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

Optimal. Leaf size=607 \[ -\frac {2 \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right ) \left (-2 a b d e-a \left (c d^2-a e^2\right )+b^2 d^2\right )}{a^3 \sqrt {d}}+\frac {\sqrt {2} \sqrt {c} \left (-a b \left (e \left (2 d \sqrt {b^2-4 a c}-a e\right )+3 c d^2\right )+a \left (a e^2 \sqrt {b^2-4 a c}-c d \left (d \sqrt {b^2-4 a c}-4 a e\right )\right )+b^2 d \left (d \sqrt {b^2-4 a c}-2 a e\right )+b^3 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )}}\right )}{a^3 \sqrt {b^2-4 a c} \sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )}}-\frac {\sqrt {2} \sqrt {c} \left (-a b \left (3 c d^2-e \left (2 d \sqrt {b^2-4 a c}+a e\right )\right )-a \left (a e^2 \sqrt {b^2-4 a c}-c d \left (d \sqrt {b^2-4 a c}+4 a e\right )\right )-b^2 d \left (d \sqrt {b^2-4 a c}+2 a e\right )+b^3 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}\right )}{a^3 \sqrt {b^2-4 a c} \sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}+\frac {\sqrt {d+e x} (b d-2 a e)}{a^2 x}-\frac {e (b d-2 a e) \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right )}{a^2 \sqrt {d}}-\frac {3 e^2 \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right )}{4 a \sqrt {d}}-\frac {d \sqrt {d+e x}}{2 a x^2}+\frac {3 e \sqrt {d+e x}}{4 a x} \]

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Rubi [A]  time = 3.93, antiderivative size = 607, normalized size of antiderivative = 1.00, number of steps used = 12, number of rules used = 6, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.240, Rules used = {897, 1287, 199, 206, 1166, 208} \begin {gather*} -\frac {2 \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right ) \left (-2 a b d e-a \left (c d^2-a e^2\right )+b^2 d^2\right )}{a^3 \sqrt {d}}+\frac {\sqrt {2} \sqrt {c} \left (-a b \left (e \left (2 d \sqrt {b^2-4 a c}-a e\right )+3 c d^2\right )+a \left (a e^2 \sqrt {b^2-4 a c}-c d \left (d \sqrt {b^2-4 a c}-4 a e\right )\right )+b^2 d \left (d \sqrt {b^2-4 a c}-2 a e\right )+b^3 d^2\right ) \tanh ^{-1}\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 )}{a^3 \sqrt {b^2-4 a c} \sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )}}-\frac {\sqrt {2} \sqrt {c} \left (-a b \left (3 c d^2-e \left (2 d \sqrt {b^2-4 a c}+a e\right )\right )-a \left (a e^2 \sqrt {b^2-4 a c}-c d \left (d \sqrt {b^2-4 a c}+4 a e\right )\right )-b^2 d \left (d \sqrt {b^2-4 a c}+2 a e\right )+b^3 d^2\right ) \tanh ^{-1}\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 )}{a^3 \sqrt {b^2-4 a c} \sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}+\frac {\sqrt {d+e x} (b d-2 a e)}{a^2 x}-\frac {e (b d-2 a e) \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right )}{a^2 \sqrt {d}}-\frac {3 e^2 \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right )}{4 a \sqrt {d}}-\frac {d \sqrt {d+e x}}{2 a x^2}+\frac {3 e \sqrt {d+e x}}{4 a x} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-(d*Sqrt[d + e*x])/(2*a*x^2) + (3*e*Sqrt[d + e*x])/(4*a*x) + ((b*d - 2*a*e)*Sqrt[d + e*x])/(a^2*x) - (3*e^2*Ar
cTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*a*Sqrt[d]) - (e*(b*d - 2*a*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(a^2*Sqrt[d]) -
(2*(b^2*d^2 - 2*a*b*d*e - a*(c*d^2 - a*e^2))*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(a^3*Sqrt[d]) + (Sqrt[2]*Sqrt[c]
*(b^3*d^2 + b^2*d*(Sqrt[b^2 - 4*a*c]*d - 2*a*e) + a*(a*Sqrt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d - 4*a*
e)) - a*b*(3*c*d^2 + e*(2*Sqrt[b^2 - 4*a*c]*d - a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b
- Sqrt[b^2 - 4*a*c])*e]])/(a^3*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (Sqrt[2]*Sqrt[c]*
(b^3*d^2 - b^2*d*(Sqrt[b^2 - 4*a*c]*d + 2*a*e) - a*b*(3*c*d^2 - e*(2*Sqrt[b^2 - 4*a*c]*d + a*e)) - a*(a*Sqrt[b
^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d + 4*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b
+ Sqrt[b^2 - 4*a*c])*e]])/(a^3*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])

Rule 199

Int[((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> -Simp[(x*(a + b*x^n)^(p + 1))/(a*n*(p + 1)), x] + Dist[(n*(p +
1) + 1)/(a*n*(p + 1)), Int[(a + b*x^n)^(p + 1), x], x] /; FreeQ[{a, b}, x] && IGtQ[n, 0] && LtQ[p, -1] && (In
tegerQ[2*p] || (n == 2 && IntegerQ[4*p]) || (n == 2 && IntegerQ[3*p]) || Denominator[p + 1/n] < Denominator[p]
)

Rule 206

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])

Rule 208

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

Rule 897

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 1166

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 1287

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*} \int \frac {(d+e x)^{3/2}}{x^3 \left (a+b x+c x^2\right )} \, dx &=\frac {2 \operatorname {Subst}\left (\int \frac {x^4}{\left (-\frac {d}{e}+\frac {x^2}{e}\right )^3 \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 )} \, dx,x,\sqrt {d+e x}\right )}{e}\\ &=\frac {2 \operatorname {Subst}\left (\int \left (-\frac {d^2 e^3}{a \left (d-x^2\right )^3}+\frac {d e^2 (-b d+2 a e)}{a^2 \left (d-x^2\right )^2}+\frac {e \left (-b^2 d^2+2 a b d e+a \left (c d^2-a e^2\right )\right )}{a^3 \left (d-x^2\right )}+\frac {e \left (\left (b^2 d-a c d-a b e\right ) \left (c d^2-b d e+a e^2\right )-c \left (b^2 d^2-2 a b d e-a \left (c d^2-a e^2\right )\right ) x^2\right )}{a^3 \left (c d^2-b d e+a e^2-(2 c d-b e) x^2+c x^4\right )}\right ) \, dx,x,\sqrt {d+e x}\right )}{e}\\ &=\frac {2 \operatorname {Subst}\left (\int \frac {\left (b^2 d-a c d-a b e\right ) \left (c d^2-b d e+a e^2\right )-c \left (b^2 d^2-2 a b d e-a \left (c d^2-a e^2\right )\right ) x^2}{c d^2-b d e+a e^2+(-2 c d+b e) x^2+c x^4} \, dx,x,\sqrt {d+e x}\right )}{a^3}-\frac {\left (2 d^2 e^2\right ) \operatorname {Subst}\left (\int \frac {1}{\left (d-x^2\right )^3} \, dx,x,\sqrt {d+e x}\right )}{a}-\frac {(2 d e (b d-2 a e)) \operatorname {Subst}\left (\int \frac {1}{\left (d-x^2\right )^2} \, dx,x,\sqrt {d+e x}\right )}{a^2}-\frac {\left (2 \left (b^2 d^2-2 a b d e-a \left (c d^2-a e^2\right )\right )\right ) \operatorname {Subst}\left (\int \frac {1}{d-x^2} \, dx,x,\sqrt {d+e x}\right )}{a^3}\\ &=-\frac {d \sqrt {d+e x}}{2 a x^2}+\frac {(b d-2 a e) \sqrt {d+e x}}{a^2 x}-\frac {2 \left (b^2 d^2-2 a b d e-a \left (c d^2-a e^2\right )\right ) \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right )}{a^3 \sqrt {d}}-\frac {\left (3 d e^2\right ) \operatorname {Subst}\left (\int \frac {1}{\left (d-x^2\right )^2} \, dx,x,\sqrt {d+e x}\right )}{2 a}-\frac {(e (b d-2 a e)) \operatorname {Subst}\left (\int \frac {1}{d-x^2} \, dx,x,\sqrt {d+e x}\right )}{a^2}-\frac {\left (c \left (b^3 d^2+b^2 d \left (\sqrt {b^2-4 a c} d-2 a e\right )+a \left (a \sqrt {b^2-4 a c} e^2-c d \left (\sqrt {b^2-4 a c} d-4 a e\right )\right )-a b \left (3 c d^2+e \left (2 \sqrt {b^2-4 a c} d-a e\right )\right )\right )\right ) \operatorname {Subst}\left (\int \frac {1}{-\frac {1}{2} \sqrt {b^2-4 a c} e+\frac {1}{2} (-2 c d+b e)+c x^2} \, dx,x,\sqrt {d+e x}\right )}{a^3 \sqrt {b^2-4 a c}}+\frac {\left (c \left (b^3 d^2-b^2 d \left (\sqrt {b^2-4 a c} d+2 a e\right )-a b \left (3 c d^2-e \left (2 \sqrt {b^2-4 a c} d+a e\right )\right )-a \left (a \sqrt {b^2-4 a c} e^2-c d \left (\sqrt {b^2-4 a c} d+4 a e\right )\right )\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {1}{2} \sqrt {b^2-4 a c} e+\frac {1}{2} (-2 c d+b e)+c x^2} \, dx,x,\sqrt {d+e x}\right )}{a^3 \sqrt {b^2-4 a c}}\\ &=-\frac {d \sqrt {d+e x}}{2 a x^2}+\frac {3 e \sqrt {d+e x}}{4 a x}+\frac {(b d-2 a e) \sqrt {d+e x}}{a^2 x}-\frac {e (b d-2 a e) \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right )}{a^2 \sqrt {d}}-\frac {2 \left (b^2 d^2-2 a b d e-a \left (c d^2-a e^2\right )\right ) \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right )}{a^3 \sqrt {d}}+\frac {\sqrt {2} \sqrt {c} \left (b^3 d^2+b^2 d \left (\sqrt {b^2-4 a c} d-2 a e\right )+a \left (a \sqrt {b^2-4 a c} e^2-c d \left (\sqrt {b^2-4 a c} d-4 a e\right )\right )-a b \left (3 c d^2+e \left (2 \sqrt {b^2-4 a c} d-a e\right )\right )\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 )}{a^3 \sqrt {b^2-4 a c} \sqrt {2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e}}-\frac {\sqrt {2} \sqrt {c} \left (b^3 d^2-b^2 d \left (\sqrt {b^2-4 a c} d+2 a e\right )-a b \left (3 c d^2-e \left (2 \sqrt {b^2-4 a c} d+a e\right )\right )-a \left (a \sqrt {b^2-4 a c} e^2-c d \left (\sqrt {b^2-4 a c} d+4 a e\right )\right )\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 )}{a^3 \sqrt {b^2-4 a c} \sqrt {2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e}}-\frac {\left (3 e^2\right ) \operatorname {Subst}\left (\int \frac {1}{d-x^2} \, dx,x,\sqrt {d+e x}\right )}{4 a}\\ &=-\frac {d \sqrt {d+e x}}{2 a x^2}+\frac {3 e \sqrt {d+e x}}{4 a x}+\frac {(b d-2 a e) \sqrt {d+e x}}{a^2 x}-\frac {3 e^2 \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right )}{4 a \sqrt {d}}-\frac {e (b d-2 a e) \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right )}{a^2 \sqrt {d}}-\frac {2 \left (b^2 d^2-2 a b d e-a \left (c d^2-a e^2\right )\right ) \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right )}{a^3 \sqrt {d}}+\frac {\sqrt {2} \sqrt {c} \left (b^3 d^2+b^2 d \left (\sqrt {b^2-4 a c} d-2 a e\right )+a \left (a \sqrt {b^2-4 a c} e^2-c d \left (\sqrt {b^2-4 a c} d-4 a e\right )\right )-a b \left (3 c d^2+e \left (2 \sqrt {b^2-4 a c} d-a e\right )\right )\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 )}{a^3 \sqrt {b^2-4 a c} \sqrt {2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e}}-\frac {\sqrt {2} \sqrt {c} \left (b^3 d^2-b^2 d \left (\sqrt {b^2-4 a c} d+2 a e\right )-a b \left (3 c d^2-e \left (2 \sqrt {b^2-4 a c} d+a e\right )\right )-a \left (a \sqrt {b^2-4 a c} e^2-c d \left (\sqrt {b^2-4 a c} d+4 a e\right )\right )\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 )}{a^3 \sqrt {b^2-4 a c} \sqrt {2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e}}\\ \end {align*}

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Mathematica [A]  time = 2.86, size = 587, normalized size = 0.97 \begin {gather*} \frac {-\frac {2 a^2 d \sqrt {d+e x}}{x^2}+3 a^2 e \left (\frac {\sqrt {d+e x}}{x}-\frac {e \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right )}{\sqrt {d}}\right )-\frac {8 \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right ) \left (-2 a b d e+a \left (a e^2-c d^2\right )+b^2 d^2\right )}{\sqrt {d}}+\frac {4 \sqrt {2} \sqrt {c} \left (a b \left (e \left (a e-2 d \sqrt {b^2-4 a c}\right )-3 c d^2\right )+a \left (c d \left (4 a e-d \sqrt {b^2-4 a c}\right )+a e^2 \sqrt {b^2-4 a c}\right )+b^2 d \left (d \sqrt {b^2-4 a c}-2 a e\right )+b^3 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {e \sqrt {b^2-4 a c}-b e+2 c d}}\right )}{\sqrt {b^2-4 a c} \sqrt {e \left (\sqrt {b^2-4 a c}-b\right )+2 c d}}-\frac {4 \sqrt {2} \sqrt {c} \left (a b \left (e \left (2 d \sqrt {b^2-4 a c}+a e\right )-3 c d^2\right )+a \left (c d \left (d \sqrt {b^2-4 a c}+4 a e\right )-a e^2 \sqrt {b^2-4 a c}\right )-b^2 d \left (d \sqrt {b^2-4 a c}+2 a e\right )+b^3 d^2\right ) \tanh ^{-1}\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 )}{\sqrt {b^2-4 a c} \sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}+\frac {4 a \sqrt {d+e x} (b d-2 a e)}{x}+\frac {4 a e (2 a e-b d) \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right )}{\sqrt {d}}}{4 a^3} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

