3.15.25 \(\int \frac {b+2 c x}{(d+e x)^{5/2} (a+b x+c x^2)} \, dx\)

Optimal. Leaf size=518 \[ \frac {2 \left (-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right )}{\sqrt {d+e x} \left (a e^2-b d e+c d^2\right )^2}-\frac {\sqrt {2} \sqrt {c} \left (2 c^2 d \left (d \sqrt {b^2-4 a c}+4 a e\right )-2 c e \left (b d \sqrt {b^2-4 a c}+a e \sqrt {b^2-4 a c}+2 a b e+b^2 d\right )+b^2 e^2 \left (\sqrt {b^2-4 a c}+b\right )\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )}}\right )}{\sqrt {b^2-4 a c} \sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )} \left (a e^2-b d e+c d^2\right )^2}+\frac {\sqrt {2} \sqrt {c} \left (-2 c^2 d \left (d \sqrt {b^2-4 a c}-4 a e\right )-2 c e \left (-b d \sqrt {b^2-4 a c}-a e \sqrt {b^2-4 a c}+2 a b e+b^2 d\right )+b^2 e^2 \left (b-\sqrt {b^2-4 a c}\right )\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}\right )}{\sqrt {b^2-4 a c} \sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )} \left (a e^2-b d e+c d^2\right )^2}+\frac {2 (2 c d-b e)}{3 (d+e x)^{3/2} \left (a e^2-b d e+c d^2\right )} \]

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Rubi [A]  time = 1.90, antiderivative size = 518, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 4, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {828, 826, 1166, 208} \begin {gather*} \frac {2 \left (-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right )}{\sqrt {d+e x} \left (a e^2-b d e+c d^2\right )^2}-\frac {\sqrt {2} \sqrt {c} \left (2 c^2 d \left (d \sqrt {b^2-4 a c}+4 a e\right )-2 c e \left (b d \sqrt {b^2-4 a c}+a e \sqrt {b^2-4 a c}+2 a b e+b^2 d\right )+b^2 e^2 \left (\sqrt {b^2-4 a c}+b\right )\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 )}{\sqrt {b^2-4 a c} \sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )} \left (a e^2-b d e+c d^2\right )^2}+\frac {\sqrt {2} \sqrt {c} \left (-2 c^2 d \left (d \sqrt {b^2-4 a c}-4 a e\right )-2 c e \left (-b d \sqrt {b^2-4 a c}-a e \sqrt {b^2-4 a c}+2 a b e+b^2 d\right )+b^2 e^2 \left (b-\sqrt {b^2-4 a c}\right )\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 )} \left (a e^2-b d e+c d^2\right )^2}+\frac {2 (2 c d-b e)}{3 (d+e x)^{3/2} \left (a e^2-b d e+c d^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(b + 2*c*x)/((d + e*x)^(5/2)*(a + b*x + c*x^2)),x]

[Out]

(2*(2*c*d - b*e))/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)) + (2*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e)))/
((c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]) - (Sqrt[2]*Sqrt[c]*(b^2*(b + Sqrt[b^2 - 4*a*c])*e^2 + 2*c^2*d*(Sqrt[
b^2 - 4*a*c]*d + 4*a*e) - 2*c*e*(b^2*d + b*Sqrt[b^2 - 4*a*c]*d + 2*a*b*e + a*Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sq
rt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sq
rt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)^2) + (Sqrt[2]*Sqrt[c]*(b^2*(b - Sqrt[b^2 - 4*a*c])*e^2 - 2*c^2*d*(
Sqrt[b^2 - 4*a*c]*d - 4*a*e) - 2*c*e*(b^2*d - b*Sqrt[b^2 - 4*a*c]*d + 2*a*b*e - a*Sqrt[b^2 - 4*a*c]*e))*ArcTan
h[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + 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]*(c*d^2 - b*d*e + a*e^2)^2)

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 826

Int[((f_.) + (g_.)*(x_))/(Sqrt[(d_.) + (e_.)*(x_)]*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)), x_Symbol] :> Dist[2,
Subst[Int[(e*f - d*g + g*x^2)/(c*d^2 - b*d*e + a*e^2 - (2*c*d - b*e)*x^2 + c*x^4), x], x, Sqrt[d + e*x]], x] /
; FreeQ[{a, b, c, d, e, f, g}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0]

Rule 828

Int[(((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_)))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Simp[((
e*f - d*g)*(d + e*x)^(m + 1))/((m + 1)*(c*d^2 - b*d*e + a*e^2)), x] + Dist[1/(c*d^2 - b*d*e + a*e^2), Int[((d
+ e*x)^(m + 1)*Simp[c*d*f - f*b*e + a*e*g - c*(e*f - d*g)*x, x])/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c,
d, e, f, g, m}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && FractionQ[m] && LtQ[m, -1]

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]

Rubi steps

\begin {align*} \int \frac {b+2 c x}{(d+e x)^{5/2} \left (a+b x+c x^2\right )} \, dx &=\frac {2 (2 c d-b e)}{3 \left (c d^2-b d e+a e^2\right ) (d+e x)^{3/2}}+\frac {\int \frac {b c d-b^2 e+2 a c e+c (2 c d-b e) x}{(d+e x)^{3/2} \left (a+b x+c x^2\right )} \, dx}{c d^2-b d e+a e^2}\\ &=\frac {2 (2 c d-b e)}{3 \left (c d^2-b d e+a e^2\right ) (d+e x)^{3/2}}+\frac {2 \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\right )}{\left (c d^2-b d e+a e^2\right )^2 \sqrt {d+e x}}+\frac {\int \frac {-2 b^2 c d e+4 a c^2 d e+b^3 e^2+b c \left (c d^2-3 a e^2\right )+c \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\right ) x}{\sqrt {d+e x} \left (a+b x+c x^2\right )} \, dx}{\left (c d^2-b d e+a e^2\right )^2}\\ &=\frac {2 (2 c d-b e)}{3 \left (c d^2-b d e+a e^2\right ) (d+e x)^{3/2}}+\frac {2 \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\right )}{\left (c d^2-b d e+a e^2\right )^2 \sqrt {d+e x}}+\frac {2 \operatorname {Subst}\left (\int \frac {-c d \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\right )+e \left (-2 b^2 c d e+4 a c^2 d e+b^3 e^2+b c \left (c d^2-3 a e^2\right )\right )+c \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\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 )}{\left (c d^2-b d e+a e^2\right )^2}\\ &=\frac {2 (2 c d-b e)}{3 \left (c d^2-b d e+a e^2\right ) (d+e x)^{3/2}}+\frac {2 \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\right )}{\left (c d^2-b d e+a e^2\right )^2 \sqrt {d+e x}}-\frac {\left (c \left (b^2 \left (b-\sqrt {b^2-4 a c}\right ) e^2-2 c^2 d \left (\sqrt {b^2-4 a c} d-4 a e\right )-2 c e \left (b^2 d-b \sqrt {b^2-4 a c} d+2 a b e-a \sqrt {b^2-4 a c} e\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 )}{\sqrt {b^2-4 a c} \left (c d^2-b d e+a e^2\right )^2}+\frac {\left (c \left (b^2 \left (b+\sqrt {b^2-4 a c}\right ) e^2+2 c^2 d \left (\sqrt {b^2-4 a c} d+4 a e\right )-2 c e \left (b^2 d+b \sqrt {b^2-4 a c} d+2 a b e+a \sqrt {b^2-4 a c} e\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 )}{\sqrt {b^2-4 a c} \left (c d^2-b d e+a e^2\right )^2}\\ &=\frac {2 (2 c d-b e)}{3 \left (c d^2-b d e+a e^2\right ) (d+e x)^{3/2}}+\frac {2 \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\right )}{\left (c d^2-b d e+a e^2\right )^2 \sqrt {d+e x}}-\frac {\sqrt {2} \sqrt {c} \left (b^2 \left (b+\sqrt {b^2-4 a c}\right ) e^2+2 c^2 d \left (\sqrt {b^2-4 a c} d+4 a e\right )-2 c e \left (b^2 d+b \sqrt {b^2-4 a c} d+2 a b e+a \sqrt {b^2-4 a c} e\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 )}{\sqrt {b^2-4 a c} \sqrt {2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e} \left (c d^2-b d e+a e^2\right )^2}+\frac {\sqrt {2} \sqrt {c} \left (b^2 \left (b-\sqrt {b^2-4 a c}\right ) e^2-2 c^2 d \left (\sqrt {b^2-4 a c} d-4 a e\right )-2 c e \left (b^2 d-b \sqrt {b^2-4 a c} d+2 a b e-a \sqrt {b^2-4 a c} e\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 )}{\sqrt {b^2-4 a c} \sqrt {2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e} \left (c d^2-b d e+a e^2\right )^2}\\ \end {align*}

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Mathematica [A]  time = 1.67, size = 481, normalized size = 0.93 \begin {gather*} \frac {2 \left (\frac {-6 c e (a e+b d)+3 b^2 e^2+6 c^2 d^2}{\sqrt {d+e x} \left (e (a e-b d)+c d^2\right )}-\frac {3 \sqrt {c} \left (-\frac {\left (2 c^2 d \left (d \sqrt {b^2-4 a c}+4 a e\right )-2 c e \left (b d \sqrt {b^2-4 a c}+a e \sqrt {b^2-4 a c}+2 a b e+b^2 d\right )+b^2 e^2 \left (\sqrt {b^2-4 a c}+b\right )\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 {e \left (\sqrt {b^2-4 a c}-b\right )+2 c d}}-\frac {\left (2 c^2 d \left (d \sqrt {b^2-4 a c}-4 a e\right )-2 c e \left (b d \sqrt {b^2-4 a c}+a e \sqrt {b^2-4 a c}-2 a b e+b^2 (-d)\right )+b^2 e^2 \left (\sqrt {b^2-4 a c}-b\right )\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 {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}\right )}{\sqrt {2} \sqrt {b^2-4 a c} \left (e (b d-a e)-c d^2\right )}+\frac {2 c d-b e}{(d+e x)^{3/2}}\right )}{3 \left (e (a e-b d)+c d^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(b + 2*c*x)/((d + e*x)^(5/2)*(a + b*x + c*x^2)),x]

[Out]

(2*((2*c*d - b*e)/(d + e*x)^(3/2) + (6*c^2*d^2 + 3*b^2*e^2 - 6*c*e*(b*d + a*e))/((c*d^2 + e*(-(b*d) + a*e))*Sq
rt[d + e*x]) - (3*Sqrt[c]*(-(((b^2*(b + Sqrt[b^2 - 4*a*c])*e^2 + 2*c^2*d*(Sqrt[b^2 - 4*a*c]*d + 4*a*e) - 2*c*e
*(b^2*d + b*Sqrt[b^2 - 4*a*c]*d + 2*a*b*e + a*Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sq
rt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]])/Sqrt[2*c*d + (-b + Sqrt[b^2 - 4*a*c])*e]) - ((b^2*(-b + Sqrt[b^2 - 4*a
*c])*e^2 + 2*c^2*d*(Sqrt[b^2 - 4*a*c]*d - 4*a*e) - 2*c*e*(-(b^2*d) + b*Sqrt[b^2 - 4*a*c]*d - 2*a*b*e + a*Sqrt[
b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/Sqrt[2*c*d
- (b + Sqrt[b^2 - 4*a*c])*e]))/(Sqrt[2]*Sqrt[b^2 - 4*a*c]*(-(c*d^2) + e*(b*d - a*e)))))/(3*(c*d^2 + e*(-(b*d)
+ a*e)))

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IntegrateAlgebraic [A]  time = 2.29, size = 690, normalized size = 1.33 \begin {gather*} \frac {2 \left (-a b e^3-6 a c e^2 (d+e x)+2 a c d e^2+3 b^2 e^2 (d+e x)+b^2 d e^2-3 b c d^2 e-6 b c d e (d+e x)+2 c^2 d^3+6 c^2 d^2 (d+e x)\right )}{3 (d+e x)^{3/2} \left (a e^2-b d e+c d^2\right )^2}+\frac {\left (2 \sqrt {2} c^{5/2} d^2 \sqrt {b^2-4 a c}-2 \sqrt {2} b c^{3/2} d e \sqrt {b^2-4 a c}-2 \sqrt {2} a c^{3/2} e^2 \sqrt {b^2-4 a c}+\sqrt {2} b^2 \sqrt {c} e^2 \sqrt {b^2-4 a c}-4 \sqrt {2} a b c^{3/2} e^2+8 \sqrt {2} a c^{5/2} d e+\sqrt {2} b^3 \sqrt {c} e^2-2 \sqrt {2} b^2 c^{3/2} d e\right ) \tan ^{-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 \sqrt {b^2-4 a c}+b e-2 c d} \left (-a e^2+b d e-c d^2\right )^2}+\frac {\left (2 \sqrt {2} c^{5/2} d^2 \sqrt {b^2-4 a c}-2 \sqrt {2} b c^{3/2} d e \sqrt {b^2-4 a c}-2 \sqrt {2} a c^{3/2} e^2 \sqrt {b^2-4 a c}+\sqrt {2} b^2 \sqrt {c} e^2 \sqrt {b^2-4 a c}+4 \sqrt {2} a b c^{3/2} e^2-8 \sqrt {2} a c^{5/2} d e-\sqrt {2} b^3 \sqrt {c} e^2+2 \sqrt {2} b^2 c^{3/2} d e\right ) \tan ^{-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 \sqrt {b^2-4 a c}+b e-2 c d} \left (-a e^2+b d e-c d^2\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[(b + 2*c*x)/((d + e*x)^(5/2)*(a + b*x + c*x^2)),x]

[Out]

(2*(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3 + 6*c^2*d^2*(d + e*x) - 6*b*c*d*e*(d + e*x) +
3*b^2*e^2*(d + e*x) - 6*a*c*e^2*(d + e*x)))/(3*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(3/2)) + ((2*Sqrt[2]*c^(5/2
)*Sqrt[b^2 - 4*a*c]*d^2 - 2*Sqrt[2]*b^2*c^(3/2)*d*e + 8*Sqrt[2]*a*c^(5/2)*d*e - 2*Sqrt[2]*b*c^(3/2)*Sqrt[b^2 -
4*a*c]*d*e + Sqrt[2]*b^3*Sqrt[c]*e^2 - 4*Sqrt[2]*a*b*c^(3/2)*e^2 + Sqrt[2]*b^2*Sqrt[c]*Sqrt[b^2 - 4*a*c]*e^2
- 2*Sqrt[2]*a*c^(3/2)*Sqrt[b^2 - 4*a*c]*e^2)*ArcTan[(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*e - Sqrt[b^2 - 4*a*c]*e]*(-(c*d^2) + b*d*e - a*e^2)^2) + (
(2*Sqrt[2]*c^(5/2)*Sqrt[b^2 - 4*a*c]*d^2 + 2*Sqrt[2]*b^2*c^(3/2)*d*e - 8*Sqrt[2]*a*c^(5/2)*d*e - 2*Sqrt[2]*b*c
^(3/2)*Sqrt[b^2 - 4*a*c]*d*e - Sqrt[2]*b^3*Sqrt[c]*e^2 + 4*Sqrt[2]*a*b*c^(3/2)*e^2 + Sqrt[2]*b^2*Sqrt[c]*Sqrt[
b^2 - 4*a*c]*e^2 - 2*Sqrt[2]*a*c^(3/2)*Sqrt[b^2 - 4*a*c]*e^2)*ArcTan[(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*e + Sqrt[b^2 - 4*a*c]*e]*(-(c*d^2) + b*d*
e - a*e^2)^2)

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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((2*c*x+b)/(e*x+d)^(5/2)/(c*x^2+b*x+a),x, algorithm="fricas")

[Out]

Timed out

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giac [B]  time = 4.00, size = 1255, normalized size = 2.42

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*c*x+b)/(e*x+d)^(5/2)/(c*x^2+b*x+a),x, algorithm="giac")

[Out]

