4*c^8*d^4*e^2 - 12*a^5*c^7*d^2*e^4 + b^8*c^4*d^4*e^2 - 4*b^9*c^3*d^3*e^3 + 6*b^10*c^2*d^2*e^4 - 12*a*b^10
*c*e^6 - 4*b^11*c*d*e^5 + 20*a^2*b^4*c^6*d^4*e^2 - 108*a^2*b^5*c^5*d^3*e^3 + 210*a^2*b^6*c^4*d^2*e^4 - 16*a^3*
b^2*c^7*d^4*e^2 + 120*a^3*b^3*c^6*d^3*e^3 - 300*a^3*b^4*c^5*d^2*e^4 + 150*a^4*b^2*c^6*d^2*e^4 + 44*a*b^9*c^2*d
*e^5 + 44*a^5*b*c^6*d*e^5 - 8*a*b^6*c^5*d^4*e^2 + 36*a*b^7*c^4*d^3*e^3 - 60*a*b^8*c^3*d^2*e^4 - 176*a^2*b^7*c^
3*d*e^5 + 308*a^3*b^5*c^4*d*e^5 - 36*a^4*b*c^7*d^3*e^3 - 220*a^4*b^3*c^5*d*e^5))/c^9)*(-(b^13*e^3 + 8*a^5*c^8*
d^3 - b^10*c^3*d^3 + b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^
2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253
*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 - a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) - b^7*c^3*
d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 - 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2)
+ 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b^2*c^4*e
^3*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^
2 - 108*a^5*b*c^7*d^2*e - 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) +
4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2
*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 + 3*a^4*c^6
*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2
)^3)^(1/2) + 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 45*a^
2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 30*a^3*b^2*c^5*d^2*
e*(-(4*a*c - b^2)^3)^(1/2) + 60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b
^2*c^12)))^(1/2)*1i - (((8*(4*a^4*c^9*e^5 - a*b^6*c^6*e^5 + b^7*c^6*d*e^4 + 7*a^2*b^4*c^7*e^5 - 13*a^3*b^2*c^8
*e^5 + 4*a^3*c^10*d^2*e^3 + b^5*c^8*d^3*e^2 - 2*b^6*c^7*d^2*e^3 - 21*a^2*b^2*c^9*d^2*e^3 - 6*a*b^5*c^7*d*e^4 +
4*a^3*b*c^9*d*e^4 - 6*a*b^3*c^9*d^3*e^2 + 13*a*b^4*c^8*d^2*e^3 + 8*a^2*b*c^10*d^3*e^2 + 7*a^2*b^3*c^8*d*e^4))
/c^9 + (8*(d + e*x)^(1/2)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 + b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*
a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d
^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3
- a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) - b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*
e^2 - 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 35*a^3*b^4*c
^3*e^3*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^8*c*e^3*(-(4*a*c - b^2)^
3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e - 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(
1/2) + 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) + 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d
^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4
*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 + 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 3*b^8*c^2*d^2*e*(-(4*a*c -
b^2)^3)^(1/2) - 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 1
5*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 63*a^2*b^5*c^3*d*
e^2*(-(4*a*c - b^2)^3)^(1/2) - 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 60*a^3*b^3*c^4*d*e^2*(-(4*a*c -
b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2)*(b^3*c^11*e^3 - 2*b^2*c^12*d*e^2 - 4*a*b*c^
12*e^3 + 8*a*c^13*d*e^2))/c^9)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 + b^10*e^3*(-(4*a*c - b^2)^3)^(1/2)
+ 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*
c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^
5*e^3 - a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) - b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12
*c*d*e^2 - 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 35*a^3*