((-2*a^2*d*Sqrt[d + e*x])/x^2 + (4*a*(b*d - 2*a*e)*Sqrt[d + e*x])/x + (4*a*e*(-(b*d) + 2*a*e)*ArcTanh[Sqrt[d +
e*x]/Sqrt[d]])/Sqrt[d] - (8*(b^2*d^2 - 2*a*b*d*e + a*(-(c*d^2) + a*e^2))*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/Sqrt
[d] + 3*a^2*e*(Sqrt[d + e*x]/x - (e*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/Sqrt[d]) + (4*Sqrt[2]*Sqrt[c]*(b^3*d^2 + b
^2*d*(Sqrt[b^2 - 4*a*c]*d - 2*a*e) + a*b*(-3*c*d^2 + e*(-2*Sqrt[b^2 - 4*a*c]*d + a*e)) + a*(a*Sqrt[b^2 - 4*a*c
]*e^2 + c*d*(-(Sqrt[b^2 - 4*a*c]*d) + 4*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - b*e + Sqrt
[b^2 - 4*a*c]*e]])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d + (-b + Sqrt[b^2 - 4*a*c])*e]) - (4*Sqrt[2]*Sqrt[c]*(b^3*d^2
- b^2*d*(Sqrt[b^2 - 4*a*c]*d + 2*a*e) + a*b*(-3*c*d^2 + e*(2*Sqrt[b^2 - 4*a*c]*d + a*e)) + a*(-(a*Sqrt[b^2 - 4
*a*c]*e^2) + c*d*(Sqrt[b^2 - 4*a*c]*d + 4*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqr
t[b^2 - 4*a*c])*e]])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]))/(4*a^3)

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IntegrateAlgebraic [C]  time = 3.20, size = 759, normalized size = 1.25 \begin {gather*} -\frac {\sqrt {d+e x} \left (5 a e (d+e x)-3 a d e+4 b d^2-4 b d (d+e x)\right )}{4 a^2 e x^2}+\frac {\tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right ) \left (-3 a^2 e^2+12 a b d e+8 a c d^2-8 b^2 d^2\right )}{4 a^3 \sqrt {d}}+\frac {\left (-\sqrt {2} a^2 \sqrt {c} e^2 \sqrt {4 a c-b^2}+i \sqrt {2} a^2 b \sqrt {c} e^2+4 i \sqrt {2} a^2 c^{3/2} d e+\sqrt {2} a c^{3/2} d^2 \sqrt {4 a c-b^2}-\sqrt {2} b^2 \sqrt {c} d^2 \sqrt {4 a c-b^2}-2 i \sqrt {2} a b^2 \sqrt {c} d e+2 \sqrt {2} a b \sqrt {c} d e \sqrt {4 a c-b^2}-3 i \sqrt {2} a b c^{3/2} d^2+i \sqrt {2} b^3 \sqrt {c} d^2\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {-i e \sqrt {4 a c-b^2}+b e-2 c d}}\right )}{a^3 \sqrt {4 a c-b^2} \sqrt {-i e \sqrt {4 a c-b^2}+b e-2 c d}}+\frac {\left (-\sqrt {2} a^2 \sqrt {c} e^2 \sqrt {4 a c-b^2}-i \sqrt {2} a^2 b \sqrt {c} e^2-4 i \sqrt {2} a^2 c^{3/2} d e+\sqrt {2} a c^{3/2} d^2 \sqrt {4 a c-b^2}-\sqrt {2} b^2 \sqrt {c} d^2 \sqrt {4 a c-b^2}+2 i \sqrt {2} a b^2 \sqrt {c} d e+2 \sqrt {2} a b \sqrt {c} d e \sqrt {4 a c-b^2}+3 i \sqrt {2} a b c^{3/2} d^2-i \sqrt {2} b^3 \sqrt {c} d^2\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {i e \sqrt {4 a c-b^2}+b e-2 c d}}\right )}{a^3 \sqrt {4 a c-b^2} \sqrt {i e \sqrt {4 a c-b^2}+b e-2 c d}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-1/4*(Sqrt[d + e*x]*(4*b*d^2 - 3*a*d*e - 4*b*d*(d + e*x) + 5*a*e*(d + e*x)))/(a^2*e*x^2) + ((I*Sqrt[2]*b^3*Sqr
t[c]*d^2 - (3*I)*Sqrt[2]*a*b*c^(3/2)*d^2 - Sqrt[2]*b^2*Sqrt[c]*Sqrt[-b^2 + 4*a*c]*d^2 + Sqrt[2]*a*c^(3/2)*Sqrt
[-b^2 + 4*a*c]*d^2 - (2*I)*Sqrt[2]*a*b^2*Sqrt[c]*d*e + (4*I)*Sqrt[2]*a^2*c^(3/2)*d*e + 2*Sqrt[2]*a*b*Sqrt[c]*S
qrt[-b^2 + 4*a*c]*d*e + I*Sqrt[2]*a^2*b*Sqrt[c]*e^2 - Sqrt[2]*a^2*Sqrt[c]*Sqrt[-b^2 + 4*a*c]*e^2)*ArcTan[(Sqrt
[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[-2*c*d + b*e - I*Sqrt[-b^2 + 4*a*c]*e]])/(a^3*Sqrt[-b^2 + 4*a*c]*Sqrt[-2*c*d +
b*e - I*Sqrt[-b^2 + 4*a*c]*e]) + (((-I)*Sqrt[2]*b^3*Sqrt[c]*d^2 + (3*I)*Sqrt[2]*a*b*c^(3/2)*d^2 - Sqrt[2]*b^2
*Sqrt[c]*Sqrt[-b^2 + 4*a*c]*d^2 + Sqrt[2]*a*c^(3/2)*Sqrt[-b^2 + 4*a*c]*d^2 + (2*I)*Sqrt[2]*a*b^2*Sqrt[c]*d*e -
(4*I)*Sqrt[2]*a^2*c^(3/2)*d*e + 2*Sqrt[2]*a*b*Sqrt[c]*Sqrt[-b^2 + 4*a*c]*d*e - I*Sqrt[2]*a^2*b*Sqrt[c]*e^2 -
Sqrt[2]*a^2*Sqrt[c]*Sqrt[-b^2 + 4*a*c]*e^2)*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[-2*c*d + b*e + I*Sqrt[
-b^2 + 4*a*c]*e]])/(a^3*Sqrt[-b^2 + 4*a*c]*Sqrt[-2*c*d + b*e + I*Sqrt[-b^2 + 4*a*c]*e]) + ((-8*b^2*d^2 + 8*a*c
*d^2 + 12*a*b*d*e - 3*a^2*e^2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*a^3*Sqrt[d])

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fricas [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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giac [B]  time = 0.61, size = 1121, normalized size = 1.85

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/4*(((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^2*e - 2*(a*b^3 - 4*a^2*b*c)*d*e^2 + (a^2*b^2 - 4*a^3*c)*e^3)*sqrt(-4*c^
2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*a^2 + 2*(sqrt(b^2 - 4*a*c)*a*b^3*d^2*e + sqrt(b^2 - 4*a*c)*a^3*b*e^3 -
(a*b^2*c - a^2*c^2)*sqrt(b^2 - 4*a*c)*d^3 - (2*a^2*b^2 - a^3*c)*sqrt(b^2 - 4*a*c)*d*e^2)*sqrt(-4*c^2*d + 2*(b*
c - sqrt(b^2 - 4*a*c)*c)*e)*abs(a) + (a^4*b^2*e^3 - 2*(a^2*b^3*c - 3*a^3*b*c^2)*d^3 + (a^2*b^4 + a^3*b^2*c - 8
*a^4*c^2)*d^2*e - 2*(a^3*b^3 - a^4*b*c)*d*e^2)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt
(1/2)*sqrt(x*e + d)/sqrt(-(2*a^3*c*d - a^3*b*e + sqrt(-4*(a^3*c*d^2 - a^3*b*d*e + a^4*e^2)*a^3*c + (2*a^3*c*d
- a^3*b*e)^2))/(a^3*c)))/((sqrt(b^2 - 4*a*c)*a^4*c*d^2 - sqrt(b^2 - 4*a*c)*a^4*b*d*e + sqrt(b^2 - 4*a*c)*a^5*e
^2)*abs(a)*abs(c)) + 1/4*(((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^2*e - 2*(a*b^3 - 4*a^2*b*c)*d*e^2 + (a^2*b^2 - 4*a^
3*c)*e^3)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*a^2 - 2*(sqrt(b^2 - 4*a*c)*a*b^3*d^2*e + sqrt(b^2 -
4*a*c)*a^3*b*e^3 - (a*b^2*c - a^2*c^2)*sqrt(b^2 - 4*a*c)*d^3 - (2*a^2*b^2 - a^3*c)*sqrt(b^2 - 4*a*c)*d*e^2)*s
qrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(a) + (a^4*b^2*e^3 - 2*(a^2*b^3*c - 3*a^3*b*c^2)*d^3 + (a^2
*b^4 + a^3*b^2*c - 8*a^4*c^2)*d^2*e - 2*(a^3*b^3 - a^4*b*c)*d*e^2)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*
c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*a^3*c*d - a^3*b*e - sqrt(-4*(a^3*c*d^2 - a^3*b*d*e + a^4*e^2)
*a^3*c + (2*a^3*c*d - a^3*b*e)^2))/(a^3*c)))/((sqrt(b^2 - 4*a*c)*a^4*c*d^2 - sqrt(b^2 - 4*a*c)*a^4*b*d*e + sqr
t(b^2 - 4*a*c)*a^5*e^2)*abs(a)*abs(c)) + 1/4*(8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e + 3*a^2*e^2)*arctan(sqrt(x*e
+ d)/sqrt(-d))/(a^3*sqrt(-d)) + 1/4*(4*(x*e + d)^(3/2)*b*d*e - 4*sqrt(x*e + d)*b*d^2*e - 5*(x*e + d)^(3/2)*a*e
^2 + 3*sqrt(x*e + d)*a*d*e^2)*e^(-2)/(a^2*x^2)

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maple [B]  time = 0.06, size = 1880, normalized size = 3.10

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/a^2*c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+
(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2+1/a^2*c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arc
tan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2+e^2/a*c*2^(1/2)/((-b*e+2*c*d+(
-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2
)*c)-e^2/a*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(
-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)-1/e/a^2/x^2*(e*x+d)^(1/2)*b*d^2+1/e/a^2/x^2*(e*x+d)^(3/2)*b*d-2/a^3*d^(3/
2)*arctanh((e*x+d)^(1/2)/d^(1/2))*b^2+2/a^2*d^(3/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c-3*e/a^2*c^2/(-(4*a*c-b^2)
*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-
(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2+e/a^3*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e
^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d^2-2*e
^2/a^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2
)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d-3*e/a^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2
)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2
)^(1/2))*c)^(1/2)*c)*b*d^2+e/a^3*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^
(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d^2-2*e^2/a^2*c/(-(
4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*
e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d-3/4*e^2*arctanh((e*x+d)^(1/2)/d^(1/2))/a/d^(1/2)+3/4*d*(e*
x+d)^(1/2)/a/x^2-5/4/a/x^2*(e*x+d)^(3/2)+3*e/a^2*d^(1/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*b+2*e/a^2*c*2^(1/2)/((
b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2)
)*c)^(1/2)*c)*b*d+e^3/a*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arc
tanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b+4*e^2/a*c^2/(-(4*a*c-b^2)*e^2)
^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4
*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-2*e/a^2*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh(
(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d+e^3/a*c/(-(4*a*c-b^2)*e^2)^(1/2)*
2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*
e^2)^(1/2))*c)^(1/2)*c)*b+4*e^2/a*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c
)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d+1/a^3*c*2^(1/2)/((-b*
e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2)
)*c)^(1/2)*c)*b^2*d^2-1/a^3*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1
/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d^2

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (e x + d\right )}^{\frac {3}{2}}}{{\left (c x^{2} + b x + a\right )} x^{3}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [B]  time = 8.19, size = 44649, normalized size = 73.56