-2*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c^3*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^3*d^5 - 5*
b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^
4 - a^2*b*e^5 + sqrt((2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^
2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5)^2 - 4*(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*
d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*(c^3*d^
4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/(c^3*d^4 - 2*b*c^2*d^3*e +
b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/((2*c^3*d^3 - 3*(b*c^2 - sqrt(b^2 - 4*a*c)*c^2)
*d^2*e + 3*(b^2*c - 2*a*c^2 - sqrt(b^2 - 4*a*c)*b*c)*d*e^2 - (b^3 - 3*a*b*c - (b^2 - a*c)*sqrt(b^2 - 4*a*c))*e
^3)*abs(c)) - 2*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c^3*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2
*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 +
2*a^2*c*d*e^4 - a^2*b*e^5 - sqrt((2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3
- 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5)^2 - 4*(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e
^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3
*e^6)*(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/(c^3*d^4 - 2*b
*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/((2*c^3*d^3 - 3*(b*c^2 + sqrt(b^2
- 4*a*c)*c^2)*d^2*e + 3*(b^2*c - 2*a*c^2 + sqrt(b^2 - 4*a*c)*b*c)*d*e^2 - (b^3 - 3*a*b*c + (b^2 - a*c)*sqrt(b^
2 - 4*a*c))*e^3)*abs(c)) + 2/3*(6*(x*e + d)*c^2*d^2 + 2*c^2*d^3 - 6*(x*e + d)*b*c*d*e - 3*b*c*d^2*e + 3*(x*e +
d)*b^2*e^2 - 6*(x*e + d)*a*c*e^2 + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3)/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 +
2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*(x*e + d)^(3/2))

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maple [B]  time = 0.14, size = 1962, normalized size = 3.79

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*c*x+b)/(e*x+d)^(5/2)/(c*x^2+b*x+a),x)

[Out]

4/(a*e^2-b*d*e+c*d^2)^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)*a
rctanh((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)*a*b*e^3-8/(a*e^2-b*d*e+c*d^2)^
2*c^3/(-(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)*a*d*e^2-1/(a*e^2-b*d*e+c*d^2)^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^3*e^3+2/(a*e^2-b*d*e+c*d^2)^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^2*d*e^2+2/(a*e^2-b*d*e+c*d^2)^2*c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arct
anh((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)*a*e^2-1/(a*e^2-b*d*e+c*d^2)^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^2*e^2+2/(a*e^2-b*d*e+c*d^2)^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)*b*d*e-2/(a*e^2-b*d*e+
c*d^2)^2*c^3*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+4/(a*e^2-b*d*e+c*d^2)^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)*a*b*e^3-8/(a*e^2-b*d*e+c*d^2)^2*c^3/(-(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)*a*d*e^2-1/(a*e
^2-b*d*e+c*d^2)^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^3*e^3+2/(a*e^2-b*d*e+c*d^2)^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^2*d*e^2-2/(a*e^2-b*d*e+c*d^2)^2*c^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)*a*e^
2+1/(a*e^2-b*d*e+c*d^2)^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^2*e^2-2/(a*e^2-b*d*e+c*d^2)^2*c^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*e+2/(a*e^2-b*d*e+c*d^2)^2*c^3*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^2-2/3/(a*e^2-b*d*e+c*d^2)/(e*x+d)^(3/2)*b*e+4/3/
(a*e^2-b*d*e+c*d^2)/(e*x+d)^(3/2)*c*d-4/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)^(1/2)*a*c*e^2+2/(a*e^2-b*d*e+c*d^2)^2/(e
*x+d)^(1/2)*b^2*e^2-4/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)^(1/2)*b*c*d*e+4/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)^(1/2)*c^2*d^
2

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, c x + b}{{\left (c x^{2} + b x + a\right )} {\left (e x + d\right )}^{\frac {5}{2}}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*c*x+b)/(e*x+d)^(5/2)/(c*x^2+b*x+a),x, algorithm="maxima")

[Out]

integrate((2*c*x + b)/((c*x^2 + b*x + a)*(e*x + d)^(5/2)), x)

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mupad [B]  time = 11.38, size = 50695, normalized size = 97.87

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b + 2*c*x)/((d + e*x)^(5/2)*(a + b*x + c*x^2)),x)

[Out]

