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

Optimal. Leaf size=673 \[ \frac {e \sqrt {d+e x} \left (c x \left (-2 c e (5 a e+b d)+3 b^2 e^2+2 c^2 d^2\right )+(c d-3 b e) \left (2 a c e+b^2 (-e)+b c d\right )+5 a c e (2 c d-b e)\right )}{4 \left (b^2-4 a c\right ) \left (a+b x+c x^2\right ) \left (a e^2-b d e+c d^2\right )^2}-\frac {\sqrt {c} e \left (-2 c^2 d e \left (-d \sqrt {b^2-4 a c}-16 a e+6 b d\right )-2 c e^2 \left (b d \sqrt {b^2-4 a c}+5 a e \sqrt {b^2-4 a c}+8 a b e+b^2 d\right )+3 b^2 e^3 \left (\sqrt {b^2-4 a c}+b\right )+8 c^3 d^3\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )}}\right )}{4 \sqrt {2} \left (b^2-4 a c\right )^{3/2} \sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )} \left (a e^2-b d e+c d^2\right )^2}+\frac {\sqrt {c} e \left (-2 c^2 d e \left (d \sqrt {b^2-4 a c}-16 a e+6 b d\right )-2 c e^2 \left (-b d \sqrt {b^2-4 a c}-5 a e \sqrt {b^2-4 a c}+8 a b e+b^2 d\right )+3 b^2 e^3 \left (b-\sqrt {b^2-4 a c}\right )+8 c^3 d^3\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}\right )}{4 \sqrt {2} \left (b^2-4 a c\right )^{3/2} \sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )} \left (a e^2-b d e+c d^2\right )^2}-\frac {\sqrt {d+e x} \left (\left (b^2-4 a c\right ) (c d-b e)-c e x \left (b^2-4 a c\right )\right )}{2 \left (b^2-4 a c\right ) \left (a+b x+c x^2\right )^2 \left (a e^2-b d e+c d^2\right )} \]

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Rubi [A]  time = 5.26, antiderivative size = 673, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 4, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {822, 826, 1166, 208} \begin {gather*} \frac {e \sqrt {d+e x} \left (c x \left (-2 c e (5 a e+b d)+3 b^2 e^2+2 c^2 d^2\right )+(c d-3 b e) \left (2 a c e+b^2 (-e)+b c d\right )+5 a c e (2 c d-b e)\right )}{4 \left (b^2-4 a c\right ) \left (a+b x+c x^2\right ) \left (a e^2-b d e+c d^2\right )^2}-\frac {\sqrt {c} e \left (-2 c^2 d e \left (-d \sqrt {b^2-4 a c}-16 a e+6 b d\right )-2 c e^2 \left (b d \sqrt {b^2-4 a c}+5 a e \sqrt {b^2-4 a c}+8 a b e+b^2 d\right )+3 b^2 e^3 \left (\sqrt {b^2-4 a c}+b\right )+8 c^3 d^3\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 )}{4 \sqrt {2} \left (b^2-4 a c\right )^{3/2} \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 {c} e \left (-2 c^2 d e \left (d \sqrt {b^2-4 a c}-16 a e+6 b d\right )-2 c e^2 \left (-b d \sqrt {b^2-4 a c}-5 a e \sqrt {b^2-4 a c}+8 a b e+b^2 d\right )+3 b^2 e^3 \left (b-\sqrt {b^2-4 a c}\right )+8 c^3 d^3\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 )}{4 \sqrt {2} \left (b^2-4 a c\right )^{3/2} \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 {\sqrt {d+e x} \left (\left (b^2-4 a c\right ) (c d-b e)-c e x \left (b^2-4 a c\right )\right )}{2 \left (b^2-4 a c\right ) \left (a+b x+c x^2\right )^2 \left (a e^2-b d e+c d^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-(Sqrt[d + e*x]*((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a
+ b*x + c*x^2)^2) + (e*Sqrt[d + e*x]*(5*a*c*e*(2*c*d - b*e) + (c*d - 3*b*e)*(b*c*d - b^2*e + 2*a*c*e) + c*(2*
c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d + 5*a*e))*x))/(4*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)) -
(Sqrt[c]*e*(8*c^3*d^3 + 3*b^2*(b + Sqrt[b^2 - 4*a*c])*e^3 - 2*c^2*d*e*(6*b*d - Sqrt[b^2 - 4*a*c]*d - 16*a*e)
- 2*c*e^2*(b^2*d + b*Sqrt[b^2 - 4*a*c]*d + 8*a*b*e + 5*a*Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d
+ e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b - Sqrt[b^2 -
4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)^2) + (Sqrt[c]*e*(8*c^3*d^3 + 3*b^2*(b - Sqrt[b^2 - 4*a*c])*e^3 - 2*c^2*d*e
*(6*b*d + Sqrt[b^2 - 4*a*c]*d - 16*a*e) - 2*c*e^2*(b^2*d - b*Sqrt[b^2 - 4*a*c]*d + 8*a*b*e - 5*a*Sqrt[b^2 - 4*
a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*(b^2 - 4
*a*c)^(3/2)*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 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}{\sqrt {d+e x} \left (a+b x+c x^2\right )^3} \, dx &=-\frac {\sqrt {d+e x} \left (\left (b^2-4 a c\right ) (c d-b e)-c \left (b^2-4 a c\right ) e x\right )}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )^2}-\frac {\int \frac {\frac {1}{2} \left (b^2-4 a c\right ) e (c d-3 b e)-\frac {5}{2} c \left (b^2-4 a c\right ) e^2 x}{\sqrt {d+e x} \left (a+b x+c x^2\right )^2} \, dx}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )}\\ &=-\frac {\sqrt {d+e x} \left (\left (b^2-4 a c\right ) (c d-b e)-c \left (b^2-4 a c\right ) e x\right )}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )^2}+\frac {e \sqrt {d+e x} \left (5 a c e (2 c d-b e)+(c d-3 b e) \left (b c d-b^2 e+2 a c e\right )+c \left (2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right ) x\right )}{4 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )^2 \left (a+b x+c x^2\right )}+\frac {\int \frac {\frac {1}{4} \left (b^2-4 a c\right ) e \left (4 c^3 d^3+3 b^3 e^3-c^2 d e (5 b d-16 a e)-b c e^2 (2 b d+13 a e)\right )+\frac {1}{4} c \left (b^2-4 a c\right ) e^2 \left (2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right ) x}{\sqrt {d+e x} \left (a+b x+c x^2\right )} \, dx}{2 \left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2}\\ &=-\frac {\sqrt {d+e x} \left (\left (b^2-4 a c\right ) (c d-b e)-c \left (b^2-4 a c\right ) e x\right )}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )^2}+\frac {e \sqrt {d+e x} \left (5 a c e (2 c d-b e)+(c d-3 b e) \left (b c d-b^2 e+2 a c e\right )+c \left (2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right ) x\right )}{4 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )^2 \left (a+b x+c x^2\right )}+\frac {\operatorname {Subst}\left (\int \frac {-\frac {1}{4} c \left (b^2-4 a c\right ) d e^2 \left (2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right )+\frac {1}{4} \left (b^2-4 a c\right ) e^2 \left (4 c^3 d^3+3 b^3 e^3-c^2 d e (5 b d-16 a e)-b c e^2 (2 b d+13 a e)\right )+\frac {1}{4} c \left (b^2-4 a c\right ) e^2 \left (2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right ) x^2}{c d^2-b d e+a e^2+(-2 c d+b e) x^2+c x^4} \, dx,x,\sqrt {d+e x}\right )}{\left (b^2-4 a c\right )^2 \left (c d^2-b d e+a e^2\right )^2}\\ &=-\frac {\sqrt {d+e x} \left (\left (b^2-4 a c\right ) (c d-b e)-c \left (b^2-4 a c\right ) e x\right )}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )^2}+\frac {e \sqrt {d+e x} \left (5 a c e (2 c d-b e)+(c d-3 b e) \left (b c d-b^2 e+2 a c e\right )+c \left (2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right ) x\right )}{4 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )^2 \left (a+b x+c x^2\right )}-\frac {\left (c e \left (8 c^3 d^3+3 b^2 \left (b-\sqrt {b^2-4 a c}\right ) e^3-2 c^2 d e \left (6 b d+\sqrt {b^2-4 a c} d-16 a e\right )-2 c e^2 \left (b^2 d-b \sqrt {b^2-4 a c} d+8 a b e-5 a \sqrt {b^2-4 a c} e\right )\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {1}{2} \sqrt {b^2-4 a c} e+\frac {1}{2} (-2 c d+b e)+c x^2} \, dx,x,\sqrt {d+e x}\right )}{8 \left (b^2-4 a c\right )^{3/2} \left (c d^2-b d e+a e^2\right )^2}+\frac {\left (c e \left (8 c^3 d^3+3 b^2 \left (b+\sqrt {b^2-4 a c}\right ) e^3-2 c^2 d e \left (6 b d-\sqrt {b^2-4 a c} d-16 a e\right )-2 c e^2 \left (b^2 d+b \sqrt {b^2-4 a c} d+8 a b e+5 a \sqrt {b^2-4 a c} e\right )\right )\right ) \operatorname {Subst}\left (\int \frac {1}{-\frac {1}{2} \sqrt {b^2-4 a c} e+\frac {1}{2} (-2 c d+b e)+c x^2} \, dx,x,\sqrt {d+e x}\right )}{8 \left (b^2-4 a c\right )^{3/2} \left (c d^2-b d e+a e^2\right )^2}\\ &=-\frac {\sqrt {d+e x} \left (\left (b^2-4 a c\right ) (c d-b e)-c \left (b^2-4 a c\right ) e x\right )}{2 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right ) \left (a+b x+c x^2\right )^2}+\frac {e \sqrt {d+e x} \left (5 a c e (2 c d-b e)+(c d-3 b e) \left (b c d-b^2 e+2 a c e\right )+c \left (2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right ) x\right )}{4 \left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )^2 \left (a+b x+c x^2\right )}-\frac {\sqrt {c} e \left (8 c^3 d^3+3 b^2 \left (b+\sqrt {b^2-4 a c}\right ) e^3-2 c^2 d e \left (6 b d-\sqrt {b^2-4 a c} d-16 a e\right )-2 c e^2 \left (b^2 d+b \sqrt {b^2-4 a c} d+8 a b e+5 a \sqrt {b^2-4 a c} e\right )\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e}}\right )}{4 \sqrt {2} \left (b^2-4 a c\right )^{3/2} \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 {c} e \left (8 c^3 d^3+3 b^2 \left (b-\sqrt {b^2-4 a c}\right ) e^3-2 c^2 d e \left (6 b d+\sqrt {b^2-4 a c} d-16 a e\right )-2 c e^2 \left (b^2 d-b \sqrt {b^2-4 a c} d+8 a b e-5 a \sqrt {b^2-4 a c} e\right )\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e}}\right )}{4 \sqrt {2} \left (b^2-4 a c\right )^{3/2} \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 = 6.20, size = 1033, normalized size = 1.53 \begin {gather*} -\frac {\sqrt {d+e x} \left (-2 a c (2 c d-b e)+b \left (-e b^2+c d b+2 a c e\right )+c (b (2 c d-b e)-2 c (b d-2 a e)) x\right )}{2 \left (b^2-4 a c\right ) \left (c d^2-b e d+a e^2\right ) \left (c x^2+b x+a\right )^2}-\frac {-\frac {\sqrt {d+e x} \left (\frac {5}{2} a c \left (b^2-4 a c\right ) (2 c d-b e) e^2+\frac {1}{2} \left (b^2-4 a c\right ) (c d-3 b e) \left (-e b^2+c d b+2 a c e\right ) e+c \left (\frac {5}{2} c \left (b^2-4 a c\right ) (b d-2 a e) e^2+\frac {1}{2} \left (b^2-4 a c\right ) (c d-3 b e) (2 c d-b e) e\right ) x\right )}{\left (b^2-4 a c\right ) \left (c d^2-b e d+a e^2\right ) \left (c x^2+b x+a\right )}-\frac {2 \left (\frac {\sqrt {2 c d-b e-\sqrt {b^2-4 a c} e} \left (\frac {1}{4} c \left (b^2-4 a c\right ) e^2 \left (2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right )-\frac {2 c \left (\frac {1}{4} \left (b^2-4 a c\right ) e^2 \left (4 c^3 d^3-c^2 e (5 b d-16 a e) d+3 b^3 e^3-b c e^2 (2 b d+13 a e)\right )-\frac {1}{4} c \left (b^2-4 a c\right ) d e^2 \left (2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right )\right )-\frac {1}{4} c \left (b^2-4 a c\right ) e^2 (b e-2 c d) \left (2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right )}{\sqrt {b^2-4 a c} e}\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-b e-\sqrt {b^2-4 a c} e}}\right )}{\sqrt {2} \sqrt {c} \left (-2 c d+b e+\sqrt {b^2-4 a c} e\right )}+\frac {\sqrt {2 c d-b e+\sqrt {b^2-4 a c} e} \left (\frac {1}{4} c \left (b^2-4 a c\right ) \left (2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right ) e^2+\frac {2 c \left (\frac {1}{4} \left (b^2-4 a c\right ) e^2 \left (4 c^3 d^3-c^2 e (5 b d-16 a e) d+3 b^3 e^3-b c e^2 (2 b d+13 a e)\right )-\frac {1}{4} c \left (b^2-4 a c\right ) d e^2 \left (2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right )\right )-\frac {1}{4} c \left (b^2-4 a c\right ) e^2 (b e-2 c d) \left (2 c^2 d^2+3 b^2 e^2-2 c e (b d+5 a e)\right )}{\sqrt {b^2-4 a c} e}\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-b e+\sqrt {b^2-4 a c} e}}\right )}{\sqrt {2} \sqrt {c} \left (-2 c d+b e-\sqrt {b^2-4 a c} e\right )}\right )}{\left (b^2-4 a c\right ) \left (c d^2-b e d+a e^2\right )}}{2 \left (b^2-4 a c\right ) \left (c d^2-b e d+a e^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-1/2*(Sqrt[d + e*x]*(-2*a*c*(2*c*d - b*e) + b*(b*c*d - b^2*e + 2*a*c*e) + c*(-2*c*(b*d - 2*a*e) + b*(2*c*d - b
*e))*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2) - (-((Sqrt[d + e*x]*((5*a*c*(b^2 - 4*a*c)
*e^2*(2*c*d - b*e))/2 + ((b^2 - 4*a*c)*e*(c*d - 3*b*e)*(b*c*d - b^2*e + 2*a*c*e))/2 + c*((5*c*(b^2 - 4*a*c)*e^
2*(b*d - 2*a*e))/2 + ((b^2 - 4*a*c)*e*(c*d - 3*b*e)*(2*c*d - b*e))/2)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^
2)*(a + b*x + c*x^2))) - (2*((Sqrt[2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e]*((c*(b^2 - 4*a*c)*e^2*(2*c^2*d^2 + 3*b^2
*e^2 - 2*c*e*(b*d + 5*a*e)))/4 - (-1/4*(c*(b^2 - 4*a*c)*e^2*(-2*c*d + b*e)*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d
+ 5*a*e))) + 2*c*(-1/4*(c*(b^2 - 4*a*c)*d*e^2*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d + 5*a*e))) + ((b^2 - 4*a*c)
*e^2*(4*c^3*d^3 + 3*b^3*e^3 - c^2*d*e*(5*b*d - 16*a*e) - b*c*e^2*(2*b*d + 13*a*e)))/4))/(Sqrt[b^2 - 4*a*c]*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]*Sqrt[c]*(-2*c*d +
b*e + Sqrt[b^2 - 4*a*c]*e)) + (Sqrt[2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e]*((c*(b^2 - 4*a*c)*e^2*(2*c^2*d^2 + 3*b^
2*e^2 - 2*c*e*(b*d + 5*a*e)))/4 + (-1/4*(c*(b^2 - 4*a*c)*e^2*(-2*c*d + b*e)*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*
d + 5*a*e))) + 2*c*(-1/4*(c*(b^2 - 4*a*c)*d*e^2*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d + 5*a*e))) + ((b^2 - 4*a*c
)*e^2*(4*c^3*d^3 + 3*b^3*e^3 - c^2*d*e*(5*b*d - 16*a*e) - b*c*e^2*(2*b*d + 13*a*e)))/4))/(Sqrt[b^2 - 4*a*c]*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]*Sqrt[c]*(-2*c*d +