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(((3*a*d*e^2 - 4*b*d^2*e)*(d + e*x)^(1/2))/(4*a^2) - ((5*a*e^2 - 4*b*d*e)*(d + e*x)^(3/2))/(4*a^2))/((d + e*x)
^2 - 2*d*(d + e*x) + d^2) + atan(((((((192*a^11*b^2*c^3*e^12 - 24*a^10*b^4*c^2*e^12 - 384*a^12*c^4*e^12 + 768*
a^10*c^6*d^4*e^8 + 384*a^11*c^5*d^2*e^10 + 128*a^8*b^4*c^4*d^4*e^8 - 96*a^8*b^5*c^3*d^3*e^9 - 32*a^8*b^6*c^2*d
^2*e^10 - 704*a^9*b^2*c^5*d^4*e^8 + 320*a^9*b^3*c^4*d^3*e^9 + 488*a^9*b^4*c^3*d^2*e^10 - 1536*a^10*b^2*c^4*d^2
*e^10 + 1408*a^11*b*c^4*d*e^11 + 56*a^9*b^5*c^2*d*e^11 + 256*a^10*b*c^5*d^3*e^9 - 576*a^10*b^3*c^3*d*e^11)/(2*
a^8) - ((d + e*x)^(1/2)*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3
*c*e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b
^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*
b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*
c*d*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(
1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^
2*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*
c)))^(1/2)*(1024*a^13*c^4*e^10 + 64*a^11*b^4*c^2*e^10 - 512*a^12*b^2*c^3*e^10 + 1536*a^12*c^5*d^2*e^8 + 128*a^
10*b^4*c^3*d^2*e^8 - 896*a^11*b^2*c^4*d^2*e^8 - 1792*a^12*b*c^4*d*e^9 - 128*a^10*b^5*c^2*d*e^9 + 960*a^11*b^3*
c^3*d*e^9))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*
e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*
c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*b^3
*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d
*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2
) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^2*e
*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c))
)^(1/2) - ((d + e*x)^(1/2)*(876*a^10*b*c^4*e^13 + 1336*a^10*c^5*d*e^12 + 73*a^8*b^5*c^2*e^13 - 511*a^9*b^3*c^3
*e^13 - 1152*a^8*c^7*d^5*e^8 + 2176*a^9*c^6*d^3*e^10 - 128*a^4*b^8*c^3*d^5*e^8 + 128*a^4*b^9*c^2*d^4*e^9 + 115
2*a^5*b^6*c^4*d^5*e^8 - 832*a^5*b^7*c^3*d^4*e^9 - 448*a^5*b^8*c^2*d^3*e^10 - 3520*a^6*b^4*c^5*d^5*e^8 + 768*a^
6*b^5*c^4*d^4*e^9 + 3520*a^6*b^6*c^3*d^3*e^10 + 576*a^6*b^7*c^2*d^2*e^11 + 4096*a^7*b^2*c^6*d^5*e^8 + 3328*a^7
*b^3*c^5*d^4*e^9 - 7824*a^7*b^4*c^4*d^3*e^10 - 4520*a^7*b^5*c^3*d^2*e^11 + 2912*a^8*b^2*c^5*d^3*e^10 + 10016*a
^8*b^3*c^4*d^2*e^11 - 328*a^7*b^6*c^2*d*e^12 - 4864*a^8*b*c^6*d^4*e^9 + 2479*a^8*b^4*c^3*d*e^12 - 4352*a^9*b*c
^5*d^2*e^11 - 5034*a^9*b^2*c^4*d*e^12))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c -
b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24
*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d
^3 - 3*a*b^7*d^2*e - 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*
b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d
*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^
3)^(1/2) + 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4
+ 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) - (216*a^9*b*c^4*e^15 + 604*a^9*c^5*d*e^14 + 15*a^7*b^5*c^2*e^15 - 114*a^8
*b^3*c^3*e^15 + 192*a^6*c^8*d^7*e^8 - 1344*a^7*c^7*d^5*e^10 - 932*a^8*c^6*d^3*e^12 + 128*a^2*b^8*c^4*d^7*e^8 -
96*a^2*b^9*c^3*d^6*e^9 - 32*a^2*b^10*c^2*d^5*e^10 - 960*a^3*b^6*c^5*d^7*e^8 + 128*a^3*b^7*c^4*d^6*e^9 + 840*a
^3*b^8*c^3*d^5*e^10 + 152*a^3*b^9*c^2*d^4*e^11 + 2176*a^4*b^4*c^6*d^7*e^8 + 2336*a^4*b^5*c^5*d^6*e^9 - 3648*a^
4*b^6*c^4*d^5*e^10 - 2496*a^4*b^7*c^3*d^4*e^11 - 280*a^4*b^8*c^2*d^3*e^12 - 1600*a^5*b^2*c^7*d^7*e^8 - 6016*a^
5*b^3*c^6*d^6*e^9 + 2328*a^5*b^4*c^5*d^5*e^10 + 10216*a^5*b^5*c^4*d^4*e^11 + 3497*a^5*b^6*c^3*d^3*e^12 + 247*a
^5*b^7*c^2*d^2*e^13 + 3744*a^6*b^2*c^6*d^5*e^10 - 10912*a^6*b^3*c^5*d^4*e^11 - 12151*a^6*b^4*c^4*d^3*e^12 - 24
98*a^6*b^5*c^3*d^2*e^13 + 10885*a^7*b^2*c^5*d^3*e^12 + 7081*a^7*b^3*c^4*d^2*e^13 + 3200*a^6*b*c^7*d^6*e^9 - 10
2*a^6*b^6*c^2*d*e^14 + 1024*a^7*b*c^6*d^4*e^11 + 867*a^7*b^4*c^3*d*e^14 - 4292*a^8*b*c^5*d^2*e^13 - 1971*a^8*b
^2*c^4*d*e^14)/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3
*c*e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b
^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*
b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*
c*d*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(
1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^
2*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*
c)))^(1/2) - ((d + e*x)^(1/2)*(82*a^8*c^5*e^16 + 192*a^4*c^9*d^8*e^8 - 608*a^5*c^8*d^6*e^10 + 1106*a^6*c^7*d^4
*e^12 + 52*a^7*c^6*d^2*e^14 + 64*b^8*c^5*d^8*e^8 + 704*a^2*b^4*c^7*d^8*e^8 + 2240*a^2*b^5*c^6*d^7*e^9 + 1344*a
^2*b^6*c^5*d^6*e^10 - 512*a^3*b^2*c^8*d^8*e^8 - 2944*a^3*b^3*c^7*d^7*e^9 - 5424*a^3*b^4*c^6*d^6*e^10 - 2248*a^
3*b^5*c^5*d^5*e^11 + 5184*a^4*b^2*c^7*d^6*e^10 + 6496*a^4*b^3*c^6*d^5*e^11 + 2409*a^4*b^4*c^5*d^4*e^12 - 3748*
a^5*b^2*c^6*d^4*e^12 - 1876*a^5*b^3*c^5*d^3*e^13 + 1110*a^6*b^2*c^5*d^2*e^14 - 436*a^7*b*c^5*d*e^15 - 384*a*b^
6*c^6*d^8*e^8 - 448*a*b^7*c^5*d^7*e^9 + 896*a^4*b*c^8*d^7*e^9 - 4048*a^5*b*c^7*d^5*e^11 + 780*a^6*b*c^6*d^3*e^
13))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 1
2*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3
- 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*b^3*c*d^3*
(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 +
60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*
a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^2*e*(-(4*a
*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2)
*1i - (((((192*a^11*b^2*c^3*e^12 - 24*a^10*b^4*c^2*e^12 - 384*a^12*c^4*e^12 + 768*a^10*c^6*d^4*e^8 + 384*a^11*
c^5*d^2*e^10 + 128*a^8*b^4*c^4*d^4*e^8 - 96*a^8*b^5*c^3*d^3*e^9 - 32*a^8*b^6*c^2*d^2*e^10 - 704*a^9*b^2*c^5*d^
4*e^8 + 320*a^9*b^3*c^4*d^3*e^9 + 488*a^9*b^4*c^3*d^2*e^10 - 1536*a^10*b^2*c^4*d^2*e^10 + 1408*a^11*b*c^4*d*e^
11 + 56*a^9*b^5*c^2*d*e^11 + 256*a^10*b*c^5*d^3*e^9 - 576*a^10*b^3*c^3*d*e^11)/(2*a^8) + ((d + e*x)^(1/2)*((b^
8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 +
a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*
d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)
^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e
+ 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e
+ 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2)
- 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2)*(1024*a^13*c^4*e^
10 + 64*a^11*b^4*c^2*e^10 - 512*a^12*b^2*c^3*e^10 + 1536*a^12*c^5*d^2*e^8 + 128*a^10*b^4*c^3*d^2*e^8 - 896*a^1
1*b^2*c^4*d^2*e^8 - 1792*a^12*b*c^4*d*e^9 - 128*a^10*b^5*c^2*d*e^9 + 960*a^11*b^3*c^3*d*e^9))/(2*a^8))*((b^8*d
^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 + a^4
*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3
- a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1
/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e +
3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 5
4*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) -
6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) + ((d + e*x)^(1/2)*(
876*a^10*b*c^4*e^13 + 1336*a^10*c^5*d*e^12 + 73*a^8*b^5*c^2*e^13 - 511*a^9*b^3*c^3*e^13 - 1152*a^8*c^7*d^5*e^8
+ 2176*a^9*c^6*d^3*e^10 - 128*a^4*b^8*c^3*d^5*e^8 + 128*a^4*b^9*c^2*d^4*e^9 + 1152*a^5*b^6*c^4*d^5*e^8 - 832*
a^5*b^7*c^3*d^4*e^9 - 448*a^5*b^8*c^2*d^3*e^10 - 3520*a^6*b^4*c^5*d^5*e^8 + 768*a^6*b^5*c^4*d^4*e^9 + 3520*a^6
*b^6*c^3*d^3*e^10 + 576*a^6*b^7*c^2*d^2*e^11 + 4096*a^7*b^2*c^6*d^5*e^8 + 3328*a^7*b^3*c^5*d^4*e^9 - 7824*a^7*
b^4*c^4*d^3*e^10 - 4520*a^7*b^5*c^3*d^2*e^11 + 2912*a^8*b^2*c^5*d^3*e^10 + 10016*a^8*b^3*c^4*d^2*e^11 - 328*a^
7*b^6*c^2*d*e^12 - 4864*a^8*b*c^6*d^4*e^9 + 2479*a^8*b^4*c^3*d*e^12 - 4352*a^9*b*c^5*d^2*e^11 - 5034*a^9*b^2*c
^4*d*e^12))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*
e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*
c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*b^3
*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d
*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2
) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^2*e
*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c))
)^(1/2) - (216*a^9*b*c^4*e^15 + 604*a^9*c^5*d*e^14 + 15*a^7*b^5*c^2*e^15 - 114*a^8*b^3*c^3*e^15 + 192*a^6*c^8*
d^7*e^8 - 1344*a^7*c^7*d^5*e^10 - 932*a^8*c^6*d^3*e^12 + 128*a^2*b^8*c^4*d^7*e^8 - 96*a^2*b^9*c^3*d^6*e^9 - 32
*a^2*b^10*c^2*d^5*e^10 - 960*a^3*b^6*c^5*d^7*e^8 + 128*a^3*b^7*c^4*d^6*e^9 + 840*a^3*b^8*c^3*d^5*e^10 + 152*a^
3*b^9*c^2*d^4*e^11 + 2176*a^4*b^4*c^6*d^7*e^8 + 2336*a^4*b^5*c^5*d^6*e^9 - 3648*a^4*b^6*c^4*d^5*e^10 - 2496*a^
4*b^7*c^3*d^4*e^11 - 280*a^4*b^8*c^2*d^3*e^12 - 1600*a^5*b^2*c^7*d^7*e^8 - 6016*a^5*b^3*c^6*d^6*e^9 + 2328*a^5
*b^4*c^5*d^5*e^10 + 10216*a^5*b^5*c^4*d^4*e^11 + 3497*a^5*b^6*c^3*d^3*e^12 + 247*a^5*b^7*c^2*d^2*e^13 + 3744*a
^6*b^2*c^6*d^5*e^10 - 10912*a^6*b^3*c^5*d^4*e^11 - 12151*a^6*b^4*c^4*d^3*e^12 - 2498*a^6*b^5*c^3*d^2*e^13 + 10
885*a^7*b^2*c^5*d^3*e^12 + 7081*a^7*b^3*c^4*d^2*e^13 + 3200*a^6*b*c^7*d^6*e^9 - 102*a^6*b^6*c^2*d*e^14 + 1024*
a^7*b*c^6*d^4*e^11 + 867*a^7*b^4*c^3*d*e^14 - 4292*a^8*b*c^5*d^2*e^13 - 1971*a^8*b^2*c^4*d*e^14)/(2*a^8))*((b^
8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 +
a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*
d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)
^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e
+ 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e
+ 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2)
- 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) + ((d + e*x)^(1/2
)*(82*a^8*c^5*e^16 + 192*a^4*c^9*d^8*e^8 - 608*a^5*c^8*d^6*e^10 + 1106*a^6*c^7*d^4*e^12 + 52*a^7*c^6*d^2*e^14
+ 64*b^8*c^5*d^8*e^8 + 704*a^2*b^4*c^7*d^8*e^8 + 2240*a^2*b^5*c^6*d^7*e^9 + 1344*a^2*b^6*c^5*d^6*e^10 - 512*a^
3*b^2*c^8*d^8*e^8 - 2944*a^3*b^3*c^7*d^7*e^9 - 5424*a^3*b^4*c^6*d^6*e^10 - 2248*a^3*b^5*c^5*d^5*e^11 + 5184*a^
4*b^2*c^7*d^6*e^10 + 6496*a^4*b^3*c^6*d^5*e^11 + 2409*a^4*b^4*c^5*d^4*e^12 - 3748*a^5*b^2*c^6*d^4*e^12 - 1876*
a^5*b^3*c^5*d^3*e^13 + 1110*a^6*b^2*c^5*d^2*e^14 - 436*a^7*b*c^5*d*e^15 - 384*a*b^6*c^6*d^8*e^8 - 448*a*b^7*c^