atan((((-(b^5*e^5 - 2*c^5*d^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) + 5*a^2*b*c^2*e^5 + 20*a*c^4*d^3*e^2 - 10*a^2*c^3*
d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) - 10*b^2*c^3*d^3*e^2 + 10*b^3*c^2*d^2*e^3 - 5*a*b^3*c*e^5 + 5*b*c^4*d^
4*e - 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5
*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) - 30*a*b*c^3*d^2*e^3 + 20*a*b^2*c^2*d*e^4 - 10*a*c^3*
d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*
(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 1
0*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3
*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 +
30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(b^5*e^5 - 2*c^
5*d^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) + 5*a^2*b*c^2*e^5 + 20*a*c^4*d^3*e^2 - 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2
- 4*a*c)^(1/2) - 10*b^2*c^3*d^3*e^2 + 10*b^3*c^2*d^2*e^3 - 5*a*b^3*c*e^5 + 5*b*c^4*d^4*e - 5*b^4*c*d*e^4 + 5*
c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5
*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) - 30*a*b*c^3*d^2*e^3 + 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1
/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b
^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a
^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d
*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 3
0*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e
^22 + 8*a^10*b^3*c^2*e^23 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^
5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5
*e^18 + 640*a^10*c^5*d^3*e^20 - 16*b^2*c^13*d^21*e^2 + 168*b^3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^
5*c^10*d^18*e^5 - 4320*b^6*c^9*d^17*e^6 + 5712*b^7*c^8*d^16*e^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^
9 - 1680*b^10*c^5*d^13*e^10 + 520*b^11*c^4*d^12*e^11 - 96*b^12*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^
2*b^2*c^11*d^17*e^6 - 59160*a^2*b^3*c^10*d^16*e^7 + 84480*a^2*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 +
23520*a^2*b^6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^
10*e^13 - 3280*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^
3*c^9*d^14*e^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 1
0560*a^3*b^7*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^1
6 + 184800*a^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^
5*c^6*d^10*e^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a
^4*b^9*c^2*d^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^1
4 - 120960*a^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^
5*e^18 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b
^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*
a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 338
40*a^8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 +
5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 760
0*a*b^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*
a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a
*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^
4*b*c^10*d^14*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a
^8*b*c^6*d^6*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c
^3*d*e^22) - 96*a^10*b*c^4*e^21 - 64*a*c^14*d^19*e^2 + 192*a^10*c^5*d*e^20 - 8*a^8*b^5*c^2*e^21 + 56*a^9*b^3*c
^3*e^21 - 320*a^2*c^13*d^17*e^4 - 256*a^3*c^12*d^15*e^6 + 1792*a^4*c^11*d^13*e^8 + 6272*a^5*c^10*d^11*e^10 + 9
856*a^6*c^9*d^9*e^12 + 8960*a^7*c^8*d^7*e^14 + 4864*a^8*c^7*d^5*e^16 + 1472*a^9*c^6*d^3*e^18 + 16*b^2*c^13*d^1
9*e^2 - 152*b^3*c^12*d^18*e^3 + 664*b^4*c^11*d^17*e^4 - 1768*b^5*c^10*d^16*e^5 + 3200*b^6*c^9*d^15*e^6 - 4144*
b^7*c^8*d^14*e^7 + 3920*b^8*c^7*d^13*e^8 - 2704*b^9*c^6*d^12*e^9 + 1328*b^10*c^5*d^11*e^10 - 440*b^11*c^4*d^10
*e^11 + 88*b^12*c^3*d^9*e^12 - 8*b^13*c^2*d^8*e^13 - 10688*a^2*b^2*c^11*d^15*e^6 + 25760*a^2*b^3*c^10*d^14*e^7
- 41888*a^2*b^4*c^9*d^13*e^8 + 46592*a^2*b^5*c^8*d^12*e^9 - 33376*a^2*b^6*c^7*d^11*e^10 + 11968*a^2*b^7*c^6*d
^10*e^11 + 1760*a^2*b^8*c^5*d^9*e^12 - 3872*a^2*b^9*c^4*d^8*e^13 + 1568*a^2*b^10*c^3*d^7*e^14 - 224*a^2*b^11*c
^2*d^6*e^15 - 8512*a^3*b^2*c^10*d^13*e^8 + 26208*a^3*b^3*c^9*d^12*e^9 - 52864*a^3*b^4*c^8*d^11*e^10 + 66528*a^
3*b^5*c^7*d^10*e^11 - 49280*a^3*b^6*c^6*d^9*e^12 + 17952*a^3*b^7*c^5*d^8*e^13 - 128*a^3*b^8*c^4*d^7*e^14 - 201
6*a^3*b^9*c^3*d^6*e^15 + 448*a^3*b^10*c^2*d^5*e^16 + 27104*a^4*b^2*c^9*d^11*e^10 - 20944*a^4*b^3*c^8*d^10*e^11
- 18480*a^4*b^4*c^7*d^9*e^12 + 48048*a^4*b^5*c^6*d^8*e^13 - 35392*a^4*b^6*c^5*d^7*e^14 + 9296*a^4*b^7*c^4*d^6
*e^15 + 784*a^4*b^8*c^3*d^5*e^16 - 560*a^4*b^9*c^2*d^4*e^17 + 71456*a^5*b^2*c^8*d^9*e^12 - 62832*a^5*b^3*c^7*d
^8*e^13 + 8064*a^5*b^4*c^6*d^7*e^14 + 23520*a^5*b^5*c^5*d^6*e^15 - 13664*a^5*b^6*c^4*d^5*e^16 + 1232*a^5*b^7*c
^3*d^4*e^17 + 448*a^5*b^8*c^2*d^3*e^18 + 73024*a^6*b^2*c^7*d^7*e^14 - 48608*a^6*b^3*c^6*d^6*e^15 + 3808*a^6*b^
4*c^5*d^5*e^16 + 8512*a^6*b^5*c^4*d^4*e^17 - 2016*a^6*b^6*c^3*d^3*e^18 - 224*a^6*b^7*c^2*d^2*e^19 + 37312*a^7*
b^2*c^6*d^5*e^16 - 14880*a^7*b^3*c^5*d^4*e^17 - 1408*a^7*b^4*c^4*d^3*e^18 + 1312*a^7*b^5*c^3*d^2*e^19 + 8848*a
^8*b^2*c^5*d^3*e^18 - 1112*a^8*b^3*c^4*d^2*e^19 + 608*a*b*c^13*d^18*e^3 - 2576*a*b^2*c^12*d^17*e^4 + 6392*a*b^
3*c^11*d^16*e^5 - 10112*a*b^4*c^10*d^15*e^6 + 10016*a*b^5*c^9*d^14*e^7 - 4704*a*b^6*c^8*d^13*e^8 - 2288*a*b^7*
c^7*d^12*e^9 + 5888*a*b^8*c^6*d^11*e^10 - 4928*a*b^9*c^5*d^10*e^11 + 2288*a*b^10*c^4*d^9*e^12 - 584*a*b^11*c^3
*d^8*e^13 + 64*a*b^12*c^2*d^7*e^14 + 2720*a^2*b*c^12*d^16*e^5 + 1920*a^3*b*c^11*d^14*e^7 - 11648*a^4*b*c^10*d^
12*e^9 - 34496*a^5*b*c^9*d^10*e^11 - 44352*a^6*b*c^8*d^8*e^13 - 31360*a^7*b*c^7*d^6*e^15 + 64*a^7*b^6*c^2*d*e^
20 - 12160*a^8*b*c^6*d^4*e^17 - 424*a^8*b^4*c^3*d*e^20 - 2208*a^9*b*c^5*d^2*e^19 + 624*a^9*b^2*c^4*d*e^20) + (
d + e*x)^(1/2)*(8*a^6*b^6*c^3*e^18 - 64*a*c^14*d^16*e^2 - 64*a^9*c^6*e^18 - 64*a^7*b^4*c^4*e^18 + 144*a^8*b^2*
c^5*e^18 + 1280*a^3*c^12*d^12*e^6 + 4096*a^4*c^11*d^10*e^8 + 5760*a^5*c^10*d^8*e^10 + 4096*a^6*c^9*d^6*e^12 +
1280*a^7*c^8*d^4*e^14 + 16*b^2*c^13*d^16*e^2 - 128*b^3*c^12*d^15*e^3 + 480*b^4*c^11*d^14*e^4 - 1120*b^5*c^10*d
^13*e^5 + 1800*b^6*c^9*d^12*e^6 - 2064*b^7*c^8*d^11*e^7 + 1688*b^8*c^7*d^10*e^8 - 960*b^9*c^6*d^9*e^9 + 360*b^
10*c^5*d^8*e^10 - 80*b^11*c^4*d^7*e^11 + 8*b^12*c^3*d^6*e^12 - 960*a^2*b^2*c^11*d^12*e^6 + 5760*a^2*b^3*c^10*d
^11*e^7 - 14304*a^2*b^4*c^9*d^10*e^8 + 18720*a^2*b^5*c^8*d^9*e^9 - 13320*a^2*b^6*c^7*d^8*e^10 + 4320*a^2*b^7*c
^6*d^7*e^11 + 240*a^2*b^8*c^5*d^6*e^12 - 576*a^2*b^9*c^4*d^5*e^13 + 120*a^2*b^10*c^3*d^4*e^14 + 17024*a^3*b^2*
c^10*d^10*e^8 - 14720*a^3*b^3*c^9*d^9*e^9 - 2880*a^3*b^4*c^8*d^8*e^10 + 15360*a^3*b^5*c^7*d^7*e^11 - 11360*a^3
*b^6*c^6*d^6*e^12 + 2976*a^3*b^7*c^5*d^5*e^13 + 160*a^3*b^8*c^4*d^4*e^14 - 160*a^3*b^9*c^3*d^3*e^15 + 38880*a^
4*b^2*c^9*d^8*e^10 - 32640*a^4*b^3*c^8*d^7*e^11 + 7200*a^4*b^4*c^7*d^6*e^12 + 6624*a^4*b^5*c^6*d^5*e^13 - 4360
*a^4*b^6*c^5*d^4*e^14 + 560*a^4*b^7*c^4*d^3*e^15 + 120*a^4*b^8*c^3*d^2*e^16 + 34176*a^5*b^2*c^8*d^6*e^12 - 218
88*a^5*b^3*c^7*d^5*e^13 + 3840*a^5*b^4*c^6*d^4*e^14 + 1920*a^5*b^5*c^5*d^3*e^15 - 720*a^5*b^6*c^4*d^2*e^16 + 1
3120*a^6*b^2*c^7*d^4*e^14 - 5760*a^6*b^3*c^6*d^3*e^15 + 480*a^6*b^4*c^5*d^2*e^16 + 1920*a^7*b^2*c^6*d^2*e^16 +
512*a*b*c^13*d^15*e^3 - 1920*a*b^2*c^12*d^14*e^4 + 4480*a*b^3*c^11*d^13*e^5 - 7040*a*b^4*c^10*d^12*e^6 + 7296
*a*b^5*c^9*d^11*e^7 - 4304*a*b^6*c^8*d^10*e^8 + 400*a*b^7*c^7*d^9*e^9 + 1440*a*b^8*c^6*d^8*e^10 - 1120*a*b^9*c
^5*d^7*e^11 + 368*a*b^10*c^4*d^6*e^12 - 48*a*b^11*c^3*d^5*e^13 - 7680*a^3*b*c^11*d^11*e^7 - 20480*a^4*b*c^10*d
^9*e^9 - 23040*a^5*b*c^9*d^7*e^11 - 48*a^5*b^7*c^3*d*e^17 - 12288*a^6*b*c^8*d^5*e^13 + 352*a^6*b^5*c^4*d*e^17
- 2560*a^7*b*c^7*d^3*e^15 - 640*a^7*b^3*c^5*d*e^17))*(-(b^5*e^5 - 2*c^5*d^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) + 5*
a^2*b*c^2*e^5 + 20*a*c^4*d^3*e^2 - 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) - 10*b^2*c^3*d^3*e^2 + 1
0*b^3*c^2*d^2*e^3 - 5*a*b^3*c*e^5 + 5*b*c^4*d^4*e - 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c
^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) - 30*a*
b*c^3*d^2*e^3 + 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/
2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d
^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10
*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^
3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e
^6)))^(1/2)*1i - ((-(b^5*e^5 - 2*c^5*d^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) + 5*a^2*b*c^2*e^5 + 20*a*c^4*d^3*e^2 -
10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) - 10*b^2*c^3*d^3*e^2 + 10*b^3*c^2*d^2*e^3 - 5*a*b^3*c*e^5 +
5*b*c^4*d^4*e - 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*
a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) - 30*a*b*c^3*d^2*e^3 + 20*a*b^2*c^2*d*e^4
- 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)
^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*
d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e
^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c
*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2)*(192*a^10*c^5*d*e^20 -
96*a^10*b*c^4*e^21 - 64*a*c^14*d^19*e^2 - (d + e*x)^(1/2)*(-(b^5*e^5 - 2*c^5*d^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2)
+ 5*a^2*b*c^2*e^5 + 20*a*c^4*d^3*e^2 - 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) - 10*b^2*c^3*d^3*e^
2 + 10*b^3*c^2*d^2*e^3 - 5*a*b^3*c*e^5 + 5*b*c^4*d^4*e - 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*
b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) -
30*a*b*c^3*d^2*e^3 + 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c
)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*
c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4
+ 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d
^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*
d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e^22 + 8*a^10*b^3*c^2*e^23 + 640*a^2
*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^
11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20 - 16*
b^2*c^13*d^21*e^2 + 168*b^3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^5*c^10*d^18*e^5 - 4320*b^6*c^9*d^17
*e^6 + 5712*b^7*c^8*d^16*e^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^9 - 1680*b^10*c^5*d^13*e^10 + 520*b
^11*c^4*d^12*e^11 - 96*b^12*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^2*b^2*c^11*d^17*e^6 - 59160*a^2*b^3
*c^10*d^16*e^7 + 84480*a^2*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 + 23520*a^2*b^6*c^7*d^13*e^10 + 15600
*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^10*e^13 - 3280*a^2*b^10*c^3*d^9*e^1
4 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^3*c^9*d^14*e^9 + 235200*a^3*b^4*c^8
*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 10560*a^3*b^7*c^5*d^10*e^13 - 19200*
a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^16 + 184800*a^4*b^2*c^9*d^13*e^10 -
327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^5*c^6*d^10*e^13 + 50400*a^4*b^6*c^5
*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^9*c^2*d^6*e^17 + 237888*a^5*b^
2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^14 - 120960*a^5*b^5*c^5*d^8*e^15 + 1
3440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198240*a^6*b^2*c^7*d^9*e^1
4 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*
d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^
4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c^5*d^5*e^18 - 17400*a^8
*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^
9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11*d^18*e^5 + 10800*a*b^4
*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^
6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2
*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^4*b*c^10*d^14*e^9 - 87360*a^5*b*c^9
*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a^8*b*c^6*d^6*e^17 - 7200*a^9*b*c^5*
d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c^3*d*e^22) - 8*a^8*b^5*c^2*e^21 + 5
6*a^9*b^3*c^3*e^21 - 320*a^2*c^13*d^17*e^4 - 256*a^3*c^12*d^15*e^6 + 1792*a^4*c^11*d^13*e^8 + 6272*a^5*c^10*d^
11*e^10 + 9856*a^6*c^9*d^9*e^12 + 8960*a^7*c^8*d^7*e^14 + 4864*a^8*c^7*d^5*e^16 + 1472*a^9*c^6*d^3*e^18 + 16*b
^2*c^13*d^19*e^2 - 152*b^3*c^12*d^18*e^3 + 664*b^4*c^11*d^17*e^4 - 1768*b^5*c^10*d^16*e^5 + 3200*b^6*c^9*d^15*
e^6 - 4144*b^7*c^8*d^14*e^7 + 3920*b^8*c^7*d^13*e^8 - 2704*b^9*c^6*d^12*e^9 + 1328*b^10*c^5*d^11*e^10 - 440*b^