b*e - Sqrt[b^2 - 4*a*c]*e))))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^
2))

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IntegrateAlgebraic [A]  time = 16.08, size = 1184, normalized size = 1.76 \begin {gather*} -\frac {\sqrt {d+e x} \left (2 c^4 d^5-5 b c^3 e d^4-6 c^4 (d+e x) d^4-36 a c^3 e^2 d^3+14 b^2 c^2 e^2 d^3+6 c^4 (d+e x)^2 d^3+12 b c^3 e (d+e x) d^3+54 a b c^2 e^3 d^2-16 b^3 c e^3 d^2-2 c^4 (d+e x)^3 d^2-9 b c^3 e (d+e x)^2 d^2+60 a c^3 e^2 (d+e x) d^2-24 b^2 c^2 e^2 (d+e x) d^2+5 b^4 e^4 d-38 a^2 c^2 e^4 d-8 a b^2 c e^4 d+2 b c^3 e (d+e x)^3 d-42 a c^3 e^2 (d+e x)^2 d+15 b^2 c^2 e^2 (d+e x)^2 d-60 a b c^2 e^3 (d+e x) d+18 b^3 c e^3 (d+e x) d-5 a b^3 e^5+19 a^2 b c e^5+10 a c^3 e^2 (d+e x)^3-3 b^2 c^2 e^2 (d+e x)^3+21 a b c^2 e^3 (d+e x)^2-6 b^3 c e^3 (d+e x)^2-3 b^4 e^4 (d+e x)+18 a^2 c^2 e^4 (d+e x)+6 a b^2 c e^4 (d+e x)\right ) e^2}{4 \left (b^2-4 a c\right ) \left (-c d^2+b e d-a e^2\right )^2 \left (-c d^2+b e d+2 c (d+e x) d-a e^2-c (d+e x)^2-b e (d+e x)\right )^2}+\frac {\left (-16 \sqrt {2} a b c^{3/2} e^4+3 \sqrt {2} b^3 \sqrt {c} e^4-10 \sqrt {2} a c^{3/2} \sqrt {b^2-4 a c} e^4+3 \sqrt {2} b^2 \sqrt {c} \sqrt {b^2-4 a c} e^4+32 \sqrt {2} a c^{5/2} d e^3-2 \sqrt {2} b^2 c^{3/2} d e^3-2 \sqrt {2} b c^{3/2} \sqrt {b^2-4 a c} d e^3-12 \sqrt {2} b c^{5/2} d^2 e^2+2 \sqrt {2} c^{5/2} \sqrt {b^2-4 a c} d^2 e^2+8 \sqrt {2} c^{7/2} d^3 e\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {-2 c d+b e-\sqrt {b^2-4 a c} e}}\right )}{8 \left (b^2-4 a c\right )^{3/2} \sqrt {-2 c d+b e-\sqrt {b^2-4 a c} e} \left (-c d^2+b e d-a e^2\right )^2}+\frac {\left (16 \sqrt {2} a b c^{3/2} e^4-3 \sqrt {2} b^3 \sqrt {c} e^4-10 \sqrt {2} a c^{3/2} \sqrt {b^2-4 a c} e^4+3 \sqrt {2} b^2 \sqrt {c} \sqrt {b^2-4 a c} e^4-32 \sqrt {2} a c^{5/2} d e^3+2 \sqrt {2} b^2 c^{3/2} d e^3-2 \sqrt {2} b c^{3/2} \sqrt {b^2-4 a c} d e^3+12 \sqrt {2} b c^{5/2} d^2 e^2+2 \sqrt {2} c^{5/2} \sqrt {b^2-4 a c} d^2 e^2-8 \sqrt {2} c^{7/2} d^3 e\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {-2 c d+b e+\sqrt {b^2-4 a c} e}}\right )}{8 \left (b^2-4 a c\right )^{3/2} \sqrt {-2 c d+b e+\sqrt {b^2-4 a c} e} \left (-c d^2+b e d-a e^2\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-1/4*(e^2*Sqrt[d + e*x]*(2*c^4*d^5 - 5*b*c^3*d^4*e + 14*b^2*c^2*d^3*e^2 - 36*a*c^3*d^3*e^2 - 16*b^3*c*d^2*e^3
+ 54*a*b*c^2*d^2*e^3 + 5*b^4*d*e^4 - 8*a*b^2*c*d*e^4 - 38*a^2*c^2*d*e^4 - 5*a*b^3*e^5 + 19*a^2*b*c*e^5 - 6*c^4
*d^4*(d + e*x) + 12*b*c^3*d^3*e*(d + e*x) - 24*b^2*c^2*d^2*e^2*(d + e*x) + 60*a*c^3*d^2*e^2*(d + e*x) + 18*b^3
*c*d*e^3*(d + e*x) - 60*a*b*c^2*d*e^3*(d + e*x) - 3*b^4*e^4*(d + e*x) + 6*a*b^2*c*e^4*(d + e*x) + 18*a^2*c^2*e
^4*(d + e*x) + 6*c^4*d^3*(d + e*x)^2 - 9*b*c^3*d^2*e*(d + e*x)^2 + 15*b^2*c^2*d*e^2*(d + e*x)^2 - 42*a*c^3*d*e
^2*(d + e*x)^2 - 6*b^3*c*e^3*(d + e*x)^2 + 21*a*b*c^2*e^3*(d + e*x)^2 - 2*c^4*d^2*(d + e*x)^3 + 2*b*c^3*d*e*(d
+ e*x)^3 - 3*b^2*c^2*e^2*(d + e*x)^3 + 10*a*c^3*e^2*(d + e*x)^3))/((b^2 - 4*a*c)*(-(c*d^2) + b*d*e - a*e^2)^2
*(-(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)^2) + ((8*Sqrt[2]*c^(7/2)*d^3*e -
12*Sqrt[2]*b*c^(5/2)*d^2*e^2 + 2*Sqrt[2]*c^(5/2)*Sqrt[b^2 - 4*a*c]*d^2*e^2 - 2*Sqrt[2]*b^2*c^(3/2)*d*e^3 + 32
*Sqrt[2]*a*c^(5/2)*d*e^3 - 2*Sqrt[2]*b*c^(3/2)*Sqrt[b^2 - 4*a*c]*d*e^3 + 3*Sqrt[2]*b^3*Sqrt[c]*e^4 - 16*Sqrt[2
]*a*b*c^(3/2)*e^4 + 3*Sqrt[2]*b^2*Sqrt[c]*Sqrt[b^2 - 4*a*c]*e^4 - 10*Sqrt[2]*a*c^(3/2)*Sqrt[b^2 - 4*a*c]*e^4)*
ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[-2*c*d + b*e - Sqrt[b^2 - 4*a*c]*e]])/(8*(b^2 - 4*a*c)^(3/2)*Sqrt[
-2*c*d + b*e - Sqrt[b^2 - 4*a*c]*e]*(-(c*d^2) + b*d*e - a*e^2)^2) + ((-8*Sqrt[2]*c^(7/2)*d^3*e + 12*Sqrt[2]*b*
c^(5/2)*d^2*e^2 + 2*Sqrt[2]*c^(5/2)*Sqrt[b^2 - 4*a*c]*d^2*e^2 + 2*Sqrt[2]*b^2*c^(3/2)*d*e^3 - 32*Sqrt[2]*a*c^(
5/2)*d*e^3 - 2*Sqrt[2]*b*c^(3/2)*Sqrt[b^2 - 4*a*c]*d*e^3 - 3*Sqrt[2]*b^3*Sqrt[c]*e^4 + 16*Sqrt[2]*a*b*c^(3/2)*
e^4 + 3*Sqrt[2]*b^2*Sqrt[c]*Sqrt[b^2 - 4*a*c]*e^4 - 10*Sqrt[2]*a*c^(3/2)*Sqrt[b^2 - 4*a*c]*e^4)*ArcTan[(Sqrt[2
]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[-2*c*d + b*e + Sqrt[b^2 - 4*a*c]*e]])/(8*(b^2 - 4*a*c)^(3/2)*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)/(c*x^2+b*x+a)^3/(e*x+d)^(1/2),x, algorithm="fricas")

[Out]

Timed out

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giac [B]  time = 10.02, size = 5779, normalized size = 8.59

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*c*x+b)/(c*x^2+b*x+a)^3/(e*x+d)^(1/2),x, algorithm="giac")

[Out]

1/32*((b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 -
8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5)^2*(2*c^2*d^2*e^2 - 2*b*c*d*e
^3 + (3*b^2 - 10*a*c)*e^4)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e) + 2*(2*sqrt(b^2 - 4*a*c)*c^5*d^7*e
^2 - 7*sqrt(b^2 - 4*a*c)*b*c^4*d^6*e^3 + 3*(b^2*c^3 + 10*a*c^4)*sqrt(b^2 - 4*a*c)*d^5*e^4 + 5*(2*b^3*c^2 - 15*
a*b*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^5 - (11*b^4*c - 48*a*b^2*c^2 - 54*a^2*c^3)*sqrt(b^2 - 4*a*c)*d^3*e^6 + 3*(b^5
+ a*b^3*c - 27*a^2*b*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^7 - (6*a*b^4 - 21*a^2*b^2*c - 26*a^3*c^2)*sqrt(b^2 - 4*a*c)
*d*e^8 + (3*a^2*b^3 - 13*a^3*b*c)*sqrt(b^2 - 4*a*c)*e^9)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(
b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*
c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5) - (16*(b^2*c^8 - 4*a*c^9)*d^12*e^2
- 96*(b^3*c^7 - 4*a*b*c^8)*d^11*e^3 + 8*(29*b^4*c^6 - 100*a*b^2*c^7 - 64*a^2*c^8)*d^10*e^4 - 40*(7*b^5*c^5 - 1
2*a*b^3*c^6 - 64*a^2*b*c^7)*d^9*e^5 + (157*b^6*c^4 + 636*a*b^4*c^5 - 4704*a^2*b^2*c^6 - 1408*a^3*c^7)*d^8*e^6
- 4*(b^7*c^3 + 300*a*b^5*c^4 - 864*a^2*b^3*c^5 - 1408*a^3*b*c^6)*d^7*e^7 - 14*(3*b^8*c^2 - 50*a*b^6*c^3 + 576*
a^3*b^2*c^5 + 128*a^4*c^6)*d^6*e^8 + 4*(5*b^9*c - 27*a*b^7*c^2 - 336*a^2*b^5*c^3 + 1120*a^3*b^3*c^4 + 1344*a^4
*b*c^5)*d^5*e^9 - (3*b^10 + 40*a*b^8*c - 590*a^2*b^6*c^2 + 120*a^3*b^4*c^3 + 5360*a^4*b^2*c^4 + 1088*a^5*c^5)*
d^4*e^10 + 4*(3*a*b^9 - 7*a^2*b^7*c - 164*a^3*b^5*c^2 + 440*a^4*b^3*c^3 + 544*a^5*b*c^4)*d^3*e^11 - 2*(9*a^2*b
^8 - 62*a^3*b^6*c - 60*a^4*b^4*c^2 + 624*a^5*b^2*c^3 + 128*a^6*c^4)*d^2*e^12 + 4*(3*a^3*b^7 - 26*a^4*b^5*c + 4
0*a^5*b^3*c^2 + 64*a^6*b*c^3)*d*e^13 - (3*a^4*b^6 - 28*a^5*b^4*c + 64*a^6*b^2*c^2)*e^14)*sqrt(-4*c^2*d + 2*(b*
c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^3*d^5 - 8*a*c^4*d^5 - 5*b^3*c^2*d
^4*e + 20*a*b*c^3*d^4*e + 4*b^4*c*d^3*e^2 - 12*a*b^2*c^2*d^3*e^2 - 16*a^2*c^3*d^3*e^2 - b^5*d^2*e^3 - 2*a*b^3*
c*d^2*e^3 + 24*a^2*b*c^2*d^2*e^3 + 2*a*b^4*d*e^4 - 6*a^2*b^2*c*d*e^4 - 8*a^3*c^2*d*e^4 - a^2*b^3*e^5 + 4*a^3*b
*c*e^5 + sqrt((2*b^2*c^3*d^5 - 8*a*c^4*d^5 - 5*b^3*c^2*d^4*e + 20*a*b*c^3*d^4*e + 4*b^4*c*d^3*e^2 - 12*a*b^2*c
^2*d^3*e^2 - 16*a^2*c^3*d^3*e^2 - b^5*d^2*e^3 - 2*a*b^3*c*d^2*e^3 + 24*a^2*b*c^2*d^2*e^3 + 2*a*b^4*d*e^4 - 6*a
^2*b^2*c*d*e^4 - 8*a^3*c^2*d*e^4 - a^2*b^3*e^5 + 4*a^3*b*c*e^5)^2 - 4*(b^2*c^3*d^6 - 4*a*c^4*d^6 - 3*b^3*c^2*d
^5*e + 12*a*b*c^3*d^5*e + 3*b^4*c*d^4*e^2 - 9*a*b^2*c^2*d^4*e^2 - 12*a^2*c^3*d^4*e^2 - b^5*d^3*e^3 - 2*a*b^3*c
*d^3*e^3 + 24*a^2*b*c^2*d^3*e^3 + 3*a*b^4*d^2*e^4 - 9*a^2*b^2*c*d^2*e^4 - 12*a^3*c^2*d^2*e^4 - 3*a^2*b^3*d*e^5
+ 12*a^3*b*c*d*e^5 + a^3*b^2*e^6 - 4*a^4*c*e^6)*(b^2*c^3*d^4 - 4*a*c^4*d^4 - 2*b^3*c^2*d^3*e + 8*a*b*c^3*d^3*
e + b^4*c*d^2*e^2 - 2*a*b^2*c^2*d^2*e^2 - 8*a^2*c^3*d^2*e^2 - 2*a*b^3*c*d*e^3 + 8*a^2*b*c^2*d*e^3 + a^2*b^2*c*
e^4 - 4*a^3*c^2*e^4)))/(b^2*c^3*d^4 - 4*a*c^4*d^4 - 2*b^3*c^2*d^3*e + 8*a*b*c^3*d^3*e + b^4*c*d^2*e^2 - 2*a*b^
2*c^2*d^2*e^2 - 8*a^2*c^3*d^2*e^2 - 2*a*b^3*c*d*e^3 + 8*a^2*b*c^2*d*e^3 + a^2*b^2*c*e^4 - 4*a^3*c^2*e^4)))/(((
b^2*c^5 - 4*a*c^6)*sqrt(b^2 - 4*a*c)*d^10 - 5*(b^3*c^4 - 4*a*b*c^5)*sqrt(b^2 - 4*a*c)*d^9*e + 5*(2*b^4*c^3 - 7
*a*b^2*c^4 - 4*a^2*c^5)*sqrt(b^2 - 4*a*c)*d^8*e^2 - 10*(b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*sqrt(b^2 - 4*a*c)
*d^7*e^3 + 5*(b^6*c + 2*a*b^4*c^2 - 22*a^2*b^2*c^3 - 8*a^3*c^4)*sqrt(b^2 - 4*a*c)*d^6*e^4 - (b^7 + 16*a*b^5*c
- 50*a^2*b^3*c^2 - 120*a^3*b*c^3)*sqrt(b^2 - 4*a*c)*d^5*e^5 + 5*(a*b^6 + 2*a^2*b^4*c - 22*a^3*b^2*c^2 - 8*a^4*
c^3)*sqrt(b^2 - 4*a*c)*d^4*e^6 - 10*(a^2*b^5 - 2*a^3*b^3*c - 8*a^4*b*c^2)*sqrt(b^2 - 4*a*c)*d^3*e^7 + 5*(2*a^3
*b^4 - 7*a^4*b^2*c - 4*a^5*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^8 - 5*(a^4*b^3 - 4*a^5*b*c)*sqrt(b^2 - 4*a*c)*d*e^9 +
(a^5*b^2 - 4*a^6*c)*sqrt(b^2 - 4*a*c)*e^10)*abs(b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^
3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 -
4*a^3*c*e^5)*abs(c)) - 1/32*((b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^
3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5)^2*(2*
c^2*d^2*e^2 - 2*b*c*d*e^3 + (3*b^2 - 10*a*c)*e^4)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e) - 2*(2*sqrt
(b^2 - 4*a*c)*c^5*d^7*e^2 - 7*sqrt(b^2 - 4*a*c)*b*c^4*d^6*e^3 + 3*(b^2*c^3 + 10*a*c^4)*sqrt(b^2 - 4*a*c)*d^5*e
^4 + 5*(2*b^3*c^2 - 15*a*b*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^5 - (11*b^4*c - 48*a*b^2*c^2 - 54*a^2*c^3)*sqrt(b^2 -
4*a*c)*d^3*e^6 + 3*(b^5 + a*b^3*c - 27*a^2*b*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^7 - (6*a*b^4 - 21*a^2*b^2*c - 26*a^3
*c^2)*sqrt(b^2 - 4*a*c)*d*e^8 + (3*a^2*b^3 - 13*a^3*b*c)*sqrt(b^2 - 4*a*c)*e^9)*sqrt(-4*c^2*d + 2*(b*c + sqrt(
b^2 - 4*a*c)*c)*e)*abs(b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a
*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5) - (16*(b^2*c
^8 - 4*a*c^9)*d^12*e^2 - 96*(b^3*c^7 - 4*a*b*c^8)*d^11*e^3 + 8*(29*b^4*c^6 - 100*a*b^2*c^7 - 64*a^2*c^8)*d^10*
e^4 - 40*(7*b^5*c^5 - 12*a*b^3*c^6 - 64*a^2*b*c^7)*d^9*e^5 + (157*b^6*c^4 + 636*a*b^4*c^5 - 4704*a^2*b^2*c^6 -
1408*a^3*c^7)*d^8*e^6 - 4*(b^7*c^3 + 300*a*b^5*c^4 - 864*a^2*b^3*c^5 - 1408*a^3*b*c^6)*d^7*e^7 - 14*(3*b^8*c^
2 - 50*a*b^6*c^3 + 576*a^3*b^2*c^5 + 128*a^4*c^6)*d^6*e^8 + 4*(5*b^9*c - 27*a*b^7*c^2 - 336*a^2*b^5*c^3 + 1120
*a^3*b^3*c^4 + 1344*a^4*b*c^5)*d^5*e^9 - (3*b^10 + 40*a*b^8*c - 590*a^2*b^6*c^2 + 120*a^3*b^4*c^3 + 5360*a^4*b
^2*c^4 + 1088*a^5*c^5)*d^4*e^10 + 4*(3*a*b^9 - 7*a^2*b^7*c - 164*a^3*b^5*c^2 + 440*a^4*b^3*c^3 + 544*a^5*b*c^4
)*d^3*e^11 - 2*(9*a^2*b^8 - 62*a^3*b^6*c - 60*a^4*b^4*c^2 + 624*a^5*b^2*c^3 + 128*a^6*c^4)*d^2*e^12 + 4*(3*a^3
*b^7 - 26*a^4*b^5*c + 40*a^5*b^3*c^2 + 64*a^6*b*c^3)*d*e^13 - (3*a^4*b^6 - 28*a^5*b^4*c + 64*a^6*b^2*c^2)*e^14
)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^3*d^5 - 8*
a*c^4*d^5 - 5*b^3*c^2*d^4*e + 20*a*b*c^3*d^4*e + 4*b^4*c*d^3*e^2 - 12*a*b^2*c^2*d^3*e^2 - 16*a^2*c^3*d^3*e^2 -
b^5*d^2*e^3 - 2*a*b^3*c*d^2*e^3 + 24*a^2*b*c^2*d^2*e^3 + 2*a*b^4*d*e^4 - 6*a^2*b^2*c*d*e^4 - 8*a^3*c^2*d*e^4
- a^2*b^3*e^5 + 4*a^3*b*c*e^5 - sqrt((2*b^2*c^3*d^5 - 8*a*c^4*d^5 - 5*b^3*c^2*d^4*e + 20*a*b*c^3*d^4*e + 4*b^4
*c*d^3*e^2 - 12*a*b^2*c^2*d^3*e^2 - 16*a^2*c^3*d^3*e^2 - b^5*d^2*e^3 - 2*a*b^3*c*d^2*e^3 + 24*a^2*b*c^2*d^2*e^
3 + 2*a*b^4*d*e^4 - 6*a^2*b^2*c*d*e^4 - 8*a^3*c^2*d*e^4 - a^2*b^3*e^5 + 4*a^3*b*c*e^5)^2 - 4*(b^2*c^3*d^6 - 4*
a*c^4*d^6 - 3*b^3*c^2*d^5*e + 12*a*b*c^3*d^5*e + 3*b^4*c*d^4*e^2 - 9*a*b^2*c^2*d^4*e^2 - 12*a^2*c^3*d^4*e^2 -
b^5*d^3*e^3 - 2*a*b^3*c*d^3*e^3 + 24*a^2*b*c^2*d^3*e^3 + 3*a*b^4*d^2*e^4 - 9*a^2*b^2*c*d^2*e^4 - 12*a^3*c^2*d^
2*e^4 - 3*a^2*b^3*d*e^5 + 12*a^3*b*c*d*e^5 + a^3*b^2*e^6 - 4*a^4*c*e^6)*(b^2*c^3*d^4 - 4*a*c^4*d^4 - 2*b^3*c^2
*d^3*e + 8*a*b*c^3*d^3*e + b^4*c*d^2*e^2 - 2*a*b^2*c^2*d^2*e^2 - 8*a^2*c^3*d^2*e^2 - 2*a*b^3*c*d*e^3 + 8*a^2*b
*c^2*d*e^3 + a^2*b^2*c*e^4 - 4*a^3*c^2*e^4)))/(b^2*c^3*d^4 - 4*a*c^4*d^4 - 2*b^3*c^2*d^3*e + 8*a*b*c^3*d^3*e +
b^4*c*d^2*e^2 - 2*a*b^2*c^2*d^2*e^2 - 8*a^2*c^3*d^2*e^2 - 2*a*b^3*c*d*e^3 + 8*a^2*b*c^2*d*e^3 + a^2*b^2*c*e^4
- 4*a^3*c^2*e^4)))/(((b^2*c^5 - 4*a*c^6)*sqrt(b^2 - 4*a*c)*d^10 - 5*(b^3*c^4 - 4*a*b*c^5)*sqrt(b^2 - 4*a*c)*d
^9*e + 5*(2*b^4*c^3 - 7*a*b^2*c^4 - 4*a^2*c^5)*sqrt(b^2 - 4*a*c)*d^8*e^2 - 10*(b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b
*c^4)*sqrt(b^2 - 4*a*c)*d^7*e^3 + 5*(b^6*c + 2*a*b^4*c^2 - 22*a^2*b^2*c^3 - 8*a^3*c^4)*sqrt(b^2 - 4*a*c)*d^6*e
^4 - (b^7 + 16*a*b^5*c - 50*a^2*b^3*c^2 - 120*a^3*b*c^3)*sqrt(b^2 - 4*a*c)*d^5*e^5 + 5*(a*b^6 + 2*a^2*b^4*c -
22*a^3*b^2*c^2 - 8*a^4*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^6 - 10*(a^2*b^5 - 2*a^3*b^3*c - 8*a^4*b*c^2)*sqrt(b^2 - 4*
a*c)*d^3*e^7 + 5*(2*a^3*b^4 - 7*a^4*b^2*c - 4*a^5*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^8 - 5*(a^4*b^3 - 4*a^5*b*c)*sqr
t(b^2 - 4*a*c)*d*e^9 + (a^5*b^2 - 4*a^6*c)*sqrt(b^2 - 4*a*c)*e^10)*abs(b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c
*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c
*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5)*abs(c)) + 1/4*(2*(x*e + d)^(7/2)*c^4*d^2*e^2 - 6*(x*e + d)^(5/2)*c^4*d^3*e
^2 + 6*(x*e + d)^(3/2)*c^4*d^4*e^2 - 2*sqrt(x*e + d)*c^4*d^5*e^2 - 2*(x*e + d)^(7/2)*b*c^3*d*e^3 + 9*(x*e + d)
