3.2294 \(\int \frac {1}{(d+e x)^{5/2} (a+b x+c x^2)} \, dx\)

Optimal. Leaf size=414 \[ -\frac {\sqrt {2} \sqrt {c} \left (-2 c e \left (d \sqrt {b^2-4 a c}+a e+b d\right )+b e^2 \left (\sqrt {b^2-4 a c}+b\right )+2 c^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )}}\right )}{\sqrt {b^2-4 a c} \sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )} \left (a e^2-b d e+c d^2\right )^2}+\frac {\sqrt {2} \sqrt {c} \left (-2 c e \left (-d \sqrt {b^2-4 a c}+a e+b d\right )+b e^2 \left (b-\sqrt {b^2-4 a c}\right )+2 c^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}\right )}{\sqrt {b^2-4 a c} \sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )} \left (a e^2-b d e+c d^2\right )^2}-\frac {2 e (2 c d-b e)}{\sqrt {d+e x} \left (a e^2-b d e+c d^2\right )^2}-\frac {2 e}{3 (d+e x)^{3/2} \left (a e^2-b d e+c d^2\right )} \]

[Out]

-2/3*e/(a*e^2-b*d*e+c*d^2)/(e*x+d)^(3/2)-2*e*(-b*e+2*c*d)/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)^(1/2)-arctanh(2^(1/2)*
c^(1/2)*(e*x+d)^(1/2)/(2*c*d-e*(b-(-4*a*c+b^2)^(1/2)))^(1/2))*2^(1/2)*c^(1/2)*(2*c^2*d^2+b*e^2*(b+(-4*a*c+b^2)
^(1/2))-2*c*e*(b*d+a*e+d*(-4*a*c+b^2)^(1/2)))/(a*e^2-b*d*e+c*d^2)^2/(-4*a*c+b^2)^(1/2)/(2*c*d-e*(b-(-4*a*c+b^2
)^(1/2)))^(1/2)+arctanh(2^(1/2)*c^(1/2)*(e*x+d)^(1/2)/(2*c*d-e*(b+(-4*a*c+b^2)^(1/2)))^(1/2))*2^(1/2)*c^(1/2)*
(2*c^2*d^2+b*e^2*(b-(-4*a*c+b^2)^(1/2))-2*c*e*(b*d+a*e-d*(-4*a*c+b^2)^(1/2)))/(a*e^2-b*d*e+c*d^2)^2/(-4*a*c+b^
2)^(1/2)/(2*c*d-e*(b+(-4*a*c+b^2)^(1/2)))^(1/2)

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Rubi [A]  time = 1.55, antiderivative size = 414, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 5, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.227, Rules used = {709, 828, 826, 1166, 208} \[ -\frac {\sqrt {2} \sqrt {c} \left (-2 c e \left (d \sqrt {b^2-4 a c}+a e+b d\right )+b e^2 \left (\sqrt {b^2-4 a c}+b\right )+2 c^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )}}\right )}{\sqrt {b^2-4 a c} \sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )} \left (a e^2-b d e+c d^2\right )^2}+\frac {\sqrt {2} \sqrt {c} \left (-2 c e \left (-d \sqrt {b^2-4 a c}+a e+b d\right )+b e^2 \left (b-\sqrt {b^2-4 a c}\right )+2 c^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}\right )}{\sqrt {b^2-4 a c} \sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )} \left (a e^2-b d e+c d^2\right )^2}-\frac {2 e (2 c d-b e)}{\sqrt {d+e x} \left (a e^2-b d e+c d^2\right )^2}-\frac {2 e}{3 (d+e x)^{3/2} \left (a e^2-b d e+c d^2\right )} \]

Antiderivative was successfully verified.

[In]

Int[1/((d + e*x)^(5/2)*(a + b*x + c*x^2)),x]

[Out]

(-2*e)/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)) - (2*e*(2*c*d - b*e))/((c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e
*x]) - (Sqrt[2]*Sqrt[c]*(2*c^2*d^2 + b*(b + Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(b*d + Sqrt[b^2 - 4*a*c]*d + a*e))*
ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(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) + (Sqrt[2]*Sqrt[c]*(2*c^2*d^2 + b*(b - Sqrt[b^2 - 4*
a*c])*e^2 - 2*c*e*(b*d - Sqrt[b^2 - 4*a*c]*d + a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b +
Sqrt[b^2 - 4*a*c])*e]])/(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 709

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

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 {1}{(d+e x)^{5/2} \left (a+b x+c x^2\right )} \, dx &=-\frac {2 e}{3 \left (c d^2-b d e+a e^2\right ) (d+e x)^{3/2}}+\frac {\int \frac {c d-b e-c 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 e}{3 \left (c d^2-b d e+a e^2\right ) (d+e x)^{3/2}}-\frac {2 e (2 c d-b e)}{\left (c d^2-b d e+a e^2\right )^2 \sqrt {d+e x}}+\frac {\int \frac {c^2 d^2+b^2 e^2-c e (2 b d+a e)-c e (2 c d-b e) 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 e}{3 \left (c d^2-b d e+a e^2\right ) (d+e x)^{3/2}}-\frac {2 e (2 c d-b e)}{\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 e (2 c d-b e)+e \left (c^2 d^2+b^2 e^2-c e (2 b d+a e)\right )-c e (2 c d-b e) 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 e}{3 \left (c d^2-b d e+a e^2\right ) (d+e x)^{3/2}}-\frac {2 e (2 c d-b e)}{\left (c d^2-b d e+a e^2\right )^2 \sqrt {d+e x}}-\frac {\left (c \left (2 c^2 d^2+b \left (b-\sqrt {b^2-4 a c}\right ) e^2-2 c e \left (b d-\sqrt {b^2-4 a c} d+a 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 (2 c^2 d^2+b \left (b+\sqrt {b^2-4 a c}\right ) e^2-2 c e \left (b d+\sqrt {b^2-4 a c} d+a 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 e}{3 \left (c d^2-b d e+a e^2\right ) (d+e x)^{3/2}}-\frac {2 e (2 c d-b e)}{\left (c d^2-b d e+a e^2\right )^2 \sqrt {d+e x}}-\frac {\sqrt {2} \sqrt {c} \left (2 c^2 d^2+b \left (b+\sqrt {b^2-4 a c}\right ) e^2-2 c e \left (b d+\sqrt {b^2-4 a c} d+a 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 (2 c^2 d^2+b \left (b-\sqrt {b^2-4 a c}\right ) e^2-2 c e \left (b d-\sqrt {b^2-4 a c} d+a 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 = 1.25, size = 377, normalized size = 0.91 \[ \frac {2 \left (-\frac {3 \sqrt {c} \left (\frac {\left (-2 c e \left (-d \sqrt {b^2-4 a c}+a e+b d\right )+b e^2 \left (b-\sqrt {b^2-4 a c}\right )+2 c^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}\right )}{\sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}-\frac {\left (-2 c e \left (d \sqrt {b^2-4 a c}+a e+b d\right )+b e^2 \left (\sqrt {b^2-4 a c}+b\right )+2 c^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {e \sqrt {b^2-4 a c}-b e+2 c d}}\right )}{\sqrt {e \left (\sqrt {b^2-4 a c}-b\right )+2 c d}}\right )}{\sqrt {2} \sqrt {b^2-4 a c} \left (e (b d-a e)-c d^2\right )}+\frac {3 e (b e-2 c d)}{\sqrt {d+e x} \left (e (a e-b d)+c d^2\right )}-\frac {e}{(d+e x)^{3/2}}\right )}{3 \left (e (a e-b d)+c d^2\right )} \]

Antiderivative was successfully verified.