11*c^4*d^10*e^11 + 88*b^12*c^3*d^9*e^12 - 8*b^13*c^2*d^8*e^13 - 10688*a^2*b^2*c^11*d^15*e^6 + 25760*a^2*b^3*c^
10*d^14*e^7 - 41888*a^2*b^4*c^9*d^13*e^8 + 46592*a^2*b^5*c^8*d^12*e^9 - 33376*a^2*b^6*c^7*d^11*e^10 + 11968*a^
2*b^7*c^6*d^10*e^11 + 1760*a^2*b^8*c^5*d^9*e^12 - 3872*a^2*b^9*c^4*d^8*e^13 + 1568*a^2*b^10*c^3*d^7*e^14 - 224
*a^2*b^11*c^2*d^6*e^15 - 8512*a^3*b^2*c^10*d^13*e^8 + 26208*a^3*b^3*c^9*d^12*e^9 - 52864*a^3*b^4*c^8*d^11*e^10
+ 66528*a^3*b^5*c^7*d^10*e^11 - 49280*a^3*b^6*c^6*d^9*e^12 + 17952*a^3*b^7*c^5*d^8*e^13 - 128*a^3*b^8*c^4*d^7
*e^14 - 2016*a^3*b^9*c^3*d^6*e^15 + 448*a^3*b^10*c^2*d^5*e^16 + 27104*a^4*b^2*c^9*d^11*e^10 - 20944*a^4*b^3*c^
8*d^10*e^11 - 18480*a^4*b^4*c^7*d^9*e^12 + 48048*a^4*b^5*c^6*d^8*e^13 - 35392*a^4*b^6*c^5*d^7*e^14 + 9296*a^4*
b^7*c^4*d^6*e^15 + 784*a^4*b^8*c^3*d^5*e^16 - 560*a^4*b^9*c^2*d^4*e^17 + 71456*a^5*b^2*c^8*d^9*e^12 - 62832*a^
5*b^3*c^7*d^8*e^13 + 8064*a^5*b^4*c^6*d^7*e^14 + 23520*a^5*b^5*c^5*d^6*e^15 - 13664*a^5*b^6*c^4*d^5*e^16 + 123
2*a^5*b^7*c^3*d^4*e^17 + 448*a^5*b^8*c^2*d^3*e^18 + 73024*a^6*b^2*c^7*d^7*e^14 - 48608*a^6*b^3*c^6*d^6*e^15 +
3808*a^6*b^4*c^5*d^5*e^16 + 8512*a^6*b^5*c^4*d^4*e^17 - 2016*a^6*b^6*c^3*d^3*e^18 - 224*a^6*b^7*c^2*d^2*e^19 +
37312*a^7*b^2*c^6*d^5*e^16 - 14880*a^7*b^3*c^5*d^4*e^17 - 1408*a^7*b^4*c^4*d^3*e^18 + 1312*a^7*b^5*c^3*d^2*e^
19 + 8848*a^8*b^2*c^5*d^3*e^18 - 1112*a^8*b^3*c^4*d^2*e^19 + 608*a*b*c^13*d^18*e^3 - 2576*a*b^2*c^12*d^17*e^4
+ 6392*a*b^3*c^11*d^16*e^5 - 10112*a*b^4*c^10*d^15*e^6 + 10016*a*b^5*c^9*d^14*e^7 - 4704*a*b^6*c^8*d^13*e^8 -
2288*a*b^7*c^7*d^12*e^9 + 5888*a*b^8*c^6*d^11*e^10 - 4928*a*b^9*c^5*d^10*e^11 + 2288*a*b^10*c^4*d^9*e^12 - 584
*a*b^11*c^3*d^8*e^13 + 64*a*b^12*c^2*d^7*e^14 + 2720*a^2*b*c^12*d^16*e^5 + 1920*a^3*b*c^11*d^14*e^7 - 11648*a^
4*b*c^10*d^12*e^9 - 34496*a^5*b*c^9*d^10*e^11 - 44352*a^6*b*c^8*d^8*e^13 - 31360*a^7*b*c^7*d^6*e^15 + 64*a^7*b
^6*c^2*d*e^20 - 12160*a^8*b*c^6*d^4*e^17 - 424*a^8*b^4*c^3*d*e^20 - 2208*a^9*b*c^5*d^2*e^19 + 624*a^9*b^2*c^4*
d*e^20) - (d + e*x)^(1/2)*(8*a^6*b^6*c^3*e^18 - 64*a*c^14*d^16*e^2 - 64*a^9*c^6*e^18 - 64*a^7*b^4*c^4*e^18 + 1
44*a^8*b^2*c^5*e^18 + 1280*a^3*c^12*d^12*e^6 + 4096*a^4*c^11*d^10*e^8 + 5760*a^5*c^10*d^8*e^10 + 4096*a^6*c^9*
d^6*e^12 + 1280*a^7*c^8*d^4*e^14 + 16*b^2*c^13*d^16*e^2 - 128*b^3*c^12*d^15*e^3 + 480*b^4*c^11*d^14*e^4 - 1120
*b^5*c^10*d^13*e^5 + 1800*b^6*c^9*d^12*e^6 - 2064*b^7*c^8*d^11*e^7 + 1688*b^8*c^7*d^10*e^8 - 960*b^9*c^6*d^9*e
^9 + 360*b^10*c^5*d^8*e^10 - 80*b^11*c^4*d^7*e^11 + 8*b^12*c^3*d^6*e^12 - 960*a^2*b^2*c^11*d^12*e^6 + 5760*a^2
*b^3*c^10*d^11*e^7 - 14304*a^2*b^4*c^9*d^10*e^8 + 18720*a^2*b^5*c^8*d^9*e^9 - 13320*a^2*b^6*c^7*d^8*e^10 + 432
0*a^2*b^7*c^6*d^7*e^11 + 240*a^2*b^8*c^5*d^6*e^12 - 576*a^2*b^9*c^4*d^5*e^13 + 120*a^2*b^10*c^3*d^4*e^14 + 170
24*a^3*b^2*c^10*d^10*e^8 - 14720*a^3*b^3*c^9*d^9*e^9 - 2880*a^3*b^4*c^8*d^8*e^10 + 15360*a^3*b^5*c^7*d^7*e^11
- 11360*a^3*b^6*c^6*d^6*e^12 + 2976*a^3*b^7*c^5*d^5*e^13 + 160*a^3*b^8*c^4*d^4*e^14 - 160*a^3*b^9*c^3*d^3*e^15
+ 38880*a^4*b^2*c^9*d^8*e^10 - 32640*a^4*b^3*c^8*d^7*e^11 + 7200*a^4*b^4*c^7*d^6*e^12 + 6624*a^4*b^5*c^6*d^5*
e^13 - 4360*a^4*b^6*c^5*d^4*e^14 + 560*a^4*b^7*c^4*d^3*e^15 + 120*a^4*b^8*c^3*d^2*e^16 + 34176*a^5*b^2*c^8*d^6
*e^12 - 21888*a^5*b^3*c^7*d^5*e^13 + 3840*a^5*b^4*c^6*d^4*e^14 + 1920*a^5*b^5*c^5*d^3*e^15 - 720*a^5*b^6*c^4*d
^2*e^16 + 13120*a^6*b^2*c^7*d^4*e^14 - 5760*a^6*b^3*c^6*d^3*e^15 + 480*a^6*b^4*c^5*d^2*e^16 + 1920*a^7*b^2*c^6
*d^2*e^16 + 512*a*b*c^13*d^15*e^3 - 1920*a*b^2*c^12*d^14*e^4 + 4480*a*b^3*c^11*d^13*e^5 - 7040*a*b^4*c^10*d^12
*e^6 + 7296*a*b^5*c^9*d^11*e^7 - 4304*a*b^6*c^8*d^10*e^8 + 400*a*b^7*c^7*d^9*e^9 + 1440*a*b^8*c^6*d^8*e^10 - 1
120*a*b^9*c^5*d^7*e^11 + 368*a*b^10*c^4*d^6*e^12 - 48*a*b^11*c^3*d^5*e^13 - 7680*a^3*b*c^11*d^11*e^7 - 20480*a
^4*b*c^10*d^9*e^9 - 23040*a^5*b*c^9*d^7*e^11 - 48*a^5*b^7*c^3*d*e^17 - 12288*a^6*b*c^8*d^5*e^13 + 352*a^6*b^5*
c^4*d*e^17 - 2560*a^7*b*c^7*d^3*e^15 - 640*a^7*b^3*c^5*d*e^17))*(-(b^5*e^5 - 2*c^5*d^5 + b^4*e^5*(b^2 - 4*a*c)
^(1/2) + 5*a^2*b*c^2*e^5 + 20*a*c^4*d^3*e^2 - 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) - 10*b^2*c^3*
d^3*e^2 + 10*b^3*c^2*d^2*e^3 - 5*a*b^3*c*e^5 + 5*b*c^4*d^4*e - 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2)
+ 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1
/2) - 30*a*b*c^3*d^2*e^3 + 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 -
4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6
+ 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d
^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b
*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*
b^2*c*d^4*e^6)))^(1/2)*1i)/(128*a^8*c^7*e^16 - ((-(b^5*e^5 - 2*c^5*d^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) + 5*a^2*b
*c^2*e^5 + 20*a*c^4*d^3*e^2 - 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) - 10*b^2*c^3*d^3*e^2 + 10*b^3
*c^2*d^2*e^3 - 5*a*b^3*c*e^5 + 5*b*c^4*d^4*e - 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^
2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) - 30*a*b*c^3
*d^2*e^3 + 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) +
10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^
2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*
c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 2
0*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))
^(1/2)*(192*a^10*c^5*d*e^20 - 96*a^10*b*c^4*e^21 - 64*a*c^14*d^19*e^2 - (d + e*x)^(1/2)*(-(b^5*e^5 - 2*c^5*d^5
+ b^4*e^5*(b^2 - 4*a*c)^(1/2) + 5*a^2*b*c^2*e^5 + 20*a*c^4*d^3*e^2 - 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*
a*c)^(1/2) - 10*b^2*c^3*d^3*e^2 + 10*b^3*c^2*d^2*e^3 - 5*a*b^3*c*e^5 + 5*b*c^4*d^4*e - 5*b^4*c*d*e^4 + 5*c^4*d
^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*
c*d*e^4*(b^2 - 4*a*c)^(1/2) - 30*a*b*c^3*d^2*e^3 + 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) -
10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^
5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^
2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9
- 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2
*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e^22 +
8*a^10*b^3*c^2*e^23 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^1
0*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18
+ 640*a^10*c^5*d^3*e^20 - 16*b^2*c^13*d^21*e^2 + 168*b^3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^5*c^1
0*d^18*e^5 - 4320*b^6*c^9*d^17*e^6 + 5712*b^7*c^8*d^16*e^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^9 - 1
680*b^10*c^5*d^13*e^10 + 520*b^11*c^4*d^12*e^11 - 96*b^12*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^2*b^2
*c^11*d^17*e^6 - 59160*a^2*b^3*c^10*d^16*e^7 + 84480*a^2*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 + 23520
*a^2*b^6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^10*e^
13 - 3280*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^3*c^9
*d^14*e^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 10560*
a^3*b^7*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^16 + 1
84800*a^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^5*c^6
*d^10*e^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^
9*c^2*d^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^14 - 1
20960*a^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^1
8 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^
4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b
^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^
8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*
a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b
^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7
*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11
*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^4*b*c
^10*d^14*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a^8*b*
c^6*d^6*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c^3*d*
e^22) - 8*a^8*b^5*c^2*e^21 + 56*a^9*b^3*c^3*e^21 - 320*a^2*c^13*d^17*e^4 - 256*a^3*c^12*d^15*e^6 + 1792*a^4*c^
11*d^13*e^8 + 6272*a^5*c^10*d^11*e^10 + 9856*a^6*c^9*d^9*e^12 + 8960*a^7*c^8*d^7*e^14 + 4864*a^8*c^7*d^5*e^16
+ 1472*a^9*c^6*d^3*e^18 + 16*b^2*c^13*d^19*e^2 - 152*b^3*c^12*d^18*e^3 + 664*b^4*c^11*d^17*e^4 - 1768*b^5*c^10
*d^16*e^5 + 3200*b^6*c^9*d^15*e^6 - 4144*b^7*c^8*d^14*e^7 + 3920*b^8*c^7*d^13*e^8 - 2704*b^9*c^6*d^12*e^9 + 13
28*b^10*c^5*d^11*e^10 - 440*b^11*c^4*d^10*e^11 + 88*b^12*c^3*d^9*e^12 - 8*b^13*c^2*d^8*e^13 - 10688*a^2*b^2*c^
11*d^15*e^6 + 25760*a^2*b^3*c^10*d^14*e^7 - 41888*a^2*b^4*c^9*d^13*e^8 + 46592*a^2*b^5*c^8*d^12*e^9 - 33376*a^
2*b^6*c^7*d^11*e^10 + 11968*a^2*b^7*c^6*d^10*e^11 + 1760*a^2*b^8*c^5*d^9*e^12 - 3872*a^2*b^9*c^4*d^8*e^13 + 15
68*a^2*b^10*c^3*d^7*e^14 - 224*a^2*b^11*c^2*d^6*e^15 - 8512*a^3*b^2*c^10*d^13*e^8 + 26208*a^3*b^3*c^9*d^12*e^9
- 52864*a^3*b^4*c^8*d^11*e^10 + 66528*a^3*b^5*c^7*d^10*e^11 - 49280*a^3*b^6*c^6*d^9*e^12 + 17952*a^3*b^7*c^5*
d^8*e^13 - 128*a^3*b^8*c^4*d^7*e^14 - 2016*a^3*b^9*c^3*d^6*e^15 + 448*a^3*b^10*c^2*d^5*e^16 + 27104*a^4*b^2*c^
9*d^11*e^10 - 20944*a^4*b^3*c^8*d^10*e^11 - 18480*a^4*b^4*c^7*d^9*e^12 + 48048*a^4*b^5*c^6*d^8*e^13 - 35392*a^
4*b^6*c^5*d^7*e^14 + 9296*a^4*b^7*c^4*d^6*e^15 + 784*a^4*b^8*c^3*d^5*e^16 - 560*a^4*b^9*c^2*d^4*e^17 + 71456*a
^5*b^2*c^8*d^9*e^12 - 62832*a^5*b^3*c^7*d^8*e^13 + 8064*a^5*b^4*c^6*d^7*e^14 + 23520*a^5*b^5*c^5*d^6*e^15 - 13
664*a^5*b^6*c^4*d^5*e^16 + 1232*a^5*b^7*c^3*d^4*e^17 + 448*a^5*b^8*c^2*d^3*e^18 + 73024*a^6*b^2*c^7*d^7*e^14 -
48608*a^6*b^3*c^6*d^6*e^15 + 3808*a^6*b^4*c^5*d^5*e^16 + 8512*a^6*b^5*c^4*d^4*e^17 - 2016*a^6*b^6*c^3*d^3*e^1
8 - 224*a^6*b^7*c^2*d^2*e^19 + 37312*a^7*b^2*c^6*d^5*e^16 - 14880*a^7*b^3*c^5*d^4*e^17 - 1408*a^7*b^4*c^4*d^3*
e^18 + 1312*a^7*b^5*c^3*d^2*e^19 + 8848*a^8*b^2*c^5*d^3*e^18 - 1112*a^8*b^3*c^4*d^2*e^19 + 608*a*b*c^13*d^18*e
^3 - 2576*a*b^2*c^12*d^17*e^4 + 6392*a*b^3*c^11*d^16*e^5 - 10112*a*b^4*c^10*d^15*e^6 + 10016*a*b^5*c^9*d^14*e^
7 - 4704*a*b^6*c^8*d^13*e^8 - 2288*a*b^7*c^7*d^12*e^9 + 5888*a*b^8*c^6*d^11*e^10 - 4928*a*b^9*c^5*d^10*e^11 +
2288*a*b^10*c^4*d^9*e^12 - 584*a*b^11*c^3*d^8*e^13 + 64*a*b^12*c^2*d^7*e^14 + 2720*a^2*b*c^12*d^16*e^5 + 1920*
a^3*b*c^11*d^14*e^7 - 11648*a^4*b*c^10*d^12*e^9 - 34496*a^5*b*c^9*d^10*e^11 - 44352*a^6*b*c^8*d^8*e^13 - 31360
*a^7*b*c^7*d^6*e^15 + 64*a^7*b^6*c^2*d*e^20 - 12160*a^8*b*c^6*d^4*e^17 - 424*a^8*b^4*c^3*d*e^20 - 2208*a^9*b*c
^5*d^2*e^19 + 624*a^9*b^2*c^4*d*e^20) - (d + e*x)^(1/2)*(8*a^6*b^6*c^3*e^18 - 64*a*c^14*d^16*e^2 - 64*a^9*c^6*
e^18 - 64*a^7*b^4*c^4*e^18 + 144*a^8*b^2*c^5*e^18 + 1280*a^3*c^12*d^12*e^6 + 4096*a^4*c^11*d^10*e^8 + 5760*a^5
*c^10*d^8*e^10 + 4096*a^6*c^9*d^6*e^12 + 1280*a^7*c^8*d^4*e^14 + 16*b^2*c^13*d^16*e^2 - 128*b^3*c^12*d^15*e^3
+ 480*b^4*c^11*d^14*e^4 - 1120*b^5*c^10*d^13*e^5 + 1800*b^6*c^9*d^12*e^6 - 2064*b^7*c^8*d^11*e^7 + 1688*b^8*c^
7*d^10*e^8 - 960*b^9*c^6*d^9*e^9 + 360*b^10*c^5*d^8*e^10 - 80*b^11*c^4*d^7*e^11 + 8*b^12*c^3*d^6*e^12 - 960*a^
2*b^2*c^11*d^12*e^6 + 5760*a^2*b^3*c^10*d^11*e^7 - 14304*a^2*b^4*c^9*d^10*e^8 + 18720*a^2*b^5*c^8*d^9*e^9 - 13
320*a^2*b^6*c^7*d^8*e^10 + 4320*a^2*b^7*c^6*d^7*e^11 + 240*a^2*b^8*c^5*d^6*e^12 - 576*a^2*b^9*c^4*d^5*e^13 + 1
20*a^2*b^10*c^3*d^4*e^14 + 17024*a^3*b^2*c^10*d^10*e^8 - 14720*a^3*b^3*c^9*d^9*e^9 - 2880*a^3*b^4*c^8*d^8*e^10
+ 15360*a^3*b^5*c^7*d^7*e^11 - 11360*a^3*b^6*c^6*d^6*e^12 + 2976*a^3*b^7*c^5*d^5*e^13 + 160*a^3*b^8*c^4*d^4*e
^14 - 160*a^3*b^9*c^3*d^3*e^15 + 38880*a^4*b^2*c^9*d^8*e^10 - 32640*a^4*b^3*c^8*d^7*e^11 + 7200*a^4*b^4*c^7*d^
6*e^12 + 6624*a^4*b^5*c^6*d^5*e^13 - 4360*a^4*b^6*c^5*d^4*e^14 + 560*a^4*b^7*c^4*d^3*e^15 + 120*a^4*b^8*c^3*d^
2*e^16 + 34176*a^5*b^2*c^8*d^6*e^12 - 21888*a^5*b^3*c^7*d^5*e^13 + 3840*a^5*b^4*c^6*d^4*e^14 + 1920*a^5*b^5*c^
5*d^3*e^15 - 720*a^5*b^6*c^4*d^2*e^16 + 13120*a^6*b^2*c^7*d^4*e^14 - 5760*a^6*b^3*c^6*d^3*e^15 + 480*a^6*b^4*c
^5*d^2*e^16 + 1920*a^7*b^2*c^6*d^2*e^16 + 512*a*b*c^13*d^15*e^3 - 1920*a*b^2*c^12*d^14*e^4 + 4480*a*b^3*c^11*d
^13*e^5 - 7040*a*b^4*c^10*d^12*e^6 + 7296*a*b^5*c^9*d^11*e^7 - 4304*a*b^6*c^8*d^10*e^8 + 400*a*b^7*c^7*d^9*e^9
+ 1440*a*b^8*c^6*d^8*e^10 - 1120*a*b^9*c^5*d^7*e^11 + 368*a*b^10*c^4*d^6*e^12 - 48*a*b^11*c^3*d^5*e^13 - 7680
*a^3*b*c^11*d^11*e^7 - 20480*a^4*b*c^10*d^9*e^9 - 23040*a^5*b*c^9*d^7*e^11 - 48*a^5*b^7*c^3*d*e^17 - 12288*a^6
*b*c^8*d^5*e^13 + 352*a^6*b^5*c^4*d*e^17 - 2560*a^7*b*c^7*d^3*e^15 - 640*a^7*b^3*c^5*d*e^17))*(-(b^5*e^5 - 2*c