^(5/2)*b*c^3*d^2*e^3 - 12*(x*e + d)^(3/2)*b*c^3*d^3*e^3 + 5*sqrt(x*e + d)*b*c^3*d^4*e^3 + 3*(x*e + d)^(7/2)*b^
2*c^2*e^4 - 10*(x*e + d)^(7/2)*a*c^3*e^4 - 15*(x*e + d)^(5/2)*b^2*c^2*d*e^4 + 42*(x*e + d)^(5/2)*a*c^3*d*e^4 +
24*(x*e + d)^(3/2)*b^2*c^2*d^2*e^4 - 60*(x*e + d)^(3/2)*a*c^3*d^2*e^4 - 14*sqrt(x*e + d)*b^2*c^2*d^3*e^4 + 36
*sqrt(x*e + d)*a*c^3*d^3*e^4 + 6*(x*e + d)^(5/2)*b^3*c*e^5 - 21*(x*e + d)^(5/2)*a*b*c^2*e^5 - 18*(x*e + d)^(3/
2)*b^3*c*d*e^5 + 60*(x*e + d)^(3/2)*a*b*c^2*d*e^5 + 16*sqrt(x*e + d)*b^3*c*d^2*e^5 - 54*sqrt(x*e + d)*a*b*c^2*
d^2*e^5 + 3*(x*e + d)^(3/2)*b^4*e^6 - 6*(x*e + d)^(3/2)*a*b^2*c*e^6 - 18*(x*e + d)^(3/2)*a^2*c^2*e^6 - 5*sqrt(
x*e + d)*b^4*d*e^6 + 8*sqrt(x*e + d)*a*b^2*c*d*e^6 + 38*sqrt(x*e + d)*a^2*c^2*d*e^6 + 5*sqrt(x*e + d)*a*b^3*e^
7 - 19*sqrt(x*e + d)*a^2*b*c*e^7)/((b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2
- 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4)*((x*e +
d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)^2)

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maple [B]  time = 0.62, size = 2743, normalized size = 4.08

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*c*x+b)/(c*x^2+b*x+a)^3/(e*x+d)^(1/2),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 11.82, size = 84064, normalized size = 124.91

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((3*(d + e*x)^(3/2)*(6*a^2*c^2*e^6 - b^4*e^6 - 2*c^4*d^4*e^2 + 20*a*c^3*d^2*e^4 + 4*b*c^3*d^3*e^3 - 8*b^2*c^2*
d^2*e^4 + 2*a*b^2*c*e^6 + 6*b^3*c*d*e^5 - 20*a*b*c^2*d*e^5))/(4*(4*a*c - b^2)*(a*e^2 + c*d^2 - b*d*e)^2) - ((d
+ e*x)^(1/2)*(5*b^3*e^5 - 2*c^3*d^3*e^2 + 3*b*c^2*d^2*e^3 - 19*a*b*c*e^5 + 38*a*c^2*d*e^4 - 11*b^2*c*d*e^4))/
(4*(4*a*c - b^2)*(a*e^2 + c*d^2 - b*d*e)) + (3*(b*e - 2*c*d)*(d + e*x)^(5/2)*(7*a*c^2*e^4 - 2*b^2*c*e^4 - c^3*
d^2*e^2 + b*c^2*d*e^3))/(4*(4*a*c - b^2)*(a*e^2 + c*d^2 - b*d*e)^2) + (c*(d + e*x)^(7/2)*(10*a*c^2*e^4 - 3*b^2
*c*e^4 - 2*c^3*d^2*e^2 + 2*b*c^2*d*e^3))/(4*(4*a*c - b^2)*(a*e^2 + c*d^2 - b*d*e)^2))/(c^2*(d + e*x)^4 - (d +
e*x)*(4*c^2*d^3 + 2*b^2*d*e^2 - 2*a*b*e^3 + 4*a*c*d*e^2 - 6*b*c*d^2*e) - (4*c^2*d - 2*b*c*e)*(d + e*x)^3 + (d
+ e*x)^2*(b^2*e^2 + 6*c^2*d^2 + 2*a*c*e^2 - 6*b*c*d*e) + a^2*e^4 + c^2*d^4 + b^2*d^2*e^2 - 2*a*b*d*e^3 - 2*b*c
*d^3*e + 2*a*c*d^2*e^2) - atan(((((106496*a^6*c^7*d*e^10 - 53248*a^6*b*c^6*e^11 - 192*a^2*b^9*c^2*e^11 + 3136*
a^3*b^7*c^3*e^11 - 19200*a^4*b^5*c^4*e^11 + 52224*a^5*b^3*c^5*e^11 + 8192*a^3*c^10*d^7*e^4 + 122880*a^4*c^9*d^
5*e^6 + 221184*a^5*c^8*d^3*e^8 - 128*b^6*c^7*d^7*e^4 + 448*b^7*c^6*d^6*e^5 - 192*b^8*c^5*d^5*e^6 - 640*b^9*c^4
*d^4*e^7 + 704*b^10*c^3*d^3*e^8 - 192*b^11*c^2*d^2*e^9 - 6144*a^2*b^2*c^9*d^7*e^4 + 21504*a^2*b^3*c^8*d^6*e^5
+ 13824*a^2*b^4*c^7*d^5*e^6 - 88320*a^2*b^5*c^6*d^4*e^7 + 67200*a^2*b^6*c^5*d^3*e^8 - 1728*a^2*b^7*c^4*d^2*e^9
- 79872*a^3*b^2*c^8*d^5*e^6 + 271360*a^3*b^3*c^7*d^4*e^7 - 151040*a^3*b^4*c^6*d^3*e^8 - 59136*a^3*b^5*c^5*d^2
*e^9 + 30720*a^4*b^2*c^7*d^3*e^8 + 261120*a^4*b^3*c^6*d^2*e^9 + 384*a*b^10*c^2*d*e^10 + 1536*a*b^4*c^8*d^7*e^4
- 5376*a*b^5*c^7*d^6*e^5 + 384*a*b^6*c^6*d^5*e^6 + 12480*a*b^7*c^5*d^4*e^7 - 11520*a*b^8*c^4*d^3*e^8 + 2112*a
*b^9*c^3*d^2*e^9 - 5952*a^2*b^8*c^3*d*e^10 - 28672*a^3*b*c^9*d^6*e^5 + 32896*a^3*b^6*c^4*d*e^10 - 307200*a^4*b
*c^8*d^4*e^7 - 69120*a^4*b^4*c^5*d*e^10 - 331776*a^5*b*c^7*d^2*e^9 + 6144*a^5*b^2*c^6*d*e^10)/(64*(64*a^3*c^7*
d^8 - a^4*b^6*e^8 + 64*a^7*c^3*e^8 - b^6*c^4*d^8 - b^10*d^4*e^4 + 12*a*b^4*c^5*d^8 + 12*a^5*b^4*c*e^8 + 4*a*b^
9*d^3*e^5 + 4*a^3*b^7*d*e^7 + 4*b^7*c^3*d^7*e + 4*b^9*c*d^5*e^3 - 48*a^2*b^2*c^6*d^8 - 48*a^6*b^2*c^2*e^8 - 6*
a^2*b^8*d^2*e^6 + 256*a^4*c^6*d^6*e^2 + 384*a^5*c^5*d^4*e^4 + 256*a^6*c^4*d^2*e^6 - 6*b^8*c^2*d^6*e^2 - 240*a^
2*b^4*c^4*d^6*e^2 + 48*a^2*b^5*c^3*d^5*e^3 + 90*a^2*b^6*c^2*d^4*e^4 + 192*a^3*b^2*c^5*d^6*e^2 + 320*a^3*b^3*c^
4*d^5*e^3 - 440*a^3*b^4*c^3*d^4*e^4 + 48*a^3*b^5*c^2*d^3*e^5 + 480*a^4*b^2*c^4*d^4*e^4 + 320*a^4*b^3*c^3*d^3*e
^5 - 240*a^4*b^4*c^2*d^2*e^6 + 192*a^5*b^2*c^3*d^2*e^6 - 48*a*b^5*c^4*d^7*e - 256*a^3*b*c^6*d^7*e - 48*a^4*b^5
*c*d*e^7 - 256*a^6*b*c^3*d*e^7 + 68*a*b^6*c^3*d^6*e^2 - 36*a*b^7*c^2*d^5*e^3 + 192*a^2*b^3*c^5*d^7*e - 36*a^2*
b^7*c*d^3*e^5 + 68*a^3*b^6*c*d^2*e^6 - 768*a^4*b*c^5*d^5*e^3 - 768*a^5*b*c^4*d^3*e^5 + 192*a^5*b^3*c^2*d*e^7))
- ((d + e*x)^(1/2)*((53760*a^6*c^7*d*e^8 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) - 26880*a^6*b*c^6*e^9 - 9*b^13*
e^9 - 2077*a^2*b^9*c^2*e^9 + 10656*a^3*b^7*c^3*e^9 - 30240*a^4*b^5*c^4*e^9 + 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^
2*e^9*(-(4*a*c - b^2)^9)^(1/2) - 2048*a^3*c^10*d^7*e^2 - 17920*a^4*c^9*d^5*e^4 - 35840*a^5*c^8*d^3*e^6 + 32*b^
6*c^7*d^7*e^2 - 112*b^7*c^6*d^6*e^3 + 98*b^8*c^5*d^5*e^4 + 35*b^9*c^4*d^4*e^5 - 70*b^10*c^3*d^3*e^6 + 14*b^11*
c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^9 + 21*b^12*c*d*e^8 + 1536*a^2*b^2*c^9*
d^7*e^2 - 5376*a^2*b^3*c^8*d^6*e^3 + 1344*a^2*b^4*c^7*d^5*e^4 + 10080*a^2*b^5*c^6*d^4*e^5 - 7840*a^2*b^6*c^5*d
^3*e^6 - 1008*a^2*b^7*c^4*d^2*e^7 + 7168*a^3*b^2*c^8*d^5*e^4 - 35840*a^3*b^3*c^7*d^4*e^5 + 17920*a^3*b^4*c^6*d
^3*e^6 + 12544*a^3*b^5*c^5*d^2*e^7 - 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) +
51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) - 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) - 38
4*a*b^4*c^8*d^7*e^2 + 1344*a*b^5*c^7*d^6*e^3 - 896*a*b^6*c^6*d^5*e^4 - 1120*a*b^7*c^5*d^4*e^5 + 1260*a*b^8*c^4
*d^3*e^6 - 98*a*b^9*c^3*d^2*e^7 + 5418*a^2*b^8*c^3*d*e^8 + 7168*a^3*b*c^9*d^6*e^3 - 28224*a^3*b^6*c^4*d*e^8 +
44800*a^4*b*c^8*d^4*e^5 + 78400*a^4*b^4*c^5*d*e^8 + 53760*a^5*b*c^7*d^2*e^7 - 107520*a^5*b^2*c^6*d*e^8 + 154*a
*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c
- b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5
- 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c
*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240
*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e
^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10
*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e
^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^
3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^
2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e
^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6
*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^
2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*
d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^
8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^
6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*
b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e -
20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^
9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*
e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400
*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*
b^3*c^5*d*e^9)))^(1/2)*(8192*a^7*c^6*d*e^10 - 4096*a^7*b*c^5*e^11 + 64*a^4*b^7*c^2*e^11 - 768*a^5*b^5*c^3*e^11
+ 3072*a^6*b^3*c^4*e^11 + 8192*a^3*c^10*d^9*e^2 + 32768*a^4*c^9*d^7*e^4 + 49152*a^5*c^8*d^5*e^6 + 32768*a^6*c
^7*d^3*e^8 - 128*b^6*c^7*d^9*e^2 + 576*b^7*c^6*d^8*e^3 - 1024*b^8*c^5*d^7*e^4 + 896*b^9*c^4*d^6*e^5 - 384*b^10
*c^3*d^5*e^6 + 64*b^11*c^2*d^4*e^7 - 6144*a^2*b^2*c^9*d^9*e^2 + 27648*a^2*b^3*c^8*d^8*e^3 - 43008*a^2*b^4*c^7*
d^7*e^4 + 21504*a^2*b^5*c^6*d^6*e^5 + 8448*a^2*b^6*c^5*d^5*e^6 - 10368*a^2*b^7*c^4*d^4*e^7 + 1536*a^2*b^8*c^3*
d^3*e^8 + 384*a^2*b^9*c^2*d^2*e^9 + 40960*a^3*b^2*c^8*d^7*e^4 + 28672*a^3*b^3*c^7*d^6*e^5 - 76800*a^3*b^4*c^6*
d^5*e^6 + 34304*a^3*b^5*c^5*d^4*e^7 + 5632*a^3*b^6*c^4*d^3*e^8 - 3840*a^3*b^7*c^3*d^2*e^9 + 110592*a^4*b^2*c^7
*d^5*e^6 + 10240*a^4*b^3*c^6*d^4*e^7 - 51200*a^4*b^4*c^5*d^3*e^8 + 9216*a^4*b^5*c^4*d^2*e^9 + 73728*a^5*b^2*c^
6*d^3*e^8 + 12288*a^5*b^3*c^5*d^2*e^9 + 1536*a*b^4*c^8*d^9*e^2 - 6912*a*b^5*c^7*d^8*e^3 + 11776*a*b^6*c^6*d^7*
e^4 - 8960*a*b^7*c^5*d^6*e^5 + 2304*a*b^8*c^4*d^5*e^6 + 512*a*b^9*c^3*d^4*e^7 - 256*a*b^10*c^2*d^3*e^8 - 36864
*a^3*b*c^9*d^8*e^3 - 256*a^3*b^8*c^2*d*e^10 - 114688*a^4*b*c^8*d^6*e^5 + 2944*a^4*b^6*c^3*d*e^10 - 122880*a^5*
b*c^7*d^4*e^7 - 10752*a^5*b^4*c^4*d*e^10 - 49152*a^6*b*c^6*d^2*e^9 + 10240*a^6*b^2*c^5*d*e^10))/(8*(16*a^2*c^6
*d^8 + a^4*b^4*e^8 + 16*a^6*c^2*e^8 + b^4*c^4*d^8 + b^8*d^4*e^4 - 8*a*b^2*c^5*d^8 - 8*a^5*b^2*c*e^8 - 4*a*b^7*
d^3*e^5 - 4*a^3*b^5*d*e^7 - 4*b^5*c^3*d^7*e - 4*b^7*c*d^5*e^3 + 6*a^2*b^6*d^2*e^6 + 64*a^3*c^5*d^6*e^2 + 96*a^
4*c^4*d^4*e^4 + 64*a^5*c^3*d^2*e^6 + 6*b^6*c^2*d^6*e^2 + 64*a^2*b^2*c^4*d^6*e^2 + 32*a^2*b^3*c^3*d^5*e^3 - 74*
a^2*b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^3*d^4*e^4 + 32*a^3*b^3*c^2*d^3*e^5 + 64*a^4*b^2*c^2*d^2*e^6 + 32*a*b^3*c^4
*d^7*e + 4*a*b^6*c*d^4*e^4 - 64*a^2*b*c^5*d^7*e + 32*a^4*b^3*c*d*e^7 - 64*a^5*b*c^2*d*e^7 - 44*a*b^4*c^3*d^6*e
^2 + 20*a*b^5*c^2*d^5*e^3 + 20*a^2*b^5*c*d^3*e^5 - 192*a^3*b*c^4*d^5*e^3 - 44*a^3*b^4*c*d^2*e^6 - 192*a^4*b*c^
3*d^3*e^5)))*((53760*a^6*c^7*d*e^8 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) - 26880*a^6*b*c^6*e^9 - 9*b^13*e^9 - 2
077*a^2*b^9*c^2*e^9 + 10656*a^3*b^7*c^3*e^9 - 30240*a^4*b^5*c^4*e^9 + 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(
-(4*a*c - b^2)^9)^(1/2) - 2048*a^3*c^10*d^7*e^2 - 17920*a^4*c^9*d^5*e^4 - 35840*a^5*c^8*d^3*e^6 + 32*b^6*c^7*d
^7*e^2 - 112*b^7*c^6*d^6*e^3 + 98*b^8*c^5*d^5*e^4 + 35*b^9*c^4*d^4*e^5 - 70*b^10*c^3*d^3*e^6 + 14*b^11*c^2*d^2
*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^9 + 21*b^12*c*d*e^8 + 1536*a^2*b^2*c^9*d^7*e^2
- 5376*a^2*b^3*c^8*d^6*e^3 + 1344*a^2*b^4*c^7*d^5*e^4 + 10080*a^2*b^5*c^6*d^4*e^5 - 7840*a^2*b^6*c^5*d^3*e^6
- 1008*a^2*b^7*c^4*d^2*e^7 + 7168*a^3*b^2*c^8*d^5*e^4 - 35840*a^3*b^3*c^7*d^4*e^5 + 17920*a^3*b^4*c^6*d^3*e^6
+ 12544*a^3*b^5*c^5*d^2*e^7 - 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b
^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) - 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4
*c^8*d^7*e^2 + 1344*a*b^5*c^7*d^6*e^3 - 896*a*b^6*c^6*d^5*e^4 - 1120*a*b^7*c^5*d^4*e^5 + 1260*a*b^8*c^4*d^3*e^
6 - 98*a*b^9*c^3*d^2*e^7 + 5418*a^2*b^8*c^3*d*e^8 + 7168*a^3*b*c^9*d^6*e^3 - 28224*a^3*b^6*c^4*d*e^8 + 44800*a
^4*b*c^8*d^4*e^5 + 78400*a^4*b^4*c^5*d*e^8 + 53760*a^5*b*c^7*d^2*e^7 - 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^
2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)
^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a
*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^
4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^
8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10
*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^
2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 49
0*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560
*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 128
00*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 19
20*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 -
32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 +
10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5
+ 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e
^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d
^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6
*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a
^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d
^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235
*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^
7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5
*d*e^9)))^(1/2) - ((d + e*x)^(1/2)*(9*b^6*c^3*e^10 - 200*a^3*c^6*e^10 + 32*c^9*d^6*e^4 - 96*a*b^4*c^4*e^10 + 2
48*a*c^8*d^4*e^6 - 96*b*c^8*d^5*e^5 - 12*b^5*c^4*d*e^9 + 298*a^2*b^2*c^5*e^10 + 592*a^2*c^7*d^2*e^8 + 58*b^2*c
^7*d^4*e^6 + 44*b^3*c^6*d^3*e^7 - 26*b^4*c^5*d^2*e^8 - 496*a*b*c^7*d^3*e^7 + 172*a*b^3*c^5*d*e^9 - 592*a^2*b*c
^6*d*e^9 + 76*a*b^2*c^6*d^2*e^8))/(8*(16*a^2*c^6*d^8 + a^4*b^4*e^8 + 16*a^6*c^2*e^8 + b^4*c^4*d^8 + b^8*d^4*e^
4 - 8*a*b^2*c^5*d^8 - 8*a^5*b^2*c*e^8 - 4*a*b^7*d^3*e^5 - 4*a^3*b^5*d*e^7 - 4*b^5*c^3*d^7*e - 4*b^7*c*d^5*e^3
+ 6*a^2*b^6*d^2*e^6 + 64*a^3*c^5*d^6*e^2 + 96*a^4*c^4*d^4*e^4 + 64*a^5*c^3*d^2*e^6 + 6*b^6*c^2*d^6*e^2 + 64*a^
2*b^2*c^4*d^6*e^2 + 32*a^2*b^3*c^3*d^5*e^3 - 74*a^2*b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^3*d^4*e^4 + 32*a^3*b^3*c^2
*d^3*e^5 + 64*a^4*b^2*c^2*d^2*e^6 + 32*a*b^3*c^4*d^7*e + 4*a*b^6*c*d^4*e^4 - 64*a^2*b*c^5*d^7*e + 32*a^4*b^3*c
*d*e^7 - 64*a^5*b*c^2*d*e^7 - 44*a*b^4*c^3*d^6*e^2 + 20*a*b^5*c^2*d^5*e^3 + 20*a^2*b^5*c*d^3*e^5 - 192*a^3*b*c
^4*d^5*e^3 - 44*a^3*b^4*c*d^2*e^6 - 192*a^4*b*c^3*d^3*e^5)))*((53760*a^6*c^7*d*e^8 - 9*b^4*e^9*(-(4*a*c - b^2)
^9)^(1/2) - 26880*a^6*b*c^6*e^9 - 9*b^13*e^9 - 2077*a^2*b^9*c^2*e^9 + 10656*a^3*b^7*c^3*e^9 - 30240*a^4*b^5*c^