[In]

Integrate[1/((d + e*x)^(5/2)*(a + b*x + c*x^2)),x]

[Out]

(2*(-(e/(d + e*x)^(3/2)) + (3*e*(-2*c*d + b*e))/((c*d^2 + e*(-(b*d) + a*e))*Sqrt[d + e*x]) - (3*Sqrt[c]*(-(((2
*c^2*d^2 + b*(b + Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(b*d + Sqrt[b^2 - 4*a*c]*d + a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*S
qrt[d + e*x])/Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]])/Sqrt[2*c*d + (-b + Sqrt[b^2 - 4*a*c])*e]) + ((2*c^2*d^
2 + b*(b - Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(b*d - Sqrt[b^2 - 4*a*c]*d + a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d +
e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/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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fricas [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x+a),x, algorithm="fricas")

[Out]

Timed out

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giac [B]  time = 3.34, size = 1287, normalized size = 3.11 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(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*sqrt(b^2 - 4*a*c)*c^3*d^3 + 3*(b^2*c^2 - 4*
a*c^3 - sqrt(b^2 - 4*a*c)*b*c^2)*d^2*e - 3*(b^3*c - 4*a*b*c^2 - (b^2*c - 2*a*c^2)*sqrt(b^2 - 4*a*c))*d*e^2 + (
b^4 - 5*a*b^2*c + 4*a^2*c^2 - (b^3 - 3*a*b*c)*sqrt(b^2 - 4*a*c))*e^3)*abs(c)) + 2*sqrt(-4*c^2*d + 2*(b*c + sqr
t(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*sqrt(b^2 - 4*a*c)*c^3*d^3 - 3*(b^2*c^2 - 4*a*c^3 + sqrt(b^2 - 4*a*c)*b*c^2
)*d^2*e + 3*(b^3*c - 4*a*b*c^2 + (b^2*c - 2*a*c^2)*sqrt(b^2 - 4*a*c))*d*e^2 - (b^4 - 5*a*b^2*c + 4*a^2*c^2 + (
b^3 - 3*a*b*c)*sqrt(b^2 - 4*a*c))*e^3)*abs(c)) - 2/3*(6*(x*e + d)*c*d*e + c*d^2*e - 3*(x*e + d)*b*e^2 - b*d*e^
2 + a*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 = 1444, normalized size = 3.49 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(e*x+d)^(5/2)/(c*x^2+b*x+a),x)

[Out]

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)*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*e^3-1/(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^2*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*d*e^2-2*e/(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)*d^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*e^2+2*e/(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)*d+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)*a*e^3-1/(
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^2*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*d*e^2-2*e/(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)*d^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)*a
rctan((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*e^2-2*e/(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)*d-2/3*e/(a*e^2-b*d*e+c*d^2)/(e*x+d)^(3/2)+2/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)^(1/2)*b*
e^2-4*e/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)^(1/2)*c*d

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (c x^{2} + b x + a\right )} {\left (e x + d\right )}^{\frac {5}{2}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x+a),x, algorithm="maxima")

[Out]

integrate(1/((c*x^2 + b*x + a)*(e*x + d)^(5/2)), x)

________________________________________________________________________________________

mupad [B]  time = 8.64, size = 58096, normalized size = 140.33 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((d + e*x)^(5/2)*(a + b*x + c*x^2)),x)

[Out]