b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^8*c*e^3*(-(4*a*c -
b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e - 3*b^9*c*d*e^2*(-(4*a*c - b^2)
^3)^(1/2) + 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) + 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*
c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 67
5*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 + 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 3*b^8*c^2*d^2*e*(-(4*
a*c - b^2)^3)^(1/2) - 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2
) - 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 63*a^2*b^5*c
^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 60*a^3*b^3*c^4*d*e^2*(-(4*
a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2) + (8*(d + e*x)^(1/2)*(b^12*e^6 + 2*a^6
*c^6*e^6 + 54*a^2*b^8*c^2*e^6 - 112*a^3*b^6*c^3*e^6 + 105*a^4*b^4*c^4*e^6 - 36*a^5*b^2*c^5*e^6 + 2*a^4*c^8*d^4
*e^2 - 12*a^5*c^7*d^2*e^4 + b^8*c^4*d^4*e^2 - 4*b^9*c^3*d^3*e^3 + 6*b^10*c^2*d^2*e^4 - 12*a*b^10*c*e^6 - 4*b^1
1*c*d*e^5 + 20*a^2*b^4*c^6*d^4*e^2 - 108*a^2*b^5*c^5*d^3*e^3 + 210*a^2*b^6*c^4*d^2*e^4 - 16*a^3*b^2*c^7*d^4*e^
2 + 120*a^3*b^3*c^6*d^3*e^3 - 300*a^3*b^4*c^5*d^2*e^4 + 150*a^4*b^2*c^6*d^2*e^4 + 44*a*b^9*c^2*d*e^5 + 44*a^5*
b*c^6*d*e^5 - 8*a*b^6*c^5*d^4*e^2 + 36*a*b^7*c^4*d^3*e^3 - 60*a*b^8*c^3*d^2*e^4 - 176*a^2*b^7*c^3*d*e^5 + 308*
a^3*b^5*c^4*d*e^5 - 36*a^4*b*c^7*d^3*e^3 - 220*a^4*b^3*c^5*d*e^5))/c^9)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3
*d^3 + b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2
*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e
^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 - a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) - b^7*c^3*d^3*(-(4*a*c -
b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 - 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 28*a^2*b^6*c
^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b^2*c^4*e^3*(-(4*a*c -
b^2)^3)^(1/2) - 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*
c^7*d^2*e - 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) + 4*a^3*b*c^6*d^
3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b
^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 + 3*a^4*c^6*d^2*e*(-(4*a*
c - b^2)^3)^(1/2) + 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 2
4*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 45*a^2*b^4*c^4*d^2*
e*(-(4*a*c - b^2)^3)^(1/2) - 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b
^2)^3)^(1/2) + 60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/
2)*1i)/((16*(a^6*b^5*e^8 - 4*a^7*b^3*c*e^8 + 3*a^8*b*c^2*e^8 - 2*a^5*b^6*d*e^7 - 2*a^8*c^3*d*e^7 + a^4*b^7*d^2
*e^6 - 2*a^6*c^5*d^5*e^3 - 4*a^7*c^4*d^3*e^5 + a^4*b^3*c^4*d^6*e^2 - 4*a^4*b^4*c^3*d^5*e^3 + 6*a^4*b^5*c^2*d^4
*e^4 + 10*a^5*b^2*c^4*d^5*e^3 - 16*a^5*b^3*c^3*d^4*e^4 + 8*a^5*b^4*c^2*d^3*e^5 + 8*a^6*b^2*c^3*d^3*e^5 - 16*a^
6*b^3*c^2*d^2*e^6 + 6*a^6*b^4*c*d*e^7 - 4*a^4*b^6*c*d^3*e^5 - 2*a^5*b*c^5*d^6*e^2 + 2*a^5*b^5*c*d^2*e^6 + 3*a^
6*b*c^4*d^4*e^4 + 8*a^7*b*c^3*d^2*e^6))/c^9 + (((8*(4*a^4*c^9*e^5 - a*b^6*c^6*e^5 + b^7*c^6*d*e^4 + 7*a^2*b^4*
c^7*e^5 - 13*a^3*b^2*c^8*e^5 + 4*a^3*c^10*d^2*e^3 + b^5*c^8*d^3*e^2 - 2*b^6*c^7*d^2*e^3 - 21*a^2*b^2*c^9*d^2*e
^3 - 6*a*b^5*c^7*d*e^4 + 4*a^3*b*c^9*d*e^4 - 6*a*b^3*c^9*d^3*e^2 + 13*a*b^4*c^8*d^2*e^3 + 8*a^2*b*c^10*d^3*e^2
+ 7*a^2*b^3*c^8*d*e^4))/c^9 - (8*(d + e*x)^(1/2)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 + b^10*e^3*(-(4*a
*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^
5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e
^3 - 231*a^5*b^3*c^5*e^3 - a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) - b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*
