∫ b+2cx______ (d+ex)3∕2(a+bx+cx2)2 dx

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

Optimal. Leaf size=469 \[ \frac {3 \sqrt {c} e \left (-2 c e \left (d \sqrt {b^2-4 a c}+a e+b d\right )+b e^2 \left (\sqrt {b^2-4 a c}+b\right )+2 c^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )}}\right )}{\sqrt {2} \sqrt {b^2-4 a c} \sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )} \left (a e^2-b d e+c d^2\right )^2}-\frac {3 \sqrt {c} e \left (-2 c e \left (-d \sqrt {b^2-4 a c}+a e+b d\right )+b e^2 \left (b-\sqrt {b^2-4 a c}\right )+2 c^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}\right )}{\sqrt {2} \sqrt {b^2-4 a c} \sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )} \left (a e^2-b d e+c d^2\right )^2}-\frac {\left (b^2-4 a c\right ) (c d-b e)-c e x \left (b^2-4 a c\right )}{\left (b^2-4 a c\right ) \sqrt {d+e x} \left (a+b x+c x^2\right ) \left (a e^2-b d e+c d^2\right )}+\frac {3 e^2 (2 c d-b e)}{\sqrt {d+e x} \left (a e^2-b d e+c d^2\right )^2} \]

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Rubi [A] time = 1.72, antiderivative size = 469, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 5, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.179, Rules used = {822, 828, 826, 1166, 208} \begin {gather*} \frac {3 \sqrt {c} e \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 {2} \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 {3 \sqrt {c} e \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} \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 {\left (b^2-4 a c\right ) (c d-b e)-c e x \left (b^2-4 a c\right )}{\left (b^2-4 a c\right ) \sqrt {d+e x} \left (a+b x+c x^2\right ) \left (a e^2-b d e+c d^2\right )}+\frac {3 e^2 (2 c d-b e)}{\sqrt {d+e x} \left (a e^2-b d e+c d^2\right )^2} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

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

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

qrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*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) - (3*Sqrt[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]*Sqr

t[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 822

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp

[((d + e*x)^(m + 1)*(f*(b*c*d - b^2*e + 2*a*c*e) - a*g*(2*c*d - b*e) + c*(f*(2*c*d - b*e) - g*(b*d - 2*a*e))*x

)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)), x] + Dist[1/((p + 1)*(b^2 - 4*a*

c)*(c*d^2 - b*d*e + a*e^2)), Int[(d + e*x)^m*(a + b*x + c*x^2)^(p + 1)*Simp[f*(b*c*d*e*(2*p - m + 2) + b^2*e^2

*(p + m + 2) - 2*c^2*d^2*(2*p + 3) - 2*a*c*e^2*(m + 2*p + 3)) - g*(a*e*(b*e - 2*c*d*m + b*e*m) - b*d*(3*c*d -

b*e + 2*c*d*p - b*e*p)) + c*e*(g*(b*d - 2*a*e) - f*(2*c*d - b*e))*(m + 2*p + 4)*x, x], 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] && LtQ[p, -1] && (IntegerQ[m] ||

IntegerQ[p] || IntegersQ[2*m, 2*p])

Rule 826

Int[((f_.) + (g_.)*(x_))/(Sqrt[(d_.) + (e_.)*(x_)]*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)), x_Symbol] :> Dist[2,

Subst[Int[(e*f - d*g + g*x^2)/(c*d^2 - b*d*e + a*e^2 - (2*c*d - b*e)*x^2 + c*x^4), x], x, Sqrt[d + e*x]], x] /

; FreeQ[{a, b, c, d, e, f, g}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0]

Rule 828

Int[(((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_)))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Simp[((

e*f - d*g)*(d + e*x)^(m + 1))/((m + 1)*(c*d^2 - b*d*e + a*e^2)), x] + Dist[1/(c*d^2 - b*d*e + a*e^2), Int[((d

+ e*x)^(m + 1)*Simp[c*d*f - f*b*e + a*e*g - c*(e*f - d*g)*x, x])/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c,

d, e, f, g, m}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && FractionQ[m] && LtQ[m, -1]

Rule 1166

Int[((d_) + (e_.)*(x_)^2)/((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4), x_Symbol] :> With[{q = Rt[b^2 - 4*a*c, 2]}, Di

st[e/2 + (2*c*d - b*e)/(2*q), Int[1/(b/2 - q/2 + c*x^2), x], x] + Dist[e/2 - (2*c*d - b*e)/(2*q), Int[1/(b/2 +

q/2 + c*x^2), x], x]] /; FreeQ[{a, b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - a*e^2, 0] && PosQ[b^

2 - 4*a*c]

Rubi steps

\begin {align*} \int \frac {b+2 c x}{(d+e x)^{3/2} \left (a+b x+c x^2\right )^2} \, dx &=-\frac {\left (b^2-4 a c\right ) (c d-b e)-c \left (b^2-4 a c\right ) e x}{\left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \sqrt {d+e x} \left (a+b x+c x^2\right )}-\frac {\int \frac {\frac {3}{2} \left (b^2-4 a c\right ) e (c d-b e)-\frac {3}{2} c \left (b^2-4 a c\right ) e^2 x}{(d+e x)^{3/2} \left (a+b x+c x^2\right )} \, dx}{\left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )}\\ &=\frac {3 e^2 (2 c d-b e)}{\left (c d^2-b d e+a e^2\right )^2 \sqrt {d+e x}}-\frac {\left (b^2-4 a c\right ) (c d-b e)-c \left (b^2-4 a c\right ) e x}{\left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \sqrt {d+e x} \left (a+b x+c x^2\right )}-\frac {\int \frac {\frac {3}{2} \left (b^2-4 a c\right ) e \left (c^2 d^2+b^2 e^2-c e (2 b d+a e)\right )-\frac {3}{2} c \left (b^2-4 a c\right ) e^2 (2 c d-b e) x}{\sqrt {d+e x} \left (a+b x+c x^2\right )} \, dx}{\left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )^2}\\ &=\frac {3 e^2 (2 c d-b e)}{\left (c d^2-b d e+a e^2\right )^2 \sqrt {d+e x}}-\frac {\left (b^2-4 a c\right ) (c d-b e)-c \left (b^2-4 a c\right ) e x}{\left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \sqrt {d+e x} \left (a+b x+c x^2\right )}-\frac {2 \operatorname {Subst}\left (\int \frac {\frac {3}{2} c \left (b^2-4 a c\right ) d e^2 (2 c d-b e)+\frac {3}{2} \left (b^2-4 a c\right ) e^2 \left (c^2 d^2+b^2 e^2-c e (2 b d+a e)\right )-\frac {3}{2} c \left (b^2-4 a c\right ) e^2 (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 (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )^2}\\ &=\frac {3 e^2 (2 c d-b e)}{\left (c d^2-b d e+a e^2\right )^2 \sqrt {d+e x}}-\frac {\left (b^2-4 a c\right ) (c d-b e)-c \left (b^2-4 a c\right ) e x}{\left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \sqrt {d+e x} \left (a+b x+c x^2\right )}+\frac {\left (3 c e \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 )}{2 \sqrt {b^2-4 a c} \left (c d^2-b d e+a e^2\right )^2}-\frac {\left (3 c e \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 )}{2 \sqrt {b^2-4 a c} \left (c d^2-b d e+a e^2\right )^2}\\ &=\frac {3 e^2 (2 c d-b e)}{\left (c d^2-b d e+a e^2\right )^2 \sqrt {d+e x}}-\frac {\left (b^2-4 a c\right ) (c d-b e)-c \left (b^2-4 a c\right ) e x}{\left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \sqrt {d+e x} \left (a+b x+c x^2\right )}+\frac {3 \sqrt {c} e \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 {2} \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 {3 \sqrt {c} e \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 {2} \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 = 2.63, size = 381, normalized size = 0.81 \begin {gather*} \frac {\frac {3 \sqrt {2} \sqrt {c} e \left (\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}}-\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 )}}\right )}{\sqrt {b^2-4 a c}}+\frac {2 \left (e (a e-b d)+c d^2\right ) (b e-c d+c e x)}{\sqrt {d+e x} (a+x (b+c x))}-\frac {6 e^2 (b e-2 c d)}{\sqrt {d+e x}}}{2 \left (e (a e-b d)+c d^2\right )^2} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

((-6*e^2*(-2*c*d + b*e))/Sqrt[d + e*x] + (2*(c*d^2 + e*(-(b*d) + a*e))*(-(c*d) + b*e + c*e*x))/(Sqrt[d + e*x]*