4*e^9 + 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) - 2048*a^3*c^10*d^7*e^2 - 17920*a^4*c^
9*d^5*e^4 - 35840*a^5*c^8*d^3*e^6 + 32*b^6*c^7*d^7*e^2 - 112*b^7*c^6*d^6*e^3 + 98*b^8*c^5*d^5*e^4 + 35*b^9*c^4
*d^4*e^5 - 70*b^10*c^3*d^3*e^6 + 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*
e^9 + 21*b^12*c*d*e^8 + 1536*a^2*b^2*c^9*d^7*e^2 - 5376*a^2*b^3*c^8*d^6*e^3 + 1344*a^2*b^4*c^7*d^5*e^4 + 10080
*a^2*b^5*c^6*d^4*e^5 - 7840*a^2*b^6*c^5*d^3*e^6 - 1008*a^2*b^7*c^4*d^2*e^7 + 7168*a^3*b^2*c^8*d^5*e^4 - 35840*
a^3*b^3*c^7*d^4*e^5 + 17920*a^3*b^4*c^6*d^3*e^6 + 12544*a^3*b^5*c^5*d^2*e^7 - 44800*a^4*b^3*c^6*d^2*e^7 + 14*b
^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) - 532*a*b^10*c^2*d*e^8 + 21*
b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7*e^2 + 1344*a*b^5*c^7*d^6*e^3 - 896*a*b^6*c^6*d^5*e^4
- 1120*a*b^7*c^5*d^4*e^5 + 1260*a*b^8*c^4*d^3*e^6 - 98*a*b^9*c^3*d^2*e^7 + 5418*a^2*b^8*c^3*d*e^8 + 7168*a^3*b
*c^9*d^6*e^3 - 28224*a^3*b^6*c^4*d*e^8 + 44800*a^4*b*c^8*d^4*e^5 + 78400*a^4*b^4*c^5*d*e^8 + 53760*a^5*b*c^7*d
^2*e^7 - 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b
^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^1
1*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4
*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^
4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6
144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6
*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b
^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*
b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^
12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4
*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^
5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a
^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 12544
0*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 116
00*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 -
15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7
- 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5
*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*
e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^
3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c
^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e
^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*1i - (((106496*a^6*c^7*d*e^10 - 53248*a^6*b*c^
6*e^11 - 192*a^2*b^9*c^2*e^11 + 3136*a^3*b^7*c^3*e^11 - 19200*a^4*b^5*c^4*e^11 + 52224*a^5*b^3*c^5*e^11 + 8192
*a^3*c^10*d^7*e^4 + 122880*a^4*c^9*d^5*e^6 + 221184*a^5*c^8*d^3*e^8 - 128*b^6*c^7*d^7*e^4 + 448*b^7*c^6*d^6*e^
5 - 192*b^8*c^5*d^5*e^6 - 640*b^9*c^4*d^4*e^7 + 704*b^10*c^3*d^3*e^8 - 192*b^11*c^2*d^2*e^9 - 6144*a^2*b^2*c^9
*d^7*e^4 + 21504*a^2*b^3*c^8*d^6*e^5 + 13824*a^2*b^4*c^7*d^5*e^6 - 88320*a^2*b^5*c^6*d^4*e^7 + 67200*a^2*b^6*c
^5*d^3*e^8 - 1728*a^2*b^7*c^4*d^2*e^9 - 79872*a^3*b^2*c^8*d^5*e^6 + 271360*a^3*b^3*c^7*d^4*e^7 - 151040*a^3*b^
4*c^6*d^3*e^8 - 59136*a^3*b^5*c^5*d^2*e^9 + 30720*a^4*b^2*c^7*d^3*e^8 + 261120*a^4*b^3*c^6*d^2*e^9 + 384*a*b^1
0*c^2*d*e^10 + 1536*a*b^4*c^8*d^7*e^4 - 5376*a*b^5*c^7*d^6*e^5 + 384*a*b^6*c^6*d^5*e^6 + 12480*a*b^7*c^5*d^4*e
^7 - 11520*a*b^8*c^4*d^3*e^8 + 2112*a*b^9*c^3*d^2*e^9 - 5952*a^2*b^8*c^3*d*e^10 - 28672*a^3*b*c^9*d^6*e^5 + 32
896*a^3*b^6*c^4*d*e^10 - 307200*a^4*b*c^8*d^4*e^7 - 69120*a^4*b^4*c^5*d*e^10 - 331776*a^5*b*c^7*d^2*e^9 + 6144
*a^5*b^2*c^6*d*e^10)/(64*(64*a^3*c^7*d^8 - a^4*b^6*e^8 + 64*a^7*c^3*e^8 - b^6*c^4*d^8 - b^10*d^4*e^4 + 12*a*b^
4*c^5*d^8 + 12*a^5*b^4*c*e^8 + 4*a*b^9*d^3*e^5 + 4*a^3*b^7*d*e^7 + 4*b^7*c^3*d^7*e + 4*b^9*c*d^5*e^3 - 48*a^2*
b^2*c^6*d^8 - 48*a^6*b^2*c^2*e^8 - 6*a^2*b^8*d^2*e^6 + 256*a^4*c^6*d^6*e^2 + 384*a^5*c^5*d^4*e^4 + 256*a^6*c^4
*d^2*e^6 - 6*b^8*c^2*d^6*e^2 - 240*a^2*b^4*c^4*d^6*e^2 + 48*a^2*b^5*c^3*d^5*e^3 + 90*a^2*b^6*c^2*d^4*e^4 + 192
*a^3*b^2*c^5*d^6*e^2 + 320*a^3*b^3*c^4*d^5*e^3 - 440*a^3*b^4*c^3*d^4*e^4 + 48*a^3*b^5*c^2*d^3*e^5 + 480*a^4*b^
2*c^4*d^4*e^4 + 320*a^4*b^3*c^3*d^3*e^5 - 240*a^4*b^4*c^2*d^2*e^6 + 192*a^5*b^2*c^3*d^2*e^6 - 48*a*b^5*c^4*d^7
*e - 256*a^3*b*c^6*d^7*e - 48*a^4*b^5*c*d*e^7 - 256*a^6*b*c^3*d*e^7 + 68*a*b^6*c^3*d^6*e^2 - 36*a*b^7*c^2*d^5*
e^3 + 192*a^2*b^3*c^5*d^7*e - 36*a^2*b^7*c*d^3*e^5 + 68*a^3*b^6*c*d^2*e^6 - 768*a^4*b*c^5*d^5*e^3 - 768*a^5*b*
c^4*d^3*e^5 + 192*a^5*b^3*c^2*d*e^7)) + ((d + e*x)^(1/2)*((53760*a^6*c^7*d*e^8 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^
(1/2) - 26880*a^6*b*c^6*e^9 - 9*b^13*e^9 - 2077*a^2*b^9*c^2*e^9 + 10656*a^3*b^7*c^3*e^9 - 30240*a^4*b^5*c^4*e^
9 + 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) - 2048*a^3*c^10*d^7*e^2 - 17920*a^4*c^9*d^
5*e^4 - 35840*a^5*c^8*d^3*e^6 + 32*b^6*c^7*d^7*e^2 - 112*b^7*c^6*d^6*e^3 + 98*b^8*c^5*d^5*e^4 + 35*b^9*c^4*d^4
*e^5 - 70*b^10*c^3*d^3*e^6 + 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^9
+ 21*b^12*c*d*e^8 + 1536*a^2*b^2*c^9*d^7*e^2 - 5376*a^2*b^3*c^8*d^6*e^3 + 1344*a^2*b^4*c^7*d^5*e^4 + 10080*a^2
*b^5*c^6*d^4*e^5 - 7840*a^2*b^6*c^5*d^3*e^6 - 1008*a^2*b^7*c^4*d^2*e^7 + 7168*a^3*b^2*c^8*d^5*e^4 - 35840*a^3*
b^3*c^7*d^4*e^5 + 17920*a^3*b^4*c^6*d^3*e^6 + 12544*a^3*b^5*c^5*d^2*e^7 - 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c
^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) - 532*a*b^10*c^2*d*e^8 + 21*b^3*
c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7*e^2 + 1344*a*b^5*c^7*d^6*e^3 - 896*a*b^6*c^6*d^5*e^4 - 11
20*a*b^7*c^5*d^4*e^5 + 1260*a*b^8*c^4*d^3*e^6 - 98*a*b^9*c^3*d^2*e^7 + 5418*a^2*b^8*c^3*d*e^8 + 7168*a^3*b*c^9
*d^6*e^3 - 28224*a^3*b^6*c^4*d*e^8 + 44800*a^4*b*c^8*d^4*e^5 + 78400*a^4*b^4*c^5*d*e^8 + 53760*a^5*b*c^7*d^2*e
^7 - 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^
9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^
6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^1
3*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^
9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*
a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4
+ 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*
c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*
c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c
^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9
*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^
5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b
^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^
6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a
^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 153
60*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 4
2240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^1
1*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3
- 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^
13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d
*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 -
81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*(8192*a^7*c^6*d*e^10 - 4096*a^7*b*c^5*e^11 + 64*a^
4*b^7*c^2*e^11 - 768*a^5*b^5*c^3*e^11 + 3072*a^6*b^3*c^4*e^11 + 8192*a^3*c^10*d^9*e^2 + 32768*a^4*c^9*d^7*e^4
+ 49152*a^5*c^8*d^5*e^6 + 32768*a^6*c^7*d^3*e^8 - 128*b^6*c^7*d^9*e^2 + 576*b^7*c^6*d^8*e^3 - 1024*b^8*c^5*d^7
*e^4 + 896*b^9*c^4*d^6*e^5 - 384*b^10*c^3*d^5*e^6 + 64*b^11*c^2*d^4*e^7 - 6144*a^2*b^2*c^9*d^9*e^2 + 27648*a^2
*b^3*c^8*d^8*e^3 - 43008*a^2*b^4*c^7*d^7*e^4 + 21504*a^2*b^5*c^6*d^6*e^5 + 8448*a^2*b^6*c^5*d^5*e^6 - 10368*a^
2*b^7*c^4*d^4*e^7 + 1536*a^2*b^8*c^3*d^3*e^8 + 384*a^2*b^9*c^2*d^2*e^9 + 40960*a^3*b^2*c^8*d^7*e^4 + 28672*a^3
*b^3*c^7*d^6*e^5 - 76800*a^3*b^4*c^6*d^5*e^6 + 34304*a^3*b^5*c^5*d^4*e^7 + 5632*a^3*b^6*c^4*d^3*e^8 - 3840*a^3
*b^7*c^3*d^2*e^9 + 110592*a^4*b^2*c^7*d^5*e^6 + 10240*a^4*b^3*c^6*d^4*e^7 - 51200*a^4*b^4*c^5*d^3*e^8 + 9216*a
^4*b^5*c^4*d^2*e^9 + 73728*a^5*b^2*c^6*d^3*e^8 + 12288*a^5*b^3*c^5*d^2*e^9 + 1536*a*b^4*c^8*d^9*e^2 - 6912*a*b
^5*c^7*d^8*e^3 + 11776*a*b^6*c^6*d^7*e^4 - 8960*a*b^7*c^5*d^6*e^5 + 2304*a*b^8*c^4*d^5*e^6 + 512*a*b^9*c^3*d^4
*e^7 - 256*a*b^10*c^2*d^3*e^8 - 36864*a^3*b*c^9*d^8*e^3 - 256*a^3*b^8*c^2*d*e^10 - 114688*a^4*b*c^8*d^6*e^5 +
2944*a^4*b^6*c^3*d*e^10 - 122880*a^5*b*c^7*d^4*e^7 - 10752*a^5*b^4*c^4*d*e^10 - 49152*a^6*b*c^6*d^2*e^9 + 1024
0*a^6*b^2*c^5*d*e^10))/(8*(16*a^2*c^6*d^8 + a^4*b^4*e^8 + 16*a^6*c^2*e^8 + b^4*c^4*d^8 + b^8*d^4*e^4 - 8*a*b^2
*c^5*d^8 - 8*a^5*b^2*c*e^8 - 4*a*b^7*d^3*e^5 - 4*a^3*b^5*d*e^7 - 4*b^5*c^3*d^7*e - 4*b^7*c*d^5*e^3 + 6*a^2*b^6
*d^2*e^6 + 64*a^3*c^5*d^6*e^2 + 96*a^4*c^4*d^4*e^4 + 64*a^5*c^3*d^2*e^6 + 6*b^6*c^2*d^6*e^2 + 64*a^2*b^2*c^4*d
^6*e^2 + 32*a^2*b^3*c^3*d^5*e^3 - 74*a^2*b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^3*d^4*e^4 + 32*a^3*b^3*c^2*d^3*e^5 +
64*a^4*b^2*c^2*d^2*e^6 + 32*a*b^3*c^4*d^7*e + 4*a*b^6*c*d^4*e^4 - 64*a^2*b*c^5*d^7*e + 32*a^4*b^3*c*d*e^7 - 64
*a^5*b*c^2*d*e^7 - 44*a*b^4*c^3*d^6*e^2 + 20*a*b^5*c^2*d^5*e^3 + 20*a^2*b^5*c*d^3*e^5 - 192*a^3*b*c^4*d^5*e^3
- 44*a^3*b^4*c*d^2*e^6 - 192*a^4*b*c^3*d^3*e^5)))*((53760*a^6*c^7*d*e^8 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) -
26880*a^6*b*c^6*e^9 - 9*b^13*e^9 - 2077*a^2*b^9*c^2*e^9 + 10656*a^3*b^7*c^3*e^9 - 30240*a^4*b^5*c^4*e^9 + 448
00*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) - 2048*a^3*c^10*d^7*e^2 - 17920*a^4*c^9*d^5*e^4 -
35840*a^5*c^8*d^3*e^6 + 32*b^6*c^7*d^7*e^2 - 112*b^7*c^6*d^6*e^3 + 98*b^8*c^5*d^5*e^4 + 35*b^9*c^4*d^4*e^5 -
70*b^10*c^3*d^3*e^6 + 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^9 + 21*b^
12*c*d*e^8 + 1536*a^2*b^2*c^9*d^7*e^2 - 5376*a^2*b^3*c^8*d^6*e^3 + 1344*a^2*b^4*c^7*d^5*e^4 + 10080*a^2*b^5*c^
6*d^4*e^5 - 7840*a^2*b^6*c^5*d^3*e^6 - 1008*a^2*b^7*c^4*d^2*e^7 + 7168*a^3*b^2*c^8*d^5*e^4 - 35840*a^3*b^3*c^7
*d^4*e^5 + 17920*a^3*b^4*c^6*d^3*e^6 + 12544*a^3*b^5*c^5*d^2*e^7 - 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*
e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) - 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8
*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7*e^2 + 1344*a*b^5*c^7*d^6*e^3 - 896*a*b^6*c^6*d^5*e^4 - 1120*a*b^
7*c^5*d^4*e^5 + 1260*a*b^8*c^4*d^3*e^6 - 98*a*b^9*c^3*d^2*e^7 + 5418*a^2*b^8*c^3*d*e^8 + 7168*a^3*b*c^9*d^6*e^
3 - 28224*a^3*b^6*c^4*d*e^8 + 44800*a^4*b*c^8*d^4*e^5 + 78400*a^4*b^4*c^5*d*e^8 + 53760*a^5*b*c^7*d^2*e^7 - 10
7520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2
) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10
+ b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9
- 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10
- 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^
2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 4096
0*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8
*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8
*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*
e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^
5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d
^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*
d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c
^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*
c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*
b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^
8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e
^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*
b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^
3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 -
81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*
a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2) + ((d + e*x)^(1/2)*(9*b^6*c^3*e^10 - 200*a^3*c^6*e^10 + 3
2*c^9*d^6*e^4 - 96*a*b^4*c^4*e^10 + 248*a*c^8*d^4*e^6 - 96*b*c^8*d^5*e^5 - 12*b^5*c^4*d*e^9 + 298*a^2*b^2*c^5*
e^10 + 592*a^2*c^7*d^2*e^8 + 58*b^2*c^7*d^4*e^6 + 44*b^3*c^6*d^3*e^7 - 26*b^4*c^5*d^2*e^8 - 496*a*b*c^7*d^3*e^
7 + 172*a*b^3*c^5*d*e^9 - 592*a^2*b*c^6*d*e^9 + 76*a*b^2*c^6*d^2*e^8))/(8*(16*a^2*c^6*d^8 + a^4*b^4*e^8 + 16*a
^6*c^2*e^8 + b^4*c^4*d^8 + b^8*d^4*e^4 - 8*a*b^2*c^5*d^8 - 8*a^5*b^2*c*e^8 - 4*a*b^7*d^3*e^5 - 4*a^3*b^5*d*e^7
- 4*b^5*c^3*d^7*e - 4*b^7*c*d^5*e^3 + 6*a^2*b^6*d^2*e^6 + 64*a^3*c^5*d^6*e^2 + 96*a^4*c^4*d^4*e^4 + 64*a^5*c^
3*d^2*e^6 + 6*b^6*c^2*d^6*e^2 + 64*a^2*b^2*c^4*d^6*e^2 + 32*a^2*b^3*c^3*d^5*e^3 - 74*a^2*b^4*c^2*d^4*e^4 + 144
*a^3*b^2*c^3*d^4*e^4 + 32*a^3*b^3*c^2*d^3*e^5 + 64*a^4*b^2*c^2*d^2*e^6 + 32*a*b^3*c^4*d^7*e + 4*a*b^6*c*d^4*e^
4 - 64*a^2*b*c^5*d^7*e + 32*a^4*b^3*c*d*e^7 - 64*a^5*b*c^2*d*e^7 - 44*a*b^4*c^3*d^6*e^2 + 20*a*b^5*c^2*d^5*e^3
+ 20*a^2*b^5*c*d^3*e^5 - 192*a^3*b*c^4*d^5*e^3 - 44*a^3*b^4*c*d^2*e^6 - 192*a^4*b*c^3*d^3*e^5)))*((53760*a^6*
c^7*d*e^8 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) - 26880*a^6*b*c^6*e^9 - 9*b^13*e^9 - 2077*a^2*b^9*c^2*e^9 + 106