5*d^7*e^9 + 896*a^4*b*c^8*d^7*e^9 - 4048*a^5*b*c^7*d^5*e^11 + 780*a^6*b*c^6*d^3*e^13))/(2*a^8))*((b^8*d^3 - a^
3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*
(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*
b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3
*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b
*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b
^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b
*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2)*1i)/((216*a^3*c^9*d^8*e^10
- 15*a^7*c^5*e^18 + 391*a^4*c^8*d^6*e^12 + 119*a^5*c^7*d^4*e^14 - 71*a^6*c^6*d^2*e^16 - 64*b^4*c^8*d^10*e^8 +
128*b^5*c^7*d^9*e^9 - 64*b^6*c^6*d^8*e^10 + 1472*a^2*b^3*c^7*d^7*e^11 - 1344*a^2*b^4*c^6*d^6*e^12 + 32*a^2*b^5
*c^5*d^5*e^13 - 1264*a^3*b^2*c^7*d^6*e^12 + 2088*a^3*b^3*c^6*d^5*e^13 - 152*a^3*b^4*c^5*d^4*e^14 - 1689*a^4*b^
2*c^6*d^4*e^14 + 280*a^4*b^3*c^5*d^3*e^15 - 247*a^5*b^2*c^5*d^2*e^16 + 102*a^6*b*c^5*d*e^17 + 64*a*b^2*c^9*d^1
0*e^8 + 192*a*b^3*c^8*d^9*e^9 - 704*a*b^4*c^7*d^8*e^10 + 448*a*b^5*c^6*d^7*e^11 - 224*a^2*b*c^9*d^9*e^9 - 504*
a^3*b*c^8*d^7*e^11 + 250*a^4*b*c^7*d^5*e^13 + 632*a^5*b*c^6*d^3*e^15)/a^8 + (((((192*a^11*b^2*c^3*e^12 - 24*a^
10*b^4*c^2*e^12 - 384*a^12*c^4*e^12 + 768*a^10*c^6*d^4*e^8 + 384*a^11*c^5*d^2*e^10 + 128*a^8*b^4*c^4*d^4*e^8 -
96*a^8*b^5*c^3*d^3*e^9 - 32*a^8*b^6*c^2*d^2*e^10 - 704*a^9*b^2*c^5*d^4*e^8 + 320*a^9*b^3*c^4*d^3*e^9 + 488*a^
9*b^4*c^3*d^2*e^10 - 1536*a^10*b^2*c^4*d^2*e^10 + 1408*a^11*b*c^4*d*e^11 + 56*a^9*b^5*c^2*d*e^11 + 256*a^10*b*
c^5*d^3*e^9 - 576*a^10*b^3*c^3*d*e^11)/(2*a^8) - ((d + e*x)^(1/2)*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^
5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a
^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/
2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3
)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1
/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e
*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1
/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2)*(1024*a^13*c^4*e^10 + 64*a^11*b^4*c^2*e^10 - 512*a^12*b^2
*c^3*e^10 + 1536*a^12*c^5*d^2*e^8 + 128*a^10*b^4*c^3*d^2*e^8 - 896*a^11*b^2*c^4*d^2*e^8 - 1792*a^12*b*c^4*d*e^
9 - 128*a^10*b^5*c^2*d*e^9 + 960*a^11*b^3*c^3*d*e^9))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d
^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*
b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2)
- 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(
1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2)
+ 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-
(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2)
)/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) - ((d + e*x)^(1/2)*(876*a^10*b*c^4*e^13 + 1336*a^10*c^5*d*e^
12 + 73*a^8*b^5*c^2*e^13 - 511*a^9*b^3*c^3*e^13 - 1152*a^8*c^7*d^5*e^8 + 2176*a^9*c^6*d^3*e^10 - 128*a^4*b^8*c
^3*d^5*e^8 + 128*a^4*b^9*c^2*d^4*e^9 + 1152*a^5*b^6*c^4*d^5*e^8 - 832*a^5*b^7*c^3*d^4*e^9 - 448*a^5*b^8*c^2*d^
3*e^10 - 3520*a^6*b^4*c^5*d^5*e^8 + 768*a^6*b^5*c^4*d^4*e^9 + 3520*a^6*b^6*c^3*d^3*e^10 + 576*a^6*b^7*c^2*d^2*
e^11 + 4096*a^7*b^2*c^6*d^5*e^8 + 3328*a^7*b^3*c^5*d^4*e^9 - 7824*a^7*b^4*c^4*d^3*e^10 - 4520*a^7*b^5*c^3*d^2*
e^11 + 2912*a^8*b^2*c^5*d^3*e^10 + 10016*a^8*b^3*c^4*d^2*e^11 - 328*a^7*b^6*c^2*d*e^12 - 4864*a^8*b*c^6*d^4*e^
9 + 2479*a^8*b^4*c^3*d*e^12 - 4352*a^9*b*c^5*d^2*e^11 - 5034*a^9*b^2*c^4*d*e^12))/(2*a^8))*((b^8*d^3 - a^3*b^5
*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*
a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e
^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^
4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*
d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^
2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*
e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) - (216*a^9*b*c^4*e^15 + 604*a^9*
c^5*d*e^14 + 15*a^7*b^5*c^2*e^15 - 114*a^8*b^3*c^3*e^15 + 192*a^6*c^8*d^7*e^8 - 1344*a^7*c^7*d^5*e^10 - 932*a^
8*c^6*d^3*e^12 + 128*a^2*b^8*c^4*d^7*e^8 - 96*a^2*b^9*c^3*d^6*e^9 - 32*a^2*b^10*c^2*d^5*e^10 - 960*a^3*b^6*c^5
*d^7*e^8 + 128*a^3*b^7*c^4*d^6*e^9 + 840*a^3*b^8*c^3*d^5*e^10 + 152*a^3*b^9*c^2*d^4*e^11 + 2176*a^4*b^4*c^6*d^
7*e^8 + 2336*a^4*b^5*c^5*d^6*e^9 - 3648*a^4*b^6*c^4*d^5*e^10 - 2496*a^4*b^7*c^3*d^4*e^11 - 280*a^4*b^8*c^2*d^3
*e^12 - 1600*a^5*b^2*c^7*d^7*e^8 - 6016*a^5*b^3*c^6*d^6*e^9 + 2328*a^5*b^4*c^5*d^5*e^10 + 10216*a^5*b^5*c^4*d^
4*e^11 + 3497*a^5*b^6*c^3*d^3*e^12 + 247*a^5*b^7*c^2*d^2*e^13 + 3744*a^6*b^2*c^6*d^5*e^10 - 10912*a^6*b^3*c^5*
d^4*e^11 - 12151*a^6*b^4*c^4*d^3*e^12 - 2498*a^6*b^5*c^3*d^2*e^13 + 10885*a^7*b^2*c^5*d^3*e^12 + 7081*a^7*b^3*
c^4*d^2*e^13 + 3200*a^6*b*c^7*d^6*e^9 - 102*a^6*b^6*c^2*d*e^14 + 1024*a^7*b*c^6*d^4*e^11 + 867*a^7*b^4*c^3*d*e
^14 - 4292*a^8*b*c^5*d^2*e^13 - 1971*a^8*b^2*c^4*d*e^14)/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^
5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a
^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/
2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3
)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1
/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e
*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1
/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) - ((d + e*x)^(1/2)*(82*a^8*c^5*e^16 + 192*a^4*c^9*d^8*e^8
- 608*a^5*c^8*d^6*e^10 + 1106*a^6*c^7*d^4*e^12 + 52*a^7*c^6*d^2*e^14 + 64*b^8*c^5*d^8*e^8 + 704*a^2*b^4*c^7*d
^8*e^8 + 2240*a^2*b^5*c^6*d^7*e^9 + 1344*a^2*b^6*c^5*d^6*e^10 - 512*a^3*b^2*c^8*d^8*e^8 - 2944*a^3*b^3*c^7*d^7
*e^9 - 5424*a^3*b^4*c^6*d^6*e^10 - 2248*a^3*b^5*c^5*d^5*e^11 + 5184*a^4*b^2*c^7*d^6*e^10 + 6496*a^4*b^3*c^6*d^
5*e^11 + 2409*a^4*b^4*c^5*d^4*e^12 - 3748*a^5*b^2*c^6*d^4*e^12 - 1876*a^5*b^3*c^5*d^3*e^13 + 1110*a^6*b^2*c^5*
d^2*e^14 - 436*a^7*b*c^5*d*e^15 - 384*a*b^6*c^6*d^8*e^8 - 448*a*b^7*c^5*d^7*e^9 + 896*a^4*b*c^8*d^7*e^9 - 4048
*a^5*b*c^7*d^5*e^11 + 780*a^6*b*c^6*d^3*e^13))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4
*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e
^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*
b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) +
27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^
2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c
- b^2)^3)^(1/2) + 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a
^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) + (((((192*a^11*b^2*c^3*e^12 - 24*a^10*b^4*c^2*e^12 - 384*a^12*c^4*
e^12 + 768*a^10*c^6*d^4*e^8 + 384*a^11*c^5*d^2*e^10 + 128*a^8*b^4*c^4*d^4*e^8 - 96*a^8*b^5*c^3*d^3*e^9 - 32*a^
8*b^6*c^2*d^2*e^10 - 704*a^9*b^2*c^5*d^4*e^8 + 320*a^9*b^3*c^4*d^3*e^9 + 488*a^9*b^4*c^3*d^2*e^10 - 1536*a^10*
b^2*c^4*d^2*e^10 + 1408*a^11*b*c^4*d*e^11 + 56*a^9*b^5*c^2*d*e^11 + 256*a^10*b*c^5*d^3*e^9 - 576*a^10*b^3*c^3*
d*e^11)/(2*a^8) + ((d + e*x)^(1/2)*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2)
+ 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2
+ 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d
^2*e - 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e -
24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c
- b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a
^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 -
8*a^7*b^2*c)))^(1/2)*(1024*a^13*c^4*e^10 + 64*a^11*b^4*c^2*e^10 - 512*a^12*b^2*c^3*e^10 + 1536*a^12*c^5*d^2*e
^8 + 128*a^10*b^4*c^3*d^2*e^8 - 896*a^11*b^2*c^4*d^2*e^8 - 1792*a^12*b*c^4*d*e^9 - 128*a^10*b^5*c^2*d*e^9 + 96
0*a^11*b^3*c^3*d*e^9))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7
*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 +
33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*
e - 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*
a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b
^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*
b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*
a^7*b^2*c)))^(1/2) + ((d + e*x)^(1/2)*(876*a^10*b*c^4*e^13 + 1336*a^10*c^5*d*e^12 + 73*a^8*b^5*c^2*e^13 - 511*
a^9*b^3*c^3*e^13 - 1152*a^8*c^7*d^5*e^8 + 2176*a^9*c^6*d^3*e^10 - 128*a^4*b^8*c^3*d^5*e^8 + 128*a^4*b^9*c^2*d^
4*e^9 + 1152*a^5*b^6*c^4*d^5*e^8 - 832*a^5*b^7*c^3*d^4*e^9 - 448*a^5*b^8*c^2*d^3*e^10 - 3520*a^6*b^4*c^5*d^5*e
^8 + 768*a^6*b^5*c^4*d^4*e^9 + 3520*a^6*b^6*c^3*d^3*e^10 + 576*a^6*b^7*c^2*d^2*e^11 + 4096*a^7*b^2*c^6*d^5*e^8
+ 3328*a^7*b^3*c^5*d^4*e^9 - 7824*a^7*b^4*c^4*d^3*e^10 - 4520*a^7*b^5*c^3*d^2*e^11 + 2912*a^8*b^2*c^5*d^3*e^1
0 + 10016*a^8*b^3*c^4*d^2*e^11 - 328*a^7*b^6*c^2*d*e^12 - 4864*a^8*b*c^6*d^4*e^9 + 2479*a^8*b^4*c^3*d*e^12 - 4
352*a^9*b*c^5*d^2*e^11 - 5034*a^9*b^2*c^4*d*e^12))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*
(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6
*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 1
0*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2
) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) +
3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*
a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(
2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) - (216*a^9*b*c^4*e^15 + 604*a^9*c^5*d*e^14 + 15*a^7*b^5*c^2*e^1
5 - 114*a^8*b^3*c^3*e^15 + 192*a^6*c^8*d^7*e^8 - 1344*a^7*c^7*d^5*e^10 - 932*a^8*c^6*d^3*e^12 + 128*a^2*b^8*c^
4*d^7*e^8 - 96*a^2*b^9*c^3*d^6*e^9 - 32*a^2*b^10*c^2*d^5*e^10 - 960*a^3*b^6*c^5*d^7*e^8 + 128*a^3*b^7*c^4*d^6*
e^9 + 840*a^3*b^8*c^3*d^5*e^10 + 152*a^3*b^9*c^2*d^4*e^11 + 2176*a^4*b^4*c^6*d^7*e^8 + 2336*a^4*b^5*c^5*d^6*e^
9 - 3648*a^4*b^6*c^4*d^5*e^10 - 2496*a^4*b^7*c^3*d^4*e^11 - 280*a^4*b^8*c^2*d^3*e^12 - 1600*a^5*b^2*c^7*d^7*e^
8 - 6016*a^5*b^3*c^6*d^6*e^9 + 2328*a^5*b^4*c^5*d^5*e^10 + 10216*a^5*b^5*c^4*d^4*e^11 + 3497*a^5*b^6*c^3*d^3*e
^12 + 247*a^5*b^7*c^2*d^2*e^13 + 3744*a^6*b^2*c^6*d^5*e^10 - 10912*a^6*b^3*c^5*d^4*e^11 - 12151*a^6*b^4*c^4*d^
3*e^12 - 2498*a^6*b^5*c^3*d^2*e^13 + 10885*a^7*b^2*c^5*d^3*e^12 + 7081*a^7*b^3*c^4*d^2*e^13 + 3200*a^6*b*c^7*d