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

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IntegrateAlgebraic [A] time = 5.02, size = 655, normalized size = 1.40 \begin {gather*} -\frac {3 \left (-2 \sqrt {2} c^{3/2} d e^2 \sqrt {b^2-4 a c}+\sqrt {2} b \sqrt {c} e^3 \sqrt {b^2-4 a c}-2 \sqrt {2} a c^{3/2} e^3+\sqrt {2} b^2 \sqrt {c} e^3-2 \sqrt {2} b c^{3/2} d e^2+2 \sqrt {2} c^{5/2} d^2 e\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {-e \sqrt {b^2-4 a c}+b e-2 c d}}\right )}{2 \sqrt {b^2-4 a c} \sqrt {-e \sqrt {b^2-4 a c}+b e-2 c d} \left (-a e^2+b d e-c d^2\right )^2}-\frac {3 \left (-2 \sqrt {2} c^{3/2} d e^2 \sqrt {b^2-4 a c}+\sqrt {2} b \sqrt {c} e^3 \sqrt {b^2-4 a c}+2 \sqrt {2} a c^{3/2} e^3-\sqrt {2} b^2 \sqrt {c} e^3+2 \sqrt {2} b c^{3/2} d e^2-2 \sqrt {2} c^{5/2} d^2 e\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {e \sqrt {b^2-4 a c}+b e-2 c d}}\right )}{2 \sqrt {b^2-4 a c} \sqrt {e \sqrt {b^2-4 a c}+b e-2 c d} \left (-a e^2+b d e-c d^2\right )^2}-\frac {e^2 \left (2 a b e^3-a c e^2 (d+e x)-4 a c d e^2+3 b^2 e^2 (d+e x)-2 b^2 d e^2+6 b c d^2 e-11 b c d e (d+e x)+3 b c e (d+e x)^2-4 c^2 d^3+11 c^2 d^2 (d+e x)-6 c^2 d (d+e x)^2\right )}{\sqrt {d+e x} \left (a e^2-b d e+c d^2\right )^2 \left (a e^2+b e (d+e x)-b d e+c d^2-2 c d (d+e x)+c (d+e x)^2\right )} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

-((e^2*(-4*c^2*d^3 + 6*b*c*d^2*e - 2*b^2*d*e^2 - 4*a*c*d*e^2 + 2*a*b*e^3 + 11*c^2*d^2*(d + e*x) - 11*b*c*d*e*(

d + e*x) + 3*b^2*e^2*(d + e*x) - a*c*e^2*(d + e*x) - 6*c^2*d*(d + e*x)^2 + 3*b*c*e*(d + e*x)^2))/((c*d^2 - b*d

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

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

Sqrt[c]*e^3 - 2*Sqrt[2]*a*c^(3/2)*e^3 + Sqrt[2]*b*Sqrt[c]*Sqrt[b^2 - 4*a*c]*e^3)*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[

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

]*e]*(-(c*d^2) + b*d*e - a*e^2)^2) - (3*(-2*Sqrt[2]*c^(5/2)*d^2*e + 2*Sqrt[2]*b*c^(3/2)*d*e^2 - 2*Sqrt[2]*c^(3

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

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

*a*c]*Sqrt[-2*c*d + b*e + Sqrt[b^2 - 4*a*c]*e]*(-(c*d^2) + b*d*e - a*e^2)^2)

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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giac [B] time = 8.04, size = 1441, normalized size = 3.07

result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*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)))*e/((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)) - 3*sqrt(-4*c^2*d + 2*(b*c + sq

rt(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)))*e/((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)) + (6*(x*e + d)^2*c^2*d*e^2 - 11*(x*e + d)*c^2*d^2*e^2 + 4*c^

2*d^3*e^2 - 3*(x*e + d)^2*b*c*e^3 + 11*(x*e + d)*b*c*d*e^3 - 6*b*c*d^2*e^3 - 3*(x*e + d)*b^2*e^4 + (x*e + d)*a

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

(x*e + d)*b*d*e + sqrt(x*e + d)*a*e^2))

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maple [B] time = 0.14, size = 1758, normalized size = 3.75

result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

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

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

/(a*e^2-b*d*e+c*d^2)^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

h((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*c^2+3/2*e^4/(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^2-3*e^3/(a*e^2-b*d*e+c*d^2)^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*c^2*d+3*e^2/(a*e^2-b*d*e+c*d^2)^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)*c^3*d^2+3/2*e^3/(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-3*e^2/(a*e^2-b*d*e+c*d^2)^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)*c^2*d-3*e^4/(a*e^2-b*d*e+c*d^2)^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*c^2+

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

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

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

e+c*d^2)^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)*c^2*d-2*e^3/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)^(1/2)*b+4*e^2/(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 \begin {gather*} \int \frac {2 \, c x + b}{{\left (c x^{2} + b x + a\right )}^{2} {\left (e x + d\right )}^{\frac {3}{2}}}\,{d x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [B] time = 10.41, size = 58573, normalized size = 124.89

result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

- atan((((-(9*(b^7*e^7 + b^4*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^7 + 8*a*c^6*d^5*e^2 + 40*a^3*c^4*d*

e^6 + 25*a^2*b^3*c^2*e^7 + a^2*c^2*e^7*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^4 - 2*b^2*c^5*d^5*e^2 + 5*b

^3*c^4*d^4*e^3 - 10*b^4*c^3*d^3*e^4 + 10*b^5*c^2*d^2*e^5 + 5*c^4*d^4*e^3*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c*

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

0*a*b*c^5*d^4*e^3 + 40*a*b^4*c^2*d*e^6 - 5*b^3*c*d*e^6*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^4 - 70*a*

b^3*c^3*d^2*e^5 + 120*a^2*b*c^4*d^2*e^5 - 90*a^2*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 1

0*b*c^3*d^3*e^4*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(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 + 6

0*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)*(-(9*(b^7*e^7 + b^4*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^7 + 8*a*c^6*d^5*e^2 + 40*a^3*c^4*d*e^

6 + 25*a^2*b^3*c^2*e^7 + a^2*c^2*e^7*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^4 - 2*b^2*c^5*d^5*e^2 + 5*b^3

*c^4*d^4*e^3 - 10*b^4*c^3*d^3*e^4 + 10*b^5*c^2*d^2*e^5 + 5*c^4*d^4*e^3*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c*e^

7 - 5*b^6*c*d*e^6 + 10*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*

a*b*c^5*d^4*e^3 + 40*a*b^4*c^2*d*e^6 - 5*b^3*c*d*e^6*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^4 - 70*a*b^

3*c^3*d^2*e^5 + 120*a^2*b*c^4*d^2*e^5 - 90*a^2*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 10*

b*c^3*d^3*e^4*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(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^1

2*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 - 2304

0*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 + 7

392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^

15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d

^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5

*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*

b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*

c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c

^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5

*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^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) - 48*a^10*c^4*e^22 + 144*a*c^13*d^18*e^4 - 12*a^8*b^4

*c^2*e^22 + 60*a^9*b^2*c^3*e^22 + 1104*a^2*c^12*d^16*e^6 + 3648*a^3*c^11*d^14*e^8 + 6720*a^4*c^10*d^12*e^10 +

7392*a^5*c^9*d^10*e^12 + 4704*a^6*c^8*d^8*e^14 + 1344*a^7*c^7*d^6*e^16 - 192*a^8*c^6*d^4*e^18 - 240*a^9*c^5*d^

2*e^20 - 36*b^2*c^12*d^18*e^4 + 324*b^3*c^11*d^17*e^5 - 1308*b^4*c^10*d^16*e^6 + 3120*b^5*c^9*d^15*e^7 - 4872*

b^6*c^8*d^14*e^8 + 5208*b^7*c^7*d^13*e^9 - 3864*b^8*c^6*d^12*e^10 + 1968*b^9*c^5*d^11*e^11 - 660*b^10*c^4*d^10

*e^12 + 132*b^11*c^3*d^9*e^13 - 12*b^12*c^2*d^8*e^14 + 30384*a^2*b^2*c^10*d^14*e^8 - 58128*a^2*b^3*c^9*d^13*e^

9 + 65856*a^2*b^4*c^8*d^12*e^10 - 41328*a^2*b^5*c^7*d^11*e^11 + 7392*a^2*b^6*c^6*d^10*e^12 + 8976*a^2*b^7*c^5*

d^9*e^13 - 7632*a^2*b^8*c^4*d^8*e^14 + 2544*a^2*b^9*c^3*d^7*e^15 - 336*a^2*b^10*c^2*d^6*e^16 + 76272*a^3*b^2*c

^9*d^12*e^10 - 125664*a^3*b^3*c^8*d^11*e^11 + 121968*a^3*b^4*c^7*d^10*e^12 - 66528*a^3*b^5*c^6*d^9*e^13 + 1377

6*a^3*b^6*c^5*d^8*e^14 + 5088*a^3*b^7*c^4*d^7*e^15 - 3696*a^3*b^8*c^3*d^6*e^16 + 672*a^3*b^9*c^2*d^5*e^17 + 10