56*a^3*b^7*c^3*e^9 - 30240*a^4*b^5*c^4*e^9 + 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) -
2048*a^3*c^10*d^7*e^2 - 17920*a^4*c^9*d^5*e^4 - 35840*a^5*c^8*d^3*e^6 + 32*b^6*c^7*d^7*e^2 - 112*b^7*c^6*d^6*
e^3 + 98*b^8*c^5*d^5*e^4 + 35*b^9*c^4*d^4*e^5 - 70*b^10*c^3*d^3*e^6 + 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(
4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^9 + 21*b^12*c*d*e^8 + 1536*a^2*b^2*c^9*d^7*e^2 - 5376*a^2*b^3*c^8*d^6*e
^3 + 1344*a^2*b^4*c^7*d^5*e^4 + 10080*a^2*b^5*c^6*d^4*e^5 - 7840*a^2*b^6*c^5*d^3*e^6 - 1008*a^2*b^7*c^4*d^2*e^
7 + 7168*a^3*b^2*c^8*d^5*e^4 - 35840*a^3*b^3*c^7*d^4*e^5 + 17920*a^3*b^4*c^6*d^3*e^6 + 12544*a^3*b^5*c^5*d^2*e
^7 - 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^
9)^(1/2) - 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7*e^2 + 1344*a*b^5
*c^7*d^6*e^3 - 896*a*b^6*c^6*d^5*e^4 - 1120*a*b^7*c^5*d^4*e^5 + 1260*a*b^8*c^4*d^3*e^6 - 98*a*b^9*c^3*d^2*e^7
+ 5418*a^2*b^8*c^3*d*e^8 + 7168*a^3*b*c^9*d^6*e^3 - 28224*a^3*b^6*c^4*d*e^8 + 44800*a^4*b*c^8*d^4*e^5 + 78400*
a^4*b^4*c^5*d*e^8 + 53760*a^5*b*c^7*d^2*e^7 - 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^
(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12
*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b
^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10
- 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6
*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480
*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e
^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 +
210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2
800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 -
16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 -
42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5
- 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^
2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*
e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d
^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^
7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5
*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b
^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*
e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 307
20*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*
b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*1i)/((((1
06496*a^6*c^7*d*e^10 - 53248*a^6*b*c^6*e^11 - 192*a^2*b^9*c^2*e^11 + 3136*a^3*b^7*c^3*e^11 - 19200*a^4*b^5*c^4
*e^11 + 52224*a^5*b^3*c^5*e^11 + 8192*a^3*c^10*d^7*e^4 + 122880*a^4*c^9*d^5*e^6 + 221184*a^5*c^8*d^3*e^8 - 128
*b^6*c^7*d^7*e^4 + 448*b^7*c^6*d^6*e^5 - 192*b^8*c^5*d^5*e^6 - 640*b^9*c^4*d^4*e^7 + 704*b^10*c^3*d^3*e^8 - 19
2*b^11*c^2*d^2*e^9 - 6144*a^2*b^2*c^9*d^7*e^4 + 21504*a^2*b^3*c^8*d^6*e^5 + 13824*a^2*b^4*c^7*d^5*e^6 - 88320*
a^2*b^5*c^6*d^4*e^7 + 67200*a^2*b^6*c^5*d^3*e^8 - 1728*a^2*b^7*c^4*d^2*e^9 - 79872*a^3*b^2*c^8*d^5*e^6 + 27136
0*a^3*b^3*c^7*d^4*e^7 - 151040*a^3*b^4*c^6*d^3*e^8 - 59136*a^3*b^5*c^5*d^2*e^9 + 30720*a^4*b^2*c^7*d^3*e^8 + 2
61120*a^4*b^3*c^6*d^2*e^9 + 384*a*b^10*c^2*d*e^10 + 1536*a*b^4*c^8*d^7*e^4 - 5376*a*b^5*c^7*d^6*e^5 + 384*a*b^
6*c^6*d^5*e^6 + 12480*a*b^7*c^5*d^4*e^7 - 11520*a*b^8*c^4*d^3*e^8 + 2112*a*b^9*c^3*d^2*e^9 - 5952*a^2*b^8*c^3*
d*e^10 - 28672*a^3*b*c^9*d^6*e^5 + 32896*a^3*b^6*c^4*d*e^10 - 307200*a^4*b*c^8*d^4*e^7 - 69120*a^4*b^4*c^5*d*e
^10 - 331776*a^5*b*c^7*d^2*e^9 + 6144*a^5*b^2*c^6*d*e^10)/(64*(64*a^3*c^7*d^8 - a^4*b^6*e^8 + 64*a^7*c^3*e^8 -
b^6*c^4*d^8 - b^10*d^4*e^4 + 12*a*b^4*c^5*d^8 + 12*a^5*b^4*c*e^8 + 4*a*b^9*d^3*e^5 + 4*a^3*b^7*d*e^7 + 4*b^7*
c^3*d^7*e + 4*b^9*c*d^5*e^3 - 48*a^2*b^2*c^6*d^8 - 48*a^6*b^2*c^2*e^8 - 6*a^2*b^8*d^2*e^6 + 256*a^4*c^6*d^6*e^
2 + 384*a^5*c^5*d^4*e^4 + 256*a^6*c^4*d^2*e^6 - 6*b^8*c^2*d^6*e^2 - 240*a^2*b^4*c^4*d^6*e^2 + 48*a^2*b^5*c^3*d
^5*e^3 + 90*a^2*b^6*c^2*d^4*e^4 + 192*a^3*b^2*c^5*d^6*e^2 + 320*a^3*b^3*c^4*d^5*e^3 - 440*a^3*b^4*c^3*d^4*e^4
+ 48*a^3*b^5*c^2*d^3*e^5 + 480*a^4*b^2*c^4*d^4*e^4 + 320*a^4*b^3*c^3*d^3*e^5 - 240*a^4*b^4*c^2*d^2*e^6 + 192*a
^5*b^2*c^3*d^2*e^6 - 48*a*b^5*c^4*d^7*e - 256*a^3*b*c^6*d^7*e - 48*a^4*b^5*c*d*e^7 - 256*a^6*b*c^3*d*e^7 + 68*
a*b^6*c^3*d^6*e^2 - 36*a*b^7*c^2*d^5*e^3 + 192*a^2*b^3*c^5*d^7*e - 36*a^2*b^7*c*d^3*e^5 + 68*a^3*b^6*c*d^2*e^6
- 768*a^4*b*c^5*d^5*e^3 - 768*a^5*b*c^4*d^3*e^5 + 192*a^5*b^3*c^2*d*e^7)) - ((d + e*x)^(1/2)*((53760*a^6*c^7*
d*e^8 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) - 26880*a^6*b*c^6*e^9 - 9*b^13*e^9 - 2077*a^2*b^9*c^2*e^9 + 10656*a
^3*b^7*c^3*e^9 - 30240*a^4*b^5*c^4*e^9 + 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) - 204
8*a^3*c^10*d^7*e^2 - 17920*a^4*c^9*d^5*e^4 - 35840*a^5*c^8*d^3*e^6 + 32*b^6*c^7*d^7*e^2 - 112*b^7*c^6*d^6*e^3
+ 98*b^8*c^5*d^5*e^4 + 35*b^9*c^4*d^4*e^5 - 70*b^10*c^3*d^3*e^6 + 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*
c - b^2)^9)^(1/2) + 213*a*b^11*c*e^9 + 21*b^12*c*d*e^8 + 1536*a^2*b^2*c^9*d^7*e^2 - 5376*a^2*b^3*c^8*d^6*e^3 +
1344*a^2*b^4*c^7*d^5*e^4 + 10080*a^2*b^5*c^6*d^4*e^5 - 7840*a^2*b^6*c^5*d^3*e^6 - 1008*a^2*b^7*c^4*d^2*e^7 +
7168*a^3*b^2*c^8*d^5*e^4 - 35840*a^3*b^3*c^7*d^4*e^5 + 17920*a^3*b^4*c^6*d^3*e^6 + 12544*a^3*b^5*c^5*d^2*e^7 -
44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(
1/2) - 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7*e^2 + 1344*a*b^5*c^7
*d^6*e^3 - 896*a*b^6*c^6*d^5*e^4 - 1120*a*b^7*c^5*d^4*e^5 + 1260*a*b^8*c^4*d^3*e^6 - 98*a*b^9*c^3*d^2*e^7 + 54
18*a^2*b^8*c^3*d*e^8 + 7168*a^3*b*c^9*d^6*e^3 - 28224*a^3*b^6*c^4*d*e^8 + 44800*a^4*b*c^8*d^4*e^5 + 78400*a^4*
b^4*c^5*d*e^8 + 53760*a^5*b*c^7*d^2*e^7 - 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2
) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^1
0 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*
c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 12
80*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3
*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7
*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 -
10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*
a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*
a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 1680
0*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 422
40*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 1
6800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 +
81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6
- 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e
^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^
4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9
*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*
c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6
+ 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a
^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^
8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*(8192*a^7*c^6
*d*e^10 - 4096*a^7*b*c^5*e^11 + 64*a^4*b^7*c^2*e^11 - 768*a^5*b^5*c^3*e^11 + 3072*a^6*b^3*c^4*e^11 + 8192*a^3*
c^10*d^9*e^2 + 32768*a^4*c^9*d^7*e^4 + 49152*a^5*c^8*d^5*e^6 + 32768*a^6*c^7*d^3*e^8 - 128*b^6*c^7*d^9*e^2 + 5
76*b^7*c^6*d^8*e^3 - 1024*b^8*c^5*d^7*e^4 + 896*b^9*c^4*d^6*e^5 - 384*b^10*c^3*d^5*e^6 + 64*b^11*c^2*d^4*e^7 -
6144*a^2*b^2*c^9*d^9*e^2 + 27648*a^2*b^3*c^8*d^8*e^3 - 43008*a^2*b^4*c^7*d^7*e^4 + 21504*a^2*b^5*c^6*d^6*e^5
+ 8448*a^2*b^6*c^5*d^5*e^6 - 10368*a^2*b^7*c^4*d^4*e^7 + 1536*a^2*b^8*c^3*d^3*e^8 + 384*a^2*b^9*c^2*d^2*e^9 +
40960*a^3*b^2*c^8*d^7*e^4 + 28672*a^3*b^3*c^7*d^6*e^5 - 76800*a^3*b^4*c^6*d^5*e^6 + 34304*a^3*b^5*c^5*d^4*e^7
+ 5632*a^3*b^6*c^4*d^3*e^8 - 3840*a^3*b^7*c^3*d^2*e^9 + 110592*a^4*b^2*c^7*d^5*e^6 + 10240*a^4*b^3*c^6*d^4*e^7
- 51200*a^4*b^4*c^5*d^3*e^8 + 9216*a^4*b^5*c^4*d^2*e^9 + 73728*a^5*b^2*c^6*d^3*e^8 + 12288*a^5*b^3*c^5*d^2*e^
9 + 1536*a*b^4*c^8*d^9*e^2 - 6912*a*b^5*c^7*d^8*e^3 + 11776*a*b^6*c^6*d^7*e^4 - 8960*a*b^7*c^5*d^6*e^5 + 2304*
a*b^8*c^4*d^5*e^6 + 512*a*b^9*c^3*d^4*e^7 - 256*a*b^10*c^2*d^3*e^8 - 36864*a^3*b*c^9*d^8*e^3 - 256*a^3*b^8*c^2
*d*e^10 - 114688*a^4*b*c^8*d^6*e^5 + 2944*a^4*b^6*c^3*d*e^10 - 122880*a^5*b*c^7*d^4*e^7 - 10752*a^5*b^4*c^4*d*
e^10 - 49152*a^6*b*c^6*d^2*e^9 + 10240*a^6*b^2*c^5*d*e^10))/(8*(16*a^2*c^6*d^8 + a^4*b^4*e^8 + 16*a^6*c^2*e^8
+ b^4*c^4*d^8 + b^8*d^4*e^4 - 8*a*b^2*c^5*d^8 - 8*a^5*b^2*c*e^8 - 4*a*b^7*d^3*e^5 - 4*a^3*b^5*d*e^7 - 4*b^5*c^
3*d^7*e - 4*b^7*c*d^5*e^3 + 6*a^2*b^6*d^2*e^6 + 64*a^3*c^5*d^6*e^2 + 96*a^4*c^4*d^4*e^4 + 64*a^5*c^3*d^2*e^6 +
6*b^6*c^2*d^6*e^2 + 64*a^2*b^2*c^4*d^6*e^2 + 32*a^2*b^3*c^3*d^5*e^3 - 74*a^2*b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^
3*d^4*e^4 + 32*a^3*b^3*c^2*d^3*e^5 + 64*a^4*b^2*c^2*d^2*e^6 + 32*a*b^3*c^4*d^7*e + 4*a*b^6*c*d^4*e^4 - 64*a^2*
b*c^5*d^7*e + 32*a^4*b^3*c*d*e^7 - 64*a^5*b*c^2*d*e^7 - 44*a*b^4*c^3*d^6*e^2 + 20*a*b^5*c^2*d^5*e^3 + 20*a^2*b
^5*c*d^3*e^5 - 192*a^3*b*c^4*d^5*e^3 - 44*a^3*b^4*c*d^2*e^6 - 192*a^4*b*c^3*d^3*e^5)))*((53760*a^6*c^7*d*e^8 -
9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) - 26880*a^6*b*c^6*e^9 - 9*b^13*e^9 - 2077*a^2*b^9*c^2*e^9 + 10656*a^3*b^7*
c^3*e^9 - 30240*a^4*b^5*c^4*e^9 + 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) - 2048*a^3*c
^10*d^7*e^2 - 17920*a^4*c^9*d^5*e^4 - 35840*a^5*c^8*d^3*e^6 + 32*b^6*c^7*d^7*e^2 - 112*b^7*c^6*d^6*e^3 + 98*b^
8*c^5*d^5*e^4 + 35*b^9*c^4*d^4*e^5 - 70*b^10*c^3*d^3*e^6 + 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2
)^9)^(1/2) + 213*a*b^11*c*e^9 + 21*b^12*c*d*e^8 + 1536*a^2*b^2*c^9*d^7*e^2 - 5376*a^2*b^3*c^8*d^6*e^3 + 1344*a
^2*b^4*c^7*d^5*e^4 + 10080*a^2*b^5*c^6*d^4*e^5 - 7840*a^2*b^6*c^5*d^3*e^6 - 1008*a^2*b^7*c^4*d^2*e^7 + 7168*a^
3*b^2*c^8*d^5*e^4 - 35840*a^3*b^3*c^7*d^4*e^5 + 17920*a^3*b^4*c^6*d^3*e^6 + 12544*a^3*b^5*c^5*d^2*e^7 - 44800*
a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) -
532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7*e^2 + 1344*a*b^5*c^7*d^6*e^
3 - 896*a*b^6*c^6*d^5*e^4 - 1120*a*b^7*c^5*d^4*e^5 + 1260*a*b^8*c^4*d^3*e^6 - 98*a*b^9*c^3*d^2*e^7 + 5418*a^2*
b^8*c^3*d*e^8 + 7168*a^3*b*c^9*d^6*e^3 - 28224*a^3*b^6*c^4*d*e^8 + 44800*a^4*b*c^8*d^4*e^5 + 78400*a^4*b^4*c^5
*d*e^8 + 53760*a^5*b*c^7*d^2*e^7 - 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*
b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 409
6*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10
+ 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*
b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 +
3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d
^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^1
5*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^1
3*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^1
1*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b
^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*
b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^
5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a
^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800
*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 12
5440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 +
81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*
a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8
*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*
a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*
c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e
^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2) - ((d + e*x)^(1/2)*(
9*b^6*c^3*e^10 - 200*a^3*c^6*e^10 + 32*c^9*d^6*e^4 - 96*a*b^4*c^4*e^10 + 248*a*c^8*d^4*e^6 - 96*b*c^8*d^5*e^5
- 12*b^5*c^4*d*e^9 + 298*a^2*b^2*c^5*e^10 + 592*a^2*c^7*d^2*e^8 + 58*b^2*c^7*d^4*e^6 + 44*b^3*c^6*d^3*e^7 - 26
*b^4*c^5*d^2*e^8 - 496*a*b*c^7*d^3*e^7 + 172*a*b^3*c^5*d*e^9 - 592*a^2*b*c^6*d*e^9 + 76*a*b^2*c^6*d^2*e^8))/(8
*(16*a^2*c^6*d^8 + a^4*b^4*e^8 + 16*a^6*c^2*e^8 + b^4*c^4*d^8 + b^8*d^4*e^4 - 8*a*b^2*c^5*d^8 - 8*a^5*b^2*c*e^
8 - 4*a*b^7*d^3*e^5 - 4*a^3*b^5*d*e^7 - 4*b^5*c^3*d^7*e - 4*b^7*c*d^5*e^3 + 6*a^2*b^6*d^2*e^6 + 64*a^3*c^5*d^6
*e^2 + 96*a^4*c^4*d^4*e^4 + 64*a^5*c^3*d^2*e^6 + 6*b^6*c^2*d^6*e^2 + 64*a^2*b^2*c^4*d^6*e^2 + 32*a^2*b^3*c^3*d
^5*e^3 - 74*a^2*b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^3*d^4*e^4 + 32*a^3*b^3*c^2*d^3*e^5 + 64*a^4*b^2*c^2*d^2*e^6 +
32*a*b^3*c^4*d^7*e + 4*a*b^6*c*d^4*e^4 - 64*a^2*b*c^5*d^7*e + 32*a^4*b^3*c*d*e^7 - 64*a^5*b*c^2*d*e^7 - 44*a*b
^4*c^3*d^6*e^2 + 20*a*b^5*c^2*d^5*e^3 + 20*a^2*b^5*c*d^3*e^5 - 192*a^3*b*c^4*d^5*e^3 - 44*a^3*b^4*c*d^2*e^6 -
192*a^4*b*c^3*d^3*e^5)))*((53760*a^6*c^7*d*e^8 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) - 26880*a^6*b*c^6*e^9 - 9*
b^13*e^9 - 2077*a^2*b^9*c^2*e^9 + 10656*a^3*b^7*c^3*e^9 - 30240*a^4*b^5*c^4*e^9 + 44800*a^5*b^3*c^5*e^9 - 25*a
^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) - 2048*a^3*c^10*d^7*e^2 - 17920*a^4*c^9*d^5*e^4 - 35840*a^5*c^8*d^3*e^6 +