b^11*c*e^3 - 3*b^12*c*d*e^2 - 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)
^3)^(1/2) - 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^
8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e - 3*b^9*c*d*
e^2*(-(4*a*c - b^2)^3)^(1/2) + 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) + 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(
1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4
*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 + 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 3*
b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 24*a*b^7*c^2*d*e^2*(-(4
*a*c - b^2)^3)^(1/2) - 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(
1/2) - 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 60*a^3*
b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2)*(b^3*c^11*e^3 - 2*b
^2*c^12*d*e^2 - 4*a*b*c^12*e^3 + 8*a*c^13*d*e^2))/c^9)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 + b^10*e^3*(
-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b
^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*
c^4*e^3 - 231*a^5*b^3*c^5*e^3 - a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) - b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) -
15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 - 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 28*a^2*b^6*c^2*e^3*(-(4*a*c -
b^2)^3)^(1/2) - 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) - 9
*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e - 3*b^9
*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) + 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)
^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 38
7*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 + 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2)
+ 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 24*a*b^7*c^2*d*e^2
*(-(4*a*c - b^2)^3)^(1/2) - 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)
^3)^(1/2) - 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 60
*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2) - (8*(d + e*x)
^(1/2)*(b^12*e^6 + 2*a^6*c^6*e^6 + 54*a^2*b^8*c^2*e^6 - 112*a^3*b^6*c^3*e^6 + 105*a^4*b^4*c^4*e^6 - 36*a^5*b^2
*c^5*e^6 + 2*a^4*c^8*d^4*e^2 - 12*a^5*c^7*d^2*e^4 + b^8*c^4*d^4*e^2 - 4*b^9*c^3*d^3*e^3 + 6*b^10*c^2*d^2*e^4 -
12*a*b^10*c*e^6 - 4*b^11*c*d*e^5 + 20*a^2*b^4*c^6*d^4*e^2 - 108*a^2*b^5*c^5*d^3*e^3 + 210*a^2*b^6*c^4*d^2*e^4
- 16*a^3*b^2*c^7*d^4*e^2 + 120*a^3*b^3*c^6*d^3*e^3 - 300*a^3*b^4*c^5*d^2*e^4 + 150*a^4*b^2*c^6*d^2*e^4 + 44*a
*b^9*c^2*d*e^5 + 44*a^5*b*c^6*d*e^5 - 8*a*b^6*c^5*d^4*e^2 + 36*a*b^7*c^4*d^3*e^3 - 60*a*b^8*c^3*d^2*e^4 - 176*
a^2*b^7*c^3*d*e^5 + 308*a^3*b^5*c^4*d*e^5 - 36*a^4*b*c^7*d^3*e^3 - 220*a^4*b^3*c^5*d*e^5))/c^9)*(-(b^13*e^3 +
8*a^5*c^8*d^3 - b^10*c^3*d^3 + b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^
6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2
*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 - a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2)
- b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 - 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)
^3)^(1/2) + 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4
*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^1
0*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e - 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3
)^(1/2) + 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b
^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 +
3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 21*a*b^6*c^3*d^2*e*(-(4
*a*c - b^2)^3)^(1/2) + 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/