1640*a^4*b^2*c^8*d^10*e^12 - 138600*a^4*b^3*c^7*d^9*e^13 + 108360*a^4*b^4*c^6*d^8*e^14 - 45360*a^4*b^5*c^5*d^7

*e^15 + 5880*a^4*b^6*c^4*d^6*e^16 + 2520*a^4*b^7*c^3*d^5*e^17 - 840*a^4*b^8*c^2*d^4*e^18 + 76104*a^5*b^2*c^7*d

^8*e^14 - 82656*a^5*b^3*c^6*d^7*e^15 + 49392*a^5*b^4*c^5*d^6*e^16 - 14112*a^5*b^5*c^4*d^5*e^17 + 168*a^5*b^6*c

^3*d^4*e^18 + 672*a^5*b^7*c^2*d^3*e^19 + 30576*a^6*b^2*c^6*d^6*e^16 - 25872*a^6*b^3*c^5*d^5*e^17 + 11424*a^6*b

^4*c^4*d^4*e^18 - 1680*a^6*b^5*c^3*d^3*e^19 - 336*a^6*b^6*c^2*d^2*e^20 + 5424*a^7*b^2*c^5*d^4*e^18 - 4128*a^7*

b^3*c^4*d^3*e^19 + 1296*a^7*b^4*c^3*d^2*e^20 + 252*a^8*b^2*c^4*d^2*e^20 - 1296*a*b*c^12*d^17*e^5 + 240*a^9*b*c

^4*d*e^21 + 4956*a*b^2*c^11*d^16*e^6 - 10272*a*b^3*c^10*d^15*e^7 + 11664*a*b^4*c^9*d^14*e^8 - 4704*a*b^5*c^8*d

^13*e^9 - 5880*a*b^6*c^7*d^12*e^10 + 10944*a*b^7*c^6*d^11*e^11 - 8448*a*b^8*c^5*d^10*e^12 + 3696*a*b^9*c^4*d^9

*e^13 - 900*a*b^10*c^3*d^8*e^14 + 96*a*b^11*c^2*d^7*e^15 - 8832*a^2*b*c^11*d^15*e^7 - 25536*a^3*b*c^10*d^13*e^

9 - 40320*a^4*b*c^9*d^11*e^11 - 36960*a^5*b*c^8*d^9*e^13 - 18816*a^6*b*c^7*d^7*e^15 - 4032*a^7*b*c^6*d^5*e^17

+ 96*a^7*b^5*c^2*d*e^21 + 384*a^8*b*c^5*d^3*e^19 - 444*a^8*b^3*c^3*d*e^21) - (d + e*x)^(1/2)*(288*b*c^12*d^15*

e^5 - 36*c^13*d^16*e^4 - 36*a^8*c^5*e^20 - 18*a^6*b^4*c^3*e^20 + 72*a^7*b^2*c^4*e^20 + 720*a^2*c^11*d^12*e^8 +

2304*a^3*c^10*d^10*e^10 + 3240*a^4*c^9*d^8*e^12 + 2304*a^5*c^8*d^6*e^14 + 720*a^6*c^7*d^4*e^16 - 1080*b^2*c^1

1*d^14*e^6 + 2520*b^3*c^10*d^13*e^7 - 4050*b^4*c^9*d^12*e^8 + 4644*b^5*c^8*d^11*e^9 - 3798*b^6*c^7*d^10*e^10 +

2160*b^7*c^6*d^9*e^11 - 810*b^8*c^5*d^8*e^12 + 180*b^9*c^4*d^7*e^13 - 18*b^10*c^3*d^6*e^14 + 10152*a^2*b^2*c^

9*d^10*e^10 - 11160*a^2*b^3*c^8*d^9*e^11 + 4050*a^2*b^4*c^7*d^8*e^12 + 3240*a^2*b^5*c^6*d^7*e^13 - 4140*a^2*b^

6*c^5*d^6*e^14 + 1728*a^2*b^7*c^4*d^5*e^15 - 270*a^2*b^8*c^3*d^4*e^16 + 22680*a^3*b^2*c^8*d^8*e^12 - 21600*a^3

*b^3*c^7*d^7*e^13 + 9000*a^3*b^4*c^6*d^6*e^14 + 216*a^3*b^5*c^5*d^5*e^15 - 1440*a^3*b^6*c^4*d^4*e^16 + 360*a^3

*b^7*c^3*d^3*e^17 + 19800*a^4*b^2*c^7*d^6*e^14 - 14040*a^4*b^3*c^6*d^5*e^15 + 4050*a^4*b^4*c^5*d^4*e^16 + 180*

a^4*b^5*c^4*d^3*e^17 - 270*a^4*b^6*c^3*d^2*e^18 + 7560*a^5*b^2*c^6*d^4*e^16 - 3600*a^5*b^3*c^5*d^3*e^17 + 540*

a^5*b^4*c^4*d^2*e^18 + 1080*a^6*b^2*c^5*d^2*e^18 - 360*a*b^2*c^10*d^12*e^8 + 2160*a*b^3*c^9*d^11*e^9 - 5508*a*

b^4*c^8*d^10*e^10 + 7740*a*b^5*c^7*d^9*e^11 - 6480*a*b^6*c^6*d^8*e^12 + 3240*a*b^7*c^5*d^7*e^13 - 900*a*b^8*c^

4*d^6*e^14 + 108*a*b^9*c^3*d^5*e^15 - 4320*a^2*b*c^10*d^11*e^9 - 11520*a^3*b*c^9*d^9*e^11 - 12960*a^4*b*c^8*d^

7*e^13 - 6912*a^5*b*c^7*d^5*e^15 + 108*a^5*b^5*c^3*d*e^19 - 1440*a^6*b*c^6*d^3*e^17 - 360*a^6*b^3*c^4*d*e^19))

*(-(9*(b^7*e^7 + b^4*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^7 + 8*a*c^6*d^5*e^2 + 40*a^3*c^4*d*e^6 + 25

*a^2*b^3*c^2*e^7 + a^2*c^2*e^7*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^4 - 2*b^2*c^5*d^5*e^2 + 5*b^3*c^4*d

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

b^6*c*d*e^6 + 10*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a*b*c^

5*d^4*e^3 + 40*a*b^4*c^2*d*e^6 - 5*b^3*c*d*e^6*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^4 - 70*a*b^3*c^3*

d^2*e^5 + 120*a^2*b*c^4*d^2*e^5 - 90*a^2*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*

d^3*e^4*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(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 - ((-(9*(b^7*e^

7 + b^4*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^7 + 8*a*c^6*d^5*e^2 + 40*a^3*c^4*d*e^6 + 25*a^2*b^3*c^2*

e^7 + a^2*c^2*e^7*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^4 - 2*b^2*c^5*d^5*e^2 + 5*b^3*c^4*d^4*e^3 - 10*b

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

10*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a*b*c^5*d^4*e^3 + 4

0*a*b^4*c^2*d*e^6 - 5*b^3*c*d*e^6*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^4 - 70*a*b^3*c^3*d^2*e^5 + 120

*a^2*b*c^4*d^2*e^5 - 90*a^2*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^4*(-(4*

a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(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)*(144*a*c^13*d^18*e^4 - 48*a^10*

c^4*e^22 - (d + e*x)^(1/2)*(-(9*(b^7*e^7 + b^4*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^7 + 8*a*c^6*d^5*e

^2 + 40*a^3*c^4*d*e^6 + 25*a^2*b^3*c^2*e^7 + a^2*c^2*e^7*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^4 - 2*b^2

*c^5*d^5*e^2 + 5*b^3*c^4*d^4*e^3 - 10*b^4*c^3*d^3*e^4 + 10*b^5*c^2*d^2*e^5 + 5*c^4*d^4*e^3*(-(4*a*c - b^2)^3)^

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

b^2)^3)^(1/2) - 20*a*b*c^5*d^4*e^3 + 40*a*b^4*c^2*d*e^6 - 5*b^3*c*d*e^6*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c

^4*d^3*e^4 - 70*a*b^3*c^3*d^2*e^5 + 120*a^2*b*c^4*d^2*e^5 - 90*a^2*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c -

b^2)^3)^(1/2) - 10*b*c^3*d^3*e^4*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(1

6*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^1

9*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 + 57

12*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^1

6*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^1

0 - 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^1

1*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 - 22680

0*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^1

7*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^1

1 - 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) - 12*a^8*b^4*c^2*e^22 + 60*a^9*b^

2*c^3*e^22 + 1104*a^2*c^12*d^16*e^6 + 3648*a^3*c^11*d^14*e^8 + 6720*a^4*c^10*d^12*e^10 + 7392*a^5*c^9*d^10*e^1

2 + 4704*a^6*c^8*d^8*e^14 + 1344*a^7*c^7*d^6*e^16 - 192*a^8*c^6*d^4*e^18 - 240*a^9*c^5*d^2*e^20 - 36*b^2*c^12*

d^18*e^4 + 324*b^3*c^11*d^17*e^5 - 1308*b^4*c^10*d^16*e^6 + 3120*b^5*c^9*d^15*e^7 - 4872*b^6*c^8*d^14*e^8 + 52