^5*d^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) + 5*a^2*b*c^2*e^5 + 20*a*c^4*d^3*e^2 - 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^
2 - 4*a*c)^(1/2) - 10*b^2*c^3*d^3*e^2 + 10*b^3*c^2*d^2*e^3 - 5*a*b^3*c*e^5 + 5*b*c^4*d^4*e - 5*b^4*c*d*e^4 + 5
*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) -
5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) - 30*a*b*c^3*d^2*e^3 + 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(
1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 -
b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*
a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*
d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 -
30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2) - ((-(b^5*e^5 - 2*c^5*d^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) +
5*a^2*b*c^2*e^5 + 20*a*c^4*d^3*e^2 - 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) - 10*b^2*c^3*d^3*e^2
+ 10*b^3*c^2*d^2*e^3 - 5*a*b^3*c*e^5 + 5*b*c^4*d^4*e - 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^
2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) - 30
*a*b*c^3*d^2*e^3 + 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^
(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^
4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 +
10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7
*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^
4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(b^5*e^5 - 2*c^5*d^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) + 5*a^2*b*c^2*e^5 + 20*a*
c^4*d^3*e^2 - 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) - 10*b^2*c^3*d^3*e^2 + 10*b^3*c^2*d^2*e^3 - 5
*a*b^3*c*e^5 + 5*b*c^4*d^4*e - 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a
*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) - 30*a*b*c^3*d^2*e^3 + 20*a*
b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4
*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*
e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10
*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^
5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2)*(64*a*c^1
4*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e^22 + 8*a^10*b^3*c^2*e^23 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*
c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^
9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20 - 16*b^2*c^13*d^21*e^2 + 168*b^
3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^5*c^10*d^18*e^5 - 4320*b^6*c^9*d^17*e^6 + 5712*b^7*c^8*d^16*e
^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^9 - 1680*b^10*c^5*d^13*e^10 + 520*b^11*c^4*d^12*e^11 - 96*b^1
2*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^2*b^2*c^11*d^17*e^6 - 59160*a^2*b^3*c^10*d^16*e^7 + 84480*a^2
*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 + 23520*a^2*b^6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 2
3040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^10*e^13 - 3280*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e
^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^3*c^9*d^14*e^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^
5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 10560*a^3*b^7*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 720
0*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^16 + 184800*a^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^
11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^5*c^6*d^10*e^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*
c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^9*c^2*d^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12 - 347424*a
^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^14 - 120960*a^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16
+ 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8
*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^
2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*
b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a
^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a
*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^
5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*
c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^1
2*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^4*b*c^10*d^14*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c
^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a^8*b*c^6*d^6*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*
d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c^3*d*e^22) - 96*a^10*b*c^4*e^21 - 64*a*c^14*d^19*e^2 + 192*a^
10*c^5*d*e^20 - 8*a^8*b^5*c^2*e^21 + 56*a^9*b^3*c^3*e^21 - 320*a^2*c^13*d^17*e^4 - 256*a^3*c^12*d^15*e^6 + 179
2*a^4*c^11*d^13*e^8 + 6272*a^5*c^10*d^11*e^10 + 9856*a^6*c^9*d^9*e^12 + 8960*a^7*c^8*d^7*e^14 + 4864*a^8*c^7*d
^5*e^16 + 1472*a^9*c^6*d^3*e^18 + 16*b^2*c^13*d^19*e^2 - 152*b^3*c^12*d^18*e^3 + 664*b^4*c^11*d^17*e^4 - 1768*
b^5*c^10*d^16*e^5 + 3200*b^6*c^9*d^15*e^6 - 4144*b^7*c^8*d^14*e^7 + 3920*b^8*c^7*d^13*e^8 - 2704*b^9*c^6*d^12*
e^9 + 1328*b^10*c^5*d^11*e^10 - 440*b^11*c^4*d^10*e^11 + 88*b^12*c^3*d^9*e^12 - 8*b^13*c^2*d^8*e^13 - 10688*a^
2*b^2*c^11*d^15*e^6 + 25760*a^2*b^3*c^10*d^14*e^7 - 41888*a^2*b^4*c^9*d^13*e^8 + 46592*a^2*b^5*c^8*d^12*e^9 -
33376*a^2*b^6*c^7*d^11*e^10 + 11968*a^2*b^7*c^6*d^10*e^11 + 1760*a^2*b^8*c^5*d^9*e^12 - 3872*a^2*b^9*c^4*d^8*e
^13 + 1568*a^2*b^10*c^3*d^7*e^14 - 224*a^2*b^11*c^2*d^6*e^15 - 8512*a^3*b^2*c^10*d^13*e^8 + 26208*a^3*b^3*c^9*
d^12*e^9 - 52864*a^3*b^4*c^8*d^11*e^10 + 66528*a^3*b^5*c^7*d^10*e^11 - 49280*a^3*b^6*c^6*d^9*e^12 + 17952*a^3*
b^7*c^5*d^8*e^13 - 128*a^3*b^8*c^4*d^7*e^14 - 2016*a^3*b^9*c^3*d^6*e^15 + 448*a^3*b^10*c^2*d^5*e^16 + 27104*a^
4*b^2*c^9*d^11*e^10 - 20944*a^4*b^3*c^8*d^10*e^11 - 18480*a^4*b^4*c^7*d^9*e^12 + 48048*a^4*b^5*c^6*d^8*e^13 -
35392*a^4*b^6*c^5*d^7*e^14 + 9296*a^4*b^7*c^4*d^6*e^15 + 784*a^4*b^8*c^3*d^5*e^16 - 560*a^4*b^9*c^2*d^4*e^17 +
71456*a^5*b^2*c^8*d^9*e^12 - 62832*a^5*b^3*c^7*d^8*e^13 + 8064*a^5*b^4*c^6*d^7*e^14 + 23520*a^5*b^5*c^5*d^6*e
^15 - 13664*a^5*b^6*c^4*d^5*e^16 + 1232*a^5*b^7*c^3*d^4*e^17 + 448*a^5*b^8*c^2*d^3*e^18 + 73024*a^6*b^2*c^7*d^
7*e^14 - 48608*a^6*b^3*c^6*d^6*e^15 + 3808*a^6*b^4*c^5*d^5*e^16 + 8512*a^6*b^5*c^4*d^4*e^17 - 2016*a^6*b^6*c^3
*d^3*e^18 - 224*a^6*b^7*c^2*d^2*e^19 + 37312*a^7*b^2*c^6*d^5*e^16 - 14880*a^7*b^3*c^5*d^4*e^17 - 1408*a^7*b^4*
c^4*d^3*e^18 + 1312*a^7*b^5*c^3*d^2*e^19 + 8848*a^8*b^2*c^5*d^3*e^18 - 1112*a^8*b^3*c^4*d^2*e^19 + 608*a*b*c^1
3*d^18*e^3 - 2576*a*b^2*c^12*d^17*e^4 + 6392*a*b^3*c^11*d^16*e^5 - 10112*a*b^4*c^10*d^15*e^6 + 10016*a*b^5*c^9
*d^14*e^7 - 4704*a*b^6*c^8*d^13*e^8 - 2288*a*b^7*c^7*d^12*e^9 + 5888*a*b^8*c^6*d^11*e^10 - 4928*a*b^9*c^5*d^10
*e^11 + 2288*a*b^10*c^4*d^9*e^12 - 584*a*b^11*c^3*d^8*e^13 + 64*a*b^12*c^2*d^7*e^14 + 2720*a^2*b*c^12*d^16*e^5
+ 1920*a^3*b*c^11*d^14*e^7 - 11648*a^4*b*c^10*d^12*e^9 - 34496*a^5*b*c^9*d^10*e^11 - 44352*a^6*b*c^8*d^8*e^13
- 31360*a^7*b*c^7*d^6*e^15 + 64*a^7*b^6*c^2*d*e^20 - 12160*a^8*b*c^6*d^4*e^17 - 424*a^8*b^4*c^3*d*e^20 - 2208
*a^9*b*c^5*d^2*e^19 + 624*a^9*b^2*c^4*d*e^20) + (d + e*x)^(1/2)*(8*a^6*b^6*c^3*e^18 - 64*a*c^14*d^16*e^2 - 64*
a^9*c^6*e^18 - 64*a^7*b^4*c^4*e^18 + 144*a^8*b^2*c^5*e^18 + 1280*a^3*c^12*d^12*e^6 + 4096*a^4*c^11*d^10*e^8 +
5760*a^5*c^10*d^8*e^10 + 4096*a^6*c^9*d^6*e^12 + 1280*a^7*c^8*d^4*e^14 + 16*b^2*c^13*d^16*e^2 - 128*b^3*c^12*d
^15*e^3 + 480*b^4*c^11*d^14*e^4 - 1120*b^5*c^10*d^13*e^5 + 1800*b^6*c^9*d^12*e^6 - 2064*b^7*c^8*d^11*e^7 + 168
8*b^8*c^7*d^10*e^8 - 960*b^9*c^6*d^9*e^9 + 360*b^10*c^5*d^8*e^10 - 80*b^11*c^4*d^7*e^11 + 8*b^12*c^3*d^6*e^12
- 960*a^2*b^2*c^11*d^12*e^6 + 5760*a^2*b^3*c^10*d^11*e^7 - 14304*a^2*b^4*c^9*d^10*e^8 + 18720*a^2*b^5*c^8*d^9*
e^9 - 13320*a^2*b^6*c^7*d^8*e^10 + 4320*a^2*b^7*c^6*d^7*e^11 + 240*a^2*b^8*c^5*d^6*e^12 - 576*a^2*b^9*c^4*d^5*
e^13 + 120*a^2*b^10*c^3*d^4*e^14 + 17024*a^3*b^2*c^10*d^10*e^8 - 14720*a^3*b^3*c^9*d^9*e^9 - 2880*a^3*b^4*c^8*
d^8*e^10 + 15360*a^3*b^5*c^7*d^7*e^11 - 11360*a^3*b^6*c^6*d^6*e^12 + 2976*a^3*b^7*c^5*d^5*e^13 + 160*a^3*b^8*c
^4*d^4*e^14 - 160*a^3*b^9*c^3*d^3*e^15 + 38880*a^4*b^2*c^9*d^8*e^10 - 32640*a^4*b^3*c^8*d^7*e^11 + 7200*a^4*b^
4*c^7*d^6*e^12 + 6624*a^4*b^5*c^6*d^5*e^13 - 4360*a^4*b^6*c^5*d^4*e^14 + 560*a^4*b^7*c^4*d^3*e^15 + 120*a^4*b^
8*c^3*d^2*e^16 + 34176*a^5*b^2*c^8*d^6*e^12 - 21888*a^5*b^3*c^7*d^5*e^13 + 3840*a^5*b^4*c^6*d^4*e^14 + 1920*a^
5*b^5*c^5*d^3*e^15 - 720*a^5*b^6*c^4*d^2*e^16 + 13120*a^6*b^2*c^7*d^4*e^14 - 5760*a^6*b^3*c^6*d^3*e^15 + 480*a
^6*b^4*c^5*d^2*e^16 + 1920*a^7*b^2*c^6*d^2*e^16 + 512*a*b*c^13*d^15*e^3 - 1920*a*b^2*c^12*d^14*e^4 + 4480*a*b^
3*c^11*d^13*e^5 - 7040*a*b^4*c^10*d^12*e^6 + 7296*a*b^5*c^9*d^11*e^7 - 4304*a*b^6*c^8*d^10*e^8 + 400*a*b^7*c^7
*d^9*e^9 + 1440*a*b^8*c^6*d^8*e^10 - 1120*a*b^9*c^5*d^7*e^11 + 368*a*b^10*c^4*d^6*e^12 - 48*a*b^11*c^3*d^5*e^1
3 - 7680*a^3*b*c^11*d^11*e^7 - 20480*a^4*b*c^10*d^9*e^9 - 23040*a^5*b*c^9*d^7*e^11 - 48*a^5*b^7*c^3*d*e^17 - 1
2288*a^6*b*c^8*d^5*e^13 + 352*a^6*b^5*c^4*d*e^17 - 2560*a^7*b*c^7*d^3*e^15 - 640*a^7*b^3*c^5*d*e^17))*(-(b^5*e
^5 - 2*c^5*d^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) + 5*a^2*b*c^2*e^5 + 20*a*c^4*d^3*e^2 - 10*a^2*c^3*d*e^4 + a^2*c^2
*e^5*(b^2 - 4*a*c)^(1/2) - 10*b^2*c^3*d^3*e^2 + 10*b^3*c^2*d^2*e^3 - 5*a*b^3*c*e^5 + 5*b*c^4*d^4*e - 5*b^4*c*d
*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^
(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) - 30*a*b*c^3*d^2*e^3 + 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 -
4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5
*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e
^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 -
5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^
6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2) - 128*a*c^14*d^14*e^2 + 16*a^6*b^4*c^5*e^16 - 96*
a^7*b^2*c^6*e^16 - 640*a^2*c^13*d^12*e^4 - 1152*a^3*c^12*d^10*e^6 - 640*a^4*c^11*d^8*e^8 + 640*a^5*c^10*d^6*e^
10 + 1152*a^6*c^9*d^4*e^12 + 640*a^7*c^8*d^2*e^14 + 32*b^2*c^13*d^14*e^2 - 224*b^3*c^12*d^13*e^3 + 688*b^4*c^1
1*d^12*e^4 - 1216*b^5*c^10*d^11*e^5 + 1360*b^6*c^9*d^10*e^6 - 992*b^7*c^8*d^9*e^7 + 464*b^8*c^7*d^8*e^8 - 128*
b^9*c^6*d^7*e^9 + 16*b^10*c^5*d^6*e^10 - 9696*a^2*b^2*c^11*d^10*e^6 + 13280*a^2*b^3*c^10*d^9*e^7 - 10320*a^2*b
^4*c^9*d^8*e^8 + 3840*a^2*b^5*c^8*d^7*e^9 + 320*a^2*b^6*c^7*d^6*e^10 - 864*a^2*b^7*c^6*d^5*e^11 + 240*a^2*b^8*
c^5*d^4*e^12 - 12320*a^3*b^2*c^10*d^8*e^8 + 14720*a^3*b^3*c^9*d^7*e^9 - 10240*a^3*b^4*c^8*d^6*e^10 + 3392*a^3*
b^5*c^7*d^5*e^11 + 160*a^3*b^6*c^6*d^4*e^12 - 320*a^3*b^7*c^5*d^3*e^13 - 5280*a^4*b^2*c^9*d^6*e^10 + 6880*a^4*
b^3*c^8*d^5*e^11 - 4720*a^4*b^4*c^7*d^4*e^12 + 960*a^4*b^5*c^6*d^3*e^13 + 240*a^4*b^6*c^5*d^2*e^14 + 672*a^5*b
^2*c^8*d^4*e^12 + 1856*a^5*b^3*c^7*d^3*e^13 - 1152*a^5*b^4*c^6*d^2*e^14 + 608*a^6*b^2*c^7*d^2*e^14 + 896*a*b*c
^13*d^13*e^3 - 640*a^7*b*c^7*d*e^15 - 2592*a*b^2*c^12*d^12*e^4 + 3904*a*b^3*c^11*d^11*e^5 - 2944*a*b^4*c^10*d^
10*e^6 + 288*a*b^5*c^9*d^9*e^7 + 1504*a*b^6*c^8*d^8*e^8 - 1408*a*b^7*c^7*d^7*e^9 + 576*a*b^8*c^6*d^6*e^10 - 96
*a*b^9*c^5*d^5*e^11 + 3840*a^2*b*c^12*d^11*e^5 + 5760*a^3*b*c^11*d^9*e^7 + 2560*a^4*b*c^10*d^7*e^9 - 1920*a^5*
b*c^9*d^5*e^11 - 96*a^5*b^5*c^5*d*e^15 - 2304*a^6*b*c^8*d^3*e^13 + 544*a^6*b^3*c^6*d*e^15))*(-(b^5*e^5 - 2*c^5
*d^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) + 5*a^2*b*c^2*e^5 + 20*a*c^4*d^3*e^2 - 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2
- 4*a*c)^(1/2) - 10*b^2*c^3*d^3*e^2 + 10*b^3*c^2*d^2*e^3 - 5*a*b^3*c*e^5 + 5*b*c^4*d^4*e - 5*b^4*c*d*e^4 + 5*c
^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*
b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) - 30*a*b*c^3*d^2*e^3 + 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/
2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^
5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^
3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*
e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30
*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2)*2i - ((2*(b*e - 2*c*d))/(3*(a*e^2 + c*d^2 - b*d*e)) - (2*(d
+ e*x)*(b^2*e^2 + 2*c^2*d^2 - 2*a*c*e^2 - 2*b*c*d*e))/(a*e^2 + c*d^2 - b*d*e)^2)/(d + e*x)^(3/2) + atan(((((2
*c^5*d^5 - b^5*e^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) - 5*a^2*b*c^2*e^5 - 20*a*c^4*d^3*e^2 + 10*a^2*c^3*d*e^4 + a^2
*c^2*e^5*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^3*d^3*e^2 - 10*b^3*c^2*d^2*e^3 + 5*a*b^3*c*e^5 - 5*b*c^4*d^4*e + 5*b^4