- atan((((d + e*x)^(1/2)*(128*b*c^12*d^15*e^3 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a
^7*b^2*c^4*e^18 + 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^
12 + 320*a^6*c^7*d^4*e^14 - 480*b^2*c^11*d^14*e^4 + 1120*b^3*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*
c^8*d^11*e^7 - 1688*b^6*c^7*d^10*e^8 + 960*b^7*c^6*d^9*e^9 - 360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^
10*c^3*d^6*e^12 + 4512*a^2*b^2*c^9*d^10*e^8 - 4960*a^2*b^3*c^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*
b^5*c^6*d^7*e^11 - 1840*a^2*b^6*c^5*d^6*e^12 + 768*a^2*b^7*c^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3
*b^2*c^8*d^8*e^10 - 9600*a^3*b^3*c^7*d^7*e^11 + 4000*a^3*b^4*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*
b^6*c^4*d^4*e^14 + 160*a^3*b^7*c^3*d^3*e^15 + 8800*a^4*b^2*c^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4
*b^4*c^5*d^4*e^14 + 80*a^4*b^5*c^4*d^3*e^15 - 120*a^4*b^6*c^3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*
b^3*c^5*d^3*e^15 + 240*a^5*b^4*c^4*d^2*e^16 + 480*a^6*b^2*c^5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c
^9*d^11*e^7 - 2448*a*b^4*c^8*d^10*e^8 + 3440*a*b^5*c^7*d^9*e^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*
e^11 - 400*a*b^8*c^4*d^6*e^12 + 48*a*b^9*c^3*d^5*e^13 - 1920*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 57
60*a^4*b*c^8*d^7*e^11 - 3072*a^5*b*c^7*d^5*e^13 + 48*a^5*b^5*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3
*c^4*d*e^17) + (-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5
+ 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5
*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b
^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)
^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2
*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3
*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10
+ 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4
*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2
+ 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 1
20*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*
b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d
^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^
2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*
d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(96*a*c^13*d^18*e^3 -
32*a^10*c^4*e^21 - (d + e*x)^(1/2)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2)
- 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c
^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 -
9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^
5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^
2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^
(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*
d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a
*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 +
80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10
*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c
^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*
e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 -
75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7
*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(6
4*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 + 28
80*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 + 84
480*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^1
4 + 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 - 3
47424*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 - 19
20*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 - 65
28*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^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21
+ 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*
c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216
*b^3*c^11*d^17*e^4 - 872*b^4*c^10*d^16*e^5 + 2080*b^5*c^9*d^15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13
*e^8 - 2576*b^8*c^6*d^12*e^9 + 1312*b^9*c^5*d^11*e^10 - 440*b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12
*c^2*d^8*e^13 + 20256*a^2*b^2*c^10*d^14*e^7 - 38752*a^2*b^3*c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*e^9 - 27552*
a^2*b^5*c^7*d^11*e^10 + 4928*a^2*b^6*c^6*d^10*e^11 + 5984*a^2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1
696*a^2*b^9*c^3*d^7*e^14 - 224*a^2*b^10*c^2*d^6*e^15 + 50848*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^1
0 + 81312*a^3*b^4*c^7*d^10*e^11 - 44352*a^3*b^5*c^6*d^9*e^12 + 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^
7*e^14 - 2464*a^3*b^8*c^3*d^6*e^15 + 448*a^3*b^9*c^2*d^5*e^16 + 67760*a^4*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^
7*d^9*e^12 + 72240*a^4*b^4*c^6*d^8*e^13 - 30240*a^4*b^5*c^5*d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^
7*c^3*d^5*e^16 - 560*a^4*b^8*c^2*d^4*e^17 + 50736*a^5*b^2*c^7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^
5*b^4*c^5*d^6*e^15 - 9408*a^5*b^5*c^4*d^5*e^16 + 112*a^5*b^6*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^18 + 20384*a
^6*b^2*c^6*d^6*e^15 - 17248*a^6*b^3*c^5*d^5*e^16 + 7616*a^6*b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224
*a^6*b^6*c^2*d^2*e^19 + 3616*a^7*b^2*c^5*d^4*e^17 - 2752*a^7*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168
*a^8*b^2*c^4*d^2*e^19 - 864*a*b*c^12*d^17*e^4 + 160*a^9*b*c^4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c
^10*d^15*e^6 + 7776*a*b^4*c^9*d^14*e^7 - 3136*a*b^5*c^8*d^13*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^
11*e^10 - 5632*a*b^8*c^5*d^10*e^11 + 2464*a*b^9*c^4*d^9*e^12 - 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^1
4 - 5888*a^2*b*c^11*d^15*e^6 - 17024*a^3*b*c^10*d^13*e^8 - 26880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^1
2 - 12544*a^6*b*c^7*d^7*e^14 - 2688*a^7*b*c^6*d^5*e^16 + 64*a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*
a^8*b^3*c^3*d*e^20))*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^
3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c
^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5
- 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b
^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c
^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c
^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4
*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 -
5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^
8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e
^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 8
0*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3
*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*
d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*
b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*1i + ((d + e*x)^
(1/2)*(128*b*c^12*d^15*e^3 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a^7*b^2*c^4*e^18 + 3
20*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^
4*e^14 - 480*b^2*c^11*d^14*e^4 + 1120*b^3*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*c^8*d^11*e^7 - 1688
*b^6*c^7*d^10*e^8 + 960*b^7*c^6*d^9*e^9 - 360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4
512*a^2*b^2*c^9*d^10*e^8 - 4960*a^2*b^3*c^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*b^5*c^6*d^7*e^11 -
1840*a^2*b^6*c^5*d^6*e^12 + 768*a^2*b^7*c^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3*b^2*c^8*d^8*e^10 -
9600*a^3*b^3*c^7*d^7*e^11 + 4000*a^3*b^4*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*b^6*c^4*d^4*e^14 +
160*a^3*b^7*c^3*d^3*e^15 + 8800*a^4*b^2*c^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4*b^4*c^5*d^4*e^14 +
80*a^4*b^5*c^4*d^3*e^15 - 120*a^4*b^6*c^3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*b^3*c^5*d^3*e^15 +
240*a^5*b^4*c^4*d^2*e^16 + 480*a^6*b^2*c^5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c^9*d^11*e^7 - 2448*
a*b^4*c^8*d^10*e^8 + 3440*a*b^5*c^7*d^9*e^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^
4*d^6*e^12 + 48*a*b^9*c^3*d^5*e^13 - 1920*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^
11 - 3072*a^5*b*c^7*d^5*e^13 + 48*a^5*b^5*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3*c^4*d*e^17) - (-(b
^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4
+ 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)
^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b
*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c
^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^
4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2
)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 +
b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*
c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e
^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*
e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 1
50*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d
^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^
7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b
*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*((d + e*x)^(1/2)*(-(b^7*e^5 + 8*a*c^6*d^5
- 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e +
5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*
d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*
c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d
*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b
^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*
c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*
d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*
d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4
*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^
3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e