2) + 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 30*a^3*b^
2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^
11 - 8*a*b^2*c^12)))^(1/2) + (((8*(4*a^4*c^9*e^5 - a*b^6*c^6*e^5 + b^7*c^6*d*e^4 + 7*a^2*b^4*c^7*e^5 - 13*a^3*
b^2*c^8*e^5 + 4*a^3*c^10*d^2*e^3 + b^5*c^8*d^3*e^2 - 2*b^6*c^7*d^2*e^3 - 21*a^2*b^2*c^9*d^2*e^3 - 6*a*b^5*c^7*
d*e^4 + 4*a^3*b*c^9*d*e^4 - 6*a*b^3*c^9*d^3*e^2 + 13*a*b^4*c^8*d^2*e^3 + 8*a^2*b*c^10*d^3*e^2 + 7*a^2*b^3*c^8*
d*e^4))/c^9 + (8*(d + e*x)^(1/2)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 + b^10*e^3*(-(4*a*c - b^2)^3)^(1/2
) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^
4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*
c^5*e^3 - a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) - b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^
12*c*d*e^2 - 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 35*a^
3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^8*c*e^3*(-(4*a*c
- b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e - 3*b^9*c*d*e^2*(-(4*a*c - b^
2)^3)^(1/2) + 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) + 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^
7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e -
675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 + 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 3*b^8*c^2*d^2*e*(-(
4*a*c - b^2)^3)^(1/2) - 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1
/2) - 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 63*a^2*b^5
*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 60*a^3*b^3*c^4*d*e^2*(-(
4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2)*(b^3*c^11*e^3 - 2*b^2*c^12*d*e^2 - 4
*a*b*c^12*e^3 + 8*a*c^13*d*e^2))/c^9)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 + b^10*e^3*(-(4*a*c - b^2)^3)
^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a
^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5
*b^3*c^5*e^3 - a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) - b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 -
3*b^12*c*d*e^2 - 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) -
35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^8*c*e^3*(-(4
*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e - 3*b^9*c*d*e^2*(-(4*a*c
- b^2)^3)^(1/2) + 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) + 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a
^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2
*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 + 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 3*b^8*c^2*d^2*
e*(-(4*a*c - b^2)^3)^(1/2) - 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^
3)^(1/2) - 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 63*a^
2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 60*a^3*b^3*c^4*d*e^
2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2) + (8*(d + e*x)^(1/2)*(b^12*e^6
+ 2*a^6*c^6*e^6 + 54*a^2*b^8*c^2*e^6 - 112*a^3*b^6*c^3*e^6 + 105*a^4*b^4*c^4*e^6 - 36*a^5*b^2*c^5*e^6 + 2*a^4*
c^8*d^4*e^2 - 12*a^5*c^7*d^2*e^4 + b^8*c^4*d^4*e^2 - 4*b^9*c^3*d^3*e^3 + 6*b^10*c^2*d^2*e^4 - 12*a*b^10*c*e^6
- 4*b^11*c*d*e^5 + 20*a^2*b^4*c^6*d^4*e^2 - 108*a^2*b^5*c^5*d^3*e^3 + 210*a^2*b^6*c^4*d^2*e^4 - 16*a^3*b^2*c^7
*d^4*e^2 + 120*a^3*b^3*c^6*d^3*e^3 - 300*a^3*b^4*c^5*d^2*e^4 + 150*a^4*b^2*c^6*d^2*e^4 + 44*a*b^9*c^2*d*e^5 +
44*a^5*b*c^6*d*e^5 - 8*a*b^6*c^5*d^4*e^2 + 36*a*b^7*c^4*d^3*e^3 - 60*a*b^8*c^3*d^2*e^4 - 176*a^2*b^7*c^3*d*e^5
+ 308*a^3*b^5*c^4*d*e^5 - 36*a^4*b*c^7*d^3*e^3 - 220*a^4*b^3*c^5*d*e^5))/c^9)*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b
^10*c^3*d^3 + b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3 + 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b