*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a
*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) + 30*a*b*c^3*d^2*e^3 - 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^
2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 +
c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d
^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^
3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^
2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*((2*c^5*d^5 - b^5*e^5 + b^4*
e^5*(b^2 - 4*a*c)^(1/2) - 5*a^2*b*c^2*e^5 - 20*a*c^4*d^3*e^2 + 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1
/2) + 10*b^2*c^3*d^3*e^2 - 10*b^3*c^2*d^2*e^3 + 5*a*b^3*c*e^5 - 5*b*c^4*d^4*e + 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b
^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4
*(b^2 - 4*a*c)^(1/2) + 30*a*b*c^3*d^2*e^3 - 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c
^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 +
5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e
^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c
^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*
d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e^22 + 8*a^10
*b^3*c^2*e^23 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*
e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*
a^10*c^5*d^3*e^20 - 16*b^2*c^13*d^21*e^2 + 168*b^3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^5*c^10*d^18*
e^5 - 4320*b^6*c^9*d^17*e^6 + 5712*b^7*c^8*d^16*e^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^9 - 1680*b^1
0*c^5*d^13*e^10 + 520*b^11*c^4*d^12*e^11 - 96*b^12*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^2*b^2*c^11*d
^17*e^6 - 59160*a^2*b^3*c^10*d^16*e^7 + 84480*a^2*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 + 23520*a^2*b^
6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^10*e^13 - 32
80*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^3*c^9*d^14*e
^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 10560*a^3*b^7
*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^16 + 184800*a
^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^5*c^6*d^10*e
^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^9*c^2*d
^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^14 - 120960*a
^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198
240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e
^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*
d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c
^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2
*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11
*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^
14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^
10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^4*b*c^10*d^1
4*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a^8*b*c^6*d^6
*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c^3*d*e^22) -
96*a^10*b*c^4*e^21 - 64*a*c^14*d^19*e^2 + 192*a^10*c^5*d*e^20 - 8*a^8*b^5*c^2*e^21 + 56*a^9*b^3*c^3*e^21 - 32
0*a^2*c^13*d^17*e^4 - 256*a^3*c^12*d^15*e^6 + 1792*a^4*c^11*d^13*e^8 + 6272*a^5*c^10*d^11*e^10 + 9856*a^6*c^9*
d^9*e^12 + 8960*a^7*c^8*d^7*e^14 + 4864*a^8*c^7*d^5*e^16 + 1472*a^9*c^6*d^3*e^18 + 16*b^2*c^13*d^19*e^2 - 152*
b^3*c^12*d^18*e^3 + 664*b^4*c^11*d^17*e^4 - 1768*b^5*c^10*d^16*e^5 + 3200*b^6*c^9*d^15*e^6 - 4144*b^7*c^8*d^14
*e^7 + 3920*b^8*c^7*d^13*e^8 - 2704*b^9*c^6*d^12*e^9 + 1328*b^10*c^5*d^11*e^10 - 440*b^11*c^4*d^10*e^11 + 88*b
^12*c^3*d^9*e^12 - 8*b^13*c^2*d^8*e^13 - 10688*a^2*b^2*c^11*d^15*e^6 + 25760*a^2*b^3*c^10*d^14*e^7 - 41888*a^2
*b^4*c^9*d^13*e^8 + 46592*a^2*b^5*c^8*d^12*e^9 - 33376*a^2*b^6*c^7*d^11*e^10 + 11968*a^2*b^7*c^6*d^10*e^11 + 1
760*a^2*b^8*c^5*d^9*e^12 - 3872*a^2*b^9*c^4*d^8*e^13 + 1568*a^2*b^10*c^3*d^7*e^14 - 224*a^2*b^11*c^2*d^6*e^15
- 8512*a^3*b^2*c^10*d^13*e^8 + 26208*a^3*b^3*c^9*d^12*e^9 - 52864*a^3*b^4*c^8*d^11*e^10 + 66528*a^3*b^5*c^7*d^
10*e^11 - 49280*a^3*b^6*c^6*d^9*e^12 + 17952*a^3*b^7*c^5*d^8*e^13 - 128*a^3*b^8*c^4*d^7*e^14 - 2016*a^3*b^9*c^
3*d^6*e^15 + 448*a^3*b^10*c^2*d^5*e^16 + 27104*a^4*b^2*c^9*d^11*e^10 - 20944*a^4*b^3*c^8*d^10*e^11 - 18480*a^4
*b^4*c^7*d^9*e^12 + 48048*a^4*b^5*c^6*d^8*e^13 - 35392*a^4*b^6*c^5*d^7*e^14 + 9296*a^4*b^7*c^4*d^6*e^15 + 784*
a^4*b^8*c^3*d^5*e^16 - 560*a^4*b^9*c^2*d^4*e^17 + 71456*a^5*b^2*c^8*d^9*e^12 - 62832*a^5*b^3*c^7*d^8*e^13 + 80
64*a^5*b^4*c^6*d^7*e^14 + 23520*a^5*b^5*c^5*d^6*e^15 - 13664*a^5*b^6*c^4*d^5*e^16 + 1232*a^5*b^7*c^3*d^4*e^17
+ 448*a^5*b^8*c^2*d^3*e^18 + 73024*a^6*b^2*c^7*d^7*e^14 - 48608*a^6*b^3*c^6*d^6*e^15 + 3808*a^6*b^4*c^5*d^5*e^
16 + 8512*a^6*b^5*c^4*d^4*e^17 - 2016*a^6*b^6*c^3*d^3*e^18 - 224*a^6*b^7*c^2*d^2*e^19 + 37312*a^7*b^2*c^6*d^5*
e^16 - 14880*a^7*b^3*c^5*d^4*e^17 - 1408*a^7*b^4*c^4*d^3*e^18 + 1312*a^7*b^5*c^3*d^2*e^19 + 8848*a^8*b^2*c^5*d
^3*e^18 - 1112*a^8*b^3*c^4*d^2*e^19 + 608*a*b*c^13*d^18*e^3 - 2576*a*b^2*c^12*d^17*e^4 + 6392*a*b^3*c^11*d^16*
e^5 - 10112*a*b^4*c^10*d^15*e^6 + 10016*a*b^5*c^9*d^14*e^7 - 4704*a*b^6*c^8*d^13*e^8 - 2288*a*b^7*c^7*d^12*e^9
+ 5888*a*b^8*c^6*d^11*e^10 - 4928*a*b^9*c^5*d^10*e^11 + 2288*a*b^10*c^4*d^9*e^12 - 584*a*b^11*c^3*d^8*e^13 +
64*a*b^12*c^2*d^7*e^14 + 2720*a^2*b*c^12*d^16*e^5 + 1920*a^3*b*c^11*d^14*e^7 - 11648*a^4*b*c^10*d^12*e^9 - 344
96*a^5*b*c^9*d^10*e^11 - 44352*a^6*b*c^8*d^8*e^13 - 31360*a^7*b*c^7*d^6*e^15 + 64*a^7*b^6*c^2*d*e^20 - 12160*a
^8*b*c^6*d^4*e^17 - 424*a^8*b^4*c^3*d*e^20 - 2208*a^9*b*c^5*d^2*e^19 + 624*a^9*b^2*c^4*d*e^20) + (d + e*x)^(1/
2)*(8*a^6*b^6*c^3*e^18 - 64*a*c^14*d^16*e^2 - 64*a^9*c^6*e^18 - 64*a^7*b^4*c^4*e^18 + 144*a^8*b^2*c^5*e^18 + 1
280*a^3*c^12*d^12*e^6 + 4096*a^4*c^11*d^10*e^8 + 5760*a^5*c^10*d^8*e^10 + 4096*a^6*c^9*d^6*e^12 + 1280*a^7*c^8
*d^4*e^14 + 16*b^2*c^13*d^16*e^2 - 128*b^3*c^12*d^15*e^3 + 480*b^4*c^11*d^14*e^4 - 1120*b^5*c^10*d^13*e^5 + 18
00*b^6*c^9*d^12*e^6 - 2064*b^7*c^8*d^11*e^7 + 1688*b^8*c^7*d^10*e^8 - 960*b^9*c^6*d^9*e^9 + 360*b^10*c^5*d^8*e
^10 - 80*b^11*c^4*d^7*e^11 + 8*b^12*c^3*d^6*e^12 - 960*a^2*b^2*c^11*d^12*e^6 + 5760*a^2*b^3*c^10*d^11*e^7 - 14
304*a^2*b^4*c^9*d^10*e^8 + 18720*a^2*b^5*c^8*d^9*e^9 - 13320*a^2*b^6*c^7*d^8*e^10 + 4320*a^2*b^7*c^6*d^7*e^11
+ 240*a^2*b^8*c^5*d^6*e^12 - 576*a^2*b^9*c^4*d^5*e^13 + 120*a^2*b^10*c^3*d^4*e^14 + 17024*a^3*b^2*c^10*d^10*e^
8 - 14720*a^3*b^3*c^9*d^9*e^9 - 2880*a^3*b^4*c^8*d^8*e^10 + 15360*a^3*b^5*c^7*d^7*e^11 - 11360*a^3*b^6*c^6*d^6
*e^12 + 2976*a^3*b^7*c^5*d^5*e^13 + 160*a^3*b^8*c^4*d^4*e^14 - 160*a^3*b^9*c^3*d^3*e^15 + 38880*a^4*b^2*c^9*d^
8*e^10 - 32640*a^4*b^3*c^8*d^7*e^11 + 7200*a^4*b^4*c^7*d^6*e^12 + 6624*a^4*b^5*c^6*d^5*e^13 - 4360*a^4*b^6*c^5
*d^4*e^14 + 560*a^4*b^7*c^4*d^3*e^15 + 120*a^4*b^8*c^3*d^2*e^16 + 34176*a^5*b^2*c^8*d^6*e^12 - 21888*a^5*b^3*c
^7*d^5*e^13 + 3840*a^5*b^4*c^6*d^4*e^14 + 1920*a^5*b^5*c^5*d^3*e^15 - 720*a^5*b^6*c^4*d^2*e^16 + 13120*a^6*b^2
*c^7*d^4*e^14 - 5760*a^6*b^3*c^6*d^3*e^15 + 480*a^6*b^4*c^5*d^2*e^16 + 1920*a^7*b^2*c^6*d^2*e^16 + 512*a*b*c^1
3*d^15*e^3 - 1920*a*b^2*c^12*d^14*e^4 + 4480*a*b^3*c^11*d^13*e^5 - 7040*a*b^4*c^10*d^12*e^6 + 7296*a*b^5*c^9*d
^11*e^7 - 4304*a*b^6*c^8*d^10*e^8 + 400*a*b^7*c^7*d^9*e^9 + 1440*a*b^8*c^6*d^8*e^10 - 1120*a*b^9*c^5*d^7*e^11
+ 368*a*b^10*c^4*d^6*e^12 - 48*a*b^11*c^3*d^5*e^13 - 7680*a^3*b*c^11*d^11*e^7 - 20480*a^4*b*c^10*d^9*e^9 - 230
40*a^5*b*c^9*d^7*e^11 - 48*a^5*b^7*c^3*d*e^17 - 12288*a^6*b*c^8*d^5*e^13 + 352*a^6*b^5*c^4*d*e^17 - 2560*a^7*b
*c^7*d^3*e^15 - 640*a^7*b^3*c^5*d*e^17))*((2*c^5*d^5 - b^5*e^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) - 5*a^2*b*c^2*e^5
- 20*a*c^4*d^3*e^2 + 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^3*d^3*e^2 - 10*b^3*c^2*d^2
*e^3 + 5*a*b^3*c*e^5 - 5*b*c^4*d^4*e + 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b
^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) + 30*a*b*c^3*d^2*e^3
- 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c
^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^
4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*
e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*
c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2)*1
i - (((2*c^5*d^5 - b^5*e^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) - 5*a^2*b*c^2*e^5 - 20*a*c^4*d^3*e^2 + 10*a^2*c^3*d*e
^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^3*d^3*e^2 - 10*b^3*c^2*d^2*e^3 + 5*a*b^3*c*e^5 - 5*b*c^4*d^4*e
+ 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b
^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) + 30*a*b*c^3*d^2*e^3 - 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2
*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^
5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a
^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^
2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*
a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2)*(192*a^10*c^5*d*e^20 - 96*a^10*b*c^4*
e^21 - 64*a*c^14*d^19*e^2 - (d + e*x)^(1/2)*((2*c^5*d^5 - b^5*e^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) - 5*a^2*b*c^2*
e^5 - 20*a*c^4*d^3*e^2 + 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^3*d^3*e^2 - 10*b^3*c^2*
d^2*e^3 + 5*a*b^3*c*e^5 - 5*b*c^4*d^4*e + 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3
*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) + 30*a*b*c^3*d^2*
e^3 - 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*
b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5
*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d
^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b
^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2
)*(64*a*c^14*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e^22 + 8*a^10*b^3*c^2*e^23 + 640*a^2*c^13*d^19*e^4
+ 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440
*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20 - 16*b^2*c^13*d^21*e
^2 + 168*b^3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^5*c^10*d^18*e^5 - 4320*b^6*c^9*d^17*e^6 + 5712*b^7
*c^8*d^16*e^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^9 - 1680*b^10*c^5*d^13*e^10 + 520*b^11*c^4*d^12*e^
11 - 96*b^12*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^2*b^2*c^11*d^17*e^6 - 59160*a^2*b^3*c^10*d^16*e^7
+ 84480*a^2*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 + 23520*a^2*b^6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^
12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^10*e^13 - 3280*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^1
1*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^3*c^9*d^14*e^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 17
4720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 10560*a^3*b^7*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9
*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^16 + 184800*a^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*
c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^5*c^6*d^10*e^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 108
00*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^9*c^2*d^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12
- 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^14 - 120960*a^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^
4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*
b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680
*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18
- 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^
19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e
^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6
- 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 1
0400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 608
0*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^4*b*c^10*d^14*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88
704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a^8*b*c^6*d^6*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a
^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c^3*d*e^22) - 8*a^8*b^5*c^2*e^21 + 56*a^9*b^3*c^3*e
^21 - 320*a^2*c^13*d^17*e^4 - 256*a^3*c^12*d^15*e^6 + 1792*a^4*c^11*d^13*e^8 + 6272*a^5*c^10*d^11*e^10 + 9856*
a^6*c^9*d^9*e^12 + 8960*a^7*c^8*d^7*e^14 + 4864*a^8*c^7*d^5*e^16 + 1472*a^9*c^6*d^3*e^18 + 16*b^2*c^13*d^19*e^
2 - 152*b^3*c^12*d^18*e^3 + 664*b^4*c^11*d^17*e^4 - 1768*b^5*c^10*d^16*e^5 + 3200*b^6*c^9*d^15*e^6 - 4144*b^7*