^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^
6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2
*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^
4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(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 + 235
20*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 + 1056
0*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 + 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 + 560
0*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) - 32*a^10*c^4*e^21 + 96*a*c^13*d^18*e^3 - 8*a^8*b^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21 + 736*a^2*c^12*d^16
*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*
a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216*b^3*c^11*d^17*e^4
- 872*b^4*c^10*d^16*e^5 + 2080*b^5*c^9*d^15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13*e^8 - 2576*b^8*c^6
*d^12*e^9 + 1312*b^9*c^5*d^11*e^10 - 440*b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12*c^2*d^8*e^13 + 202
56*a^2*b^2*c^10*d^14*e^7 - 38752*a^2*b^3*c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*e^9 - 27552*a^2*b^5*c^7*d^11*e^
10 + 4928*a^2*b^6*c^6*d^10*e^11 + 5984*a^2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1696*a^2*b^9*c^3*d^7
*e^14 - 224*a^2*b^10*c^2*d^6*e^15 + 50848*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^10 + 81312*a^3*b^4*c
^7*d^10*e^11 - 44352*a^3*b^5*c^6*d^9*e^12 + 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^7*e^14 - 2464*a^3*b
^8*c^3*d^6*e^15 + 448*a^3*b^9*c^2*d^5*e^16 + 67760*a^4*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^7*d^9*e^12 + 72240*
a^4*b^4*c^6*d^8*e^13 - 30240*a^4*b^5*c^5*d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^7*c^3*d^5*e^16 - 56
0*a^4*b^8*c^2*d^4*e^17 + 50736*a^5*b^2*c^7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^5*b^4*c^5*d^6*e^15
- 9408*a^5*b^5*c^4*d^5*e^16 + 112*a^5*b^6*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^18 + 20384*a^6*b^2*c^6*d^6*e^15
- 17248*a^6*b^3*c^5*d^5*e^16 + 7616*a^6*b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224*a^6*b^6*c^2*d^2*e^
19 + 3616*a^7*b^2*c^5*d^4*e^17 - 2752*a^7*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168*a^8*b^2*c^4*d^2*e^
19 - 864*a*b*c^12*d^17*e^4 + 160*a^9*b*c^4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c^10*d^15*e^6 + 7776
*a*b^4*c^9*d^14*e^7 - 3136*a*b^5*c^8*d^13*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^11*e^10 - 5632*a*b^
8*c^5*d^10*e^11 + 2464*a*b^9*c^4*d^9*e^12 - 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^14 - 5888*a^2*b*c^11
*d^15*e^6 - 17024*a^3*b*c^10*d^13*e^8 - 26880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^12 - 12544*a^6*b*c^7
*d^7*e^14 - 2688*a^7*b*c^6*d^5*e^16 + 64*a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*a^8*b^3*c^3*d*e^20)
)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*
d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b
^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 -
20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a
*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^
2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c
- b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*
e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 -
5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5
*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^
5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e
^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b
^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*
c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480
*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*1i)/(((d + e*x)^(1/2)*(128*b*c^12*d
^15*e^3 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a^7*b^2*c^4*e^18 + 320*a^2*c^11*d^12*e^
6 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14 - 480*b^2*c^
11*d^14*e^4 + 1120*b^3*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*c^8*d^11*e^7 - 1688*b^6*c^7*d^10*e^8 +
960*b^7*c^6*d^9*e^9 - 360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4512*a^2*b^2*c^9*d^1
0*e^8 - 4960*a^2*b^3*c^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*b^5*c^6*d^7*e^11 - 1840*a^2*b^6*c^5*d^
6*e^12 + 768*a^2*b^7*c^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3*b^2*c^8*d^8*e^10 - 9600*a^3*b^3*c^7*d
^7*e^11 + 4000*a^3*b^4*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*b^6*c^4*d^4*e^14 + 160*a^3*b^7*c^3*d^3
*e^15 + 8800*a^4*b^2*c^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4*b^4*c^5*d^4*e^14 + 80*a^4*b^5*c^4*d^3
*e^15 - 120*a^4*b^6*c^3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*b^3*c^5*d^3*e^15 + 240*a^5*b^4*c^4*d^2
*e^16 + 480*a^6*b^2*c^5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c^9*d^11*e^7 - 2448*a*b^4*c^8*d^10*e^8
+ 3440*a*b^5*c^7*d^9*e^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^4*d^6*e^12 + 48*a*b
^9*c^3*d^5*e^13 - 1920*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^11 - 3072*a^5*b*c^7
*d^5*e^13 + 48*a^5*b^5*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3*c^4*d*e^17) - (-(b^7*e^5 + 8*a*c^6*d^
5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e +
5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5
*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2
*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*
d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*
b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b
*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9
*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c
*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^
4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c
^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*
e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c
^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^
2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a
^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*((d + e*x)^(1/2)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 +
b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*
c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^
3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*
c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2
)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a
*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c
- b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c
^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^
7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d
^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2
*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^
3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^
3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b
^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 3
20*a^5*b*c^3*d^3*e^7)))^(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 + 161
28*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^1
0*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 + 23520
0*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 + 5040
0*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^1
8 - 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 - 1
6800*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 - 87
360*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 - 72
00*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) - 32*a^10*c
^4*e^21 + 96*a*c^13*d^18*e^3 - 8*a^8*b^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^1
1*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 -
128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216*b^3*c^11*d^17*e^4 - 872*b^4*c^10*d^16
*e^5 + 2080*b^5*c^9*d^15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13*e^8 - 2576*b^8*c^6*d^12*e^9 + 1312*b^
9*c^5*d^11*e^10 - 440*b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12*c^2*d^8*e^13 + 20256*a^2*b^2*c^10*d^1
4*e^7 - 38752*a^2*b^3*c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*e^9 - 27552*a^2*b^5*c^7*d^11*e^10 + 4928*a^2*b^6*c
^6*d^10*e^11 + 5984*a^2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1696*a^2*b^9*c^3*d^7*e^14 - 224*a^2*b^1
0*c^2*d^6*e^15 + 50848*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^10 + 81312*a^3*b^4*c^7*d^10*e^11 - 4435
2*a^3*b^5*c^6*d^9*e^12 + 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^7*e^14 - 2464*a^3*b^8*c^3*d^6*e^15 + 4
48*a^3*b^9*c^2*d^5*e^16 + 67760*a^4*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^7*d^9*e^12 + 72240*a^4*b^4*c^6*d^8*e^1
3 - 30240*a^4*b^5*c^5*d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^7*c^3*d^5*e^16 - 560*a^4*b^8*c^2*d^4*e
^17 + 50736*a^5*b^2*c^7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^5*b^4*c^5*d^6*e^15 - 9408*a^5*b^5*c^4*
d^5*e^16 + 112*a^5*b^6*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^18 + 20384*a^6*b^2*c^6*d^6*e^15 - 17248*a^6*b^3*c^
5*d^5*e^16 + 7616*a^6*b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224*a^6*b^6*c^2*d^2*e^19 + 3616*a^7*b^2*c
^5*d^4*e^17 - 2752*a^7*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168*a^8*b^2*c^4*d^2*e^19 - 864*a*b*c^12*d
^17*e^4 + 160*a^9*b*c^4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c^10*d^15*e^6 + 7776*a*b^4*c^9*d^14*e^7
- 3136*a*b^5*c^8*d^13*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^11*e^10 - 5632*a*b^8*c^5*d^10*e^11 + 2
464*a*b^9*c^4*d^9*e^12 - 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^14 - 5888*a^2*b*c^11*d^15*e^6 - 17024*a
^3*b*c^10*d^13*e^8 - 26880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^12 - 12544*a^6*b*c^7*d^7*e^14 - 2688*a^