08*b^7*c^7*d^13*e^9 - 3864*b^8*c^6*d^12*e^10 + 1968*b^9*c^5*d^11*e^11 - 660*b^10*c^4*d^10*e^12 + 132*b^11*c^3*

d^9*e^13 - 12*b^12*c^2*d^8*e^14 + 30384*a^2*b^2*c^10*d^14*e^8 - 58128*a^2*b^3*c^9*d^13*e^9 + 65856*a^2*b^4*c^8

*d^12*e^10 - 41328*a^2*b^5*c^7*d^11*e^11 + 7392*a^2*b^6*c^6*d^10*e^12 + 8976*a^2*b^7*c^5*d^9*e^13 - 7632*a^2*b

^8*c^4*d^8*e^14 + 2544*a^2*b^9*c^3*d^7*e^15 - 336*a^2*b^10*c^2*d^6*e^16 + 76272*a^3*b^2*c^9*d^12*e^10 - 125664

*a^3*b^3*c^8*d^11*e^11 + 121968*a^3*b^4*c^7*d^10*e^12 - 66528*a^3*b^5*c^6*d^9*e^13 + 13776*a^3*b^6*c^5*d^8*e^1

4 + 5088*a^3*b^7*c^4*d^7*e^15 - 3696*a^3*b^8*c^3*d^6*e^16 + 672*a^3*b^9*c^2*d^5*e^17 + 101640*a^4*b^2*c^8*d^10

*e^12 - 138600*a^4*b^3*c^7*d^9*e^13 + 108360*a^4*b^4*c^6*d^8*e^14 - 45360*a^4*b^5*c^5*d^7*e^15 + 5880*a^4*b^6*

c^4*d^6*e^16 + 2520*a^4*b^7*c^3*d^5*e^17 - 840*a^4*b^8*c^2*d^4*e^18 + 76104*a^5*b^2*c^7*d^8*e^14 - 82656*a^5*b

^3*c^6*d^7*e^15 + 49392*a^5*b^4*c^5*d^6*e^16 - 14112*a^5*b^5*c^4*d^5*e^17 + 168*a^5*b^6*c^3*d^4*e^18 + 672*a^5

*b^7*c^2*d^3*e^19 + 30576*a^6*b^2*c^6*d^6*e^16 - 25872*a^6*b^3*c^5*d^5*e^17 + 11424*a^6*b^4*c^4*d^4*e^18 - 168

0*a^6*b^5*c^3*d^3*e^19 - 336*a^6*b^6*c^2*d^2*e^20 + 5424*a^7*b^2*c^5*d^4*e^18 - 4128*a^7*b^3*c^4*d^3*e^19 + 12

96*a^7*b^4*c^3*d^2*e^20 + 252*a^8*b^2*c^4*d^2*e^20 - 1296*a*b*c^12*d^17*e^5 + 240*a^9*b*c^4*d*e^21 + 4956*a*b^

2*c^11*d^16*e^6 - 10272*a*b^3*c^10*d^15*e^7 + 11664*a*b^4*c^9*d^14*e^8 - 4704*a*b^5*c^8*d^13*e^9 - 5880*a*b^6*

c^7*d^12*e^10 + 10944*a*b^7*c^6*d^11*e^11 - 8448*a*b^8*c^5*d^10*e^12 + 3696*a*b^9*c^4*d^9*e^13 - 900*a*b^10*c^

3*d^8*e^14 + 96*a*b^11*c^2*d^7*e^15 - 8832*a^2*b*c^11*d^15*e^7 - 25536*a^3*b*c^10*d^13*e^9 - 40320*a^4*b*c^9*d

^11*e^11 - 36960*a^5*b*c^8*d^9*e^13 - 18816*a^6*b*c^7*d^7*e^15 - 4032*a^7*b*c^6*d^5*e^17 + 96*a^7*b^5*c^2*d*e^

21 + 384*a^8*b*c^5*d^3*e^19 - 444*a^8*b^3*c^3*d*e^21) + (d + e*x)^(1/2)*(288*b*c^12*d^15*e^5 - 36*c^13*d^16*e^

4 - 36*a^8*c^5*e^20 - 18*a^6*b^4*c^3*e^20 + 72*a^7*b^2*c^4*e^20 + 720*a^2*c^11*d^12*e^8 + 2304*a^3*c^10*d^10*e

^10 + 3240*a^4*c^9*d^8*e^12 + 2304*a^5*c^8*d^6*e^14 + 720*a^6*c^7*d^4*e^16 - 1080*b^2*c^11*d^14*e^6 + 2520*b^3

*c^10*d^13*e^7 - 4050*b^4*c^9*d^12*e^8 + 4644*b^5*c^8*d^11*e^9 - 3798*b^6*c^7*d^10*e^10 + 2160*b^7*c^6*d^9*e^1

1 - 810*b^8*c^5*d^8*e^12 + 180*b^9*c^4*d^7*e^13 - 18*b^10*c^3*d^6*e^14 + 10152*a^2*b^2*c^9*d^10*e^10 - 11160*a

^2*b^3*c^8*d^9*e^11 + 4050*a^2*b^4*c^7*d^8*e^12 + 3240*a^2*b^5*c^6*d^7*e^13 - 4140*a^2*b^6*c^5*d^6*e^14 + 1728

*a^2*b^7*c^4*d^5*e^15 - 270*a^2*b^8*c^3*d^4*e^16 + 22680*a^3*b^2*c^8*d^8*e^12 - 21600*a^3*b^3*c^7*d^7*e^13 + 9

000*a^3*b^4*c^6*d^6*e^14 + 216*a^3*b^5*c^5*d^5*e^15 - 1440*a^3*b^6*c^4*d^4*e^16 + 360*a^3*b^7*c^3*d^3*e^17 + 1

9800*a^4*b^2*c^7*d^6*e^14 - 14040*a^4*b^3*c^6*d^5*e^15 + 4050*a^4*b^4*c^5*d^4*e^16 + 180*a^4*b^5*c^4*d^3*e^17

- 270*a^4*b^6*c^3*d^2*e^18 + 7560*a^5*b^2*c^6*d^4*e^16 - 3600*a^5*b^3*c^5*d^3*e^17 + 540*a^5*b^4*c^4*d^2*e^18

+ 1080*a^6*b^2*c^5*d^2*e^18 - 360*a*b^2*c^10*d^12*e^8 + 2160*a*b^3*c^9*d^11*e^9 - 5508*a*b^4*c^8*d^10*e^10 + 7

740*a*b^5*c^7*d^9*e^11 - 6480*a*b^6*c^6*d^8*e^12 + 3240*a*b^7*c^5*d^7*e^13 - 900*a*b^8*c^4*d^6*e^14 + 108*a*b^

9*c^3*d^5*e^15 - 4320*a^2*b*c^10*d^11*e^9 - 11520*a^3*b*c^9*d^9*e^11 - 12960*a^4*b*c^8*d^7*e^13 - 6912*a^5*b*c

^7*d^5*e^15 + 108*a^5*b^5*c^3*d*e^19 - 1440*a^6*b*c^6*d^3*e^17 - 360*a^6*b^3*c^4*d*e^19))*(-(9*(b^7*e^7 + b^4*

e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^7 + 8*a*c^6*d^5*e^2 + 40*a^3*c^4*d*e^6 + 25*a^2*b^3*c^2*e^7 + a^

2*c^2*e^7*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^4 - 2*b^2*c^5*d^5*e^2 + 5*b^3*c^4*d^4*e^3 - 10*b^4*c^3*d

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

c^2*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a*b*c^5*d^4*e^3 + 40*a*b^4*

c^2*d*e^6 - 5*b^3*c*d*e^6*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^4 - 70*a*b^3*c^3*d^2*e^5 + 120*a^2*b*c

^4*d^2*e^5 - 90*a^2*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^4*(-(4*a*c - b^

2)^3)^(1/2) + 10*a*b*c^2*d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(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)/(108*c^12*d^13*e^6 - ((-(9*(b^7*e^7

+ b^4*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^7 + 8*a*c^6*d^5*e^2 + 40*a^3*c^4*d*e^6 + 25*a^2*b^3*c^2*e

^7 + a^2*c^2*e^7*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^4 - 2*b^2*c^5*d^5*e^2 + 5*b^3*c^4*d^4*e^3 - 10*b^

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

10*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a*b*c^5*d^4*e^3 + 40

*a*b^4*c^2*d*e^6 - 5*b^3*c*d*e^6*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^4 - 70*a*b^3*c^3*d^2*e^5 + 120*

a^2*b*c^4*d^2*e^5 - 90*a^2*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^4*(-(4*a