c^8*d^14*e^7 + 3920*b^8*c^7*d^13*e^8 - 2704*b^9*c^6*d^12*e^9 + 1328*b^10*c^5*d^11*e^10 - 440*b^11*c^4*d^10*e^1
1 + 88*b^12*c^3*d^9*e^12 - 8*b^13*c^2*d^8*e^13 - 10688*a^2*b^2*c^11*d^15*e^6 + 25760*a^2*b^3*c^10*d^14*e^7 - 4
1888*a^2*b^4*c^9*d^13*e^8 + 46592*a^2*b^5*c^8*d^12*e^9 - 33376*a^2*b^6*c^7*d^11*e^10 + 11968*a^2*b^7*c^6*d^10*
e^11 + 1760*a^2*b^8*c^5*d^9*e^12 - 3872*a^2*b^9*c^4*d^8*e^13 + 1568*a^2*b^10*c^3*d^7*e^14 - 224*a^2*b^11*c^2*d
^6*e^15 - 8512*a^3*b^2*c^10*d^13*e^8 + 26208*a^3*b^3*c^9*d^12*e^9 - 52864*a^3*b^4*c^8*d^11*e^10 + 66528*a^3*b^
5*c^7*d^10*e^11 - 49280*a^3*b^6*c^6*d^9*e^12 + 17952*a^3*b^7*c^5*d^8*e^13 - 128*a^3*b^8*c^4*d^7*e^14 - 2016*a^
3*b^9*c^3*d^6*e^15 + 448*a^3*b^10*c^2*d^5*e^16 + 27104*a^4*b^2*c^9*d^11*e^10 - 20944*a^4*b^3*c^8*d^10*e^11 - 1
8480*a^4*b^4*c^7*d^9*e^12 + 48048*a^4*b^5*c^6*d^8*e^13 - 35392*a^4*b^6*c^5*d^7*e^14 + 9296*a^4*b^7*c^4*d^6*e^1
5 + 784*a^4*b^8*c^3*d^5*e^16 - 560*a^4*b^9*c^2*d^4*e^17 + 71456*a^5*b^2*c^8*d^9*e^12 - 62832*a^5*b^3*c^7*d^8*e
^13 + 8064*a^5*b^4*c^6*d^7*e^14 + 23520*a^5*b^5*c^5*d^6*e^15 - 13664*a^5*b^6*c^4*d^5*e^16 + 1232*a^5*b^7*c^3*d
^4*e^17 + 448*a^5*b^8*c^2*d^3*e^18 + 73024*a^6*b^2*c^7*d^7*e^14 - 48608*a^6*b^3*c^6*d^6*e^15 + 3808*a^6*b^4*c^
5*d^5*e^16 + 8512*a^6*b^5*c^4*d^4*e^17 - 2016*a^6*b^6*c^3*d^3*e^18 - 224*a^6*b^7*c^2*d^2*e^19 + 37312*a^7*b^2*
c^6*d^5*e^16 - 14880*a^7*b^3*c^5*d^4*e^17 - 1408*a^7*b^4*c^4*d^3*e^18 + 1312*a^7*b^5*c^3*d^2*e^19 + 8848*a^8*b
^2*c^5*d^3*e^18 - 1112*a^8*b^3*c^4*d^2*e^19 + 608*a*b*c^13*d^18*e^3 - 2576*a*b^2*c^12*d^17*e^4 + 6392*a*b^3*c^
11*d^16*e^5 - 10112*a*b^4*c^10*d^15*e^6 + 10016*a*b^5*c^9*d^14*e^7 - 4704*a*b^6*c^8*d^13*e^8 - 2288*a*b^7*c^7*
d^12*e^9 + 5888*a*b^8*c^6*d^11*e^10 - 4928*a*b^9*c^5*d^10*e^11 + 2288*a*b^10*c^4*d^9*e^12 - 584*a*b^11*c^3*d^8
*e^13 + 64*a*b^12*c^2*d^7*e^14 + 2720*a^2*b*c^12*d^16*e^5 + 1920*a^3*b*c^11*d^14*e^7 - 11648*a^4*b*c^10*d^12*e
^9 - 34496*a^5*b*c^9*d^10*e^11 - 44352*a^6*b*c^8*d^8*e^13 - 31360*a^7*b*c^7*d^6*e^15 + 64*a^7*b^6*c^2*d*e^20 -
12160*a^8*b*c^6*d^4*e^17 - 424*a^8*b^4*c^3*d*e^20 - 2208*a^9*b*c^5*d^2*e^19 + 624*a^9*b^2*c^4*d*e^20) - (d +
e*x)^(1/2)*(8*a^6*b^6*c^3*e^18 - 64*a*c^14*d^16*e^2 - 64*a^9*c^6*e^18 - 64*a^7*b^4*c^4*e^18 + 144*a^8*b^2*c^5*
e^18 + 1280*a^3*c^12*d^12*e^6 + 4096*a^4*c^11*d^10*e^8 + 5760*a^5*c^10*d^8*e^10 + 4096*a^6*c^9*d^6*e^12 + 1280
*a^7*c^8*d^4*e^14 + 16*b^2*c^13*d^16*e^2 - 128*b^3*c^12*d^15*e^3 + 480*b^4*c^11*d^14*e^4 - 1120*b^5*c^10*d^13*
e^5 + 1800*b^6*c^9*d^12*e^6 - 2064*b^7*c^8*d^11*e^7 + 1688*b^8*c^7*d^10*e^8 - 960*b^9*c^6*d^9*e^9 + 360*b^10*c
^5*d^8*e^10 - 80*b^11*c^4*d^7*e^11 + 8*b^12*c^3*d^6*e^12 - 960*a^2*b^2*c^11*d^12*e^6 + 5760*a^2*b^3*c^10*d^11*
e^7 - 14304*a^2*b^4*c^9*d^10*e^8 + 18720*a^2*b^5*c^8*d^9*e^9 - 13320*a^2*b^6*c^7*d^8*e^10 + 4320*a^2*b^7*c^6*d
^7*e^11 + 240*a^2*b^8*c^5*d^6*e^12 - 576*a^2*b^9*c^4*d^5*e^13 + 120*a^2*b^10*c^3*d^4*e^14 + 17024*a^3*b^2*c^10
*d^10*e^8 - 14720*a^3*b^3*c^9*d^9*e^9 - 2880*a^3*b^4*c^8*d^8*e^10 + 15360*a^3*b^5*c^7*d^7*e^11 - 11360*a^3*b^6
*c^6*d^6*e^12 + 2976*a^3*b^7*c^5*d^5*e^13 + 160*a^3*b^8*c^4*d^4*e^14 - 160*a^3*b^9*c^3*d^3*e^15 + 38880*a^4*b^
2*c^9*d^8*e^10 - 32640*a^4*b^3*c^8*d^7*e^11 + 7200*a^4*b^4*c^7*d^6*e^12 + 6624*a^4*b^5*c^6*d^5*e^13 - 4360*a^4
*b^6*c^5*d^4*e^14 + 560*a^4*b^7*c^4*d^3*e^15 + 120*a^4*b^8*c^3*d^2*e^16 + 34176*a^5*b^2*c^8*d^6*e^12 - 21888*a
^5*b^3*c^7*d^5*e^13 + 3840*a^5*b^4*c^6*d^4*e^14 + 1920*a^5*b^5*c^5*d^3*e^15 - 720*a^5*b^6*c^4*d^2*e^16 + 13120
*a^6*b^2*c^7*d^4*e^14 - 5760*a^6*b^3*c^6*d^3*e^15 + 480*a^6*b^4*c^5*d^2*e^16 + 1920*a^7*b^2*c^6*d^2*e^16 + 512
*a*b*c^13*d^15*e^3 - 1920*a*b^2*c^12*d^14*e^4 + 4480*a*b^3*c^11*d^13*e^5 - 7040*a*b^4*c^10*d^12*e^6 + 7296*a*b
^5*c^9*d^11*e^7 - 4304*a*b^6*c^8*d^10*e^8 + 400*a*b^7*c^7*d^9*e^9 + 1440*a*b^8*c^6*d^8*e^10 - 1120*a*b^9*c^5*d
^7*e^11 + 368*a*b^10*c^4*d^6*e^12 - 48*a*b^11*c^3*d^5*e^13 - 7680*a^3*b*c^11*d^11*e^7 - 20480*a^4*b*c^10*d^9*e
^9 - 23040*a^5*b*c^9*d^7*e^11 - 48*a^5*b^7*c^3*d*e^17 - 12288*a^6*b*c^8*d^5*e^13 + 352*a^6*b^5*c^4*d*e^17 - 25
60*a^7*b*c^7*d^3*e^15 - 640*a^7*b^3*c^5*d*e^17))*((2*c^5*d^5 - b^5*e^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) - 5*a^2*b
*c^2*e^5 - 20*a*c^4*d^3*e^2 + 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^3*d^3*e^2 - 10*b^3
*c^2*d^2*e^3 + 5*a*b^3*c*e^5 - 5*b*c^4*d^4*e + 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^
2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) + 30*a*b*c^3
*d^2*e^3 - 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) +
10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^
2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*
c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 2
0*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))
^(1/2)*1i)/(128*a^8*c^7*e^16 - (((2*c^5*d^5 - b^5*e^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) - 5*a^2*b*c^2*e^5 - 20*a*c
^4*d^3*e^2 + 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^3*d^3*e^2 - 10*b^3*c^2*d^2*e^3 + 5*
a*b^3*c*e^5 - 5*b*c^4*d^4*e + 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*
c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) + 30*a*b*c^3*d^2*e^3 - 20*a*b
^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*
(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e
^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*
b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5
- 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2)*(192*a^10*
c^5*d*e^20 - 96*a^10*b*c^4*e^21 - 64*a*c^14*d^19*e^2 - (d + e*x)^(1/2)*((2*c^5*d^5 - b^5*e^5 + b^4*e^5*(b^2 -
4*a*c)^(1/2) - 5*a^2*b*c^2*e^5 - 20*a*c^4*d^3*e^2 + 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) + 10*b^
2*c^3*d^3*e^2 - 10*b^3*c^2*d^2*e^3 + 5*a*b^3*c*e^5 - 5*b*c^4*d^4*e + 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)
^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a
*c)^(1/2) + 30*a*b*c^3*d^2*e^3 - 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*
(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^
4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2
*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e -
20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 3
0*a^2*b^2*c*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e^22 + 8*a^10*b^3*c^2*e^
23 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 1612
8*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^
3*e^20 - 16*b^2*c^13*d^21*e^2 + 168*b^3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^5*c^10*d^18*e^5 - 4320*
b^6*c^9*d^17*e^6 + 5712*b^7*c^8*d^16*e^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^9 - 1680*b^10*c^5*d^13*
e^10 + 520*b^11*c^4*d^12*e^11 - 96*b^12*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^2*b^2*c^11*d^17*e^6 - 5
9160*a^2*b^3*c^10*d^16*e^7 + 84480*a^2*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 + 23520*a^2*b^6*c^7*d^13*
e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^10*e^13 - 3280*a^2*b^10
*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^3*c^9*d^14*e^9 + 235200
*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 10560*a^3*b^7*c^5*d^10*e
^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^16 + 184800*a^4*b^2*c^9*
d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^5*c^6*d^10*e^13 + 50400
*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^9*c^2*d^6*e^17 + 2
37888*a^5*b^2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^14 - 120960*a^5*b^5*c^5*
d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198240*a^6*b^2
*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e^17 - 2016*
a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*d^6*e^17 +
31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c^5*d^5*e^18
- 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2*c^4*d^3*e^
20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11*d^18*e^5 +
10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^14*e^9 - 16
800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^10*e^13 - 8
0*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^4*b*c^10*d^14*e^9 - 873
60*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a^8*b*c^6*d^6*e^17 - 720
0*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c^3*d*e^22) - 8*a^8*b^5*
c^2*e^21 + 56*a^9*b^3*c^3*e^21 - 320*a^2*c^13*d^17*e^4 - 256*a^3*c^12*d^15*e^6 + 1792*a^4*c^11*d^13*e^8 + 6272
*a^5*c^10*d^11*e^10 + 9856*a^6*c^9*d^9*e^12 + 8960*a^7*c^8*d^7*e^14 + 4864*a^8*c^7*d^5*e^16 + 1472*a^9*c^6*d^3
*e^18 + 16*b^2*c^13*d^19*e^2 - 152*b^3*c^12*d^18*e^3 + 664*b^4*c^11*d^17*e^4 - 1768*b^5*c^10*d^16*e^5 + 3200*b
^6*c^9*d^15*e^6 - 4144*b^7*c^8*d^14*e^7 + 3920*b^8*c^7*d^13*e^8 - 2704*b^9*c^6*d^12*e^9 + 1328*b^10*c^5*d^11*e
^10 - 440*b^11*c^4*d^10*e^11 + 88*b^12*c^3*d^9*e^12 - 8*b^13*c^2*d^8*e^13 - 10688*a^2*b^2*c^11*d^15*e^6 + 2576
0*a^2*b^3*c^10*d^14*e^7 - 41888*a^2*b^4*c^9*d^13*e^8 + 46592*a^2*b^5*c^8*d^12*e^9 - 33376*a^2*b^6*c^7*d^11*e^1
0 + 11968*a^2*b^7*c^6*d^10*e^11 + 1760*a^2*b^8*c^5*d^9*e^12 - 3872*a^2*b^9*c^4*d^8*e^13 + 1568*a^2*b^10*c^3*d^
7*e^14 - 224*a^2*b^11*c^2*d^6*e^15 - 8512*a^3*b^2*c^10*d^13*e^8 + 26208*a^3*b^3*c^9*d^12*e^9 - 52864*a^3*b^4*c
^8*d^11*e^10 + 66528*a^3*b^5*c^7*d^10*e^11 - 49280*a^3*b^6*c^6*d^9*e^12 + 17952*a^3*b^7*c^5*d^8*e^13 - 128*a^3
*b^8*c^4*d^7*e^14 - 2016*a^3*b^9*c^3*d^6*e^15 + 448*a^3*b^10*c^2*d^5*e^16 + 27104*a^4*b^2*c^9*d^11*e^10 - 2094
4*a^4*b^3*c^8*d^10*e^11 - 18480*a^4*b^4*c^7*d^9*e^12 + 48048*a^4*b^5*c^6*d^8*e^13 - 35392*a^4*b^6*c^5*d^7*e^14
+ 9296*a^4*b^7*c^4*d^6*e^15 + 784*a^4*b^8*c^3*d^5*e^16 - 560*a^4*b^9*c^2*d^4*e^17 + 71456*a^5*b^2*c^8*d^9*e^1
2 - 62832*a^5*b^3*c^7*d^8*e^13 + 8064*a^5*b^4*c^6*d^7*e^14 + 23520*a^5*b^5*c^5*d^6*e^15 - 13664*a^5*b^6*c^4*d^
5*e^16 + 1232*a^5*b^7*c^3*d^4*e^17 + 448*a^5*b^8*c^2*d^3*e^18 + 73024*a^6*b^2*c^7*d^7*e^14 - 48608*a^6*b^3*c^6
*d^6*e^15 + 3808*a^6*b^4*c^5*d^5*e^16 + 8512*a^6*b^5*c^4*d^4*e^17 - 2016*a^6*b^6*c^3*d^3*e^18 - 224*a^6*b^7*c^
2*d^2*e^19 + 37312*a^7*b^2*c^6*d^5*e^16 - 14880*a^7*b^3*c^5*d^4*e^17 - 1408*a^7*b^4*c^4*d^3*e^18 + 1312*a^7*b^
5*c^3*d^2*e^19 + 8848*a^8*b^2*c^5*d^3*e^18 - 1112*a^8*b^3*c^4*d^2*e^19 + 608*a*b*c^13*d^18*e^3 - 2576*a*b^2*c^
12*d^17*e^4 + 6392*a*b^3*c^11*d^16*e^5 - 10112*a*b^4*c^10*d^15*e^6 + 10016*a*b^5*c^9*d^14*e^7 - 4704*a*b^6*c^8
*d^13*e^8 - 2288*a*b^7*c^7*d^12*e^9 + 5888*a*b^8*c^6*d^11*e^10 - 4928*a*b^9*c^5*d^10*e^11 + 2288*a*b^10*c^4*d^
9*e^12 - 584*a*b^11*c^3*d^8*e^13 + 64*a*b^12*c^2*d^7*e^14 + 2720*a^2*b*c^12*d^16*e^5 + 1920*a^3*b*c^11*d^14*e^
7 - 11648*a^4*b*c^10*d^12*e^9 - 34496*a^5*b*c^9*d^10*e^11 - 44352*a^6*b*c^8*d^8*e^13 - 31360*a^7*b*c^7*d^6*e^1
5 + 64*a^7*b^6*c^2*d*e^20 - 12160*a^8*b*c^6*d^4*e^17 - 424*a^8*b^4*c^3*d*e^20 - 2208*a^9*b*c^5*d^2*e^19 + 624*
a^9*b^2*c^4*d*e^20) - (d + e*x)^(1/2)*(8*a^6*b^6*c^3*e^18 - 64*a*c^14*d^16*e^2 - 64*a^9*c^6*e^18 - 64*a^7*b^4*
c^4*e^18 + 144*a^8*b^2*c^5*e^18 + 1280*a^3*c^12*d^12*e^6 + 4096*a^4*c^11*d^10*e^8 + 5760*a^5*c^10*d^8*e^10 + 4
096*a^6*c^9*d^6*e^12 + 1280*a^7*c^8*d^4*e^14 + 16*b^2*c^13*d^16*e^2 - 128*b^3*c^12*d^15*e^3 + 480*b^4*c^11*d^1
4*e^4 - 1120*b^5*c^10*d^13*e^5 + 1800*b^6*c^9*d^12*e^6 - 2064*b^7*c^8*d^11*e^7 + 1688*b^8*c^7*d^10*e^8 - 960*b
^9*c^6*d^9*e^9 + 360*b^10*c^5*d^8*e^10 - 80*b^11*c^4*d^7*e^11 + 8*b^12*c^3*d^6*e^12 - 960*a^2*b^2*c^11*d^12*e^
6 + 5760*a^2*b^3*c^10*d^11*e^7 - 14304*a^2*b^4*c^9*d^10*e^8 + 18720*a^2*b^5*c^8*d^9*e^9 - 13320*a^2*b^6*c^7*d^
8*e^10 + 4320*a^2*b^7*c^6*d^7*e^11 + 240*a^2*b^8*c^5*d^6*e^12 - 576*a^2*b^9*c^4*d^5*e^13 + 120*a^2*b^10*c^3*d^
4*e^14 + 17024*a^3*b^2*c^10*d^10*e^8 - 14720*a^3*b^3*c^9*d^9*e^9 - 2880*a^3*b^4*c^8*d^8*e^10 + 15360*a^3*b^5*c
^7*d^7*e^11 - 11360*a^3*b^6*c^6*d^6*e^12 + 2976*a^3*b^7*c^5*d^5*e^13 + 160*a^3*b^8*c^4*d^4*e^14 - 160*a^3*b^9*
c^3*d^3*e^15 + 38880*a^4*b^2*c^9*d^8*e^10 - 32640*a^4*b^3*c^8*d^7*e^11 + 7200*a^4*b^4*c^7*d^6*e^12 + 6624*a^4*
b^5*c^6*d^5*e^13 - 4360*a^4*b^6*c^5*d^4*e^14 + 560*a^4*b^7*c^4*d^3*e^15 + 120*a^4*b^8*c^3*d^2*e^16 + 34176*a^5
*b^2*c^8*d^6*e^12 - 21888*a^5*b^3*c^7*d^5*e^13 + 3840*a^5*b^4*c^6*d^4*e^14 + 1920*a^5*b^5*c^5*d^3*e^15 - 720*a
^5*b^6*c^4*d^2*e^16 + 13120*a^6*b^2*c^7*d^4*e^14 - 5760*a^6*b^3*c^6*d^3*e^15 + 480*a^6*b^4*c^5*d^2*e^16 + 1920
*a^7*b^2*c^6*d^2*e^16 + 512*a*b*c^13*d^15*e^3 - 1920*a*b^2*c^12*d^14*e^4 + 4480*a*b^3*c^11*d^13*e^5 - 7040*a*b
^4*c^10*d^12*e^6 + 7296*a*b^5*c^9*d^11*e^7 - 4304*a*b^6*c^8*d^10*e^8 + 400*a*b^7*c^7*d^9*e^9 + 1440*a*b^8*c^6*
d^8*e^10 - 1120*a*b^9*c^5*d^7*e^11 + 368*a*b^10*c^4*d^6*e^12 - 48*a*b^11*c^3*d^5*e^13 - 7680*a^3*b*c^11*d^11*e