32*b^6*c^7*d^7*e^2 - 112*b^7*c^6*d^6*e^3 + 98*b^8*c^5*d^5*e^4 + 35*b^9*c^4*d^4*e^5 - 70*b^10*c^3*d^3*e^6 + 14*
b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^9 + 21*b^12*c*d*e^8 + 1536*a^2*b^2
*c^9*d^7*e^2 - 5376*a^2*b^3*c^8*d^6*e^3 + 1344*a^2*b^4*c^7*d^5*e^4 + 10080*a^2*b^5*c^6*d^4*e^5 - 7840*a^2*b^6*
c^5*d^3*e^6 - 1008*a^2*b^7*c^4*d^2*e^7 + 7168*a^3*b^2*c^8*d^5*e^4 - 35840*a^3*b^3*c^7*d^4*e^5 + 17920*a^3*b^4*
c^6*d^3*e^6 + 12544*a^3*b^5*c^5*d^2*e^7 - 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1
/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) - 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2)
- 384*a*b^4*c^8*d^7*e^2 + 1344*a*b^5*c^7*d^6*e^3 - 896*a*b^6*c^6*d^5*e^4 - 1120*a*b^7*c^5*d^4*e^5 + 1260*a*b^
8*c^4*d^3*e^6 - 98*a*b^9*c^3*d^2*e^7 + 5418*a^2*b^8*c^3*d*e^8 + 7168*a^3*b*c^9*d^6*e^3 - 28224*a^3*b^6*c^4*d*e
^8 + 44800*a^4*b*c^8*d^4*e^5 + 78400*a^4*b^4*c^5*d*e^8 + 53760*a^5*b*c^7*d^2*e^7 - 107520*a^5*b^2*c^6*d*e^8 +
154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(
4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^
5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b
^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10
+ 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*
d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480
*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*
d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d
^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d
^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*
d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^
6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c
^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5
*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b
^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a
^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240
*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9
*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a
^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8
*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 +
6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720
*a^9*b^3*c^5*d*e^9)))^(1/2) - (1000*a^2*c^7*e^10 + 63*b^4*c^5*e^10 - 32*c^9*d^4*e^6 - 510*a*b^2*c^6*e^10 - 40*
a*c^8*d^2*e^8 + 64*b*c^8*d^3*e^7 + 6*b^3*c^6*d*e^9 - 38*b^2*c^7*d^2*e^8 + 40*a*b*c^7*d*e^9)/(32*(64*a^3*c^7*d^
8 - a^4*b^6*e^8 + 64*a^7*c^3*e^8 - b^6*c^4*d^8 - b^10*d^4*e^4 + 12*a*b^4*c^5*d^8 + 12*a^5*b^4*c*e^8 + 4*a*b^9*
d^3*e^5 + 4*a^3*b^7*d*e^7 + 4*b^7*c^3*d^7*e + 4*b^9*c*d^5*e^3 - 48*a^2*b^2*c^6*d^8 - 48*a^6*b^2*c^2*e^8 - 6*a^
2*b^8*d^2*e^6 + 256*a^4*c^6*d^6*e^2 + 384*a^5*c^5*d^4*e^4 + 256*a^6*c^4*d^2*e^6 - 6*b^8*c^2*d^6*e^2 - 240*a^2*
b^4*c^4*d^6*e^2 + 48*a^2*b^5*c^3*d^5*e^3 + 90*a^2*b^6*c^2*d^4*e^4 + 192*a^3*b^2*c^5*d^6*e^2 + 320*a^3*b^3*c^4*
d^5*e^3 - 440*a^3*b^4*c^3*d^4*e^4 + 48*a^3*b^5*c^2*d^3*e^5 + 480*a^4*b^2*c^4*d^4*e^4 + 320*a^4*b^3*c^3*d^3*e^5
- 240*a^4*b^4*c^2*d^2*e^6 + 192*a^5*b^2*c^3*d^2*e^6 - 48*a*b^5*c^4*d^7*e - 256*a^3*b*c^6*d^7*e - 48*a^4*b^5*c
*d*e^7 - 256*a^6*b*c^3*d*e^7 + 68*a*b^6*c^3*d^6*e^2 - 36*a*b^7*c^2*d^5*e^3 + 192*a^2*b^3*c^5*d^7*e - 36*a^2*b^
7*c*d^3*e^5 + 68*a^3*b^6*c*d^2*e^6 - 768*a^4*b*c^5*d^5*e^3 - 768*a^5*b*c^4*d^3*e^5 + 192*a^5*b^3*c^2*d*e^7)) +
(((106496*a^6*c^7*d*e^10 - 53248*a^6*b*c^6*e^11 - 192*a^2*b^9*c^2*e^11 + 3136*a^3*b^7*c^3*e^11 - 19200*a^4*b^
5*c^4*e^11 + 52224*a^5*b^3*c^5*e^11 + 8192*a^3*c^10*d^7*e^4 + 122880*a^4*c^9*d^5*e^6 + 221184*a^5*c^8*d^3*e^8
- 128*b^6*c^7*d^7*e^4 + 448*b^7*c^6*d^6*e^5 - 192*b^8*c^5*d^5*e^6 - 640*b^9*c^4*d^4*e^7 + 704*b^10*c^3*d^3*e^8
- 192*b^11*c^2*d^2*e^9 - 6144*a^2*b^2*c^9*d^7*e^4 + 21504*a^2*b^3*c^8*d^6*e^5 + 13824*a^2*b^4*c^7*d^5*e^6 - 8
8320*a^2*b^5*c^6*d^4*e^7 + 67200*a^2*b^6*c^5*d^3*e^8 - 1728*a^2*b^7*c^4*d^2*e^9 - 79872*a^3*b^2*c^8*d^5*e^6 +
271360*a^3*b^3*c^7*d^4*e^7 - 151040*a^3*b^4*c^6*d^3*e^8 - 59136*a^3*b^5*c^5*d^2*e^9 + 30720*a^4*b^2*c^7*d^3*e^
8 + 261120*a^4*b^3*c^6*d^2*e^9 + 384*a*b^10*c^2*d*e^10 + 1536*a*b^4*c^8*d^7*e^4 - 5376*a*b^5*c^7*d^6*e^5 + 384
*a*b^6*c^6*d^5*e^6 + 12480*a*b^7*c^5*d^4*e^7 - 11520*a*b^8*c^4*d^3*e^8 + 2112*a*b^9*c^3*d^2*e^9 - 5952*a^2*b^8
*c^3*d*e^10 - 28672*a^3*b*c^9*d^6*e^5 + 32896*a^3*b^6*c^4*d*e^10 - 307200*a^4*b*c^8*d^4*e^7 - 69120*a^4*b^4*c^
5*d*e^10 - 331776*a^5*b*c^7*d^2*e^9 + 6144*a^5*b^2*c^6*d*e^10)/(64*(64*a^3*c^7*d^8 - a^4*b^6*e^8 + 64*a^7*c^3*
e^8 - b^6*c^4*d^8 - b^10*d^4*e^4 + 12*a*b^4*c^5*d^8 + 12*a^5*b^4*c*e^8 + 4*a*b^9*d^3*e^5 + 4*a^3*b^7*d*e^7 + 4
*b^7*c^3*d^7*e + 4*b^9*c*d^5*e^3 - 48*a^2*b^2*c^6*d^8 - 48*a^6*b^2*c^2*e^8 - 6*a^2*b^8*d^2*e^6 + 256*a^4*c^6*d
^6*e^2 + 384*a^5*c^5*d^4*e^4 + 256*a^6*c^4*d^2*e^6 - 6*b^8*c^2*d^6*e^2 - 240*a^2*b^4*c^4*d^6*e^2 + 48*a^2*b^5*
c^3*d^5*e^3 + 90*a^2*b^6*c^2*d^4*e^4 + 192*a^3*b^2*c^5*d^6*e^2 + 320*a^3*b^3*c^4*d^5*e^3 - 440*a^3*b^4*c^3*d^4
*e^4 + 48*a^3*b^5*c^2*d^3*e^5 + 480*a^4*b^2*c^4*d^4*e^4 + 320*a^4*b^3*c^3*d^3*e^5 - 240*a^4*b^4*c^2*d^2*e^6 +
192*a^5*b^2*c^3*d^2*e^6 - 48*a*b^5*c^4*d^7*e - 256*a^3*b*c^6*d^7*e - 48*a^4*b^5*c*d*e^7 - 256*a^6*b*c^3*d*e^7
+ 68*a*b^6*c^3*d^6*e^2 - 36*a*b^7*c^2*d^5*e^3 + 192*a^2*b^3*c^5*d^7*e - 36*a^2*b^7*c*d^3*e^5 + 68*a^3*b^6*c*d^
2*e^6 - 768*a^4*b*c^5*d^5*e^3 - 768*a^5*b*c^4*d^3*e^5 + 192*a^5*b^3*c^2*d*e^7)) + ((d + e*x)^(1/2)*((53760*a^6
*c^7*d*e^8 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) - 26880*a^6*b*c^6*e^9 - 9*b^13*e^9 - 2077*a^2*b^9*c^2*e^9 + 10
656*a^3*b^7*c^3*e^9 - 30240*a^4*b^5*c^4*e^9 + 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2)
- 2048*a^3*c^10*d^7*e^2 - 17920*a^4*c^9*d^5*e^4 - 35840*a^5*c^8*d^3*e^6 + 32*b^6*c^7*d^7*e^2 - 112*b^7*c^6*d^6
*e^3 + 98*b^8*c^5*d^5*e^4 + 35*b^9*c^4*d^4*e^5 - 70*b^10*c^3*d^3*e^6 + 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-
(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^9 + 21*b^12*c*d*e^8 + 1536*a^2*b^2*c^9*d^7*e^2 - 5376*a^2*b^3*c^8*d^6*
e^3 + 1344*a^2*b^4*c^7*d^5*e^4 + 10080*a^2*b^5*c^6*d^4*e^5 - 7840*a^2*b^6*c^5*d^3*e^6 - 1008*a^2*b^7*c^4*d^2*e
^7 + 7168*a^3*b^2*c^8*d^5*e^4 - 35840*a^3*b^3*c^7*d^4*e^5 + 17920*a^3*b^4*c^6*d^3*e^6 + 12544*a^3*b^5*c^5*d^2*
e^7 - 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)
^9)^(1/2) - 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7*e^2 + 1344*a*b^
5*c^7*d^6*e^3 - 896*a*b^6*c^6*d^5*e^4 - 1120*a*b^7*c^5*d^4*e^5 + 1260*a*b^8*c^4*d^3*e^6 - 98*a*b^9*c^3*d^2*e^7
+ 5418*a^2*b^8*c^3*d*e^8 + 7168*a^3*b*c^9*d^6*e^3 - 28224*a^3*b^6*c^4*d*e^8 + 44800*a^4*b*c^8*d^4*e^5 + 78400
*a^4*b^4*c^5*d*e^8 + 53760*a^5*b*c^7*d^2*e^7 - 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)
^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^1
2*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*
b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10
- 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^
6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 2048
0*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*
e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 +
210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 -
2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 -
16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7
- 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^
5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e
^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4
*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*
d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c
^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^
5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*
b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4
*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30
720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8
*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*(8192*a^
7*c^6*d*e^10 - 4096*a^7*b*c^5*e^11 + 64*a^4*b^7*c^2*e^11 - 768*a^5*b^5*c^3*e^11 + 3072*a^6*b^3*c^4*e^11 + 8192
*a^3*c^10*d^9*e^2 + 32768*a^4*c^9*d^7*e^4 + 49152*a^5*c^8*d^5*e^6 + 32768*a^6*c^7*d^3*e^8 - 128*b^6*c^7*d^9*e^
2 + 576*b^7*c^6*d^8*e^3 - 1024*b^8*c^5*d^7*e^4 + 896*b^9*c^4*d^6*e^5 - 384*b^10*c^3*d^5*e^6 + 64*b^11*c^2*d^4*
e^7 - 6144*a^2*b^2*c^9*d^9*e^2 + 27648*a^2*b^3*c^8*d^8*e^3 - 43008*a^2*b^4*c^7*d^7*e^4 + 21504*a^2*b^5*c^6*d^6
*e^5 + 8448*a^2*b^6*c^5*d^5*e^6 - 10368*a^2*b^7*c^4*d^4*e^7 + 1536*a^2*b^8*c^3*d^3*e^8 + 384*a^2*b^9*c^2*d^2*e
^9 + 40960*a^3*b^2*c^8*d^7*e^4 + 28672*a^3*b^3*c^7*d^6*e^5 - 76800*a^3*b^4*c^6*d^5*e^6 + 34304*a^3*b^5*c^5*d^4
*e^7 + 5632*a^3*b^6*c^4*d^3*e^8 - 3840*a^3*b^7*c^3*d^2*e^9 + 110592*a^4*b^2*c^7*d^5*e^6 + 10240*a^4*b^3*c^6*d^
4*e^7 - 51200*a^4*b^4*c^5*d^3*e^8 + 9216*a^4*b^5*c^4*d^2*e^9 + 73728*a^5*b^2*c^6*d^3*e^8 + 12288*a^5*b^3*c^5*d
^2*e^9 + 1536*a*b^4*c^8*d^9*e^2 - 6912*a*b^5*c^7*d^8*e^3 + 11776*a*b^6*c^6*d^7*e^4 - 8960*a*b^7*c^5*d^6*e^5 +
2304*a*b^8*c^4*d^5*e^6 + 512*a*b^9*c^3*d^4*e^7 - 256*a*b^10*c^2*d^3*e^8 - 36864*a^3*b*c^9*d^8*e^3 - 256*a^3*b^
8*c^2*d*e^10 - 114688*a^4*b*c^8*d^6*e^5 + 2944*a^4*b^6*c^3*d*e^10 - 122880*a^5*b*c^7*d^4*e^7 - 10752*a^5*b^4*c
^4*d*e^10 - 49152*a^6*b*c^6*d^2*e^9 + 10240*a^6*b^2*c^5*d*e^10))/(8*(16*a^2*c^6*d^8 + a^4*b^4*e^8 + 16*a^6*c^2
*e^8 + b^4*c^4*d^8 + b^8*d^4*e^4 - 8*a*b^2*c^5*d^8 - 8*a^5*b^2*c*e^8 - 4*a*b^7*d^3*e^5 - 4*a^3*b^5*d*e^7 - 4*b
^5*c^3*d^7*e - 4*b^7*c*d^5*e^3 + 6*a^2*b^6*d^2*e^6 + 64*a^3*c^5*d^6*e^2 + 96*a^4*c^4*d^4*e^4 + 64*a^5*c^3*d^2*
e^6 + 6*b^6*c^2*d^6*e^2 + 64*a^2*b^2*c^4*d^6*e^2 + 32*a^2*b^3*c^3*d^5*e^3 - 74*a^2*b^4*c^2*d^4*e^4 + 144*a^3*b
^2*c^3*d^4*e^4 + 32*a^3*b^3*c^2*d^3*e^5 + 64*a^4*b^2*c^2*d^2*e^6 + 32*a*b^3*c^4*d^7*e + 4*a*b^6*c*d^4*e^4 - 64
*a^2*b*c^5*d^7*e + 32*a^4*b^3*c*d*e^7 - 64*a^5*b*c^2*d*e^7 - 44*a*b^4*c^3*d^6*e^2 + 20*a*b^5*c^2*d^5*e^3 + 20*
a^2*b^5*c*d^3*e^5 - 192*a^3*b*c^4*d^5*e^3 - 44*a^3*b^4*c*d^2*e^6 - 192*a^4*b*c^3*d^3*e^5)))*((53760*a^6*c^7*d*
e^8 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) - 26880*a^6*b*c^6*e^9 - 9*b^13*e^9 - 2077*a^2*b^9*c^2*e^9 + 10656*a^3
*b^7*c^3*e^9 - 30240*a^4*b^5*c^4*e^9 + 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) - 2048*
a^3*c^10*d^7*e^2 - 17920*a^4*c^9*d^5*e^4 - 35840*a^5*c^8*d^3*e^6 + 32*b^6*c^7*d^7*e^2 - 112*b^7*c^6*d^6*e^3 +
98*b^8*c^5*d^5*e^4 + 35*b^9*c^4*d^4*e^5 - 70*b^10*c^3*d^3*e^6 + 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c
- b^2)^9)^(1/2) + 213*a*b^11*c*e^9 + 21*b^12*c*d*e^8 + 1536*a^2*b^2*c^9*d^7*e^2 - 5376*a^2*b^3*c^8*d^6*e^3 + 1
344*a^2*b^4*c^7*d^5*e^4 + 10080*a^2*b^5*c^6*d^4*e^5 - 7840*a^2*b^6*c^5*d^3*e^6 - 1008*a^2*b^7*c^4*d^2*e^7 + 71
68*a^3*b^2*c^8*d^5*e^4 - 35840*a^3*b^3*c^7*d^4*e^5 + 17920*a^3*b^4*c^6*d^3*e^6 + 12544*a^3*b^5*c^5*d^2*e^7 - 4
4800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/
2) - 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7*e^2 + 1344*a*b^5*c^7*d
^6*e^3 - 896*a*b^6*c^6*d^5*e^4 - 1120*a*b^7*c^5*d^4*e^5 + 1260*a*b^8*c^4*d^3*e^6 - 98*a*b^9*c^3*d^2*e^7 + 5418
*a^2*b^8*c^3*d*e^8 + 7168*a^3*b*c^9*d^6*e^3 - 28224*a^3*b^6*c^4*d*e^8 + 44800*a^4*b*c^8*d^4*e^5 + 78400*a^4*b^
4*c^5*d*e^8 + 53760*a^5*b*c^7*d^2*e^7 - 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2)
- 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10
+ 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*
e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280
*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e
^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c
^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 1
0*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^
2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^
3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*
a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240
*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 168
00*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81
920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 -
12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5
- 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*
e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e
+ 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^
4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 +
6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5
*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*
d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2) + ((d + e*x)^(1
/2)*(9*b^6*c^3*e^10 - 200*a^3*c^6*e^10 + 32*c^9*d^6*e^4 - 96*a*b^4*c^4*e^10 + 248*a*c^8*d^4*e^6 - 96*b*c^8*d^5
*e^5 - 12*b^5*c^4*d*e^9 + 298*a^2*b^2*c^5*e^10 + 592*a^2*c^7*d^2*e^8 + 58*b^2*c^7*d^4*e^6 + 44*b^3*c^6*d^3*e^7
- 26*b^4*c^5*d^2*e^8 - 496*a*b*c^7*d^3*e^7 + 172*a*b^3*c^5*d*e^9 - 592*a^2*b*c^6*d*e^9 + 76*a*b^2*c^6*d^2*e^8