7*b*c^6*d^5*e^16 + 64*a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*a^8*b^3*c^3*d*e^20))*(-(b^7*e^5 + 8*a*
c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d
^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a
^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e +
10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*
b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 9
0*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) +
10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10
- b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5
*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*
c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2
*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^
2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a
^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*
b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5
- 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2) - ((d + e*x)^(1/2)*(128*b*c^12*d^15*e^3 - 16*c^13*d^16
*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a^7*b^2*c^4*e^18 + 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10
*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14 - 480*b^2*c^11*d^14*e^4 + 1120*b^3
*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*c^8*d^11*e^7 - 1688*b^6*c^7*d^10*e^8 + 960*b^7*c^6*d^9*e^9 -
360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4512*a^2*b^2*c^9*d^10*e^8 - 4960*a^2*b^3*c
^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*b^5*c^6*d^7*e^11 - 1840*a^2*b^6*c^5*d^6*e^12 + 768*a^2*b^7*c
^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3*b^2*c^8*d^8*e^10 - 9600*a^3*b^3*c^7*d^7*e^11 + 4000*a^3*b^4
*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*b^6*c^4*d^4*e^14 + 160*a^3*b^7*c^3*d^3*e^15 + 8800*a^4*b^2*c
^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4*b^4*c^5*d^4*e^14 + 80*a^4*b^5*c^4*d^3*e^15 - 120*a^4*b^6*c^
3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*b^3*c^5*d^3*e^15 + 240*a^5*b^4*c^4*d^2*e^16 + 480*a^6*b^2*c^
5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c^9*d^11*e^7 - 2448*a*b^4*c^8*d^10*e^8 + 3440*a*b^5*c^7*d^9*e
^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^4*d^6*e^12 + 48*a*b^9*c^3*d^5*e^13 - 1920
*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^11 - 3072*a^5*b*c^7*d^5*e^13 + 48*a^5*b^5
*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3*c^4*d*e^17) + (-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^
4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c
- b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*
d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c
- b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^
3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c
^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c -
b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6
*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*
d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2
*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b
^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*
d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*
c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6
*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320
*a^5*b*c^3*d^3*e^7)))^(1/2)*(96*a*c^13*d^18*e^3 - 32*a^10*c^4*e^21 - (d + e*x)^(1/2)*(-(b^7*e^5 + 8*a*c^6*d^5
- 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5
*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d
^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c
^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*
e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^
2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c
^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d
^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d
^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*
e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3
*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^
6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6
*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*
d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4
*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(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^1
8 + 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 + 2352
0*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 + 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^1
1*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^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*
c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 -
160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216*b^3*c^11*d^17*e^4 - 872*b^4*c^10*d^16*e^5 + 2080*b^5*c^9*d^
15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13*e^8 - 2576*b^8*c^6*d^12*e^9 + 1312*b^9*c^5*d^11*e^10 - 440*
b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12*c^2*d^8*e^13 + 20256*a^2*b^2*c^10*d^14*e^7 - 38752*a^2*b^3*
c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*e^9 - 27552*a^2*b^5*c^7*d^11*e^10 + 4928*a^2*b^6*c^6*d^10*e^11 + 5984*a^
2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1696*a^2*b^9*c^3*d^7*e^14 - 224*a^2*b^10*c^2*d^6*e^15 + 50848
*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^10 + 81312*a^3*b^4*c^7*d^10*e^11 - 44352*a^3*b^5*c^6*d^9*e^12
+ 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^7*e^14 - 2464*a^3*b^8*c^3*d^6*e^15 + 448*a^3*b^9*c^2*d^5*e^1
6 + 67760*a^4*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^7*d^9*e^12 + 72240*a^4*b^4*c^6*d^8*e^13 - 30240*a^4*b^5*c^5*
d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^7*c^3*d^5*e^16 - 560*a^4*b^8*c^2*d^4*e^17 + 50736*a^5*b^2*c^
7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^5*b^4*c^5*d^6*e^15 - 9408*a^5*b^5*c^4*d^5*e^16 + 112*a^5*b^6
*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^18 + 20384*a^6*b^2*c^6*d^6*e^15 - 17248*a^6*b^3*c^5*d^5*e^16 + 7616*a^6*
b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224*a^6*b^6*c^2*d^2*e^19 + 3616*a^7*b^2*c^5*d^4*e^17 - 2752*a^7
*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168*a^8*b^2*c^4*d^2*e^19 - 864*a*b*c^12*d^17*e^4 + 160*a^9*b*c^
4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c^10*d^15*e^6 + 7776*a*b^4*c^9*d^14*e^7 - 3136*a*b^5*c^8*d^13
*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^11*e^10 - 5632*a*b^8*c^5*d^10*e^11 + 2464*a*b^9*c^4*d^9*e^12
- 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^14 - 5888*a^2*b*c^11*d^15*e^6 - 17024*a^3*b*c^10*d^13*e^8 - 2
6880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^12 - 12544*a^6*b*c^7*d^7*e^14 - 2688*a^7*b*c^6*d^5*e^16 + 64*
a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*a^8*b^3*c^3*d*e^20))*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^
5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(
4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^
4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(
4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c -
b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 -
10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*
a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b
^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^
2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c
^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114
*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^
2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^
5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a
^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8
- 320*a^5*b*c^3*d^3*e^7)))^(1/2) + 32*c^12*d^13*e^3 - 16*a^6*b*c^5*e^16 + 192*a*c^11*d^11*e^5 + 32*a^6*c^6*d*
e^15 - 208*b*c^11*d^12*e^4 + 480*a^2*c^10*d^9*e^7 + 640*a^3*c^9*d^7*e^9 + 480*a^4*c^8*d^5*e^11 + 192*a^5*c^7*d
^3*e^13 + 576*b^2*c^10*d^11*e^5 - 880*b^3*c^9*d^10*e^6 + 800*b^4*c^8*d^9*e^7 - 432*b^5*c^7*d^8*e^8 + 128*b^6*c
^6*d^7*e^9 - 16*b^7*c^5*d^6*e^10 + 3840*a^2*b^2*c^8*d^7*e^9 - 3360*a^2*b^3*c^7*d^6*e^10 + 1440*a^2*b^4*c^6*d^5
*e^11 - 240*a^2*b^5*c^5*d^4*e^12 + 2880*a^3*b^2*c^7*d^5*e^11 - 1600*a^3*b^3*c^6*d^4*e^12 + 320*a^3*b^4*c^5*d^3
*e^13 + 960*a^4*b^2*c^6*d^3*e^13 - 240*a^4*b^3*c^5*d^2*e^14 - 1056*a*b*c^10*d^10*e^6 + 2400*a*b^2*c^9*d^9*e^7
- 2880*a*b^3*c^8*d^8*e^8 + 1920*a*b^4*c^7*d^7*e^9 - 672*a*b^5*c^6*d^6*e^10 + 96*a*b^6*c^5*d^5*e^11 - 2160*a^2*
b*c^9*d^8*e^8 - 2240*a^3*b*c^8*d^6*e^10 - 1200*a^4*b*c^7*d^4*e^12 - 288*a^5*b*c^6*d^2*e^14 + 96*a^5*b^2*c^5*d*
e^15))*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3
*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*
c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e
^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) +
40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 1
20*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(
4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7
*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e
^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^
4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b
^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*
d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 1
2*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a
*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7
- 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*2i - atan((((d + e*x)^(1/2)*(1
28*b*c^12*d^15*e^3 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a^7*b^2*c^4*e^18 + 320*a^2*c
^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14 -
480*b^2*c^11*d^14*e^4 + 1120*b^3*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*c^8*d^11*e^7 - 1688*b^6*c^7