^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^
7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 - a^5*c^5*e^3*(-(4*a*c - b^2)^3)^(1/2) - b^7*c^3*d^3*(-(
4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 - 10*a^2*b^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 28*a^
2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 35*a^3*b^4*c^3*e^3*(-(4*a*c - b^2)^3)^(1/2) + 15*a^4*b^2*c^4*e^3*(-(4
*a*c - b^2)^3)^(1/2) - 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108
*a^5*b*c^7*d^2*e - 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 6*a*b^5*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) + 4*a^3*b
*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 57
0*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2 + 306*a^5*b^2*c^6*d*e^2 + 3*a^4*c^6*d^2*e*
(-(4*a*c - b^2)^3)^(1/2) + 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1
/2) + 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 15*a^4*b*c^5*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 45*a^2*b^4*c
^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 63*a^2*b^5*c^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 30*a^3*b^2*c^5*d^2*e*(-(4*
a*c - b^2)^3)^(1/2) + 60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12
)))^(1/2)))*(-(b^13*e^3 + 8*a^5*c^8*d^3 - b^10*c^3*d^3 + b^10*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^8*c^4*d^3
+ 44*a^6*b*c^6*e^3 - 24*a^6*c^7*d*e^2 + 3*b^11*c^2*d^2*e - 52*a^2*b^6*c^5*d^3 + 96*a^3*b^4*c^6*d^3 - 66*a^4*b^
2*c^7*d^3 + 88*a^2*b^9*c^2*e^3 - 253*a^3*b^7*c^3*e^3 + 363*a^4*b^5*c^4*e^3 - 231*a^5*b^3*c^5*e^3 - a^5*c^5*e^3
*(-(4*a*c - b^2)^3)^(1/2) - b^7*c^3*d^3*(-(4*a*c - b^2)^3)^(1/2) - 15*a*b^11*c*e^3 - 3*b^12*c*d*e^2 - 10*a^2*b
^3*c^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 28*a^2*b^6*c^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 35*a^3*b^4*c^3*e^3*(-(4*a*
c - b^2)^3)^(1/2) + 15*a^4*b^2*c^4*e^3*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^8*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 39*
a*b^9*c^3*d^2*e + 42*a*b^10*c^2*d*e^2 - 108*a^5*b*c^7*d^2*e - 3*b^9*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 6*a*b^5
*c^4*d^3*(-(4*a*c - b^2)^3)^(1/2) + 4*a^3*b*c^6*d^3*(-(4*a*c - b^2)^3)^(1/2) + 189*a^2*b^7*c^4*d^2*e - 225*a^2
*b^8*c^3*d*e^2 - 414*a^3*b^5*c^5*d^2*e + 570*a^3*b^6*c^4*d*e^2 + 387*a^4*b^3*c^6*d^2*e - 675*a^4*b^4*c^5*d*e^2
+ 306*a^5*b^2*c^6*d*e^2 + 3*a^4*c^6*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 3*b^8*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2)
- 21*a*b^6*c^3*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 24*a*b^7*c^2*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 15*a^4*b*c^5*d*
e^2*(-(4*a*c - b^2)^3)^(1/2) + 45*a^2*b^4*c^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 63*a^2*b^5*c^3*d*e^2*(-(4*a*c -
b^2)^3)^(1/2) - 30*a^3*b^2*c^5*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 60*a^3*b^3*c^4*d*e^2*(-(4*a*c - b^2)^3)^(1/2)
)/(2*(16*a^2*c^13 + b^4*c^11 - 8*a*b^2*c^12)))^(1/2)*2i - ((8*d)/(7*c*e^3) + (2*(b*e^4 - 2*c*d*e^3))/(7*c^2*e^
6))*(d + e*x)^(7/2) + (d + e*x)^(5/2)*((12*d^2)/(5*c*e^3) - (2*(a*e^5 + c*d^2*e^3 - b*d*e^4))/(5*c^2*e^6) + ((
(8*d)/(c*e^3) + (2*(b*e^4 - 2*c*d*e^3))/(c^2*e^6))*(b*e^4 - 2*c*d*e^3))/(5*c*e^3)) - (d + e*x)^(3/2)*((8*d^3)/
(3*c*e^3) - (((8*d)/(c*e^3) + (2*(b*e^4 - 2*c*d*e^3))/(c^2*e^6))*(a*e^5 + c*d^2*e^3 - b*d*e^4))/(3*c*e^3) + ((
b*e^4 - 2*c*d*e^3)*((12*d^2)/(c*e^3) - (2*(a*e^5 + c*d^2*e^3 - b*d*e^4))/(c^2*e^6) + (((8*d)/(c*e^3) + (2*(b*e
^4 - 2*c*d*e^3))/(c^2*e^6))*(b*e^4 - 2*c*d*e^3))/(c*e^3)))/(3*c*e^3)) + (2*(d + e*x)^(9/2))/(9*c*e^3)