*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(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)*(144*a*c^13*d^18*e^4 - 48*a^10*c

^4*e^22 - (d + e*x)^(1/2)*(-(9*(b^7*e^7 + b^4*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^7 + 8*a*c^6*d^5*e^

2 + 40*a^3*c^4*d*e^6 + 25*a^2*b^3*c^2*e^7 + a^2*c^2*e^7*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^4 - 2*b^2*

c^5*d^5*e^2 + 5*b^3*c^4*d^4*e^3 - 10*b^4*c^3*d^3*e^4 + 10*b^5*c^2*d^2*e^5 + 5*c^4*d^4*e^3*(-(4*a*c - b^2)^3)^(

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

b^2)^3)^(1/2) - 20*a*b*c^5*d^4*e^3 + 40*a*b^4*c^2*d*e^6 - 5*b^3*c*d*e^6*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^

4*d^3*e^4 - 70*a*b^3*c^3*d^2*e^5 + 120*a^2*b*c^4*d^2*e^5 - 90*a^2*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c -

b^2)^3)^(1/2) - 10*b*c^3*d^3*e^4*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(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 + 571

2*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 - 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^1

0 + 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) - 12*a^8*b^4*c^2*e^22 + 60*a^9*b^2

*c^3*e^22 + 1104*a^2*c^12*d^16*e^6 + 3648*a^3*c^11*d^14*e^8 + 6720*a^4*c^10*d^12*e^10 + 7392*a^5*c^9*d^10*e^12

+ 4704*a^6*c^8*d^8*e^14 + 1344*a^7*c^7*d^6*e^16 - 192*a^8*c^6*d^4*e^18 - 240*a^9*c^5*d^2*e^20 - 36*b^2*c^12*d

^18*e^4 + 324*b^3*c^11*d^17*e^5 - 1308*b^4*c^10*d^16*e^6 + 3120*b^5*c^9*d^15*e^7 - 4872*b^6*c^8*d^14*e^8 + 520

8*b^7*c^7*d^13*e^9 - 3864*b^8*c^6*d^12*e^10 + 1968*b^9*c^5*d^11*e^11 - 660*b^10*c^4*d^10*e^12 + 132*b^11*c^3*d

^9*e^13 - 12*b^12*c^2*d^8*e^14 + 30384*a^2*b^2*c^10*d^14*e^8 - 58128*a^2*b^3*c^9*d^13*e^9 + 65856*a^2*b^4*c^8*

d^12*e^10 - 41328*a^2*b^5*c^7*d^11*e^11 + 7392*a^2*b^6*c^6*d^10*e^12 + 8976*a^2*b^7*c^5*d^9*e^13 - 7632*a^2*b^

8*c^4*d^8*e^14 + 2544*a^2*b^9*c^3*d^7*e^15 - 336*a^2*b^10*c^2*d^6*e^16 + 76272*a^3*b^2*c^9*d^12*e^10 - 125664*

a^3*b^3*c^8*d^11*e^11 + 121968*a^3*b^4*c^7*d^10*e^12 - 66528*a^3*b^5*c^6*d^9*e^13 + 13776*a^3*b^6*c^5*d^8*e^14

+ 5088*a^3*b^7*c^4*d^7*e^15 - 3696*a^3*b^8*c^3*d^6*e^16 + 672*a^3*b^9*c^2*d^5*e^17 + 101640*a^4*b^2*c^8*d^10*

e^12 - 138600*a^4*b^3*c^7*d^9*e^13 + 108360*a^4*b^4*c^6*d^8*e^14 - 45360*a^4*b^5*c^5*d^7*e^15 + 5880*a^4*b^6*c

^4*d^6*e^16 + 2520*a^4*b^7*c^3*d^5*e^17 - 840*a^4*b^8*c^2*d^4*e^18 + 76104*a^5*b^2*c^7*d^8*e^14 - 82656*a^5*b^

3*c^6*d^7*e^15 + 49392*a^5*b^4*c^5*d^6*e^16 - 14112*a^5*b^5*c^4*d^5*e^17 + 168*a^5*b^6*c^3*d^4*e^18 + 672*a^5*

b^7*c^2*d^3*e^19 + 30576*a^6*b^2*c^6*d^6*e^16 - 25872*a^6*b^3*c^5*d^5*e^17 + 11424*a^6*b^4*c^4*d^4*e^18 - 1680

*a^6*b^5*c^3*d^3*e^19 - 336*a^6*b^6*c^2*d^2*e^20 + 5424*a^7*b^2*c^5*d^4*e^18 - 4128*a^7*b^3*c^4*d^3*e^19 + 129

6*a^7*b^4*c^3*d^2*e^20 + 252*a^8*b^2*c^4*d^2*e^20 - 1296*a*b*c^12*d^17*e^5 + 240*a^9*b*c^4*d*e^21 + 4956*a*b^2

*c^11*d^16*e^6 - 10272*a*b^3*c^10*d^15*e^7 + 11664*a*b^4*c^9*d^14*e^8 - 4704*a*b^5*c^8*d^13*e^9 - 5880*a*b^6*c

^7*d^12*e^10 + 10944*a*b^7*c^6*d^11*e^11 - 8448*a*b^8*c^5*d^10*e^12 + 3696*a*b^9*c^4*d^9*e^13 - 900*a*b^10*c^3

*d^8*e^14 + 96*a*b^11*c^2*d^7*e^15 - 8832*a^2*b*c^11*d^15*e^7 - 25536*a^3*b*c^10*d^13*e^9 - 40320*a^4*b*c^9*d^

11*e^11 - 36960*a^5*b*c^8*d^9*e^13 - 18816*a^6*b*c^7*d^7*e^15 - 4032*a^7*b*c^6*d^5*e^17 + 96*a^7*b^5*c^2*d*e^2

1 + 384*a^8*b*c^5*d^3*e^19 - 444*a^8*b^3*c^3*d*e^21) + (d + e*x)^(1/2)*(288*b*c^12*d^15*e^5 - 36*c^13*d^16*e^4

- 36*a^8*c^5*e^20 - 18*a^6*b^4*c^3*e^20 + 72*a^7*b^2*c^4*e^20 + 720*a^2*c^11*d^12*e^8 + 2304*a^3*c^10*d^10*e^

10 + 3240*a^4*c^9*d^8*e^12 + 2304*a^5*c^8*d^6*e^14 + 720*a^6*c^7*d^4*e^16 - 1080*b^2*c^11*d^14*e^6 + 2520*b^3*

c^10*d^13*e^7 - 4050*b^4*c^9*d^12*e^8 + 4644*b^5*c^8*d^11*e^9 - 3798*b^6*c^7*d^10*e^10 + 2160*b^7*c^6*d^9*e^11

- 810*b^8*c^5*d^8*e^12 + 180*b^9*c^4*d^7*e^13 - 18*b^10*c^3*d^6*e^14 + 10152*a^2*b^2*c^9*d^10*e^10 - 11160*a^

2*b^3*c^8*d^9*e^11 + 4050*a^2*b^4*c^7*d^8*e^12 + 3240*a^2*b^5*c^6*d^7*e^13 - 4140*a^2*b^6*c^5*d^6*e^14 + 1728*

a^2*b^7*c^4*d^5*e^15 - 270*a^2*b^8*c^3*d^4*e^16 + 22680*a^3*b^2*c^8*d^8*e^12 - 21600*a^3*b^3*c^7*d^7*e^13 + 90

00*a^3*b^4*c^6*d^6*e^14 + 216*a^3*b^5*c^5*d^5*e^15 - 1440*a^3*b^6*c^4*d^4*e^16 + 360*a^3*b^7*c^3*d^3*e^17 + 19

800*a^4*b^2*c^7*d^6*e^14 - 14040*a^4*b^3*c^6*d^5*e^15 + 4050*a^4*b^4*c^5*d^4*e^16 + 180*a^4*b^5*c^4*d^3*e^17 -

270*a^4*b^6*c^3*d^2*e^18 + 7560*a^5*b^2*c^6*d^4*e^16 - 3600*a^5*b^3*c^5*d^3*e^17 + 540*a^5*b^4*c^4*d^2*e^18 +

1080*a^6*b^2*c^5*d^2*e^18 - 360*a*b^2*c^10*d^12*e^8 + 2160*a*b^3*c^9*d^11*e^9 - 5508*a*b^4*c^8*d^10*e^10 + 77

40*a*b^5*c^7*d^9*e^11 - 6480*a*b^6*c^6*d^8*e^12 + 3240*a*b^7*c^5*d^7*e^13 - 900*a*b^8*c^4*d^6*e^14 + 108*a*b^9

*c^3*d^5*e^15 - 4320*a^2*b*c^10*d^11*e^9 - 11520*a^3*b*c^9*d^9*e^11 - 12960*a^4*b*c^8*d^7*e^13 - 6912*a^5*b*c^