*d^10*e^8 + 960*b^7*c^6*d^9*e^9 - 360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4512*a^2*
b^2*c^9*d^10*e^8 - 4960*a^2*b^3*c^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*b^5*c^6*d^7*e^11 - 1840*a^2
*b^6*c^5*d^6*e^12 + 768*a^2*b^7*c^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3*b^2*c^8*d^8*e^10 - 9600*a^
3*b^3*c^7*d^7*e^11 + 4000*a^3*b^4*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*b^6*c^4*d^4*e^14 + 160*a^3*
b^7*c^3*d^3*e^15 + 8800*a^4*b^2*c^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4*b^4*c^5*d^4*e^14 + 80*a^4*
b^5*c^4*d^3*e^15 - 120*a^4*b^6*c^3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*b^3*c^5*d^3*e^15 + 240*a^5*
b^4*c^4*d^2*e^16 + 480*a^6*b^2*c^5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c^9*d^11*e^7 - 2448*a*b^4*c^
8*d^10*e^8 + 3440*a*b^5*c^7*d^9*e^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^4*d^6*e^
12 + 48*a*b^9*c^3*d^5*e^13 - 1920*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^11 - 307
2*a^5*b*c^7*d^5*e^13 + 48*a^5*b^5*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3*c^4*d*e^17) + ((2*b^2*c^5*
d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c
^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) +
80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*
e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4
- 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3
+ 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2
) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*
d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e
+ 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*
a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150
*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^
4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 -
80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 1
0*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*
e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(96*a*c^13*d^18*e^3 - 32*a^10*c^4*e^21 - (d + e*x)
^(1/2)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*
c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c
- b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^
4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) -
40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 12
0*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4
*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*
c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^
9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4
*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^
2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d
^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12
*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*
b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 -
480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(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 - 70
560*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 + 6048
0*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 + 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 + 304
0*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^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21 + 736*a^2*c^12*d^16*e^5 + 243
2*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^
6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216*b^3*c^11*d^17*e^4 - 872*b^4*
c^10*d^16*e^5 + 2080*b^5*c^9*d^15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13*e^8 - 2576*b^8*c^6*d^12*e^9
+ 1312*b^9*c^5*d^11*e^10 - 440*b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12*c^2*d^8*e^13 + 20256*a^2*b^2
*c^10*d^14*e^7 - 38752*a^2*b^3*c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*e^9 - 27552*a^2*b^5*c^7*d^11*e^10 + 4928*
a^2*b^6*c^6*d^10*e^11 + 5984*a^2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1696*a^2*b^9*c^3*d^7*e^14 - 22
4*a^2*b^10*c^2*d^6*e^15 + 50848*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^10 + 81312*a^3*b^4*c^7*d^10*e^
11 - 44352*a^3*b^5*c^6*d^9*e^12 + 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^7*e^14 - 2464*a^3*b^8*c^3*d^6
*e^15 + 448*a^3*b^9*c^2*d^5*e^16 + 67760*a^4*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^7*d^9*e^12 + 72240*a^4*b^4*c^
6*d^8*e^13 - 30240*a^4*b^5*c^5*d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^7*c^3*d^5*e^16 - 560*a^4*b^8*
c^2*d^4*e^17 + 50736*a^5*b^2*c^7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^5*b^4*c^5*d^6*e^15 - 9408*a^5
*b^5*c^4*d^5*e^16 + 112*a^5*b^6*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^18 + 20384*a^6*b^2*c^6*d^6*e^15 - 17248*a
^6*b^3*c^5*d^5*e^16 + 7616*a^6*b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224*a^6*b^6*c^2*d^2*e^19 + 3616*
a^7*b^2*c^5*d^4*e^17 - 2752*a^7*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168*a^8*b^2*c^4*d^2*e^19 - 864*a
*b*c^12*d^17*e^4 + 160*a^9*b*c^4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c^10*d^15*e^6 + 7776*a*b^4*c^9
*d^14*e^7 - 3136*a*b^5*c^8*d^13*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^11*e^10 - 5632*a*b^8*c^5*d^10
*e^11 + 2464*a*b^9*c^4*d^9*e^12 - 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^14 - 5888*a^2*b*c^11*d^15*e^6
- 17024*a^3*b*c^10*d^13*e^8 - 26880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^12 - 12544*a^6*b*c^7*d^7*e^14
- 2688*a^7*b*c^6*d^5*e^16 + 64*a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*a^8*b^3*c^3*d*e^20))*((2*b^2*
c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b
^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2
) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*
d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*
e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2
*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^
(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*
c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d
^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 +
160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 -
150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^
3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^
5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3
- 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*
d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*1i + ((d + e*x)^(1/2)*(128*b*c^12*d^15*e^3 - 1
6*c^13*d^16*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a^7*b^2*c^4*e^18 + 320*a^2*c^11*d^12*e^6 + 1024*a^
3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14 - 480*b^2*c^11*d^14*e^4
+ 1120*b^3*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*c^8*d^11*e^7 - 1688*b^6*c^7*d^10*e^8 + 960*b^7*c^
6*d^9*e^9 - 360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4512*a^2*b^2*c^9*d^10*e^8 - 496
0*a^2*b^3*c^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*b^5*c^6*d^7*e^11 - 1840*a^2*b^6*c^5*d^6*e^12 + 76
8*a^2*b^7*c^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3*b^2*c^8*d^8*e^10 - 9600*a^3*b^3*c^7*d^7*e^11 + 4
000*a^3*b^4*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*b^6*c^4*d^4*e^14 + 160*a^3*b^7*c^3*d^3*e^15 + 880
0*a^4*b^2*c^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4*b^4*c^5*d^4*e^14 + 80*a^4*b^5*c^4*d^3*e^15 - 120
*a^4*b^6*c^3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*b^3*c^5*d^3*e^15 + 240*a^5*b^4*c^4*d^2*e^16 + 480
*a^6*b^2*c^5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c^9*d^11*e^7 - 2448*a*b^4*c^8*d^10*e^8 + 3440*a*b^
5*c^7*d^9*e^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^4*d^6*e^12 + 48*a*b^9*c^3*d^5*
e^13 - 1920*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^11 - 3072*a^5*b*c^7*d^5*e^13 +
48*a^5*b^5*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3*c^4*d*e^17) - ((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^
7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e
*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 1
0*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3
*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a
*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^
4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(
-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8
*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 1
0*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a
^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 +
114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^
4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 4
0*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 -
10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2
*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*((d + e*x)^(1/2)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*
a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(
1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 1
0*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(
1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) -
60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*
(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/
2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a
^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 1
0*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b
^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*
e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 1
20*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 8
0*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6
- 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*
d^3*e^7)))^(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) - 32*a^10*c^4*e^21 + 96*
a*c^13*d^18*e^3 - 8*a^8*b^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 +