^7 - 20480*a^4*b*c^10*d^9*e^9 - 23040*a^5*b*c^9*d^7*e^11 - 48*a^5*b^7*c^3*d*e^17 - 12288*a^6*b*c^8*d^5*e^13 +
352*a^6*b^5*c^4*d*e^17 - 2560*a^7*b*c^7*d^3*e^15 - 640*a^7*b^3*c^5*d*e^17))*((2*c^5*d^5 - b^5*e^5 + b^4*e^5*(b
^2 - 4*a*c)^(1/2) - 5*a^2*b*c^2*e^5 - 20*a*c^4*d^3*e^2 + 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) +
10*b^2*c^3*d^3*e^2 - 10*b^3*c^2*d^2*e^3 + 5*a*b^3*c*e^5 - 5*b*c^4*d^4*e + 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4
*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2
- 4*a*c)^(1/2) + 30*a*b*c^3*d^2*e^3 - 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3
*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b
^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 1
0*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9
*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^
5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2) - (((2*c^5*d^5 - b^5*e^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) - 5*a^2*b*c^2*e^5 - 2
0*a*c^4*d^3*e^2 + 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^3*d^3*e^2 - 10*b^3*c^2*d^2*e^3
+ 5*a*b^3*c*e^5 - 5*b*c^4*d^4*e + 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 -
4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) + 30*a*b*c^3*d^2*e^3 - 2
0*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d
*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*
d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6
+ 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^
5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2)*((d +
e*x)^(1/2)*((2*c^5*d^5 - b^5*e^5 + b^4*e^5*(b^2 - 4*a*c)^(1/2) - 5*a^2*b*c^2*e^5 - 20*a*c^4*d^3*e^2 + 10*a^2*
c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^3*d^3*e^2 - 10*b^3*c^2*d^2*e^3 + 5*a*b^3*c*e^5 - 5*b*c^
4*d^4*e + 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c
*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*c)^(1/2) + 30*a*b*c^3*d^2*e^3 - 20*a*b^2*c^2*d*e^4 - 10*a*
c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))
/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4
- 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10
*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^
7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 - 32*a^11*
b*c^3*e^23 + 64*a^11*c^4*d*e^22 + 8*a^10*b^3*c^2*e^23 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*
a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7
*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20 - 16*b^2*c^13*d^21*e^2 + 168*b^3*c^12*d^20*e^3 - 800
*b^4*c^11*d^19*e^4 + 2280*b^5*c^10*d^18*e^5 - 4320*b^6*c^9*d^17*e^6 + 5712*b^7*c^8*d^16*e^7 - 5376*b^8*c^7*d^1
5*e^8 + 3600*b^9*c^6*d^14*e^9 - 1680*b^10*c^5*d^13*e^10 + 520*b^11*c^4*d^12*e^11 - 96*b^12*c^3*d^11*e^12 + 8*b
^13*c^2*d^10*e^13 + 25200*a^2*b^2*c^11*d^17*e^6 - 59160*a^2*b^3*c^10*d^16*e^7 + 84480*a^2*b^4*c^9*d^15*e^8 - 7
0560*a^2*b^5*c^8*d^14*e^9 + 23520*a^2*b^6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11
*e^12 + 12320*a^2*b^9*c^4*d^10*e^13 - 3280*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c
^10*d^15*e^8 - 187200*a^3*b^3*c^9*d^14*e^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 604
80*a^3*b^6*c^6*d^11*e^12 + 10560*a^3*b^7*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^1
5 - 960*a^3*b^10*c^2*d^7*e^16 + 184800*a^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c
^7*d^11*e^12 - 203280*a^4*b^5*c^6*d^10*e^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a
^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^9*c^2*d^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13
+ 285600*a^5*b^4*c^6*d^9*e^14 - 120960*a^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^
6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^
4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a
^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 96
0*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 +
360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 30
40*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376
*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*
a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^
3*b*c^11*d^16*e^7 - 57600*a^4*b*c^10*d^14*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*
a^7*b*c^7*d^8*e^15 - 26880*a^8*b*c^6*d^6*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c
^4*d^2*e^21 + 304*a^10*b^2*c^3*d*e^22) - 96*a^10*b*c^4*e^21 - 64*a*c^14*d^19*e^2 + 192*a^10*c^5*d*e^20 - 8*a^8
*b^5*c^2*e^21 + 56*a^9*b^3*c^3*e^21 - 320*a^2*c^13*d^17*e^4 - 256*a^3*c^12*d^15*e^6 + 1792*a^4*c^11*d^13*e^8 +
6272*a^5*c^10*d^11*e^10 + 9856*a^6*c^9*d^9*e^12 + 8960*a^7*c^8*d^7*e^14 + 4864*a^8*c^7*d^5*e^16 + 1472*a^9*c^
6*d^3*e^18 + 16*b^2*c^13*d^19*e^2 - 152*b^3*c^12*d^18*e^3 + 664*b^4*c^11*d^17*e^4 - 1768*b^5*c^10*d^16*e^5 + 3
200*b^6*c^9*d^15*e^6 - 4144*b^7*c^8*d^14*e^7 + 3920*b^8*c^7*d^13*e^8 - 2704*b^9*c^6*d^12*e^9 + 1328*b^10*c^5*d
^11*e^10 - 440*b^11*c^4*d^10*e^11 + 88*b^12*c^3*d^9*e^12 - 8*b^13*c^2*d^8*e^13 - 10688*a^2*b^2*c^11*d^15*e^6 +
25760*a^2*b^3*c^10*d^14*e^7 - 41888*a^2*b^4*c^9*d^13*e^8 + 46592*a^2*b^5*c^8*d^12*e^9 - 33376*a^2*b^6*c^7*d^1
1*e^10 + 11968*a^2*b^7*c^6*d^10*e^11 + 1760*a^2*b^8*c^5*d^9*e^12 - 3872*a^2*b^9*c^4*d^8*e^13 + 1568*a^2*b^10*c
^3*d^7*e^14 - 224*a^2*b^11*c^2*d^6*e^15 - 8512*a^3*b^2*c^10*d^13*e^8 + 26208*a^3*b^3*c^9*d^12*e^9 - 52864*a^3*
b^4*c^8*d^11*e^10 + 66528*a^3*b^5*c^7*d^10*e^11 - 49280*a^3*b^6*c^6*d^9*e^12 + 17952*a^3*b^7*c^5*d^8*e^13 - 12
8*a^3*b^8*c^4*d^7*e^14 - 2016*a^3*b^9*c^3*d^6*e^15 + 448*a^3*b^10*c^2*d^5*e^16 + 27104*a^4*b^2*c^9*d^11*e^10 -
20944*a^4*b^3*c^8*d^10*e^11 - 18480*a^4*b^4*c^7*d^9*e^12 + 48048*a^4*b^5*c^6*d^8*e^13 - 35392*a^4*b^6*c^5*d^7
*e^14 + 9296*a^4*b^7*c^4*d^6*e^15 + 784*a^4*b^8*c^3*d^5*e^16 - 560*a^4*b^9*c^2*d^4*e^17 + 71456*a^5*b^2*c^8*d^
9*e^12 - 62832*a^5*b^3*c^7*d^8*e^13 + 8064*a^5*b^4*c^6*d^7*e^14 + 23520*a^5*b^5*c^5*d^6*e^15 - 13664*a^5*b^6*c
^4*d^5*e^16 + 1232*a^5*b^7*c^3*d^4*e^17 + 448*a^5*b^8*c^2*d^3*e^18 + 73024*a^6*b^2*c^7*d^7*e^14 - 48608*a^6*b^
3*c^6*d^6*e^15 + 3808*a^6*b^4*c^5*d^5*e^16 + 8512*a^6*b^5*c^4*d^4*e^17 - 2016*a^6*b^6*c^3*d^3*e^18 - 224*a^6*b
^7*c^2*d^2*e^19 + 37312*a^7*b^2*c^6*d^5*e^16 - 14880*a^7*b^3*c^5*d^4*e^17 - 1408*a^7*b^4*c^4*d^3*e^18 + 1312*a
^7*b^5*c^3*d^2*e^19 + 8848*a^8*b^2*c^5*d^3*e^18 - 1112*a^8*b^3*c^4*d^2*e^19 + 608*a*b*c^13*d^18*e^3 - 2576*a*b
^2*c^12*d^17*e^4 + 6392*a*b^3*c^11*d^16*e^5 - 10112*a*b^4*c^10*d^15*e^6 + 10016*a*b^5*c^9*d^14*e^7 - 4704*a*b^
6*c^8*d^13*e^8 - 2288*a*b^7*c^7*d^12*e^9 + 5888*a*b^8*c^6*d^11*e^10 - 4928*a*b^9*c^5*d^10*e^11 + 2288*a*b^10*c
^4*d^9*e^12 - 584*a*b^11*c^3*d^8*e^13 + 64*a*b^12*c^2*d^7*e^14 + 2720*a^2*b*c^12*d^16*e^5 + 1920*a^3*b*c^11*d^
14*e^7 - 11648*a^4*b*c^10*d^12*e^9 - 34496*a^5*b*c^9*d^10*e^11 - 44352*a^6*b*c^8*d^8*e^13 - 31360*a^7*b*c^7*d^
6*e^15 + 64*a^7*b^6*c^2*d*e^20 - 12160*a^8*b*c^6*d^4*e^17 - 424*a^8*b^4*c^3*d*e^20 - 2208*a^9*b*c^5*d^2*e^19 +
624*a^9*b^2*c^4*d*e^20) + (d + e*x)^(1/2)*(8*a^6*b^6*c^3*e^18 - 64*a*c^14*d^16*e^2 - 64*a^9*c^6*e^18 - 64*a^7
*b^4*c^4*e^18 + 144*a^8*b^2*c^5*e^18 + 1280*a^3*c^12*d^12*e^6 + 4096*a^4*c^11*d^10*e^8 + 5760*a^5*c^10*d^8*e^1
0 + 4096*a^6*c^9*d^6*e^12 + 1280*a^7*c^8*d^4*e^14 + 16*b^2*c^13*d^16*e^2 - 128*b^3*c^12*d^15*e^3 + 480*b^4*c^1
1*d^14*e^4 - 1120*b^5*c^10*d^13*e^5 + 1800*b^6*c^9*d^12*e^6 - 2064*b^7*c^8*d^11*e^7 + 1688*b^8*c^7*d^10*e^8 -
960*b^9*c^6*d^9*e^9 + 360*b^10*c^5*d^8*e^10 - 80*b^11*c^4*d^7*e^11 + 8*b^12*c^3*d^6*e^12 - 960*a^2*b^2*c^11*d^
12*e^6 + 5760*a^2*b^3*c^10*d^11*e^7 - 14304*a^2*b^4*c^9*d^10*e^8 + 18720*a^2*b^5*c^8*d^9*e^9 - 13320*a^2*b^6*c
^7*d^8*e^10 + 4320*a^2*b^7*c^6*d^7*e^11 + 240*a^2*b^8*c^5*d^6*e^12 - 576*a^2*b^9*c^4*d^5*e^13 + 120*a^2*b^10*c
^3*d^4*e^14 + 17024*a^3*b^2*c^10*d^10*e^8 - 14720*a^3*b^3*c^9*d^9*e^9 - 2880*a^3*b^4*c^8*d^8*e^10 + 15360*a^3*
b^5*c^7*d^7*e^11 - 11360*a^3*b^6*c^6*d^6*e^12 + 2976*a^3*b^7*c^5*d^5*e^13 + 160*a^3*b^8*c^4*d^4*e^14 - 160*a^3
*b^9*c^3*d^3*e^15 + 38880*a^4*b^2*c^9*d^8*e^10 - 32640*a^4*b^3*c^8*d^7*e^11 + 7200*a^4*b^4*c^7*d^6*e^12 + 6624
*a^4*b^5*c^6*d^5*e^13 - 4360*a^4*b^6*c^5*d^4*e^14 + 560*a^4*b^7*c^4*d^3*e^15 + 120*a^4*b^8*c^3*d^2*e^16 + 3417
6*a^5*b^2*c^8*d^6*e^12 - 21888*a^5*b^3*c^7*d^5*e^13 + 3840*a^5*b^4*c^6*d^4*e^14 + 1920*a^5*b^5*c^5*d^3*e^15 -
720*a^5*b^6*c^4*d^2*e^16 + 13120*a^6*b^2*c^7*d^4*e^14 - 5760*a^6*b^3*c^6*d^3*e^15 + 480*a^6*b^4*c^5*d^2*e^16 +
1920*a^7*b^2*c^6*d^2*e^16 + 512*a*b*c^13*d^15*e^3 - 1920*a*b^2*c^12*d^14*e^4 + 4480*a*b^3*c^11*d^13*e^5 - 704
0*a*b^4*c^10*d^12*e^6 + 7296*a*b^5*c^9*d^11*e^7 - 4304*a*b^6*c^8*d^10*e^8 + 400*a*b^7*c^7*d^9*e^9 + 1440*a*b^8
*c^6*d^8*e^10 - 1120*a*b^9*c^5*d^7*e^11 + 368*a*b^10*c^4*d^6*e^12 - 48*a*b^11*c^3*d^5*e^13 - 7680*a^3*b*c^11*d
^11*e^7 - 20480*a^4*b*c^10*d^9*e^9 - 23040*a^5*b*c^9*d^7*e^11 - 48*a^5*b^7*c^3*d*e^17 - 12288*a^6*b*c^8*d^5*e^
13 + 352*a^6*b^5*c^4*d*e^17 - 2560*a^7*b*c^7*d^3*e^15 - 640*a^7*b^3*c^5*d*e^17))*((2*c^5*d^5 - b^5*e^5 + b^4*e
^5*(b^2 - 4*a*c)^(1/2) - 5*a^2*b*c^2*e^5 - 20*a*c^4*d^3*e^2 + 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/
2) + 10*b^2*c^3*d^3*e^2 - 10*b^3*c^2*d^2*e^3 + 5*a*b^3*c*e^5 - 5*b*c^4*d^4*e + 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^
2 - 4*a*c)^(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*
(b^2 - 4*a*c)^(1/2) + 30*a*b*c^3*d^2*e^3 - 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^
3*d^3*e^2*(b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 +
5*a*b^4*d^4*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^
8 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^
4*d^9*e - 20*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d
^5*e^5 + 30*a^2*b^2*c*d^4*e^6)))^(1/2) - 128*a*c^14*d^14*e^2 + 16*a^6*b^4*c^5*e^16 - 96*a^7*b^2*c^6*e^16 - 640
*a^2*c^13*d^12*e^4 - 1152*a^3*c^12*d^10*e^6 - 640*a^4*c^11*d^8*e^8 + 640*a^5*c^10*d^6*e^10 + 1152*a^6*c^9*d^4*
e^12 + 640*a^7*c^8*d^2*e^14 + 32*b^2*c^13*d^14*e^2 - 224*b^3*c^12*d^13*e^3 + 688*b^4*c^11*d^12*e^4 - 1216*b^5*
c^10*d^11*e^5 + 1360*b^6*c^9*d^10*e^6 - 992*b^7*c^8*d^9*e^7 + 464*b^8*c^7*d^8*e^8 - 128*b^9*c^6*d^7*e^9 + 16*b
^10*c^5*d^6*e^10 - 9696*a^2*b^2*c^11*d^10*e^6 + 13280*a^2*b^3*c^10*d^9*e^7 - 10320*a^2*b^4*c^9*d^8*e^8 + 3840*
a^2*b^5*c^8*d^7*e^9 + 320*a^2*b^6*c^7*d^6*e^10 - 864*a^2*b^7*c^6*d^5*e^11 + 240*a^2*b^8*c^5*d^4*e^12 - 12320*a
^3*b^2*c^10*d^8*e^8 + 14720*a^3*b^3*c^9*d^7*e^9 - 10240*a^3*b^4*c^8*d^6*e^10 + 3392*a^3*b^5*c^7*d^5*e^11 + 160
*a^3*b^6*c^6*d^4*e^12 - 320*a^3*b^7*c^5*d^3*e^13 - 5280*a^4*b^2*c^9*d^6*e^10 + 6880*a^4*b^3*c^8*d^5*e^11 - 472
0*a^4*b^4*c^7*d^4*e^12 + 960*a^4*b^5*c^6*d^3*e^13 + 240*a^4*b^6*c^5*d^2*e^14 + 672*a^5*b^2*c^8*d^4*e^12 + 1856
*a^5*b^3*c^7*d^3*e^13 - 1152*a^5*b^4*c^6*d^2*e^14 + 608*a^6*b^2*c^7*d^2*e^14 + 896*a*b*c^13*d^13*e^3 - 640*a^7
*b*c^7*d*e^15 - 2592*a*b^2*c^12*d^12*e^4 + 3904*a*b^3*c^11*d^11*e^5 - 2944*a*b^4*c^10*d^10*e^6 + 288*a*b^5*c^9
*d^9*e^7 + 1504*a*b^6*c^8*d^8*e^8 - 1408*a*b^7*c^7*d^7*e^9 + 576*a*b^8*c^6*d^6*e^10 - 96*a*b^9*c^5*d^5*e^11 +
3840*a^2*b*c^12*d^11*e^5 + 5760*a^3*b*c^11*d^9*e^7 + 2560*a^4*b*c^10*d^7*e^9 - 1920*a^5*b*c^9*d^5*e^11 - 96*a^
5*b^5*c^5*d*e^15 - 2304*a^6*b*c^8*d^3*e^13 + 544*a^6*b^3*c^6*d*e^15))*((2*c^5*d^5 - b^5*e^5 + b^4*e^5*(b^2 - 4
*a*c)^(1/2) - 5*a^2*b*c^2*e^5 - 20*a*c^4*d^3*e^2 + 10*a^2*c^3*d*e^4 + a^2*c^2*e^5*(b^2 - 4*a*c)^(1/2) + 10*b^2
*c^3*d^3*e^2 - 10*b^3*c^2*d^2*e^3 + 5*a*b^3*c*e^5 - 5*b*c^4*d^4*e + 5*b^4*c*d*e^4 + 5*c^4*d^4*e*(b^2 - 4*a*c)^
(1/2) + 10*b^2*c^2*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 3*a*b^2*c*e^5*(b^2 - 4*a*c)^(1/2) - 5*b^3*c*d*e^4*(b^2 - 4*a*
c)^(1/2) + 30*a*b*c^3*d^2*e^3 - 20*a*b^2*c^2*d*e^4 - 10*a*c^3*d^2*e^3*(b^2 - 4*a*c)^(1/2) - 10*b*c^3*d^3*e^2*(
b^2 - 4*a*c)^(1/2) + 10*a*b*c^2*d*e^4*(b^2 - 4*a*c)^(1/2))/(2*(a^5*e^10 + c^5*d^10 - b^5*d^5*e^5 + 5*a*b^4*d^4
*e^6 + 5*a*c^4*d^8*e^2 + 5*a^4*c*d^2*e^8 + 5*b^4*c*d^6*e^4 - 10*a^2*b^3*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 10*a^2*
c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 10*b^2*c^3*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 5*a^4*b*d*e^9 - 5*b*c^4*d^9*e - 2
0*a*b*c^3*d^7*e^3 - 20*a*b^3*c*d^5*e^5 - 20*a^3*b*c*d^3*e^7 + 30*a*b^2*c^2*d^6*e^4 - 30*a^2*b*c^2*d^5*e^5 + 30
*a^2*b^2*c*d^4*e^6)))^(1/2)*2i

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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((2*c*x+b)/(e*x+d)**(5/2)/(c*x**2+b*x+a),x)

[Out]

Timed out

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