7*d^5*e^15 + 108*a^5*b^5*c^3*d*e^19 - 1440*a^6*b*c^6*d^3*e^17 - 360*a^6*b^3*c^4*d*e^19))*(-(9*(b^7*e^7 + b^4*e

^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^7 + 8*a*c^6*d^5*e^2 + 40*a^3*c^4*d*e^6 + 25*a^2*b^3*c^2*e^7 + a^2

*c^2*e^7*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^4 - 2*b^2*c^5*d^5*e^2 + 5*b^3*c^4*d^4*e^3 - 10*b^4*c^3*d^

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

^2*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a*b*c^5*d^4*e^3 + 40*a*b^4*c

^2*d*e^6 - 5*b^3*c*d*e^6*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^4 - 70*a*b^3*c^3*d^2*e^5 + 120*a^2*b*c^

4*d^2*e^5 - 90*a^2*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^4*(-(4*a*c - b^2

)^3)^(1/2) + 10*a*b*c^2*d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(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) - ((-(9*(b^7*e^7 + b^4*e^7*(-(4*a*c - b^

2)^3)^(1/2) - 20*a^3*b*c^3*e^7 + 8*a*c^6*d^5*e^2 + 40*a^3*c^4*d*e^6 + 25*a^2*b^3*c^2*e^7 + a^2*c^2*e^7*(-(4*a*

c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^4 - 2*b^2*c^5*d^5*e^2 + 5*b^3*c^4*d^4*e^3 - 10*b^4*c^3*d^3*e^4 + 10*b^5*c

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

a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a*b*c^5*d^4*e^3 + 40*a*b^4*c^2*d*e^6 - 5*b^3

*c*d*e^6*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^4 - 70*a*b^3*c^3*d^2*e^5 + 120*a^2*b*c^4*d^2*e^5 - 90*a

^2*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^4*(-(4*a*c - b^2)^3)^(1/2) + 10*

a*b*c^2*d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(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)*(-(9*(b^7*e^7 + b^4*e^7*(-(4*a*c - b^2)

^3)^(1/2) - 20*a^3*b*c^3*e^7 + 8*a*c^6*d^5*e^2 + 40*a^3*c^4*d*e^6 + 25*a^2*b^3*c^2*e^7 + a^2*c^2*e^7*(-(4*a*c

- b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^4 - 2*b^2*c^5*d^5*e^2 + 5*b^3*c^4*d^4*e^3 - 10*b^4*c^3*d^3*e^4 + 10*b^5*c^2

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

c - b^2)^3)^(1/2) - 3*a*b^2*c*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a*b*c^5*d^4*e^3 + 40*a*b^4*c^2*d*e^6 - 5*b^3*c

*d*e^6*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^4 - 70*a*b^3*c^3*d^2*e^5 + 120*a^2*b*c^4*d^2*e^5 - 90*a^2

*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^4*(-(4*a*c - b^2)^3)^(1/2) + 10*a*

b*c^2*d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(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 +

23520*a^2*b^6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^

10*e^13 - 3280*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^

3*c^9*d^14*e^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 1

0560*a^3*b^7*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^1

6 + 184800*a^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^

5*c^6*d^10*e^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a

^4*b^9*c^2*d^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^1

4 - 120960*a^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^

5*e^18 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b

^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*

a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 338

40*a^8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 +

5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 760

0*a*b^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*

a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a

*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^

4*b*c^10*d^14*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a

^8*b*c^6*d^6*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c

^3*d*e^22) - 48*a^10*c^4*e^22 + 144*a*c^13*d^18*e^4 - 12*a^8*b^4*c^2*e^22 + 60*a^9*b^2*c^3*e^22 + 1104*a^2*c^1

2*d^16*e^6 + 3648*a^3*c^11*d^14*e^8 + 6720*a^4*c^10*d^12*e^10 + 7392*a^5*c^9*d^10*e^12 + 4704*a^6*c^8*d^8*e^14

+ 1344*a^7*c^7*d^6*e^16 - 192*a^8*c^6*d^4*e^18 - 240*a^9*c^5*d^2*e^20 - 36*b^2*c^12*d^18*e^4 + 324*b^3*c^11*d

^17*e^5 - 1308*b^4*c^10*d^16*e^6 + 3120*b^5*c^9*d^15*e^7 - 4872*b^6*c^8*d^14*e^8 + 5208*b^7*c^7*d^13*e^9 - 386

4*b^8*c^6*d^12*e^10 + 1968*b^9*c^5*d^11*e^11 - 660*b^10*c^4*d^10*e^12 + 132*b^11*c^3*d^9*e^13 - 12*b^12*c^2*d^

8*e^14 + 30384*a^2*b^2*c^10*d^14*e^8 - 58128*a^2*b^3*c^9*d^13*e^9 + 65856*a^2*b^4*c^8*d^12*e^10 - 41328*a^2*b^

5*c^7*d^11*e^11 + 7392*a^2*b^6*c^6*d^10*e^12 + 8976*a^2*b^7*c^5*d^9*e^13 - 7632*a^2*b^8*c^4*d^8*e^14 + 2544*a^

2*b^9*c^3*d^7*e^15 - 336*a^2*b^10*c^2*d^6*e^16 + 76272*a^3*b^2*c^9*d^12*e^10 - 125664*a^3*b^3*c^8*d^11*e^11 +

121968*a^3*b^4*c^7*d^10*e^12 - 66528*a^3*b^5*c^6*d^9*e^13 + 13776*a^3*b^6*c^5*d^8*e^14 + 5088*a^3*b^7*c^4*d^7*

e^15 - 3696*a^3*b^8*c^3*d^6*e^16 + 672*a^3*b^9*c^2*d^5*e^17 + 101640*a^4*b^2*c^8*d^10*e^12 - 138600*a^4*b^3*c^

7*d^9*e^13 + 108360*a^4*b^4*c^6*d^8*e^14 - 45360*a^4*b^5*c^5*d^7*e^15 + 5880*a^4*b^6*c^4*d^6*e^16 + 2520*a^4*b

^7*c^3*d^5*e^17 - 840*a^4*b^8*c^2*d^4*e^18 + 76104*a^5*b^2*c^7*d^8*e^14 - 82656*a^5*b^3*c^6*d^7*e^15 + 49392*a

^5*b^4*c^5*d^6*e^16 - 14112*a^5*b^5*c^4*d^5*e^17 + 168*a^5*b^6*c^3*d^4*e^18 + 672*a^5*b^7*c^2*d^3*e^19 + 30576

*a^6*b^2*c^6*d^6*e^16 - 25872*a^6*b^3*c^5*d^5*e^17 + 11424*a^6*b^4*c^4*d^4*e^18 - 1680*a^6*b^5*c^3*d^3*e^19 -

336*a^6*b^6*c^2*d^2*e^20 + 5424*a^7*b^2*c^5*d^4*e^18 - 4128*a^7*b^3*c^4*d^3*e^19 + 1296*a^7*b^4*c^3*d^2*e^20 +

252*a^8*b^2*c^4*d^2*e^20 - 1296*a*b*c^12*d^17*e^5 + 240*a^9*b*c^4*d*e^21 + 4956*a*b^2*c^11*d^16*e^6 - 10272*a

*b^3*c^10*d^15*e^7 + 11664*a*b^4*c^9*d^14*e^8 - 4704*a*b^5*c^8*d^13*e^9 - 5880*a*b^6*c^7*d^12*e^10 + 10944*a*b

^7*c^6*d^11*e^11 - 8448*a*b^8*c^5*d^10*e^12 + 3696*a*b^9*c^4*d^9*e^13 - 900*a*b^10*c^3*d^8*e^14 + 96*a*b^11*c^

2*d^7*e^15 - 8832*a^2*b*c^11*d^15*e^7 - 25536*a^3*b*c^10*d^13*e^9 - 40320*a^4*b*c^9*d^11*e^11 - 36960*a^5*b*c^

8*d^9*e^13 - 18816*a^6*b*c^7*d^7*e^15 - 4032*a^7*b*c^6*d^5*e^17 + 96*a^7*b^5*c^2*d*e^21 + 384*a^8*b*c^5*d^3*e^

19 - 444*a^8*b^3*c^3*d*e^21) - (d + e*x)^(1/2)*(288*b*c^12*d^15*e^5 - 36*c^13*d^16*e^4 - 36*a^8*c^5*e^20 - 18*

a^6*b^4*c^3*e^20 + 72*a^7*b^2*c^4*e^20 + 720*a^2*c^11*d^12*e^8 + 2304*a^3*c^10*d^10*e^10 + 3240*a^4*c^9*d^8*e^

12 + 2304*a^5*c^8*d^6*e^14 + 720*a^6*c^7*d^4*e^16 - 1080*b^2*c^11*d^14*e^6 + 2520*b^3*c^10*d^13*e^7 - 4050*b^4