4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d
^4*e^17 - 160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216*b^3*c^11*d^17*e^4 - 872*b^4*c^10*d^16*e^5 + 2080*b
^5*c^9*d^15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13*e^8 - 2576*b^8*c^6*d^12*e^9 + 1312*b^9*c^5*d^11*e^
10 - 440*b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12*c^2*d^8*e^13 + 20256*a^2*b^2*c^10*d^14*e^7 - 38752
*a^2*b^3*c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*e^9 - 27552*a^2*b^5*c^7*d^11*e^10 + 4928*a^2*b^6*c^6*d^10*e^11
+ 5984*a^2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1696*a^2*b^9*c^3*d^7*e^14 - 224*a^2*b^10*c^2*d^6*e^1
5 + 50848*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^10 + 81312*a^3*b^4*c^7*d^10*e^11 - 44352*a^3*b^5*c^6
*d^9*e^12 + 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^7*e^14 - 2464*a^3*b^8*c^3*d^6*e^15 + 448*a^3*b^9*c^
2*d^5*e^16 + 67760*a^4*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^7*d^9*e^12 + 72240*a^4*b^4*c^6*d^8*e^13 - 30240*a^4
*b^5*c^5*d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^7*c^3*d^5*e^16 - 560*a^4*b^8*c^2*d^4*e^17 + 50736*a
^5*b^2*c^7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^5*b^4*c^5*d^6*e^15 - 9408*a^5*b^5*c^4*d^5*e^16 + 11
2*a^5*b^6*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^18 + 20384*a^6*b^2*c^6*d^6*e^15 - 17248*a^6*b^3*c^5*d^5*e^16 +
7616*a^6*b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224*a^6*b^6*c^2*d^2*e^19 + 3616*a^7*b^2*c^5*d^4*e^17 -
2752*a^7*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168*a^8*b^2*c^4*d^2*e^19 - 864*a*b*c^12*d^17*e^4 + 160
*a^9*b*c^4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c^10*d^15*e^6 + 7776*a*b^4*c^9*d^14*e^7 - 3136*a*b^5
*c^8*d^13*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^11*e^10 - 5632*a*b^8*c^5*d^10*e^11 + 2464*a*b^9*c^4
*d^9*e^12 - 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^14 - 5888*a^2*b*c^11*d^15*e^6 - 17024*a^3*b*c^10*d^1
3*e^8 - 26880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^12 - 12544*a^6*b*c^7*d^7*e^14 - 2688*a^7*b*c^6*d^5*e
^16 + 64*a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*a^8*b^3*c^3*d*e^20))*((2*b^2*c^5*d^5 - 8*a*c^6*d^5
- b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d
^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2
+ 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2
*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-
(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*
d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e
^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5
- 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4
- 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 +
80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e
^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 40
0*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e
+ 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^
4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c
*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*1i)/(((d + e*x)^(1/2)*(128*b*c^12*d^15*e^3 - 16*c^13*d^16*e^2 - 16*a
^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a^7*b^2*c^4*e^18 + 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 + 1440
*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14 - 480*b^2*c^11*d^14*e^4 + 1120*b^3*c^10*d^13*
e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*c^8*d^11*e^7 - 1688*b^6*c^7*d^10*e^8 + 960*b^7*c^6*d^9*e^9 - 360*b^8*c^
5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4512*a^2*b^2*c^9*d^10*e^8 - 4960*a^2*b^3*c^8*d^9*e^9
+ 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*b^5*c^6*d^7*e^11 - 1840*a^2*b^6*c^5*d^6*e^12 + 768*a^2*b^7*c^4*d^5*e^13
- 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3*b^2*c^8*d^8*e^10 - 9600*a^3*b^3*c^7*d^7*e^11 + 4000*a^3*b^4*c^6*d^6*e^
12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*b^6*c^4*d^4*e^14 + 160*a^3*b^7*c^3*d^3*e^15 + 8800*a^4*b^2*c^7*d^6*e^12
- 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4*b^4*c^5*d^4*e^14 + 80*a^4*b^5*c^4*d^3*e^15 - 120*a^4*b^6*c^3*d^2*e^16
+ 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*b^3*c^5*d^3*e^15 + 240*a^5*b^4*c^4*d^2*e^16 + 480*a^6*b^2*c^5*d^2*e^16
- 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c^9*d^11*e^7 - 2448*a*b^4*c^8*d^10*e^8 + 3440*a*b^5*c^7*d^9*e^9 - 2880*a
*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^4*d^6*e^12 + 48*a*b^9*c^3*d^5*e^13 - 1920*a^2*b*c^10
*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^11 - 3072*a^5*b*c^7*d^5*e^13 + 48*a^5*b^5*c^3*d*e^17
- 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3*c^4*d*e^17) - ((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a
*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1
/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10
*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1
/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 6
0*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(
-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2
))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^
6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10
*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^
6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e
^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 12
0*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80
*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 -
320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d
^3*e^7)))^(1/2)*((d + e*x)^(1/2)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) +
20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*
e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*
a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(
-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 +
70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/
2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^1
0 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^
8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80
*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^
7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*
d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8
+ 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75
*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^
3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(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 + 16
8*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 + 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^1
2*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 - 3474
24*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 + 24
00*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 - 6
72*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) - 32*a^10*c^4*e^21 + 96*a*c^13*d^18*e^3 - 8*a^
8*b^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9
+ 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*
d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216*b^3*c^11*d^17*e^4 - 872*b^4*c^10*d^16*e^5 + 2080*b^5*c^9*d^15*e^6 - 3248
*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13*e^8 - 2576*b^8*c^6*d^12*e^9 + 1312*b^9*c^5*d^11*e^10 - 440*b^10*c^4*d^10
*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12*c^2*d^8*e^13 + 20256*a^2*b^2*c^10*d^14*e^7 - 38752*a^2*b^3*c^9*d^13*e^8
+ 43904*a^2*b^4*c^8*d^12*e^9 - 27552*a^2*b^5*c^7*d^11*e^10 + 4928*a^2*b^6*c^6*d^10*e^11 + 5984*a^2*b^7*c^5*d^9
*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1696*a^2*b^9*c^3*d^7*e^14 - 224*a^2*b^10*c^2*d^6*e^15 + 50848*a^3*b^2*c^9*
d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^10 + 81312*a^3*b^4*c^7*d^10*e^11 - 44352*a^3*b^5*c^6*d^9*e^12 + 9184*a^3*b
^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^7*e^14 - 2464*a^3*b^8*c^3*d^6*e^15 + 448*a^3*b^9*c^2*d^5*e^16 + 67760*a^4
*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^7*d^9*e^12 + 72240*a^4*b^4*c^6*d^8*e^13 - 30240*a^4*b^5*c^5*d^7*e^14 + 39
20*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^7*c^3*d^5*e^16 - 560*a^4*b^8*c^2*d^4*e^17 + 50736*a^5*b^2*c^7*d^8*e^13 -
55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^5*b^4*c^5*d^6*e^15 - 9408*a^5*b^5*c^4*d^5*e^16 + 112*a^5*b^6*c^3*d^4*e^17
+ 448*a^5*b^7*c^2*d^3*e^18 + 20384*a^6*b^2*c^6*d^6*e^15 - 17248*a^6*b^3*c^5*d^5*e^16 + 7616*a^6*b^4*c^4*d^4*e
^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224*a^6*b^6*c^2*d^2*e^19 + 3616*a^7*b^2*c^5*d^4*e^17 - 2752*a^7*b^3*c^4*d^3*
e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168*a^8*b^2*c^4*d^2*e^19 - 864*a*b*c^12*d^17*e^4 + 160*a^9*b*c^4*d*e^20 + 33
04*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c^10*d^15*e^6 + 7776*a*b^4*c^9*d^14*e^7 - 3136*a*b^5*c^8*d^13*e^8 - 3920*a
*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^11*e^10 - 5632*a*b^8*c^5*d^10*e^11 + 2464*a*b^9*c^4*d^9*e^12 - 600*a*b^10
*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^14 - 5888*a^2*b*c^11*d^15*e^6 - 17024*a^3*b*c^10*d^13*e^8 - 26880*a^4*b*c^
9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^12 - 12544*a^6*b*c^7*d^7*e^14 - 2688*a^7*b*c^6*d^5*e^16 + 64*a^7*b^5*c^2*d
*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*a^8*b^3*c^3*d*e^20))*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-
(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3
)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2
- 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3
)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2)
- 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e
^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^