^6*e^9 - 102*a^6*b^6*c^2*d*e^14 + 1024*a^7*b*c^6*d^4*e^11 + 867*a^7*b^4*c^3*d*e^14 - 4292*a^8*b*c^5*d^2*e^13 -
1971*a^8*b^2*c^4*d*e^14)/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2)
+ 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2
+ 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d
^2*e - 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e -
24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c
- b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a
^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 -
8*a^7*b^2*c)))^(1/2) + ((d + e*x)^(1/2)*(82*a^8*c^5*e^16 + 192*a^4*c^9*d^8*e^8 - 608*a^5*c^8*d^6*e^10 + 1106*
a^6*c^7*d^4*e^12 + 52*a^7*c^6*d^2*e^14 + 64*b^8*c^5*d^8*e^8 + 704*a^2*b^4*c^7*d^8*e^8 + 2240*a^2*b^5*c^6*d^7*e
^9 + 1344*a^2*b^6*c^5*d^6*e^10 - 512*a^3*b^2*c^8*d^8*e^8 - 2944*a^3*b^3*c^7*d^7*e^9 - 5424*a^3*b^4*c^6*d^6*e^1
0 - 2248*a^3*b^5*c^5*d^5*e^11 + 5184*a^4*b^2*c^7*d^6*e^10 + 6496*a^4*b^3*c^6*d^5*e^11 + 2409*a^4*b^4*c^5*d^4*e
^12 - 3748*a^5*b^2*c^6*d^4*e^12 - 1876*a^5*b^3*c^5*d^3*e^13 + 1110*a^6*b^2*c^5*d^2*e^14 - 436*a^7*b*c^5*d*e^15
- 384*a*b^6*c^6*d^8*e^8 - 448*a*b^7*c^5*d^7*e^9 + 896*a^4*b*c^8*d^7*e^9 - 4048*a^5*b*c^7*d^5*e^11 + 780*a^6*b
*c^6*d^3*e^13))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^
3*c*e^3 - 12*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*
b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a
*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4
*c*d*e^2 + 60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^
(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d
^2*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2
*c)))^(1/2)))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 + b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 1
2*a^5*b*c^2*e^3 + a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3
- 38*a^3*b^2*c^3*d^3 - a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e - 4*a*b^3*c*d^3*
(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 +
60*a^4*b*c^3*d^2*e + 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*
a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 - 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 9*a^2*b^2*c*d^2*e*(-(4*a
*c - b^2)^3)^(1/2) - 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2)
*2i + atan(((((((192*a^11*b^2*c^3*e^12 - 24*a^10*b^4*c^2*e^12 - 384*a^12*c^4*e^12 + 768*a^10*c^6*d^4*e^8 + 384
*a^11*c^5*d^2*e^10 + 128*a^8*b^4*c^4*d^4*e^8 - 96*a^8*b^5*c^3*d^3*e^9 - 32*a^8*b^6*c^2*d^2*e^10 - 704*a^9*b^2*
c^5*d^4*e^8 + 320*a^9*b^3*c^4*d^3*e^9 + 488*a^9*b^4*c^3*d^2*e^10 - 1536*a^10*b^2*c^4*d^2*e^10 + 1408*a^11*b*c^
4*d*e^11 + 56*a^9*b^5*c^2*d*e^11 + 256*a^10*b*c^5*d^3*e^9 - 576*a^10*b^3*c^3*d*e^11)/(2*a^8) - ((d + e*x)^(1/2
)*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*
e^3 - a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^
2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b
^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3
*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*
d^2*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)
^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2)*(1024*a^13*
c^4*e^10 + 64*a^11*b^4*c^2*e^10 - 512*a^12*b^2*c^3*e^10 + 1536*a^12*c^5*d^2*e^8 + 128*a^10*b^4*c^3*d^2*e^8 - 8
96*a^11*b^2*c^4*d^2*e^8 - 1792*a^12*b*c^4*d*e^9 - 128*a^10*b^5*c^2*d*e^9 + 960*a^11*b^3*c^3*d*e^9))/(2*a^8))*(
(b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3
- a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c
^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b^2)
^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^
2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2
*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1
/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) - ((d + e*x)^(
1/2)*(876*a^10*b*c^4*e^13 + 1336*a^10*c^5*d*e^12 + 73*a^8*b^5*c^2*e^13 - 511*a^9*b^3*c^3*e^13 - 1152*a^8*c^7*d
^5*e^8 + 2176*a^9*c^6*d^3*e^10 - 128*a^4*b^8*c^3*d^5*e^8 + 128*a^4*b^9*c^2*d^4*e^9 + 1152*a^5*b^6*c^4*d^5*e^8
- 832*a^5*b^7*c^3*d^4*e^9 - 448*a^5*b^8*c^2*d^3*e^10 - 3520*a^6*b^4*c^5*d^5*e^8 + 768*a^6*b^5*c^4*d^4*e^9 + 35
20*a^6*b^6*c^3*d^3*e^10 + 576*a^6*b^7*c^2*d^2*e^11 + 4096*a^7*b^2*c^6*d^5*e^8 + 3328*a^7*b^3*c^5*d^4*e^9 - 782
4*a^7*b^4*c^4*d^3*e^10 - 4520*a^7*b^5*c^3*d^2*e^11 + 2912*a^8*b^2*c^5*d^3*e^10 + 10016*a^8*b^3*c^4*d^2*e^11 -
328*a^7*b^6*c^2*d*e^12 - 4864*a^8*b*c^6*d^4*e^9 + 2479*a^8*b^4*c^3*d*e^12 - 4352*a^9*b*c^5*d^2*e^11 - 5034*a^9
*b^2*c^4*d*e^12))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*
b^3*c*e^3 - 12*a^5*b*c^2*e^3 - a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^
2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4
*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b
^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3
)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c
*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b
^2*c)))^(1/2) - (216*a^9*b*c^4*e^15 + 604*a^9*c^5*d*e^14 + 15*a^7*b^5*c^2*e^15 - 114*a^8*b^3*c^3*e^15 + 192*a^
6*c^8*d^7*e^8 - 1344*a^7*c^7*d^5*e^10 - 932*a^8*c^6*d^3*e^12 + 128*a^2*b^8*c^4*d^7*e^8 - 96*a^2*b^9*c^3*d^6*e^
9 - 32*a^2*b^10*c^2*d^5*e^10 - 960*a^3*b^6*c^5*d^7*e^8 + 128*a^3*b^7*c^4*d^6*e^9 + 840*a^3*b^8*c^3*d^5*e^10 +
152*a^3*b^9*c^2*d^4*e^11 + 2176*a^4*b^4*c^6*d^7*e^8 + 2336*a^4*b^5*c^5*d^6*e^9 - 3648*a^4*b^6*c^4*d^5*e^10 - 2
496*a^4*b^7*c^3*d^4*e^11 - 280*a^4*b^8*c^2*d^3*e^12 - 1600*a^5*b^2*c^7*d^7*e^8 - 6016*a^5*b^3*c^6*d^6*e^9 + 23
28*a^5*b^4*c^5*d^5*e^10 + 10216*a^5*b^5*c^4*d^4*e^11 + 3497*a^5*b^6*c^3*d^3*e^12 + 247*a^5*b^7*c^2*d^2*e^13 +
3744*a^6*b^2*c^6*d^5*e^10 - 10912*a^6*b^3*c^5*d^4*e^11 - 12151*a^6*b^4*c^4*d^3*e^12 - 2498*a^6*b^5*c^3*d^2*e^1
3 + 10885*a^7*b^2*c^5*d^3*e^12 + 7081*a^7*b^3*c^4*d^2*e^13 + 3200*a^6*b*c^7*d^6*e^9 - 102*a^6*b^6*c^2*d*e^14 +
1024*a^7*b*c^6*d^4*e^11 + 867*a^7*b^4*c^3*d*e^14 - 4292*a^8*b*c^5*d^2*e^13 - 1971*a^8*b^2*c^4*d*e^14)/(2*a^8)
)*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*
e^3 - a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^
2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b
^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3
*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*
d^2*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)
^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) - ((d + e*x
)^(1/2)*(82*a^8*c^5*e^16 + 192*a^4*c^9*d^8*e^8 - 608*a^5*c^8*d^6*e^10 + 1106*a^6*c^7*d^4*e^12 + 52*a^7*c^6*d^2
*e^14 + 64*b^8*c^5*d^8*e^8 + 704*a^2*b^4*c^7*d^8*e^8 + 2240*a^2*b^5*c^6*d^7*e^9 + 1344*a^2*b^6*c^5*d^6*e^10 -
512*a^3*b^2*c^8*d^8*e^8 - 2944*a^3*b^3*c^7*d^7*e^9 - 5424*a^3*b^4*c^6*d^6*e^10 - 2248*a^3*b^5*c^5*d^5*e^11 + 5
184*a^4*b^2*c^7*d^6*e^10 + 6496*a^4*b^3*c^6*d^5*e^11 + 2409*a^4*b^4*c^5*d^4*e^12 - 3748*a^5*b^2*c^6*d^4*e^12 -
1876*a^5*b^3*c^5*d^3*e^13 + 1110*a^6*b^2*c^5*d^2*e^14 - 436*a^7*b*c^5*d*e^15 - 384*a*b^6*c^6*d^8*e^8 - 448*a*
b^7*c^5*d^7*e^9 + 896*a^4*b*c^8*d^7*e^9 - 4048*a^5*b*c^7*d^5*e^11 + 780*a^6*b*c^6*d^3*e^13))/(2*a^8))*((b^8*d^
3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 - a^4*
c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3
+ a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/
2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e - 3
*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54
*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 6
*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2)*1i - (((((192*a^11*b^
2*c^3*e^12 - 24*a^10*b^4*c^2*e^12 - 384*a^12*c^4*e^12 + 768*a^10*c^6*d^4*e^8 + 384*a^11*c^5*d^2*e^10 + 128*a^8
*b^4*c^4*d^4*e^8 - 96*a^8*b^5*c^3*d^3*e^9 - 32*a^8*b^6*c^2*d^2*e^10 - 704*a^9*b^2*c^5*d^4*e^8 + 320*a^9*b^3*c^
4*d^3*e^9 + 488*a^9*b^4*c^3*d^2*e^10 - 1536*a^10*b^2*c^4*d^2*e^10 + 1408*a^11*b*c^4*d*e^11 + 56*a^9*b^5*c^2*d*
e^11 + 256*a^10*b*c^5*d^3*e^9 - 576*a^10*b^3*c^3*d*e^11)/(2*a^8) + ((d + e*x)^(1/2)*((b^8*d^3 - a^3*b^5*e^3 +
8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 - a^4*c*e^3*(-(4*a*c - b
^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 + a^3*b^2*e^3*(-(4
*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a*b^4*d^2*e
*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e - 3*a^2*b*c^2*d^3*(-(
4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2
+ 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^3*b*c*d*e^2*(-(
4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2)*(1024*a^13*c^4*e^10 + 64*a^11*b^4*c^2*e
^10 - 512*a^12*b^2*c^3*e^10 + 1536*a^12*c^5*d^2*e^8 + 128*a^10*b^4*c^3*d^2*e^8 - 896*a^11*b^2*c^4*d^2*e^8 - 17
92*a^12*b*c^4*d*e^9 - 128*a^10*b^5*c^2*d*e^9 + 960*a^11*b^3*c^3*d*e^9))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a
^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 - a^4*c*e^3*(-(4*a*c - b^2)
^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*
c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-
(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a
*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 +
3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a
*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) + ((d + e*x)^(1/2)*(876*a^10*b*c^4*e^13 +
1336*a^10*c^5*d*e^12 + 73*a^8*b^5*c^2*e^13 - 511*a^9*b^3*c^3*e^13 - 1152*a^8*c^7*d^5*e^8 + 2176*a^9*c^6*d^3*e^
10 - 128*a^4*b^8*c^3*d^5*e^8 + 128*a^4*b^9*c^2*d^4*e^9 + 1152*a^5*b^6*c^4*d^5*e^8 - 832*a^5*b^7*c^3*d^4*e^9 -
448*a^5*b^8*c^2*d^3*e^10 - 3520*a^6*b^4*c^5*d^5*e^8 + 768*a^6*b^5*c^4*d^4*e^9 + 3520*a^6*b^6*c^3*d^3*e^10 + 57
6*a^6*b^7*c^2*d^2*e^11 + 4096*a^7*b^2*c^6*d^5*e^8 + 3328*a^7*b^3*c^5*d^4*e^9 - 7824*a^7*b^4*c^4*d^3*e^10 - 452
0*a^7*b^5*c^3*d^2*e^11 + 2912*a^8*b^2*c^5*d^3*e^10 + 10016*a^8*b^3*c^4*d^2*e^11 - 328*a^7*b^6*c^2*d*e^12 - 486
4*a^8*b*c^6*d^4*e^9 + 2479*a^8*b^4*c^3*d*e^12 - 4352*a^9*b*c^5*d^2*e^11 - 5034*a^9*b^2*c^4*d*e^12))/(2*a^8))*(
(b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3
- a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c
^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b^2)
^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^