))/(8*(16*a^2*c^6*d^8 + a^4*b^4*e^8 + 16*a^6*c^2*e^8 + b^4*c^4*d^8 + b^8*d^4*e^4 - 8*a*b^2*c^5*d^8 - 8*a^5*b^2
*c*e^8 - 4*a*b^7*d^3*e^5 - 4*a^3*b^5*d*e^7 - 4*b^5*c^3*d^7*e - 4*b^7*c*d^5*e^3 + 6*a^2*b^6*d^2*e^6 + 64*a^3*c^
5*d^6*e^2 + 96*a^4*c^4*d^4*e^4 + 64*a^5*c^3*d^2*e^6 + 6*b^6*c^2*d^6*e^2 + 64*a^2*b^2*c^4*d^6*e^2 + 32*a^2*b^3*
c^3*d^5*e^3 - 74*a^2*b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^3*d^4*e^4 + 32*a^3*b^3*c^2*d^3*e^5 + 64*a^4*b^2*c^2*d^2*e
^6 + 32*a*b^3*c^4*d^7*e + 4*a*b^6*c*d^4*e^4 - 64*a^2*b*c^5*d^7*e + 32*a^4*b^3*c*d*e^7 - 64*a^5*b*c^2*d*e^7 - 4
4*a*b^4*c^3*d^6*e^2 + 20*a*b^5*c^2*d^5*e^3 + 20*a^2*b^5*c*d^3*e^5 - 192*a^3*b*c^4*d^5*e^3 - 44*a^3*b^4*c*d^2*e
^6 - 192*a^4*b*c^3*d^3*e^5)))*((53760*a^6*c^7*d*e^8 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) - 26880*a^6*b*c^6*e^9
- 9*b^13*e^9 - 2077*a^2*b^9*c^2*e^9 + 10656*a^3*b^7*c^3*e^9 - 30240*a^4*b^5*c^4*e^9 + 44800*a^5*b^3*c^5*e^9 -
25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) - 2048*a^3*c^10*d^7*e^2 - 17920*a^4*c^9*d^5*e^4 - 35840*a^5*c^8*d^3*e
^6 + 32*b^6*c^7*d^7*e^2 - 112*b^7*c^6*d^6*e^3 + 98*b^8*c^5*d^5*e^4 + 35*b^9*c^4*d^4*e^5 - 70*b^10*c^3*d^3*e^6
+ 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^9 + 21*b^12*c*d*e^8 + 1536*a^
2*b^2*c^9*d^7*e^2 - 5376*a^2*b^3*c^8*d^6*e^3 + 1344*a^2*b^4*c^7*d^5*e^4 + 10080*a^2*b^5*c^6*d^4*e^5 - 7840*a^2
*b^6*c^5*d^3*e^6 - 1008*a^2*b^7*c^4*d^2*e^7 + 7168*a^3*b^2*c^8*d^5*e^4 - 35840*a^3*b^3*c^7*d^4*e^5 + 17920*a^3
*b^4*c^6*d^3*e^6 + 12544*a^3*b^5*c^5*d^2*e^7 - 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^
9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) - 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^
(1/2) - 384*a*b^4*c^8*d^7*e^2 + 1344*a*b^5*c^7*d^6*e^3 - 896*a*b^6*c^6*d^5*e^4 - 1120*a*b^7*c^5*d^4*e^5 + 1260
*a*b^8*c^4*d^3*e^6 - 98*a*b^9*c^3*d^2*e^7 + 5418*a^2*b^8*c^3*d*e^8 + 7168*a^3*b*c^9*d^6*e^3 - 28224*a^3*b^6*c^
4*d*e^8 + 44800*a^4*b*c^8*d^4*e^5 + 78400*a^4*b^4*c^5*d*e^8 + 53760*a^5*b*c^7*d^2*e^7 - 107520*a^5*b^2*c^6*d*e
^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^
8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^
17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e
+ 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*
d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*
b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 +
20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11
*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*
c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*
c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10
*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b
^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b
^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^
6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*
a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32
000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 +
10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^1
0*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1
200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^
5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*
e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 +
30720*a^9*b^3*c^5*d*e^9)))^(1/2)))*((53760*a^6*c^7*d*e^8 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) - 26880*a^6*b*c^
6*e^9 - 9*b^13*e^9 - 2077*a^2*b^9*c^2*e^9 + 10656*a^3*b^7*c^3*e^9 - 30240*a^4*b^5*c^4*e^9 + 44800*a^5*b^3*c^5*
e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) - 2048*a^3*c^10*d^7*e^2 - 17920*a^4*c^9*d^5*e^4 - 35840*a^5*c^8*
d^3*e^6 + 32*b^6*c^7*d^7*e^2 - 112*b^7*c^6*d^6*e^3 + 98*b^8*c^5*d^5*e^4 + 35*b^9*c^4*d^4*e^5 - 70*b^10*c^3*d^3
*e^6 + 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^9 + 21*b^12*c*d*e^8 + 15
36*a^2*b^2*c^9*d^7*e^2 - 5376*a^2*b^3*c^8*d^6*e^3 + 1344*a^2*b^4*c^7*d^5*e^4 + 10080*a^2*b^5*c^6*d^4*e^5 - 784
0*a^2*b^6*c^5*d^3*e^6 - 1008*a^2*b^7*c^4*d^2*e^7 + 7168*a^3*b^2*c^8*d^5*e^4 - 35840*a^3*b^3*c^7*d^4*e^5 + 1792
0*a^3*b^4*c^6*d^3*e^6 + 12544*a^3*b^5*c^5*d^2*e^7 - 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c -
b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) - 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2
)^9)^(1/2) - 384*a*b^4*c^8*d^7*e^2 + 1344*a*b^5*c^7*d^6*e^3 - 896*a*b^6*c^6*d^5*e^4 - 1120*a*b^7*c^5*d^4*e^5 +
1260*a*b^8*c^4*d^3*e^6 - 98*a*b^9*c^3*d^2*e^7 + 5418*a^2*b^8*c^3*d*e^8 + 7168*a^3*b*c^9*d^6*e^3 - 28224*a^3*b
^6*c^4*d*e^8 + 44800*a^4*b*c^8*d^4*e^5 + 78400*a^4*b^4*c^5*d*e^8 + 53760*a^5*b*c^7*d^2*e^7 - 107520*a^5*b^2*c^
6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2
*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10
- b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d
^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*
c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10
*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e
^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2
*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3
*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4
*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4
*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*
a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*
a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 35
84*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 6
1440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7
+ 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e
^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*
b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^
4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a
^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9
*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e
^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*2i - atan(((((106496*a^6*c^7*d*e^10 - 53248*a^6*b*c^6*e^11 - 192*a^2*b^9
*c^2*e^11 + 3136*a^3*b^7*c^3*e^11 - 19200*a^4*b^5*c^4*e^11 + 52224*a^5*b^3*c^5*e^11 + 8192*a^3*c^10*d^7*e^4 +
122880*a^4*c^9*d^5*e^6 + 221184*a^5*c^8*d^3*e^8 - 128*b^6*c^7*d^7*e^4 + 448*b^7*c^6*d^6*e^5 - 192*b^8*c^5*d^5*
e^6 - 640*b^9*c^4*d^4*e^7 + 704*b^10*c^3*d^3*e^8 - 192*b^11*c^2*d^2*e^9 - 6144*a^2*b^2*c^9*d^7*e^4 + 21504*a^2
*b^3*c^8*d^6*e^5 + 13824*a^2*b^4*c^7*d^5*e^6 - 88320*a^2*b^5*c^6*d^4*e^7 + 67200*a^2*b^6*c^5*d^3*e^8 - 1728*a^
2*b^7*c^4*d^2*e^9 - 79872*a^3*b^2*c^8*d^5*e^6 + 271360*a^3*b^3*c^7*d^4*e^7 - 151040*a^3*b^4*c^6*d^3*e^8 - 5913
6*a^3*b^5*c^5*d^2*e^9 + 30720*a^4*b^2*c^7*d^3*e^8 + 261120*a^4*b^3*c^6*d^2*e^9 + 384*a*b^10*c^2*d*e^10 + 1536*
a*b^4*c^8*d^7*e^4 - 5376*a*b^5*c^7*d^6*e^5 + 384*a*b^6*c^6*d^5*e^6 + 12480*a*b^7*c^5*d^4*e^7 - 11520*a*b^8*c^4
*d^3*e^8 + 2112*a*b^9*c^3*d^2*e^9 - 5952*a^2*b^8*c^3*d*e^10 - 28672*a^3*b*c^9*d^6*e^5 + 32896*a^3*b^6*c^4*d*e^
10 - 307200*a^4*b*c^8*d^4*e^7 - 69120*a^4*b^4*c^5*d*e^10 - 331776*a^5*b*c^7*d^2*e^9 + 6144*a^5*b^2*c^6*d*e^10)
/(64*(64*a^3*c^7*d^8 - a^4*b^6*e^8 + 64*a^7*c^3*e^8 - b^6*c^4*d^8 - b^10*d^4*e^4 + 12*a*b^4*c^5*d^8 + 12*a^5*b
^4*c*e^8 + 4*a*b^9*d^3*e^5 + 4*a^3*b^7*d*e^7 + 4*b^7*c^3*d^7*e + 4*b^9*c*d^5*e^3 - 48*a^2*b^2*c^6*d^8 - 48*a^6
*b^2*c^2*e^8 - 6*a^2*b^8*d^2*e^6 + 256*a^4*c^6*d^6*e^2 + 384*a^5*c^5*d^4*e^4 + 256*a^6*c^4*d^2*e^6 - 6*b^8*c^2
*d^6*e^2 - 240*a^2*b^4*c^4*d^6*e^2 + 48*a^2*b^5*c^3*d^5*e^3 + 90*a^2*b^6*c^2*d^4*e^4 + 192*a^3*b^2*c^5*d^6*e^2
+ 320*a^3*b^3*c^4*d^5*e^3 - 440*a^3*b^4*c^3*d^4*e^4 + 48*a^3*b^5*c^2*d^3*e^5 + 480*a^4*b^2*c^4*d^4*e^4 + 320*
a^4*b^3*c^3*d^3*e^5 - 240*a^4*b^4*c^2*d^2*e^6 + 192*a^5*b^2*c^3*d^2*e^6 - 48*a*b^5*c^4*d^7*e - 256*a^3*b*c^6*d
^7*e - 48*a^4*b^5*c*d*e^7 - 256*a^6*b*c^3*d*e^7 + 68*a*b^6*c^3*d^6*e^2 - 36*a*b^7*c^2*d^5*e^3 + 192*a^2*b^3*c^
5*d^7*e - 36*a^2*b^7*c*d^3*e^5 + 68*a^3*b^6*c*d^2*e^6 - 768*a^4*b*c^5*d^5*e^3 - 768*a^5*b*c^4*d^3*e^5 + 192*a^
5*b^3*c^2*d*e^7)) - ((d + e*x)^(1/2)*(-(9*b^13*e^9 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) + 26880*a^6*b*c^6*e^9
- 53760*a^6*c^7*d*e^8 + 2077*a^2*b^9*c^2*e^9 - 10656*a^3*b^7*c^3*e^9 + 30240*a^4*b^5*c^4*e^9 - 44800*a^5*b^3*c
^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^10*d^7*e^2 + 17920*a^4*c^9*d^5*e^4 + 35840*a^5*c
^8*d^3*e^6 - 32*b^6*c^7*d^7*e^2 + 112*b^7*c^6*d^6*e^3 - 98*b^8*c^5*d^5*e^4 - 35*b^9*c^4*d^4*e^5 + 70*b^10*c^3*
d^3*e^6 - 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^9 - 21*b^12*c*d*e^8 -
1536*a^2*b^2*c^9*d^7*e^2 + 5376*a^2*b^3*c^8*d^6*e^3 - 1344*a^2*b^4*c^7*d^5*e^4 - 10080*a^2*b^5*c^6*d^4*e^5 +
7840*a^2*b^6*c^5*d^3*e^6 + 1008*a^2*b^7*c^4*d^2*e^7 - 7168*a^3*b^2*c^8*d^5*e^4 + 35840*a^3*b^3*c^7*d^4*e^5 - 1
7920*a^3*b^4*c^6*d^3*e^6 - 12544*a^3*b^5*c^5*d^2*e^7 + 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c
- b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) + 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c -
b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7*e^2 - 1344*a*b^5*c^7*d^6*e^3 + 896*a*b^6*c^6*d^5*e^4 + 1120*a*b^7*c^5*d^4*e^
5 - 1260*a*b^8*c^4*d^3*e^6 + 98*a*b^9*c^3*d^2*e^7 - 5418*a^2*b^8*c^3*d*e^8 - 7168*a^3*b*c^9*d^6*e^3 + 28224*a^
3*b^6*c^4*d*e^8 - 44800*a^4*b*c^8*d^4*e^5 - 78400*a^4*b^4*c^5*d*e^8 - 53760*a^5*b*c^7*d^2*e^7 + 107520*a^5*b^2
*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*
c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d
^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^
4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b
^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 -
10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^
4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*
a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*
a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*
a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*
a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 716
80*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 22
80*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 +
3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8
+ 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*
e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^
2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a
^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6
*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 1920
0*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*
c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^
3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*(8192*a^7*c^6*d*e^10 - 4096*a^7*b*c^5*e^11 + 64*a^4*b^7*c^2*e^11 - 76
8*a^5*b^5*c^3*e^11 + 3072*a^6*b^3*c^4*e^11 + 8192*a^3*c^10*d^9*e^2 + 32768*a^4*c^9*d^7*e^4 + 49152*a^5*c^8*d^5
*e^6 + 32768*a^6*c^7*d^3*e^8 - 128*b^6*c^7*d^9*e^2 + 576*b^7*c^6*d^8*e^3 - 1024*b^8*c^5*d^7*e^4 + 896*b^9*c^4*
d^6*e^5 - 384*b^10*c^3*d^5*e^6 + 64*b^11*c^2*d^4*e^7 - 6144*a^2*b^2*c^9*d^9*e^2 + 27648*a^2*b^3*c^8*d^8*e^3 -
43008*a^2*b^4*c^7*d^7*e^4 + 21504*a^2*b^5*c^6*d^6*e^5 + 8448*a^2*b^6*c^5*d^5*e^6 - 10368*a^2*b^7*c^4*d^4*e^7 +
1536*a^2*b^8*c^3*d^3*e^8 + 384*a^2*b^9*c^2*d^2*e^9 + 40960*a^3*b^2*c^8*d^7*e^4 + 28672*a^3*b^3*c^7*d^6*e^5 -
76800*a^3*b^4*c^6*d^5*e^6 + 34304*a^3*b^5*c^5*d^4*e^7 + 5632*a^3*b^6*c^4*d^3*e^8 - 3840*a^3*b^7*c^3*d^2*e^9 +
110592*a^4*b^2*c^7*d^5*e^6 + 10240*a^4*b^3*c^6*d^4*e^7 - 51200*a^4*b^4*c^5*d^3*e^8 + 9216*a^4*b^5*c^4*d^2*e^9
+ 73728*a^5*b^2*c^6*d^3*e^8 + 12288*a^5*b^3*c^5*d^2*e^9 + 1536*a*b^4*c^8*d^9*e^2 - 6912*a*b^5*c^7*d^8*e^3 + 11
776*a*b^6*c^6*d^7*e^4 - 8960*a*b^7*c^5*d^6*e^5 + 2304*a*b^8*c^4*d^5*e^6 + 512*a*b^9*c^3*d^4*e^7 - 256*a*b^10*c
^2*d^3*e^8 - 36864*a^3*b*c^9*d^8*e^3 - 256*a^3*b^8*c^2*d*e^10 - 114688*a^4*b*c^8*d^6*e^5 + 2944*a^4*b^6*c^3*d*
e^10 - 122880*a^5*b*c^7*d^4*e^7 - 10752*a^5*b^4*c^4*d*e^10 - 49152*a^6*b*c^6*d^2*e^9 + 10240*a^6*b^2*c^5*d*e^1
0))/(8*(16*a^2*c^6*d^8 + a^4*b^4*e^8 + 16*a^6*c^2*e^8 + b^4*c^4*d^8 + b^8*d^4*e^4 - 8*a*b^2*c^5*d^8 - 8*a^5*b^
2*c*e^8 - 4*a*b^7*d^3*e^5 - 4*a^3*b^5*d*e^7 - 4*b^5*c^3*d^7*e - 4*b^7*c*d^5*e^3 + 6*a^2*b^6*d^2*e^6 + 64*a^3*c
^5*d^6*e^2 + 96*a^4*c^4*d^4*e^4 + 64*a^5*c^3*d^2*e^6 + 6*b^6*c^2*d^6*e^2 + 64*a^2*b^2*c^4*d^6*e^2 + 32*a^2*b^3
*c^3*d^5*e^3 - 74*a^2*b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^3*d^4*e^4 + 32*a^3*b^3*c^2*d^3*e^5 + 64*a^4*b^2*c^2*d^2*
e^6 + 32*a*b^3*c^4*d^7*e + 4*a*b^6*c*d^4*e^4 - 64*a^2*b*c^5*d^7*e + 32*a^4*b^3*c*d*e^7 - 64*a^5*b*c^2*d*e^7 -
44*a*b^4*c^3*d^6*e^2 + 20*a*b^5*c^2*d^5*e^3 + 20*a^2*b^5*c*d^3*e^5 - 192*a^3*b*c^4*d^5*e^3 - 44*a^3*b^4*c*d^2*
e^6 - 192*a^4*b*c^3*d^3*e^5)))*(-(9*b^13*e^9 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) + 26880*a^6*b*c^6*e^9 - 5376
0*a^6*c^7*d*e^8 + 2077*a^2*b^9*c^2*e^9 - 10656*a^3*b^7*c^3*e^9 + 30240*a^4*b^5*c^4*e^9 - 44800*a^5*b^3*c^5*e^9
- 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^10*d^7*e^2 + 17920*a^4*c^9*d^5*e^4 + 35840*a^5*c^8*d^3