(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 -
8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7
+ 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 1
0*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d
^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6
+ 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9
- 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e
^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c
^3*d^3*e^7)))^(1/2) - ((d + e*x)^(1/2)*(128*b*c^12*d^15*e^3 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c
^3*e^18 + 32*a^7*b^2*c^4*e^18 + 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*
a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14 - 480*b^2*c^11*d^14*e^4 + 1120*b^3*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e
^6 + 2064*b^5*c^8*d^11*e^7 - 1688*b^6*c^7*d^10*e^8 + 960*b^7*c^6*d^9*e^9 - 360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d
^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4512*a^2*b^2*c^9*d^10*e^8 - 4960*a^2*b^3*c^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^
10 + 1440*a^2*b^5*c^6*d^7*e^11 - 1840*a^2*b^6*c^5*d^6*e^12 + 768*a^2*b^7*c^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^
14 + 10080*a^3*b^2*c^8*d^8*e^10 - 9600*a^3*b^3*c^7*d^7*e^11 + 4000*a^3*b^4*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e
^13 - 640*a^3*b^6*c^4*d^4*e^14 + 160*a^3*b^7*c^3*d^3*e^15 + 8800*a^4*b^2*c^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e
^13 + 1800*a^4*b^4*c^5*d^4*e^14 + 80*a^4*b^5*c^4*d^3*e^15 - 120*a^4*b^6*c^3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^
14 - 1600*a^5*b^3*c^5*d^3*e^15 + 240*a^5*b^4*c^4*d^2*e^16 + 480*a^6*b^2*c^5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6
+ 960*a*b^3*c^9*d^11*e^7 - 2448*a*b^4*c^8*d^10*e^8 + 3440*a*b^5*c^7*d^9*e^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*
a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^4*d^6*e^12 + 48*a*b^9*c^3*d^5*e^13 - 1920*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^
9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^11 - 3072*a^5*b*c^7*d^5*e^13 + 48*a^5*b^5*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15
- 160*a^6*b^3*c^4*d*e^17) + ((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a
^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5
+ a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^
5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*
a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*
a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) -
10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 +
a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^
4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3
*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^
2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*
e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 4
0*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b
^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 +
60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(96*a*c^1
3*d^18*e^3 - 32*a^10*c^4*e^21 - (d + e*x)^(1/2)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b
^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) -
25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c
^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) -
3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^
2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*
c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*
(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*
c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b
^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*
d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 4
00*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*
b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b
*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a
^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7
)))^(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^1
3*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 + 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 + 198240*a^6*b^2*c^7*d^9*e^14 - 226
800*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^1
8 + 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^1
9 - 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^4*c^2*e^21 + 40*a^9*b
^2*c^3*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11
+ 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^
18*e^3 + 216*b^3*c^11*d^17*e^4 - 872*b^4*c^10*d^16*e^5 + 2080*b^5*c^9*d^15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*
b^7*c^7*d^13*e^8 - 2576*b^8*c^6*d^12*e^9 + 1312*b^9*c^5*d^11*e^10 - 440*b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e
^12 - 8*b^12*c^2*d^8*e^13 + 20256*a^2*b^2*c^10*d^14*e^7 - 38752*a^2*b^3*c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*
e^9 - 27552*a^2*b^5*c^7*d^11*e^10 + 4928*a^2*b^6*c^6*d^10*e^11 + 5984*a^2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*
d^8*e^13 + 1696*a^2*b^9*c^3*d^7*e^14 - 224*a^2*b^10*c^2*d^6*e^15 + 50848*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*
c^8*d^11*e^10 + 81312*a^3*b^4*c^7*d^10*e^11 - 44352*a^3*b^5*c^6*d^9*e^12 + 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^
3*b^7*c^4*d^7*e^14 - 2464*a^3*b^8*c^3*d^6*e^15 + 448*a^3*b^9*c^2*d^5*e^16 + 67760*a^4*b^2*c^8*d^10*e^11 - 9240
0*a^4*b^3*c^7*d^9*e^12 + 72240*a^4*b^4*c^6*d^8*e^13 - 30240*a^4*b^5*c^5*d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 +
1680*a^4*b^7*c^3*d^5*e^16 - 560*a^4*b^8*c^2*d^4*e^17 + 50736*a^5*b^2*c^7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^1
4 + 32928*a^5*b^4*c^5*d^6*e^15 - 9408*a^5*b^5*c^4*d^5*e^16 + 112*a^5*b^6*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^
18 + 20384*a^6*b^2*c^6*d^6*e^15 - 17248*a^6*b^3*c^5*d^5*e^16 + 7616*a^6*b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^
3*e^18 - 224*a^6*b^6*c^2*d^2*e^19 + 3616*a^7*b^2*c^5*d^4*e^17 - 2752*a^7*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^
2*e^19 + 168*a^8*b^2*c^4*d^2*e^19 - 864*a*b*c^12*d^17*e^4 + 160*a^9*b*c^4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 -
6848*a*b^3*c^10*d^15*e^6 + 7776*a*b^4*c^9*d^14*e^7 - 3136*a*b^5*c^8*d^13*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*
a*b^7*c^6*d^11*e^10 - 5632*a*b^8*c^5*d^10*e^11 + 2464*a*b^9*c^4*d^9*e^12 - 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11
*c^2*d^7*e^14 - 5888*a^2*b*c^11*d^15*e^6 - 17024*a^3*b*c^10*d^13*e^8 - 26880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b
*c^8*d^9*e^12 - 12544*a^6*b*c^7*d^7*e^14 - 2688*a^7*b*c^6*d^5*e^16 + 64*a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3
*e^18 - 296*a^8*b^3*c^3*d*e^20))*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) +
20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*
e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*
a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(
-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 +
70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/
2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^1
0 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^
8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80
*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^
7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*
d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8
+ 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75
*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^
3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2) + 32*
c^12*d^13*e^3 - 16*a^6*b*c^5*e^16 + 192*a*c^11*d^11*e^5 + 32*a^6*c^6*d*e^15 - 208*b*c^11*d^12*e^4 + 480*a^2*c^
10*d^9*e^7 + 640*a^3*c^9*d^7*e^9 + 480*a^4*c^8*d^5*e^11 + 192*a^5*c^7*d^3*e^13 + 576*b^2*c^10*d^11*e^5 - 880*b
^3*c^9*d^10*e^6 + 800*b^4*c^8*d^9*e^7 - 432*b^5*c^7*d^8*e^8 + 128*b^6*c^6*d^7*e^9 - 16*b^7*c^5*d^6*e^10 + 3840
*a^2*b^2*c^8*d^7*e^9 - 3360*a^2*b^3*c^7*d^6*e^10 + 1440*a^2*b^4*c^6*d^5*e^11 - 240*a^2*b^5*c^5*d^4*e^12 + 2880
*a^3*b^2*c^7*d^5*e^11 - 1600*a^3*b^3*c^6*d^4*e^12 + 320*a^3*b^4*c^5*d^3*e^13 + 960*a^4*b^2*c^6*d^3*e^13 - 240*
a^4*b^3*c^5*d^2*e^14 - 1056*a*b*c^10*d^10*e^6 + 2400*a*b^2*c^9*d^9*e^7 - 2880*a*b^3*c^8*d^8*e^8 + 1920*a*b^4*c
^7*d^7*e^9 - 672*a*b^5*c^6*d^6*e^10 + 96*a*b^6*c^5*d^5*e^11 - 2160*a^2*b*c^9*d^8*e^8 - 2240*a^3*b*c^8*d^6*e^10
- 1200*a^4*b*c^7*d^4*e^12 - 288*a^5*b*c^6*d^2*e^14 + 96*a^5*b^2*c^5*d*e^15))*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 -
b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4
*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 +
10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e
^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4
*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*
e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4
*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 -
8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 -
10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80
*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4
+ 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*
a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e +
40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4
- 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d
^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*2i - ((2*e)/(3*(a*e^2 + c*d^2 - b*d*e)) - (2*e*(b*e - 2*c*d)*(d + e*x)
)/(a*e^2 + c*d^2 - b*d*e)^2)/(d + e*x)^(3/2)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)**(5/2)/(c*x**2+b*x+a),x)

[Out]

Timed out

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