2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2
*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1
/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) - (216*a^9*b*c
^4*e^15 + 604*a^9*c^5*d*e^14 + 15*a^7*b^5*c^2*e^15 - 114*a^8*b^3*c^3*e^15 + 192*a^6*c^8*d^7*e^8 - 1344*a^7*c^7
*d^5*e^10 - 932*a^8*c^6*d^3*e^12 + 128*a^2*b^8*c^4*d^7*e^8 - 96*a^2*b^9*c^3*d^6*e^9 - 32*a^2*b^10*c^2*d^5*e^10
- 960*a^3*b^6*c^5*d^7*e^8 + 128*a^3*b^7*c^4*d^6*e^9 + 840*a^3*b^8*c^3*d^5*e^10 + 152*a^3*b^9*c^2*d^4*e^11 + 2
176*a^4*b^4*c^6*d^7*e^8 + 2336*a^4*b^5*c^5*d^6*e^9 - 3648*a^4*b^6*c^4*d^5*e^10 - 2496*a^4*b^7*c^3*d^4*e^11 - 2
80*a^4*b^8*c^2*d^3*e^12 - 1600*a^5*b^2*c^7*d^7*e^8 - 6016*a^5*b^3*c^6*d^6*e^9 + 2328*a^5*b^4*c^5*d^5*e^10 + 10
216*a^5*b^5*c^4*d^4*e^11 + 3497*a^5*b^6*c^3*d^3*e^12 + 247*a^5*b^7*c^2*d^2*e^13 + 3744*a^6*b^2*c^6*d^5*e^10 -
10912*a^6*b^3*c^5*d^4*e^11 - 12151*a^6*b^4*c^4*d^3*e^12 - 2498*a^6*b^5*c^3*d^2*e^13 + 10885*a^7*b^2*c^5*d^3*e^
12 + 7081*a^7*b^3*c^4*d^2*e^13 + 3200*a^6*b*c^7*d^6*e^9 - 102*a^6*b^6*c^2*d*e^14 + 1024*a^7*b*c^6*d^4*e^11 + 8
67*a^7*b^4*c^3*d*e^14 - 4292*a^8*b*c^5*d^2*e^13 - 1971*a^8*b^2*c^4*d*e^14)/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 +
8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 - a^4*c*e^3*(-(4*a*c - b
^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 + a^3*b^2*e^3*(-(4
*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a*b^4*d^2*e
*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e - 3*a^2*b*c^2*d^3*(-(
4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2
+ 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^3*b*c*d*e^2*(-(
4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) + ((d + e*x)^(1/2)*(82*a^8*c^5*e^16 + 1
92*a^4*c^9*d^8*e^8 - 608*a^5*c^8*d^6*e^10 + 1106*a^6*c^7*d^4*e^12 + 52*a^7*c^6*d^2*e^14 + 64*b^8*c^5*d^8*e^8 +
704*a^2*b^4*c^7*d^8*e^8 + 2240*a^2*b^5*c^6*d^7*e^9 + 1344*a^2*b^6*c^5*d^6*e^10 - 512*a^3*b^2*c^8*d^8*e^8 - 29
44*a^3*b^3*c^7*d^7*e^9 - 5424*a^3*b^4*c^6*d^6*e^10 - 2248*a^3*b^5*c^5*d^5*e^11 + 5184*a^4*b^2*c^7*d^6*e^10 + 6
496*a^4*b^3*c^6*d^5*e^11 + 2409*a^4*b^4*c^5*d^4*e^12 - 3748*a^5*b^2*c^6*d^4*e^12 - 1876*a^5*b^3*c^5*d^3*e^13 +
1110*a^6*b^2*c^5*d^2*e^14 - 436*a^7*b*c^5*d*e^15 - 384*a*b^6*c^6*d^8*e^8 - 448*a*b^7*c^5*d^7*e^9 + 896*a^4*b*
c^8*d^7*e^9 - 4048*a^5*b*c^7*d^5*e^11 + 780*a^6*b*c^6*d^3*e^13))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*
d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 - a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/
2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2
)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c
- b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^
2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c
^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^
2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2)*1i)/((216*a^3*c^9*d^8*e^10 - 15*a^7*c^5*e^18 + 39
1*a^4*c^8*d^6*e^12 + 119*a^5*c^7*d^4*e^14 - 71*a^6*c^6*d^2*e^16 - 64*b^4*c^8*d^10*e^8 + 128*b^5*c^7*d^9*e^9 -
64*b^6*c^6*d^8*e^10 + 1472*a^2*b^3*c^7*d^7*e^11 - 1344*a^2*b^4*c^6*d^6*e^12 + 32*a^2*b^5*c^5*d^5*e^13 - 1264*a
^3*b^2*c^7*d^6*e^12 + 2088*a^3*b^3*c^6*d^5*e^13 - 152*a^3*b^4*c^5*d^4*e^14 - 1689*a^4*b^2*c^6*d^4*e^14 + 280*a
^4*b^3*c^5*d^3*e^15 - 247*a^5*b^2*c^5*d^2*e^16 + 102*a^6*b*c^5*d*e^17 + 64*a*b^2*c^9*d^10*e^8 + 192*a*b^3*c^8*
d^9*e^9 - 704*a*b^4*c^7*d^8*e^10 + 448*a*b^5*c^6*d^7*e^11 - 224*a^2*b*c^9*d^9*e^9 - 504*a^3*b*c^8*d^7*e^11 + 2
50*a^4*b*c^7*d^5*e^13 + 632*a^5*b*c^6*d^3*e^15)/a^8 + (((((192*a^11*b^2*c^3*e^12 - 24*a^10*b^4*c^2*e^12 - 384*
a^12*c^4*e^12 + 768*a^10*c^6*d^4*e^8 + 384*a^11*c^5*d^2*e^10 + 128*a^8*b^4*c^4*d^4*e^8 - 96*a^8*b^5*c^3*d^3*e^
9 - 32*a^8*b^6*c^2*d^2*e^10 - 704*a^9*b^2*c^5*d^4*e^8 + 320*a^9*b^3*c^4*d^3*e^9 + 488*a^9*b^4*c^3*d^2*e^10 - 1
536*a^10*b^2*c^4*d^2*e^10 + 1408*a^11*b*c^4*d*e^11 + 56*a^9*b^5*c^2*d*e^11 + 256*a^10*b*c^5*d^3*e^9 - 576*a^10
*b^3*c^3*d*e^11)/(2*a^8) - ((d + e*x)^(1/2)*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^
3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 - a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*
c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 -
3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c
*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*
(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1
/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*
a^8*c^2 - 8*a^7*b^2*c)))^(1/2)*(1024*a^13*c^4*e^10 + 64*a^11*b^4*c^2*e^10 - 512*a^12*b^2*c^3*e^10 + 1536*a^12*
c^5*d^2*e^8 + 128*a^10*b^4*c^3*d^2*e^8 - 896*a^11*b^2*c^4*d^2*e^8 - 1792*a^12*b*c^4*d*e^9 - 128*a^10*b^5*c^2*d
*e^9 + 960*a^11*b^3*c^3*d*e^9))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^
(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 - a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3
*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a
*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^
2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(
4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2)
- 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8
*c^2 - 8*a^7*b^2*c)))^(1/2) - ((d + e*x)^(1/2)*(876*a^10*b*c^4*e^13 + 1336*a^10*c^5*d*e^12 + 73*a^8*b^5*c^2*e^
13 - 511*a^9*b^3*c^3*e^13 - 1152*a^8*c^7*d^5*e^8 + 2176*a^9*c^6*d^3*e^10 - 128*a^4*b^8*c^3*d^5*e^8 + 128*a^4*b
^9*c^2*d^4*e^9 + 1152*a^5*b^6*c^4*d^5*e^8 - 832*a^5*b^7*c^3*d^4*e^9 - 448*a^5*b^8*c^2*d^3*e^10 - 3520*a^6*b^4*
c^5*d^5*e^8 + 768*a^6*b^5*c^4*d^4*e^9 + 3520*a^6*b^6*c^3*d^3*e^10 + 576*a^6*b^7*c^2*d^2*e^11 + 4096*a^7*b^2*c^
6*d^5*e^8 + 3328*a^7*b^3*c^5*d^4*e^9 - 7824*a^7*b^4*c^4*d^3*e^10 - 4520*a^7*b^5*c^3*d^2*e^11 + 2912*a^8*b^2*c^
5*d^3*e^10 + 10016*a^8*b^3*c^4*d^2*e^11 - 328*a^7*b^6*c^2*d*e^12 - 4864*a^8*b*c^6*d^4*e^9 + 2479*a^8*b^4*c^3*d
*e^12 - 4352*a^9*b*c^5*d^2*e^11 - 5034*a^9*b^2*c^4*d*e^12))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 -
b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 - a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) +
3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^
(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2
)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)
^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^
2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)
^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) - (216*a^9*b*c^4*e^15 + 604*a^9*c^5*d*e^14 + 15*a^7*b^
5*c^2*e^15 - 114*a^8*b^3*c^3*e^15 + 192*a^6*c^8*d^7*e^8 - 1344*a^7*c^7*d^5*e^10 - 932*a^8*c^6*d^3*e^12 + 128*a
^2*b^8*c^4*d^7*e^8 - 96*a^2*b^9*c^3*d^6*e^9 - 32*a^2*b^10*c^2*d^5*e^10 - 960*a^3*b^6*c^5*d^7*e^8 + 128*a^3*b^7
*c^4*d^6*e^9 + 840*a^3*b^8*c^3*d^5*e^10 + 152*a^3*b^9*c^2*d^4*e^11 + 2176*a^4*b^4*c^6*d^7*e^8 + 2336*a^4*b^5*c
^5*d^6*e^9 - 3648*a^4*b^6*c^4*d^5*e^10 - 2496*a^4*b^7*c^3*d^4*e^11 - 280*a^4*b^8*c^2*d^3*e^12 - 1600*a^5*b^2*c
^7*d^7*e^8 - 6016*a^5*b^3*c^6*d^6*e^9 + 2328*a^5*b^4*c^5*d^5*e^10 + 10216*a^5*b^5*c^4*d^4*e^11 + 3497*a^5*b^6*
c^3*d^3*e^12 + 247*a^5*b^7*c^2*d^2*e^13 + 3744*a^6*b^2*c^6*d^5*e^10 - 10912*a^6*b^3*c^5*d^4*e^11 - 12151*a^6*b
^4*c^4*d^3*e^12 - 2498*a^6*b^5*c^3*d^2*e^13 + 10885*a^7*b^2*c^5*d^3*e^12 + 7081*a^7*b^3*c^4*d^2*e^13 + 3200*a^
6*b*c^7*d^6*e^9 - 102*a^6*b^6*c^2*d*e^14 + 1024*a^7*b*c^6*d^4*e^11 + 867*a^7*b^4*c^3*d*e^14 - 4292*a^8*b*c^5*d
^2*e^13 - 1971*a^8*b^2*c^4*d*e^14)/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^
3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 - a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*
c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 -
3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c
*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*
(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1
/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*
a^8*c^2 - 8*a^7*b^2*c)))^(1/2) - ((d + e*x)^(1/2)*(82*a^8*c^5*e^16 + 192*a^4*c^9*d^8*e^8 - 608*a^5*c^8*d^6*e^1
0 + 1106*a^6*c^7*d^4*e^12 + 52*a^7*c^6*d^2*e^14 + 64*b^8*c^5*d^8*e^8 + 704*a^2*b^4*c^7*d^8*e^8 + 2240*a^2*b^5*
c^6*d^7*e^9 + 1344*a^2*b^6*c^5*d^6*e^10 - 512*a^3*b^2*c^8*d^8*e^8 - 2944*a^3*b^3*c^7*d^7*e^9 - 5424*a^3*b^4*c^
6*d^6*e^10 - 2248*a^3*b^5*c^5*d^5*e^11 + 5184*a^4*b^2*c^7*d^6*e^10 + 6496*a^4*b^3*c^6*d^5*e^11 + 2409*a^4*b^4*
c^5*d^4*e^12 - 3748*a^5*b^2*c^6*d^4*e^12 - 1876*a^5*b^3*c^5*d^3*e^13 + 1110*a^6*b^2*c^5*d^2*e^14 - 436*a^7*b*c
^5*d*e^15 - 384*a*b^6*c^6*d^8*e^8 - 448*a*b^7*c^5*d^7*e^9 + 896*a^4*b*c^8*d^7*e^9 - 4048*a^5*b*c^7*d^5*e^11 +
780*a^6*b*c^6*d^3*e^13))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) +
7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 - a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2
+ 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^
2*e + 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 2
4*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c -
b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^
2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 -
8*a^7*b^2*c)))^(1/2) + (((((192*a^11*b^2*c^3*e^12 - 24*a^10*b^4*c^2*e^12 - 384*a^12*c^4*e^12 + 768*a^10*c^6*d^
4*e^8 + 384*a^11*c^5*d^2*e^10 + 128*a^8*b^4*c^4*d^4*e^8 - 96*a^8*b^5*c^3*d^3*e^9 - 32*a^8*b^6*c^2*d^2*e^10 - 7
04*a^9*b^2*c^5*d^4*e^8 + 320*a^9*b^3*c^4*d^3*e^9 + 488*a^9*b^4*c^3*d^2*e^10 - 1536*a^10*b^2*c^4*d^2*e^10 + 140
8*a^11*b*c^4*d*e^11 + 56*a^9*b^5*c^2*d*e^11 + 256*a^10*b*c^5*d^3*e^9 - 576*a^10*b^3*c^3*d*e^11)/(2*a^8) + ((d
+ e*x)^(1/2)*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12
*a^5*b*c^2*e^3 - a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3
- 38*a^3*b^2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(
-(4*a*c - b^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 6
0*a^4*b*c^3*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a
^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*
c - b^2)^3)^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2)*