*c^9*d^12*e^8 + 4644*b^5*c^8*d^11*e^9 - 3798*b^6*c^7*d^10*e^10 + 2160*b^7*c^6*d^9*e^11 - 810*b^8*c^5*d^8*e^12

+ 180*b^9*c^4*d^7*e^13 - 18*b^10*c^3*d^6*e^14 + 10152*a^2*b^2*c^9*d^10*e^10 - 11160*a^2*b^3*c^8*d^9*e^11 + 405

0*a^2*b^4*c^7*d^8*e^12 + 3240*a^2*b^5*c^6*d^7*e^13 - 4140*a^2*b^6*c^5*d^6*e^14 + 1728*a^2*b^7*c^4*d^5*e^15 - 2

70*a^2*b^8*c^3*d^4*e^16 + 22680*a^3*b^2*c^8*d^8*e^12 - 21600*a^3*b^3*c^7*d^7*e^13 + 9000*a^3*b^4*c^6*d^6*e^14

+ 216*a^3*b^5*c^5*d^5*e^15 - 1440*a^3*b^6*c^4*d^4*e^16 + 360*a^3*b^7*c^3*d^3*e^17 + 19800*a^4*b^2*c^7*d^6*e^14

- 14040*a^4*b^3*c^6*d^5*e^15 + 4050*a^4*b^4*c^5*d^4*e^16 + 180*a^4*b^5*c^4*d^3*e^17 - 270*a^4*b^6*c^3*d^2*e^1

8 + 7560*a^5*b^2*c^6*d^4*e^16 - 3600*a^5*b^3*c^5*d^3*e^17 + 540*a^5*b^4*c^4*d^2*e^18 + 1080*a^6*b^2*c^5*d^2*e^

18 - 360*a*b^2*c^10*d^12*e^8 + 2160*a*b^3*c^9*d^11*e^9 - 5508*a*b^4*c^8*d^10*e^10 + 7740*a*b^5*c^7*d^9*e^11 -

6480*a*b^6*c^6*d^8*e^12 + 3240*a*b^7*c^5*d^7*e^13 - 900*a*b^8*c^4*d^6*e^14 + 108*a*b^9*c^3*d^5*e^15 - 4320*a^2

*b*c^10*d^11*e^9 - 11520*a^3*b*c^9*d^9*e^11 - 12960*a^4*b*c^8*d^7*e^13 - 6912*a^5*b*c^7*d^5*e^15 + 108*a^5*b^5

*c^3*d*e^19 - 1440*a^6*b*c^6*d^3*e^17 - 360*a^6*b^3*c^4*d*e^19))*(-(9*(b^7*e^7 + b^4*e^7*(-(4*a*c - b^2)^3)^(1

/2) - 20*a^3*b*c^3*e^7 + 8*a*c^6*d^5*e^2 + 40*a^3*c^4*d*e^6 + 25*a^2*b^3*c^2*e^7 + a^2*c^2*e^7*(-(4*a*c - b^2)

^3)^(1/2) - 80*a^2*c^5*d^3*e^4 - 2*b^2*c^5*d^5*e^2 + 5*b^3*c^4*d^4*e^3 - 10*b^4*c^3*d^3*e^4 + 10*b^5*c^2*d^2*e

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

2)^3)^(1/2) - 3*a*b^2*c*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a*b*c^5*d^4*e^3 + 40*a*b^4*c^2*d*e^6 - 5*b^3*c*d*e^6

*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^4 - 70*a*b^3*c^3*d^2*e^5 + 120*a^2*b*c^4*d^2*e^5 - 90*a^2*b^2*c

^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^4*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*

d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(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) - 54*a^6*b*c^5*e^19 + 648*a*c^11*d^11*e^8 + 108*a^6*c^6*d*e^18 -

702*b*c^11*d^12*e^7 + 1620*a^2*c^10*d^9*e^10 + 2160*a^3*c^9*d^7*e^12 + 1620*a^4*c^8*d^5*e^14 + 648*a^5*c^7*d^

3*e^16 + 1944*b^2*c^10*d^11*e^8 - 2970*b^3*c^9*d^10*e^9 + 2700*b^4*c^8*d^9*e^10 - 1458*b^5*c^7*d^8*e^11 + 432*

b^6*c^6*d^7*e^12 - 54*b^7*c^5*d^6*e^13 + 12960*a^2*b^2*c^8*d^7*e^12 - 11340*a^2*b^3*c^7*d^6*e^13 + 4860*a^2*b^

4*c^6*d^5*e^14 - 810*a^2*b^5*c^5*d^4*e^15 + 9720*a^3*b^2*c^7*d^5*e^14 - 5400*a^3*b^3*c^6*d^4*e^15 + 1080*a^3*b

^4*c^5*d^3*e^16 + 3240*a^4*b^2*c^6*d^3*e^16 - 810*a^4*b^3*c^5*d^2*e^17 - 3564*a*b*c^10*d^10*e^9 + 8100*a*b^2*c

^9*d^9*e^10 - 9720*a*b^3*c^8*d^8*e^11 + 6480*a*b^4*c^7*d^7*e^12 - 2268*a*b^5*c^6*d^6*e^13 + 324*a*b^6*c^5*d^5*

e^14 - 7290*a^2*b*c^9*d^8*e^11 - 7560*a^3*b*c^8*d^6*e^13 - 4050*a^4*b*c^7*d^4*e^15 - 972*a^5*b*c^6*d^2*e^17 +

324*a^5*b^2*c^5*d*e^18))*(-(9*(b^7*e^7 + b^4*e^7*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^7 + 8*a*c^6*d^5*e^2

+ 40*a^3*c^4*d*e^6 + 25*a^2*b^3*c^2*e^7 + a^2*c^2*e^7*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^4 - 2*b^2*c

^5*d^5*e^2 + 5*b^3*c^4*d^4*e^3 - 10*b^4*c^3*d^3*e^4 + 10*b^5*c^2*d^2*e^5 + 5*c^4*d^4*e^3*(-(4*a*c - b^2)^3)^(1

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

^2)^3)^(1/2) - 20*a*b*c^5*d^4*e^3 + 40*a*b^4*c^2*d*e^6 - 5*b^3*c*d*e^6*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4

*d^3*e^4 - 70*a*b^3*c^3*d^2*e^5 + 120*a^2*b*c^4*d^2*e^5 - 90*a^2*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c - b

^2)^3)^(1/2) - 10*b*c^3*d^3*e^4*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(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 - atan(((((9*(b^4*e^7*(-(4*a*c - b^2)^3)^(1/2) - b^7*e^7 + 20*a^3*b*c^3*e^7 - 8*a*c^6*d^5*e^2 - 40*a^

3*c^4*d*e^6 - 25*a^2*b^3*c^2*e^7 + a^2*c^2*e^7*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^4 + 2*b^2*c^5*d^5*e

^2 - 5*b^3*c^4*d^4*e^3 + 10*b^4*c^3*d^3*e^4 - 10*b^5*c^2*d^2*e^5 + 5*c^4*d^4*e^3*(-(4*a*c - b^2)^3)^(1/2) + 9*

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

1/2) + 20*a*b*c^5*d^4*e^3 - 40*a*b^4*c^2*d*e^6 - 5*b^3*c*d*e^6*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^4

+ 70*a*b^3*c^3*d^2*e^5 - 120*a^2*b*c^4*d^2*e^5 + 90*a^2*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c - b^2)^3)^(

1/2) - 10*b*c^3*d^3*e^4*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(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)*((9*(b^4*e^7*(-(4*a*c - b^2)^3)^(1/2) - b^7*e^7 + 20*a^3*b*c^3*e^7 - 8*a*c^6*d^5*e^2 - 40*a^3*c

^4*d*e^6 - 25*a^2*b^3*c^2*e^7 + a^2*c^2*e^7*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^4 + 2*b^2*c^5*d^5*e^2

- 5*b^3*c^4*d^4*e^3 + 10*b^4*c^3*d^3*e^4 - 10*b^5*c^2*d^2*e^5 + 5*c^4*d^4*e^3*(-(4*a*c - b^2)^3)^(1/2) + 9*a*b

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

) + 20*a*b*c^5*d^4*e^3 - 40*a*b^4*c^2*d*e^6 - 5*b^3*c*d*e^6*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^4 +

70*a*b^3*c^3*d^2*e^5 - 120*a^2*b*c^4*d^2*e^5 + 90*a^2*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2

) - 10*b*c^3*d^3*e^4*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^6*(-(4*a*c - b^2)^3)^(1/2)))/(8*(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) - 48*a^10*c^4*e^22 + 144*a*c^13*d^18*e^4 - 12*

a^8*b^4*c^2*e^22 + 60*a^9*b^2*c^3*e^22 + 1104*a^2*c^12*d^16*e^6 + 3648*a^3*c^11*d^14*e^8 + 6720*a^4*c^10*d^12*

e^10 + 7392*a^5*c^9*d^10*e^12 + 4704*a^6*c^8*d^8*e^14 + 1344*a^7*c^7*d^6*e^16 - 192*a^8*c^6*d^4*e^18 - 240*a^9