(1024*a^13*c^4*e^10 + 64*a^11*b^4*c^2*e^10 - 512*a^12*b^2*c^3*e^10 + 1536*a^12*c^5*d^2*e^8 + 128*a^10*b^4*c^3*
d^2*e^8 - 896*a^11*b^2*c^4*d^2*e^8 - 1792*a^12*b*c^4*d*e^9 - 128*a^10*b^5*c^2*d*e^9 + 960*a^11*b^3*c^3*d*e^9))
/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^
5*b*c^2*e^3 - a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 3
8*a^3*b^2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4
*a*c - b^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a
^4*b*c^3*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*
b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c -
b^2)^3)^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2) + (
(d + e*x)^(1/2)*(876*a^10*b*c^4*e^13 + 1336*a^10*c^5*d*e^12 + 73*a^8*b^5*c^2*e^13 - 511*a^9*b^3*c^3*e^13 - 115
2*a^8*c^7*d^5*e^8 + 2176*a^9*c^6*d^3*e^10 - 128*a^4*b^8*c^3*d^5*e^8 + 128*a^4*b^9*c^2*d^4*e^9 + 1152*a^5*b^6*c
^4*d^5*e^8 - 832*a^5*b^7*c^3*d^4*e^9 - 448*a^5*b^8*c^2*d^3*e^10 - 3520*a^6*b^4*c^5*d^5*e^8 + 768*a^6*b^5*c^4*d
^4*e^9 + 3520*a^6*b^6*c^3*d^3*e^10 + 576*a^6*b^7*c^2*d^2*e^11 + 4096*a^7*b^2*c^6*d^5*e^8 + 3328*a^7*b^3*c^5*d^
4*e^9 - 7824*a^7*b^4*c^4*d^3*e^10 - 4520*a^7*b^5*c^3*d^2*e^11 + 2912*a^8*b^2*c^5*d^3*e^10 + 10016*a^8*b^3*c^4*
d^2*e^11 - 328*a^7*b^6*c^2*d*e^12 - 4864*a^8*b*c^6*d^4*e^9 + 2479*a^8*b^4*c^3*d*e^12 - 4352*a^9*b*c^5*d^2*e^11
- 5034*a^9*b^2*c^4*d*e^12))/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/
2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 - a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*
e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^
7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e
- 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a
*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) -
9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^
2 - 8*a^7*b^2*c)))^(1/2) - (216*a^9*b*c^4*e^15 + 604*a^9*c^5*d*e^14 + 15*a^7*b^5*c^2*e^15 - 114*a^8*b^3*c^3*e^
15 + 192*a^6*c^8*d^7*e^8 - 1344*a^7*c^7*d^5*e^10 - 932*a^8*c^6*d^3*e^12 + 128*a^2*b^8*c^4*d^7*e^8 - 96*a^2*b^9
*c^3*d^6*e^9 - 32*a^2*b^10*c^2*d^5*e^10 - 960*a^3*b^6*c^5*d^7*e^8 + 128*a^3*b^7*c^4*d^6*e^9 + 840*a^3*b^8*c^3*
d^5*e^10 + 152*a^3*b^9*c^2*d^4*e^11 + 2176*a^4*b^4*c^6*d^7*e^8 + 2336*a^4*b^5*c^5*d^6*e^9 - 3648*a^4*b^6*c^4*d
^5*e^10 - 2496*a^4*b^7*c^3*d^4*e^11 - 280*a^4*b^8*c^2*d^3*e^12 - 1600*a^5*b^2*c^7*d^7*e^8 - 6016*a^5*b^3*c^6*d
^6*e^9 + 2328*a^5*b^4*c^5*d^5*e^10 + 10216*a^5*b^5*c^4*d^4*e^11 + 3497*a^5*b^6*c^3*d^3*e^12 + 247*a^5*b^7*c^2*
d^2*e^13 + 3744*a^6*b^2*c^6*d^5*e^10 - 10912*a^6*b^3*c^5*d^4*e^11 - 12151*a^6*b^4*c^4*d^3*e^12 - 2498*a^6*b^5*
c^3*d^2*e^13 + 10885*a^7*b^2*c^5*d^3*e^12 + 7081*a^7*b^3*c^4*d^2*e^13 + 3200*a^6*b*c^7*d^6*e^9 - 102*a^6*b^6*c
^2*d*e^14 + 1024*a^7*b*c^6*d^4*e^11 + 867*a^7*b^4*c^3*d*e^14 - 4292*a^8*b*c^5*d^2*e^13 - 1971*a^8*b^2*c^4*d*e^
14)/(2*a^8))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12
*a^5*b*c^2*e^3 - a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3
- 38*a^3*b^2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(
-(4*a*c - b^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 6
0*a^4*b*c^3*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a
^3*b^3*c^2*d^2*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*
c - b^2)^3)^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2)
+ ((d + e*x)^(1/2)*(82*a^8*c^5*e^16 + 192*a^4*c^9*d^8*e^8 - 608*a^5*c^8*d^6*e^10 + 1106*a^6*c^7*d^4*e^12 + 52*
a^7*c^6*d^2*e^14 + 64*b^8*c^5*d^8*e^8 + 704*a^2*b^4*c^7*d^8*e^8 + 2240*a^2*b^5*c^6*d^7*e^9 + 1344*a^2*b^6*c^5*
d^6*e^10 - 512*a^3*b^2*c^8*d^8*e^8 - 2944*a^3*b^3*c^7*d^7*e^9 - 5424*a^3*b^4*c^6*d^6*e^10 - 2248*a^3*b^5*c^5*d
^5*e^11 + 5184*a^4*b^2*c^7*d^6*e^10 + 6496*a^4*b^3*c^6*d^5*e^11 + 2409*a^4*b^4*c^5*d^4*e^12 - 3748*a^5*b^2*c^6
*d^4*e^12 - 1876*a^5*b^3*c^5*d^3*e^13 + 1110*a^6*b^2*c^5*d^2*e^14 - 436*a^7*b*c^5*d*e^15 - 384*a*b^6*c^6*d^8*e
^8 - 448*a*b^7*c^5*d^7*e^9 + 896*a^4*b*c^8*d^7*e^9 - 4048*a^5*b*c^7*d^5*e^11 + 780*a^6*b*c^6*d^3*e^13))/(2*a^8
))*((b^8*d^3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2
*e^3 - a^4*c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b
^2*c^3*d^3 + a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c -
b^2)^3)^(1/2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^
3*d^2*e - 3*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2
*d^2*e + 54*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3
)^(1/2) + 6*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2)))*((b^8*d^
3 - a^3*b^5*e^3 + 8*a^4*c^4*d^3 - b^5*d^3*(-(4*a*c - b^2)^3)^(1/2) + 7*a^4*b^3*c*e^3 - 12*a^5*b*c^2*e^3 - a^4*
c*e^3*(-(4*a*c - b^2)^3)^(1/2) + 3*a^2*b^6*d*e^2 - 24*a^5*c^3*d*e^2 + 33*a^2*b^4*c^2*d^3 - 38*a^3*b^2*c^3*d^3
+ a^3*b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^6*c*d^3 - 3*a*b^7*d^2*e + 4*a*b^3*c*d^3*(-(4*a*c - b^2)^3)^(1/
2) + 3*a*b^4*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 27*a^2*b^5*c*d^2*e - 24*a^3*b^4*c*d*e^2 + 60*a^4*b*c^3*d^2*e - 3
*a^2*b*c^2*d^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a^2*b^3*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 75*a^3*b^3*c^2*d^2*e + 54
*a^4*b^2*c^2*d*e^2 + 3*a^3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 9*a^2*b^2*c*d^2*e*(-(4*a*c - b^2)^3)^(1/2) + 6
*a^3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2))/(2*(a^6*b^4 + 16*a^8*c^2 - 8*a^7*b^2*c)))^(1/2)*2i - (atan((((((d + e
*x)^(1/2)*(82*a^8*c^5*e^16 + 192*a^4*c^9*d^8*e^8 - 608*a^5*c^8*d^6*e^10 + 1106*a^6*c^7*d^4*e^12 + 52*a^7*c^6*d
^2*e^14 + 64*b^8*c^5*d^8*e^8 + 704*a^2*b^4*c^7*d^8*e^8 + 2240*a^2*b^5*c^6*d^7*e^9 + 1344*a^2*b^6*c^5*d^6*e^10
- 512*a^3*b^2*c^8*d^8*e^8 - 2944*a^3*b^3*c^7*d^7*e^9 - 5424*a^3*b^4*c^6*d^6*e^10 - 2248*a^3*b^5*c^5*d^5*e^11 +
5184*a^4*b^2*c^7*d^6*e^10 + 6496*a^4*b^3*c^6*d^5*e^11 + 2409*a^4*b^4*c^5*d^4*e^12 - 3748*a^5*b^2*c^6*d^4*e^12
- 1876*a^5*b^3*c^5*d^3*e^13 + 1110*a^6*b^2*c^5*d^2*e^14 - 436*a^7*b*c^5*d*e^15 - 384*a*b^6*c^6*d^8*e^8 - 448*
a*b^7*c^5*d^7*e^9 + 896*a^4*b*c^8*d^7*e^9 - 4048*a^5*b*c^7*d^5*e^11 + 780*a^6*b*c^6*d^3*e^13))/(2*a^8) + (((10
8*a^9*b*c^4*e^15 + 302*a^9*c^5*d*e^14 + (15*a^7*b^5*c^2*e^15)/2 - 57*a^8*b^3*c^3*e^15 + 96*a^6*c^8*d^7*e^8 - 6
72*a^7*c^7*d^5*e^10 - 466*a^8*c^6*d^3*e^12 + 64*a^2*b^8*c^4*d^7*e^8 - 48*a^2*b^9*c^3*d^6*e^9 - 16*a^2*b^10*c^2
*d^5*e^10 - 480*a^3*b^6*c^5*d^7*e^8 + 64*a^3*b^7*c^4*d^6*e^9 + 420*a^3*b^8*c^3*d^5*e^10 + 76*a^3*b^9*c^2*d^4*e
^11 + 1088*a^4*b^4*c^6*d^7*e^8 + 1168*a^4*b^5*c^5*d^6*e^9 - 1824*a^4*b^6*c^4*d^5*e^10 - 1248*a^4*b^7*c^3*d^4*e
^11 - 140*a^4*b^8*c^2*d^3*e^12 - 800*a^5*b^2*c^7*d^7*e^8 - 3008*a^5*b^3*c^6*d^6*e^9 + 1164*a^5*b^4*c^5*d^5*e^1
0 + 5108*a^5*b^5*c^4*d^4*e^11 + (3497*a^5*b^6*c^3*d^3*e^12)/2 + (247*a^5*b^7*c^2*d^2*e^13)/2 + 1872*a^6*b^2*c^
6*d^5*e^10 - 5456*a^6*b^3*c^5*d^4*e^11 - (12151*a^6*b^4*c^4*d^3*e^12)/2 - 1249*a^6*b^5*c^3*d^2*e^13 + (10885*a
^7*b^2*c^5*d^3*e^12)/2 + (7081*a^7*b^3*c^4*d^2*e^13)/2 + 1600*a^6*b*c^7*d^6*e^9 - 51*a^6*b^6*c^2*d*e^14 + 512*
a^7*b*c^6*d^4*e^11 + (867*a^7*b^4*c^3*d*e^14)/2 - 2146*a^8*b*c^5*d^2*e^13 - (1971*a^8*b^2*c^4*d*e^14)/2)/a^8 +
((((d + e*x)^(1/2)*(876*a^10*b*c^4*e^13 + 1336*a^10*c^5*d*e^12 + 73*a^8*b^5*c^2*e^13 - 511*a^9*b^3*c^3*e^13 -
1152*a^8*c^7*d^5*e^8 + 2176*a^9*c^6*d^3*e^10 - 128*a^4*b^8*c^3*d^5*e^8 + 128*a^4*b^9*c^2*d^4*e^9 + 1152*a^5*b
^6*c^4*d^5*e^8 - 832*a^5*b^7*c^3*d^4*e^9 - 448*a^5*b^8*c^2*d^3*e^10 - 3520*a^6*b^4*c^5*d^5*e^8 + 768*a^6*b^5*c
^4*d^4*e^9 + 3520*a^6*b^6*c^3*d^3*e^10 + 576*a^6*b^7*c^2*d^2*e^11 + 4096*a^7*b^2*c^6*d^5*e^8 + 3328*a^7*b^3*c^
5*d^4*e^9 - 7824*a^7*b^4*c^4*d^3*e^10 - 4520*a^7*b^5*c^3*d^2*e^11 + 2912*a^8*b^2*c^5*d^3*e^10 + 10016*a^8*b^3*
c^4*d^2*e^11 - 328*a^7*b^6*c^2*d*e^12 - 4864*a^8*b*c^6*d^4*e^9 + 2479*a^8*b^4*c^3*d*e^12 - 4352*a^9*b*c^5*d^2*
e^11 - 5034*a^9*b^2*c^4*d*e^12))/(2*a^8) - (((96*a^11*b^2*c^3*e^12 - 12*a^10*b^4*c^2*e^12 - 192*a^12*c^4*e^12
+ 384*a^10*c^6*d^4*e^8 + 192*a^11*c^5*d^2*e^10 + 64*a^8*b^4*c^4*d^4*e^8 - 48*a^8*b^5*c^3*d^3*e^9 - 16*a^8*b^6*
c^2*d^2*e^10 - 352*a^9*b^2*c^5*d^4*e^8 + 160*a^9*b^3*c^4*d^3*e^9 + 244*a^9*b^4*c^3*d^2*e^10 - 768*a^10*b^2*c^4
*d^2*e^10 + 704*a^11*b*c^4*d*e^11 + 28*a^9*b^5*c^2*d*e^11 + 128*a^10*b*c^5*d^3*e^9 - 288*a^10*b^3*c^3*d*e^11)/
a^8 - ((d + e*x)^(1/2)*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e)*(1024*a^13*c^4*e^10 + 64*a^11*b^4*c^2*
e^10 - 512*a^12*b^2*c^3*e^10 + 1536*a^12*c^5*d^2*e^8 + 128*a^10*b^4*c^3*d^2*e^8 - 896*a^11*b^2*c^4*d^2*e^8 - 1
792*a^12*b*c^4*d*e^9 - 128*a^10*b^5*c^2*d*e^9 + 960*a^11*b^3*c^3*d*e^9))/(16*a^11*d^(1/2)))*(3*a^2*e^2 + 8*b^2
*d^2 - 8*a*c*d^2 - 12*a*b*d*e))/(8*a^3*d^(1/2)))*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e))/(8*a^3*d^(1
/2)))*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e))/(8*a^3*d^(1/2)))*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 -
12*a*b*d*e)*1i)/(8*a^3*d^(1/2)) + ((((d + e*x)^(1/2)*(82*a^8*c^5*e^16 + 192*a^4*c^9*d^8*e^8 - 608*a^5*c^8*d^6*
e^10 + 1106*a^6*c^7*d^4*e^12 + 52*a^7*c^6*d^2*e^14 + 64*b^8*c^5*d^8*e^8 + 704*a^2*b^4*c^7*d^8*e^8 + 2240*a^2*b
^5*c^6*d^7*e^9 + 1344*a^2*b^6*c^5*d^6*e^10 - 512*a^3*b^2*c^8*d^8*e^8 - 2944*a^3*b^3*c^7*d^7*e^9 - 5424*a^3*b^4
*c^6*d^6*e^10 - 2248*a^3*b^5*c^5*d^5*e^11 + 5184*a^4*b^2*c^7*d^6*e^10 + 6496*a^4*b^3*c^6*d^5*e^11 + 2409*a^4*b
^4*c^5*d^4*e^12 - 3748*a^5*b^2*c^6*d^4*e^12 - 1876*a^5*b^3*c^5*d^3*e^13 + 1110*a^6*b^2*c^5*d^2*e^14 - 436*a^7*
b*c^5*d*e^15 - 384*a*b^6*c^6*d^8*e^8 - 448*a*b^7*c^5*d^7*e^9 + 896*a^4*b*c^8*d^7*e^9 - 4048*a^5*b*c^7*d^5*e^11
+ 780*a^6*b*c^6*d^3*e^13))/(2*a^8) - (((108*a^9*b*c^4*e^15 + 302*a^9*c^5*d*e^14 + (15*a^7*b^5*c^2*e^15)/2 - 5
7*a^8*b^3*c^3*e^15 + 96*a^6*c^8*d^7*e^8 - 672*a^7*c^7*d^5*e^10 - 466*a^8*c^6*d^3*e^12 + 64*a^2*b^8*c^4*d^7*e^8
- 48*a^2*b^9*c^3*d^6*e^9 - 16*a^2*b^10*c^2*d^5*e^10 - 480*a^3*b^6*c^5*d^7*e^8 + 64*a^3*b^7*c^4*d^6*e^9 + 420*
a^3*b^8*c^3*d^5*e^10 + 76*a^3*b^9*c^2*d^4*e^11 + 1088*a^4*b^4*c^6*d^7*e^8 + 1168*a^4*b^5*c^5*d^6*e^9 - 1824*a^
4*b^6*c^4*d^5*e^10 - 1248*a^4*b^7*c^3*d^4*e^11 - 140*a^4*b^8*c^2*d^3*e^12 - 800*a^5*b^2*c^7*d^7*e^8 - 3008*a^5
*b^3*c^6*d^6*e^9 + 1164*a^5*b^4*c^5*d^5*e^10 + 5108*a^5*b^5*c^4*d^4*e^11 + (3497*a^5*b^6*c^3*d^3*e^12)/2 + (24
7*a^5*b^7*c^2*d^2*e^13)/2 + 1872*a^6*b^2*c^6*d^5*e^10 - 5456*a^6*b^3*c^5*d^4*e^11 - (12151*a^6*b^4*c^4*d^3*e^1
2)/2 - 1249*a^6*b^5*c^3*d^2*e^13 + (10885*a^7*b^2*c^5*d^3*e^12)/2 + (7081*a^7*b^3*c^4*d^2*e^13)/2 + 1600*a^6*b
*c^7*d^6*e^9 - 51*a^6*b^6*c^2*d*e^14 + 512*a^7*b*c^6*d^4*e^11 + (867*a^7*b^4*c^3*d*e^14)/2 - 2146*a^8*b*c^5*d^
2*e^13 - (1971*a^8*b^2*c^4*d*e^14)/2)/a^8 - ((((d + e*x)^(1/2)*(876*a^10*b*c^4*e^13 + 1336*a^10*c^5*d*e^12 + 7
3*a^8*b^5*c^2*e^13 - 511*a^9*b^3*c^3*e^13 - 1152*a^8*c^7*d^5*e^8 + 2176*a^9*c^6*d^3*e^10 - 128*a^4*b^8*c^3*d^5
*e^8 + 128*a^4*b^9*c^2*d^4*e^9 + 1152*a^5*b^6*c^4*d^5*e^8 - 832*a^5*b^7*c^3*d^4*e^9 - 448*a^5*b^8*c^2*d^3*e^10
- 3520*a^6*b^4*c^5*d^5*e^8 + 768*a^6*b^5*c^4*d^4*e^9 + 3520*a^6*b^6*c^3*d^3*e^10 + 576*a^6*b^7*c^2*d^2*e^11 +
4096*a^7*b^2*c^6*d^5*e^8 + 3328*a^7*b^3*c^5*d^4*e^9 - 7824*a^7*b^4*c^4*d^3*e^10 - 4520*a^7*b^5*c^3*d^2*e^11 +
2912*a^8*b^2*c^5*d^3*e^10 + 10016*a^8*b^3*c^4*d^2*e^11 - 328*a^7*b^6*c^2*d*e^12 - 4864*a^8*b*c^6*d^4*e^9 + 24
79*a^8*b^4*c^3*d*e^12 - 4352*a^9*b*c^5*d^2*e^11 - 5034*a^9*b^2*c^4*d*e^12))/(2*a^8) + (((96*a^11*b^2*c^3*e^12
- 12*a^10*b^4*c^2*e^12 - 192*a^12*c^4*e^12 + 384*a^10*c^6*d^4*e^8 + 192*a^11*c^5*d^2*e^10 + 64*a^8*b^4*c^4*d^4
*e^8 - 48*a^8*b^5*c^3*d^3*e^9 - 16*a^8*b^6*c^2*d^2*e^10 - 352*a^9*b^2*c^5*d^4*e^8 + 160*a^9*b^3*c^4*d^3*e^9 +
244*a^9*b^4*c^3*d^2*e^10 - 768*a^10*b^2*c^4*d^2*e^10 + 704*a^11*b*c^4*d*e^11 + 28*a^9*b^5*c^2*d*e^11 + 128*a^1
0*b*c^5*d^3*e^9 - 288*a^10*b^3*c^3*d*e^11)/a^8 + ((d + e*x)^(1/2)*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*
d*e)*(1024*a^13*c^4*e^10 + 64*a^11*b^4*c^2*e^10 - 512*a^12*b^2*c^3*e^10 + 1536*a^12*c^5*d^2*e^8 + 128*a^10*b^4
*c^3*d^2*e^8 - 896*a^11*b^2*c^4*d^2*e^8 - 1792*a^12*b*c^4*d*e^9 - 128*a^10*b^5*c^2*d*e^9 + 960*a^11*b^3*c^3*d*
e^9))/(16*a^11*d^(1/2)))*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e))/(8*a^3*d^(1/2)))*(3*a^2*e^2 + 8*b^2
*d^2 - 8*a*c*d^2 - 12*a*b*d*e))/(8*a^3*d^(1/2)))*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e))/(8*a^3*d^(1
/2)))*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e)*1i)/(8*a^3*d^(1/2)))/((216*a^3*c^9*d^8*e^10 - 15*a^7*c^
5*e^18 + 391*a^4*c^8*d^6*e^12 + 119*a^5*c^7*d^4*e^14 - 71*a^6*c^6*d^2*e^16 - 64*b^4*c^8*d^10*e^8 + 128*b^5*c^7
*d^9*e^9 - 64*b^6*c^6*d^8*e^10 + 1472*a^2*b^3*c^7*d^7*e^11 - 1344*a^2*b^4*c^6*d^6*e^12 + 32*a^2*b^5*c^5*d^5*e^
13 - 1264*a^3*b^2*c^7*d^6*e^12 + 2088*a^3*b^3*c^6*d^5*e^13 - 152*a^3*b^4*c^5*d^4*e^14 - 1689*a^4*b^2*c^6*d^4*e
^14 + 280*a^4*b^3*c^5*d^3*e^15 - 247*a^5*b^2*c^5*d^2*e^16 + 102*a^6*b*c^5*d*e^17 + 64*a*b^2*c^9*d^10*e^8 + 192
*a*b^3*c^8*d^9*e^9 - 704*a*b^4*c^7*d^8*e^10 + 448*a*b^5*c^6*d^7*e^11 - 224*a^2*b*c^9*d^9*e^9 - 504*a^3*b*c^8*d
^7*e^11 + 250*a^4*b*c^7*d^5*e^13 + 632*a^5*b*c^6*d^3*e^15)/a^8 - ((((d + e*x)^(1/2)*(82*a^8*c^5*e^16 + 192*a^4
*c^9*d^8*e^8 - 608*a^5*c^8*d^6*e^10 + 1106*a^6*c^7*d^4*e^12 + 52*a^7*c^6*d^2*e^14 + 64*b^8*c^5*d^8*e^8 + 704*a
^2*b^4*c^7*d^8*e^8 + 2240*a^2*b^5*c^6*d^7*e^9 + 1344*a^2*b^6*c^5*d^6*e^10 - 512*a^3*b^2*c^8*d^8*e^8 - 2944*a^3
*b^3*c^7*d^7*e^9 - 5424*a^3*b^4*c^6*d^6*e^10 - 2248*a^3*b^5*c^5*d^5*e^11 + 5184*a^4*b^2*c^7*d^6*e^10 + 6496*a^
4*b^3*c^6*d^5*e^11 + 2409*a^4*b^4*c^5*d^4*e^12 - 3748*a^5*b^2*c^6*d^4*e^12 - 1876*a^5*b^3*c^5*d^3*e^13 + 1110*
a^6*b^2*c^5*d^2*e^14 - 436*a^7*b*c^5*d*e^15 - 384*a*b^6*c^6*d^8*e^8 - 448*a*b^7*c^5*d^7*e^9 + 896*a^4*b*c^8*d^
7*e^9 - 4048*a^5*b*c^7*d^5*e^11 + 780*a^6*b*c^6*d^3*e^13))/(2*a^8) + (((108*a^9*b*c^4*e^15 + 302*a^9*c^5*d*e^1
4 + (15*a^7*b^5*c^2*e^15)/2 - 57*a^8*b^3*c^3*e^15 + 96*a^6*c^8*d^7*e^8 - 672*a^7*c^7*d^5*e^10 - 466*a^8*c^6*d^
3*e^12 + 64*a^2*b^8*c^4*d^7*e^8 - 48*a^2*b^9*c^3*d^6*e^9 - 16*a^2*b^10*c^2*d^5*e^10 - 480*a^3*b^6*c^5*d^7*e^8
+ 64*a^3*b^7*c^4*d^6*e^9 + 420*a^3*b^8*c^3*d^5*e^10 + 76*a^3*b^9*c^2*d^4*e^11 + 1088*a^4*b^4*c^6*d^7*e^8 + 116
8*a^4*b^5*c^5*d^6*e^9 - 1824*a^4*b^6*c^4*d^5*e^10 - 1248*a^4*b^7*c^3*d^4*e^11 - 140*a^4*b^8*c^2*d^3*e^12 - 800
*a^5*b^2*c^7*d^7*e^8 - 3008*a^5*b^3*c^6*d^6*e^9 + 1164*a^5*b^4*c^5*d^5*e^10 + 5108*a^5*b^5*c^4*d^4*e^11 + (349
7*a^5*b^6*c^3*d^3*e^12)/2 + (247*a^5*b^7*c^2*d^2*e^13)/2 + 1872*a^6*b^2*c^6*d^5*e^10 - 5456*a^6*b^3*c^5*d^4*e^
11 - (12151*a^6*b^4*c^4*d^3*e^12)/2 - 1249*a^6*b^5*c^3*d^2*e^13 + (10885*a^7*b^2*c^5*d^3*e^12)/2 + (7081*a^7*b
^3*c^4*d^2*e^13)/2 + 1600*a^6*b*c^7*d^6*e^9 - 51*a^6*b^6*c^2*d*e^14 + 512*a^7*b*c^6*d^4*e^11 + (867*a^7*b^4*c^
3*d*e^14)/2 - 2146*a^8*b*c^5*d^2*e^13 - (1971*a^8*b^2*c^4*d*e^14)/2)/a^8 + ((((d + e*x)^(1/2)*(876*a^10*b*c^4*
e^13 + 1336*a^10*c^5*d*e^12 + 73*a^8*b^5*c^2*e^13 - 511*a^9*b^3*c^3*e^13 - 1152*a^8*c^7*d^5*e^8 + 2176*a^9*c^6
*d^3*e^10 - 128*a^4*b^8*c^3*d^5*e^8 + 128*a^4*b^9*c^2*d^4*e^9 + 1152*a^5*b^6*c^4*d^5*e^8 - 832*a^5*b^7*c^3*d^4
*e^9 - 448*a^5*b^8*c^2*d^3*e^10 - 3520*a^6*b^4*c^5*d^5*e^8 + 768*a^6*b^5*c^4*d^4*e^9 + 3520*a^6*b^6*c^3*d^3*e^
10 + 576*a^6*b^7*c^2*d^2*e^11 + 4096*a^7*b^2*c^6*d^5*e^8 + 3328*a^7*b^3*c^5*d^4*e^9 - 7824*a^7*b^4*c^4*d^3*e^1
0 - 4520*a^7*b^5*c^3*d^2*e^11 + 2912*a^8*b^2*c^5*d^3*e^10 + 10016*a^8*b^3*c^4*d^2*e^11 - 328*a^7*b^6*c^2*d*e^1
2 - 4864*a^8*b*c^6*d^4*e^9 + 2479*a^8*b^4*c^3*d*e^12 - 4352*a^9*b*c^5*d^2*e^11 - 5034*a^9*b^2*c^4*d*e^12))/(2*
a^8) - (((96*a^11*b^2*c^3*e^12 - 12*a^10*b^4*c^2*e^12 - 192*a^12*c^4*e^12 + 384*a^10*c^6*d^4*e^8 + 192*a^11*c^
5*d^2*e^10 + 64*a^8*b^4*c^4*d^4*e^8 - 48*a^8*b^5*c^3*d^3*e^9 - 16*a^8*b^6*c^2*d^2*e^10 - 352*a^9*b^2*c^5*d^4*e
^8 + 160*a^9*b^3*c^4*d^3*e^9 + 244*a^9*b^4*c^3*d^2*e^10 - 768*a^10*b^2*c^4*d^2*e^10 + 704*a^11*b*c^4*d*e^11 +
28*a^9*b^5*c^2*d*e^11 + 128*a^10*b*c^5*d^3*e^9 - 288*a^10*b^3*c^3*d*e^11)/a^8 - ((d + e*x)^(1/2)*(3*a^2*e^2 +
8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e)*(1024*a^13*c^4*e^10 + 64*a^11*b^4*c^2*e^10 - 512*a^12*b^2*c^3*e^10 + 1536*
a^12*c^5*d^2*e^8 + 128*a^10*b^4*c^3*d^2*e^8 - 896*a^11*b^2*c^4*d^2*e^8 - 1792*a^12*b*c^4*d*e^9 - 128*a^10*b^5*
c^2*d*e^9 + 960*a^11*b^3*c^3*d*e^9))/(16*a^11*d^(1/2)))*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e))/(8*a
^3*d^(1/2)))*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e))/(8*a^3*d^(1/2)))*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c
*d^2 - 12*a*b*d*e))/(8*a^3*d^(1/2)))*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e))/(8*a^3*d^(1/2)) + ((((d
+ e*x)^(1/2)*(82*a^8*c^5*e^16 + 192*a^4*c^9*d^8*e^8 - 608*a^5*c^8*d^6*e^10 + 1106*a^6*c^7*d^4*e^12 + 52*a^7*c
^6*d^2*e^14 + 64*b^8*c^5*d^8*e^8 + 704*a^2*b^4*c^7*d^8*e^8 + 2240*a^2*b^5*c^6*d^7*e^9 + 1344*a^2*b^6*c^5*d^6*e
^10 - 512*a^3*b^2*c^8*d^8*e^8 - 2944*a^3*b^3*c^7*d^7*e^9 - 5424*a^3*b^4*c^6*d^6*e^10 - 2248*a^3*b^5*c^5*d^5*e^
11 + 5184*a^4*b^2*c^7*d^6*e^10 + 6496*a^4*b^3*c^6*d^5*e^11 + 2409*a^4*b^4*c^5*d^4*e^12 - 3748*a^5*b^2*c^6*d^4*
e^12 - 1876*a^5*b^3*c^5*d^3*e^13 + 1110*a^6*b^2*c^5*d^2*e^14 - 436*a^7*b*c^5*d*e^15 - 384*a*b^6*c^6*d^8*e^8 -
448*a*b^7*c^5*d^7*e^9 + 896*a^4*b*c^8*d^7*e^9 - 4048*a^5*b*c^7*d^5*e^11 + 780*a^6*b*c^6*d^3*e^13))/(2*a^8) - (
((108*a^9*b*c^4*e^15 + 302*a^9*c^5*d*e^14 + (15*a^7*b^5*c^2*e^15)/2 - 57*a^8*b^3*c^3*e^15 + 96*a^6*c^8*d^7*e^8
- 672*a^7*c^7*d^5*e^10 - 466*a^8*c^6*d^3*e^12 + 64*a^2*b^8*c^4*d^7*e^8 - 48*a^2*b^9*c^3*d^6*e^9 - 16*a^2*b^10
*c^2*d^5*e^10 - 480*a^3*b^6*c^5*d^7*e^8 + 64*a^3*b^7*c^4*d^6*e^9 + 420*a^3*b^8*c^3*d^5*e^10 + 76*a^3*b^9*c^2*d
^4*e^11 + 1088*a^4*b^4*c^6*d^7*e^8 + 1168*a^4*b^5*c^5*d^6*e^9 - 1824*a^4*b^6*c^4*d^5*e^10 - 1248*a^4*b^7*c^3*d
^4*e^11 - 140*a^4*b^8*c^2*d^3*e^12 - 800*a^5*b^2*c^7*d^7*e^8 - 3008*a^5*b^3*c^6*d^6*e^9 + 1164*a^5*b^4*c^5*d^5
*e^10 + 5108*a^5*b^5*c^4*d^4*e^11 + (3497*a^5*b^6*c^3*d^3*e^12)/2 + (247*a^5*b^7*c^2*d^2*e^13)/2 + 1872*a^6*b^
2*c^6*d^5*e^10 - 5456*a^6*b^3*c^5*d^4*e^11 - (12151*a^6*b^4*c^4*d^3*e^12)/2 - 1249*a^6*b^5*c^3*d^2*e^13 + (108
85*a^7*b^2*c^5*d^3*e^12)/2 + (7081*a^7*b^3*c^4*d^2*e^13)/2 + 1600*a^6*b*c^7*d^6*e^9 - 51*a^6*b^6*c^2*d*e^14 +
512*a^7*b*c^6*d^4*e^11 + (867*a^7*b^4*c^3*d*e^14)/2 - 2146*a^8*b*c^5*d^2*e^13 - (1971*a^8*b^2*c^4*d*e^14)/2)/a
^8 - ((((d + e*x)^(1/2)*(876*a^10*b*c^4*e^13 + 1336*a^10*c^5*d*e^12 + 73*a^8*b^5*c^2*e^13 - 511*a^9*b^3*c^3*e^
13 - 1152*a^8*c^7*d^5*e^8 + 2176*a^9*c^6*d^3*e^10 - 128*a^4*b^8*c^3*d^5*e^8 + 128*a^4*b^9*c^2*d^4*e^9 + 1152*a
^5*b^6*c^4*d^5*e^8 - 832*a^5*b^7*c^3*d^4*e^9 - 448*a^5*b^8*c^2*d^3*e^10 - 3520*a^6*b^4*c^5*d^5*e^8 + 768*a^6*b
^5*c^4*d^4*e^9 + 3520*a^6*b^6*c^3*d^3*e^10 + 576*a^6*b^7*c^2*d^2*e^11 + 4096*a^7*b^2*c^6*d^5*e^8 + 3328*a^7*b^
3*c^5*d^4*e^9 - 7824*a^7*b^4*c^4*d^3*e^10 - 4520*a^7*b^5*c^3*d^2*e^11 + 2912*a^8*b^2*c^5*d^3*e^10 + 10016*a^8*
b^3*c^4*d^2*e^11 - 328*a^7*b^6*c^2*d*e^12 - 4864*a^8*b*c^6*d^4*e^9 + 2479*a^8*b^4*c^3*d*e^12 - 4352*a^9*b*c^5*
d^2*e^11 - 5034*a^9*b^2*c^4*d*e^12))/(2*a^8) + (((96*a^11*b^2*c^3*e^12 - 12*a^10*b^4*c^2*e^12 - 192*a^12*c^4*e
^12 + 384*a^10*c^6*d^4*e^8 + 192*a^11*c^5*d^2*e^10 + 64*a^8*b^4*c^4*d^4*e^8 - 48*a^8*b^5*c^3*d^3*e^9 - 16*a^8*
b^6*c^2*d^2*e^10 - 352*a^9*b^2*c^5*d^4*e^8 + 160*a^9*b^3*c^4*d^3*e^9 + 244*a^9*b^4*c^3*d^2*e^10 - 768*a^10*b^2
*c^4*d^2*e^10 + 704*a^11*b*c^4*d*e^11 + 28*a^9*b^5*c^2*d*e^11 + 128*a^10*b*c^5*d^3*e^9 - 288*a^10*b^3*c^3*d*e^
11)/a^8 + ((d + e*x)^(1/2)*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e)*(1024*a^13*c^4*e^10 + 64*a^11*b^4*
c^2*e^10 - 512*a^12*b^2*c^3*e^10 + 1536*a^12*c^5*d^2*e^8 + 128*a^10*b^4*c^3*d^2*e^8 - 896*a^11*b^2*c^4*d^2*e^8
- 1792*a^12*b*c^4*d*e^9 - 128*a^10*b^5*c^2*d*e^9 + 960*a^11*b^3*c^3*d*e^9))/(16*a^11*d^(1/2)))*(3*a^2*e^2 + 8
*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e))/(8*a^3*d^(1/2)))*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e))/(8*a^3*
d^(1/2)))*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e))/(8*a^3*d^(1/2)))*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^
2 - 12*a*b*d*e))/(8*a^3*d^(1/2))))*(3*a^2*e^2 + 8*b^2*d^2 - 8*a*c*d^2 - 12*a*b*d*e)*1i)/(4*a^3*d^(1/2))

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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