*c^5*d^2*e^20 - 36*b^2*c^12*d^18*e^4 + 324*b^3*c^11*d^17*e^5 - 1308*b^4*c^10*d^16*e^6 + 3120*b^5*c^9*d^15*e^7

- 4872*b^6*c^8*d^14*e^8 + 5208*b^7*c^7*d^13*e^9 - 3864*b^8*c^6*d^12*e^10 + 1968*b^9*c^5*d^11*e^11 - 660*b^10*c

^4*d^10*e^12 + 132*b^11*c^3*d^9*e^13 - 12*b^12*c^2*d^8*e^14 + 30384*a^2*b^2*c^10*d^14*e^8 - 58128*a^2*b^3*c^9*

d^13*e^9 + 65856*a^2*b^4*c^8*d^12*e^10 - 41328*a^2*b^5*c^7*d^11*e^11 + 7392*a^2*b^6*c^6*d^10*e^12 + 8976*a^2*b

^7*c^5*d^9*e^13 - 7632*a^2*b^8*c^4*d^8*e^14 + 2544*a^2*b^9*c^3*d^7*e^15 - 336*a^2*b^10*c^2*d^6*e^16 + 76272*a^

3*b^2*c^9*d^12*e^10 - 125664*a^3*b^3*c^8*d^11*e^11 + 121968*a^3*b^4*c^7*d^10*e^12 - 66528*a^3*b^5*c^6*d^9*e^13

+ 13776*a^3*b^6*c^5*d^8*e^14 + 5088*a^3*b^7*c^4*d^7*e^15 - 3696*a^3*b^8*c^3*d^6*e^16 + 672*a^3*b^9*c^2*d^5*e^

17 + 101640*a^4*b^2*c^8*d^10*e^12 - 138600*a^4*b^3*c^7*d^9*e^13 + 108360*a^4*b^4*c^6*d^8*e^14 - 45360*a^4*b^5*

c^5*d^7*e^15 + 5880*a^4*b^6*c^4*d^6*e^16 + 2520*a^4*b^7*c^3*d^5*e^17 - 840*a^4*b^8*c^2*d^4*e^18 + 76104*a^5*b^

2*c^7*d^8*e^14 - 82656*a^5*b^3*c^6*d^7*e^15 + 49392*a^5*b^4*c^5*d^6*e^16 - 14112*a^5*b^5*c^4*d^5*e^17 + 168*a^

5*b^6*c^3*d^4*e^18 + 672*a^5*b^7*c^2*d^3*e^19 + 30576*a^6*b^2*c^6*d^6*e^16 - 25872*a^6*b^3*c^5*d^5*e^17 + 1142

4*a^6*b^4*c^4*d^4*e^18 - 1680*a^6*b^5*c^3*d^3*e^19 - 336*a^6*b^6*c^2*d^2*e^20 + 5424*a^7*b^2*c^5*d^4*e^18 - 41

28*a^7*b^3*c^4*d^3*e^19 + 1296*a^7*b^4*c^3*d^2*e^20 + 252*a^8*b^2*c^4*d^2*e^20 - 1296*a*b*c^12*d^17*e^5 + 240*

a^9*b*c^4*d*e^21 + 4956*a*b^2*c^11*d^16*e^6 - 10272*a*b^3*c^10*d^15*e^7 + 11664*a*b^4*c^9*d^14*e^8 - 4704*a*b^

5*c^8*d^13*e^9 - 5880*a*b^6*c^7*d^12*e^10 + 10944*a*b^7*c^6*d^11*e^11 - 8448*a*b^8*c^5*d^10*e^12 + 3696*a*b^9*

c^4*d^9*e^13 - 900*a*b^10*c^3*d^8*e^14 + 96*a*b^11*c^2*d^7*e^15 - 8832*a^2*b*c^11*d^15*e^7 - 25536*a^3*b*c^10*

d^13*e^9 - 40320*a^4*b*c^9*d^11*e^11 - 36960*a^5*b*c^8*d^9*e^13 - 18816*a^6*b*c^7*d^7*e^15 - 4032*a^7*b*c^6*d^

5*e^17 + 96*a^7*b^5*c^2*d*e^21 + 384*a^8*b*c^5*d^3*e^19 - 444*a^8*b^3*c^3*d*e^21) - (d + e*x)^(1/2)*(288*b*c^1

2*d^15*e^5 - 36*c^13*d^16*e^4 - 36*a^8*c^5*e^20 - 18*a^6*b^4*c^3*e^20 + 72*a^7*b^2*c^4*e^20 + 720*a^2*c^11*d^1

2*e^8 + 2304*a^3*c^10*d^10*e^10 + 3240*a^4*c^9*d^8*e^12 + 2304*a^5*c^8*d^6*e^14 + 720*a^6*c^7*d^4*e^16 - 1080*

b^2*c^11*d^14*e^6 + 2520*b^3*c^10*d^13*e^7 - 4050*b^4*c^9*d^12*e^8 + 4644*b^5*c^8*d^11*e^9 - 3798*b^6*c^7*d^10

*e^10 + 2160*b^7*c^6*d^9*e^11 - 810*b^8*c^5*d^8*e^12 + 180*b^9*c^4*d^7*e^13 - 18*b^10*c^3*d^6*e^14 + 10152*a^2

*b^2*c^9*d^10*e^10 - 11160*a^2*b^3*c^8*d^9*e^11 + 4050*a^2*b^4*c^7*d^8*e^12 + 3240*a^2*b^5*c^6*d^7*e^13 - 4140

*a^2*b^6*c^5*d^6*e^14 + 1728*a^2*b^7*c^4*d^5*e^15 - 270*a^2*b^8*c^3*d^4*e^16 + 22680*a^3*b^2*c^8*d^8*e^12 - 21

600*a^3*b^3*c^7*d^7*e^13 + 9000*a^3*b^4*c^6*d^6*e^14 + 216*a^3*b^5*c^5*d^5*e^15 - 1440*a^3*b^6*c^4*d^4*e^16 +

360*a^3*b^7*c^3*d^3*e^17 + 19800*a^4*b^2*c^7*d^6*e^14 - 14040*a^4*b^3*c^6*d^5*e^15 + 4050*a^4*b^4*c^5*d^4*e^16

+ 180*a^4*b^5*c^4*d^3*e^17 - 270*a^4*b^6*c^3*d^2*e^18 + 7560*a^5*b^2*c^6*d^4*e^16 - 3600*a^5*b^3*c^5*d^3*e^17

+ 540*a^5*b^4*c^4*d^2*e^18 + 1080*a^6*b^2*c^5*d^2*e^18 - 360*a*b^2*c^10*d^12*e^8 + 2160*a*b^3*c^9*d^11*e^9 -

5508*a*b^4*c^8*d^10*e^10 + 7740*a*b^5*c^7*d^9*e^11 - 6480*a*b^6*c^6*d^8*e^12 + 3240*a*b^7*c^5*d^7*e^13 - 900*a

*b^8*c^4*d^6*e^14 + 108*a*b^9*c^3*d^5*e^15 - 4320*a^2*b*c^10*d^11*e^9 - 11520*a^3*b*c^9*d^9*e^11 - 12960*a^4*b

*c^8*d^7*e^13 - 6912*a^5*b*c^7*d^5*e^15 + 108*a^5*b^5*c^3*d*e^19 - 1440*a^6*b*c^6*d^3*e^17 - 360*a^6*b^3*c^4*d

*e^19))*((9*(b^4*e^7*(-(4*a*c - b^2)^3)^(1/2) - b^7*e^7 + 20*a^3*b*c^3*e^7 - 8*a*c^6*d^5*e^2 - 40*a^3*c^4*d*e^

6 - 25*a^2*b^3*c^2*e^7 + a^2*c^2*e^7*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^4 + 2*b^2*c^5*d^5*e^2 - 5*b^3

*c^4*d^4*e^3 + 10*b^4*c^3*d^3*e^4 - 10*b^5*c^2*d^2*e^5 + 5*c^4*d^4*e^3*(-(4*a*c - b^2)^3)^(1/2) + 9*a*b^5*c*e^

7 + 5*b^6*c*d*e^6 + 10*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^7*(-(4*a*c - b^2)^3)^(1/2) + 20*

a*b*c^5*d^4*e^3 - 40*a*b^4*c^2*d*e^6 - 5*b^3*c*d*e^6*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^4 + 70*a*b^

3*c^3*d^2*e^5 - 120*a^2*b*c^4*d^2*e^5 + 90*a^2*b^2*c^3*d*e^6 - 10*a*c^3*d^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 10*