*e^6 - 32*b^6*c^7*d^7*e^2 + 112*b^7*c^6*d^6*e^3 - 98*b^8*c^5*d^5*e^4 - 35*b^9*c^4*d^4*e^5 + 70*b^10*c^3*d^3*e^
6 - 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^9 - 21*b^12*c*d*e^8 - 1536*
a^2*b^2*c^9*d^7*e^2 + 5376*a^2*b^3*c^8*d^6*e^3 - 1344*a^2*b^4*c^7*d^5*e^4 - 10080*a^2*b^5*c^6*d^4*e^5 + 7840*a
^2*b^6*c^5*d^3*e^6 + 1008*a^2*b^7*c^4*d^2*e^7 - 7168*a^3*b^2*c^8*d^5*e^4 + 35840*a^3*b^3*c^7*d^4*e^5 - 17920*a
^3*b^4*c^6*d^3*e^6 - 12544*a^3*b^5*c^5*d^2*e^7 + 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2
)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) + 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9
)^(1/2) + 384*a*b^4*c^8*d^7*e^2 - 1344*a*b^5*c^7*d^6*e^3 + 896*a*b^6*c^6*d^5*e^4 + 1120*a*b^7*c^5*d^4*e^5 - 12
60*a*b^8*c^4*d^3*e^6 + 98*a*b^9*c^3*d^2*e^7 - 5418*a^2*b^8*c^3*d*e^8 - 7168*a^3*b*c^9*d^6*e^3 + 28224*a^3*b^6*
c^4*d*e^8 - 44800*a^4*b*c^8*d^4*e^5 - 78400*a^4*b^4*c^5*d*e^8 - 53760*a^5*b*c^7*d^2*e^7 + 107520*a^5*b^2*c^6*d
*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*
e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 -
b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*
e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^1
0*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^
2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6
+ 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^
11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^
9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^
6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^
10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5
*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5
*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*
a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 6144
0*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 +
32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8
+ 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c
^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 -
1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*
b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^
7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7
+ 30720*a^9*b^3*c^5*d*e^9)))^(1/2) - ((d + e*x)^(1/2)*(9*b^6*c^3*e^10 - 200*a^3*c^6*e^10 + 32*c^9*d^6*e^4 - 96
*a*b^4*c^4*e^10 + 248*a*c^8*d^4*e^6 - 96*b*c^8*d^5*e^5 - 12*b^5*c^4*d*e^9 + 298*a^2*b^2*c^5*e^10 + 592*a^2*c^7
*d^2*e^8 + 58*b^2*c^7*d^4*e^6 + 44*b^3*c^6*d^3*e^7 - 26*b^4*c^5*d^2*e^8 - 496*a*b*c^7*d^3*e^7 + 172*a*b^3*c^5*
d*e^9 - 592*a^2*b*c^6*d*e^9 + 76*a*b^2*c^6*d^2*e^8))/(8*(16*a^2*c^6*d^8 + a^4*b^4*e^8 + 16*a^6*c^2*e^8 + b^4*c
^4*d^8 + b^8*d^4*e^4 - 8*a*b^2*c^5*d^8 - 8*a^5*b^2*c*e^8 - 4*a*b^7*d^3*e^5 - 4*a^3*b^5*d*e^7 - 4*b^5*c^3*d^7*e
- 4*b^7*c*d^5*e^3 + 6*a^2*b^6*d^2*e^6 + 64*a^3*c^5*d^6*e^2 + 96*a^4*c^4*d^4*e^4 + 64*a^5*c^3*d^2*e^6 + 6*b^6*
c^2*d^6*e^2 + 64*a^2*b^2*c^4*d^6*e^2 + 32*a^2*b^3*c^3*d^5*e^3 - 74*a^2*b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^3*d^4*e
^4 + 32*a^3*b^3*c^2*d^3*e^5 + 64*a^4*b^2*c^2*d^2*e^6 + 32*a*b^3*c^4*d^7*e + 4*a*b^6*c*d^4*e^4 - 64*a^2*b*c^5*d
^7*e + 32*a^4*b^3*c*d*e^7 - 64*a^5*b*c^2*d*e^7 - 44*a*b^4*c^3*d^6*e^2 + 20*a*b^5*c^2*d^5*e^3 + 20*a^2*b^5*c*d^
3*e^5 - 192*a^3*b*c^4*d^5*e^3 - 44*a^3*b^4*c*d^2*e^6 - 192*a^4*b*c^3*d^3*e^5)))*(-(9*b^13*e^9 - 9*b^4*e^9*(-(4
*a*c - b^2)^9)^(1/2) + 26880*a^6*b*c^6*e^9 - 53760*a^6*c^7*d*e^8 + 2077*a^2*b^9*c^2*e^9 - 10656*a^3*b^7*c^3*e^
9 + 30240*a^4*b^5*c^4*e^9 - 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^10*d^
7*e^2 + 17920*a^4*c^9*d^5*e^4 + 35840*a^5*c^8*d^3*e^6 - 32*b^6*c^7*d^7*e^2 + 112*b^7*c^6*d^6*e^3 - 98*b^8*c^5*
d^5*e^4 - 35*b^9*c^4*d^4*e^5 + 70*b^10*c^3*d^3*e^6 - 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(
1/2) - 213*a*b^11*c*e^9 - 21*b^12*c*d*e^8 - 1536*a^2*b^2*c^9*d^7*e^2 + 5376*a^2*b^3*c^8*d^6*e^3 - 1344*a^2*b^4
*c^7*d^5*e^4 - 10080*a^2*b^5*c^6*d^4*e^5 + 7840*a^2*b^6*c^5*d^3*e^6 + 1008*a^2*b^7*c^4*d^2*e^7 - 7168*a^3*b^2*
c^8*d^5*e^4 + 35840*a^3*b^3*c^7*d^4*e^5 - 17920*a^3*b^4*c^6*d^3*e^6 - 12544*a^3*b^5*c^5*d^2*e^7 + 44800*a^4*b^
3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) + 532*a*
b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7*e^2 - 1344*a*b^5*c^7*d^6*e^3 + 89
6*a*b^6*c^6*d^5*e^4 + 1120*a*b^7*c^5*d^4*e^5 - 1260*a*b^8*c^4*d^3*e^6 + 98*a*b^9*c^3*d^2*e^7 - 5418*a^2*b^8*c^
3*d*e^8 - 7168*a^3*b*c^9*d^6*e^3 + 28224*a^3*b^6*c^4*d*e^8 - 44800*a^4*b*c^8*d^4*e^5 - 78400*a^4*b^4*c^5*d*e^8
- 53760*a^5*b*c^7*d^2*e^7 + 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*
d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*
c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*
b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^
8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*
a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2
+ 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*
d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*
d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*
d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5
*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^
8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*
c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3
*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b
^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a
^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920
*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15
*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 +
220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^
7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^
9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 1
9200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*1i - (((106496*a^6*c^7*d*e
^10 - 53248*a^6*b*c^6*e^11 - 192*a^2*b^9*c^2*e^11 + 3136*a^3*b^7*c^3*e^11 - 19200*a^4*b^5*c^4*e^11 + 52224*a^5
*b^3*c^5*e^11 + 8192*a^3*c^10*d^7*e^4 + 122880*a^4*c^9*d^5*e^6 + 221184*a^5*c^8*d^3*e^8 - 128*b^6*c^7*d^7*e^4
+ 448*b^7*c^6*d^6*e^5 - 192*b^8*c^5*d^5*e^6 - 640*b^9*c^4*d^4*e^7 + 704*b^10*c^3*d^3*e^8 - 192*b^11*c^2*d^2*e^
9 - 6144*a^2*b^2*c^9*d^7*e^4 + 21504*a^2*b^3*c^8*d^6*e^5 + 13824*a^2*b^4*c^7*d^5*e^6 - 88320*a^2*b^5*c^6*d^4*e
^7 + 67200*a^2*b^6*c^5*d^3*e^8 - 1728*a^2*b^7*c^4*d^2*e^9 - 79872*a^3*b^2*c^8*d^5*e^6 + 271360*a^3*b^3*c^7*d^4
*e^7 - 151040*a^3*b^4*c^6*d^3*e^8 - 59136*a^3*b^5*c^5*d^2*e^9 + 30720*a^4*b^2*c^7*d^3*e^8 + 261120*a^4*b^3*c^6
*d^2*e^9 + 384*a*b^10*c^2*d*e^10 + 1536*a*b^4*c^8*d^7*e^4 - 5376*a*b^5*c^7*d^6*e^5 + 384*a*b^6*c^6*d^5*e^6 + 1
2480*a*b^7*c^5*d^4*e^7 - 11520*a*b^8*c^4*d^3*e^8 + 2112*a*b^9*c^3*d^2*e^9 - 5952*a^2*b^8*c^3*d*e^10 - 28672*a^
3*b*c^9*d^6*e^5 + 32896*a^3*b^6*c^4*d*e^10 - 307200*a^4*b*c^8*d^4*e^7 - 69120*a^4*b^4*c^5*d*e^10 - 331776*a^5*
b*c^7*d^2*e^9 + 6144*a^5*b^2*c^6*d*e^10)/(64*(64*a^3*c^7*d^8 - a^4*b^6*e^8 + 64*a^7*c^3*e^8 - b^6*c^4*d^8 - b^
10*d^4*e^4 + 12*a*b^4*c^5*d^8 + 12*a^5*b^4*c*e^8 + 4*a*b^9*d^3*e^5 + 4*a^3*b^7*d*e^7 + 4*b^7*c^3*d^7*e + 4*b^9
*c*d^5*e^3 - 48*a^2*b^2*c^6*d^8 - 48*a^6*b^2*c^2*e^8 - 6*a^2*b^8*d^2*e^6 + 256*a^4*c^6*d^6*e^2 + 384*a^5*c^5*d
^4*e^4 + 256*a^6*c^4*d^2*e^6 - 6*b^8*c^2*d^6*e^2 - 240*a^2*b^4*c^4*d^6*e^2 + 48*a^2*b^5*c^3*d^5*e^3 + 90*a^2*b
^6*c^2*d^4*e^4 + 192*a^3*b^2*c^5*d^6*e^2 + 320*a^3*b^3*c^4*d^5*e^3 - 440*a^3*b^4*c^3*d^4*e^4 + 48*a^3*b^5*c^2*
d^3*e^5 + 480*a^4*b^2*c^4*d^4*e^4 + 320*a^4*b^3*c^3*d^3*e^5 - 240*a^4*b^4*c^2*d^2*e^6 + 192*a^5*b^2*c^3*d^2*e^
6 - 48*a*b^5*c^4*d^7*e - 256*a^3*b*c^6*d^7*e - 48*a^4*b^5*c*d*e^7 - 256*a^6*b*c^3*d*e^7 + 68*a*b^6*c^3*d^6*e^2
- 36*a*b^7*c^2*d^5*e^3 + 192*a^2*b^3*c^5*d^7*e - 36*a^2*b^7*c*d^3*e^5 + 68*a^3*b^6*c*d^2*e^6 - 768*a^4*b*c^5*
d^5*e^3 - 768*a^5*b*c^4*d^3*e^5 + 192*a^5*b^3*c^2*d*e^7)) + ((d + e*x)^(1/2)*(-(9*b^13*e^9 - 9*b^4*e^9*(-(4*a*
c - b^2)^9)^(1/2) + 26880*a^6*b*c^6*e^9 - 53760*a^6*c^7*d*e^8 + 2077*a^2*b^9*c^2*e^9 - 10656*a^3*b^7*c^3*e^9 +
30240*a^4*b^5*c^4*e^9 - 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^10*d^7*e
^2 + 17920*a^4*c^9*d^5*e^4 + 35840*a^5*c^8*d^3*e^6 - 32*b^6*c^7*d^7*e^2 + 112*b^7*c^6*d^6*e^3 - 98*b^8*c^5*d^5
*e^4 - 35*b^9*c^4*d^4*e^5 + 70*b^10*c^3*d^3*e^6 - 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2
) - 213*a*b^11*c*e^9 - 21*b^12*c*d*e^8 - 1536*a^2*b^2*c^9*d^7*e^2 + 5376*a^2*b^3*c^8*d^6*e^3 - 1344*a^2*b^4*c^
7*d^5*e^4 - 10080*a^2*b^5*c^6*d^4*e^5 + 7840*a^2*b^6*c^5*d^3*e^6 + 1008*a^2*b^7*c^4*d^2*e^7 - 7168*a^3*b^2*c^8
*d^5*e^4 + 35840*a^3*b^3*c^7*d^4*e^5 - 17920*a^3*b^4*c^6*d^3*e^6 - 12544*a^3*b^5*c^5*d^2*e^7 + 44800*a^4*b^3*c
^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) + 532*a*b^1
0*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7*e^2 - 1344*a*b^5*c^7*d^6*e^3 + 896*a
*b^6*c^6*d^5*e^4 + 1120*a*b^7*c^5*d^4*e^5 - 1260*a*b^8*c^4*d^3*e^6 + 98*a*b^9*c^3*d^2*e^7 - 5418*a^2*b^8*c^3*d
*e^8 - 7168*a^3*b*c^9*d^6*e^3 + 28224*a^3*b^6*c^4*d*e^8 - 44800*a^4*b*c^8*d^4*e^5 - 78400*a^4*b^4*c^5*d*e^8 -
53760*a^5*b*c^7*d^2*e^7 + 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3
*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^1
1*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^1
6*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d
^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9
*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 +
40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7
*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5
*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5
*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^
6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d
^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4
*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^
8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*
c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*
b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^
8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*
d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 22
0*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c
^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e
- 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 1920
0*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*(8192*a^7*c^6*d*e^10 - 4096*a
^7*b*c^5*e^11 + 64*a^4*b^7*c^2*e^11 - 768*a^5*b^5*c^3*e^11 + 3072*a^6*b^3*c^4*e^11 + 8192*a^3*c^10*d^9*e^2 + 3
2768*a^4*c^9*d^7*e^4 + 49152*a^5*c^8*d^5*e^6 + 32768*a^6*c^7*d^3*e^8 - 128*b^6*c^7*d^9*e^2 + 576*b^7*c^6*d^8*e
^3 - 1024*b^8*c^5*d^7*e^4 + 896*b^9*c^4*d^6*e^5 - 384*b^10*c^3*d^5*e^6 + 64*b^11*c^2*d^4*e^7 - 6144*a^2*b^2*c^
9*d^9*e^2 + 27648*a^2*b^3*c^8*d^8*e^3 - 43008*a^2*b^4*c^7*d^7*e^4 + 21504*a^2*b^5*c^6*d^6*e^5 + 8448*a^2*b^6*c
^5*d^5*e^6 - 10368*a^2*b^7*c^4*d^4*e^7 + 1536*a^2*b^8*c^3*d^3*e^8 + 384*a^2*b^9*c^2*d^2*e^9 + 40960*a^3*b^2*c^
8*d^7*e^4 + 28672*a^3*b^3*c^7*d^6*e^5 - 76800*a^3*b^4*c^6*d^5*e^6 + 34304*a^3*b^5*c^5*d^4*e^7 + 5632*a^3*b^6*c
^4*d^3*e^8 - 3840*a^3*b^7*c^3*d^2*e^9 + 110592*a^4*b^2*c^7*d^5*e^6 + 10240*a^4*b^3*c^6*d^4*e^7 - 51200*a^4*b^4
*c^5*d^3*e^8 + 9216*a^4*b^5*c^4*d^2*e^9 + 73728*a^5*b^2*c^6*d^3*e^8 + 12288*a^5*b^3*c^5*d^2*e^9 + 1536*a*b^4*c
^8*d^9*e^2 - 6912*a*b^5*c^7*d^8*e^3 + 11776*a*b^6*c^6*d^7*e^4 - 8960*a*b^7*c^5*d^6*e^5 + 2304*a*b^8*c^4*d^5*e^
6 + 512*a*b^9*c^3*d^4*e^7 - 256*a*b^10*c^2*d^3*e^8 - 36864*a^3*b*c^9*d^8*e^3 - 256*a^3*b^8*c^2*d*e^10 - 114688
*a^4*b*c^8*d^6*e^5 + 2944*a^4*b^6*c^3*d*e^10 - 122880*a^5*b*c^7*d^4*e^7 - 10752*a^5*b^4*c^4*d*e^10 - 49152*a^6
*b*c^6*d^2*e^9 + 10240*a^6*b^2*c^5*d*e^10))/(8*(16*a^2*c^6*d^8 + a^4*b^4*e^8 + 16*a^6*c^2*e^8 + b^4*c^4*d^8 +
b^8*d^4*e^4 - 8*a*b^2*c^5*d^8 - 8*a^5*b^2*c*e^8 - 4*a*b^7*d^3*e^5 - 4*a^3*b^5*d*e^7 - 4*b^5*c^3*d^7*e - 4*b^7*
c*d^5*e^3 + 6*a^2*b^6*d^2*e^6 + 64*a^3*c^5*d^6*e^2 + 96*a^4*c^4*d^4*e^4 + 64*a^5*c^3*d^2*e^6 + 6*b^6*c^2*d^6*e
^2 + 64*a^2*b^2*c^4*d^6*e^2 + 32*a^2*b^3*c^3*d^5*e^3 - 74*a^2*b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^3*d^4*e^4 + 32*a
^3*b^3*c^2*d^3*e^5 + 64*a^4*b^2*c^2*d^2*e^6 + 32*a*b^3*c^4*d^7*e + 4*a*b^6*c*d^4*e^4 - 64*a^2*b*c^5*d^7*e + 32
*a^4*b^3*c*d*e^7 - 64*a^5*b*c^2*d*e^7 - 44*a*b^4*c^3*d^6*e^2 + 20*a*b^5*c^2*d^5*e^3 + 20*a^2*b^5*c*d^3*e^5 - 1
92*a^3*b*c^4*d^5*e^3 - 44*a^3*b^4*c*d^2*e^6 - 192*a^4*b*c^3*d^3*e^5)))*(-(9*b^13*e^9 - 9*b^4*e^9*(-(4*a*c - b^
2)^9)^(1/2) + 26880*a^6*b*c^6*e^9 - 53760*a^6*c^7*d*e^8 + 2077*a^2*b^9*c^2*e^9 - 10656*a^3*b^7*c^3*e^9 + 30240
*a^4*b^5*c^4*e^9 - 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^10*d^7*e^2 + 1
7920*a^4*c^9*d^5*e^4 + 35840*a^5*c^8*d^3*e^6 - 32*b^6*c^7*d^7*e^2 + 112*b^7*c^6*d^6*e^3 - 98*b^8*c^5*d^5*e^4 -
35*b^9*c^4*d^4*e^5 + 70*b^10*c^3*d^3*e^6 - 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) - 21
3*a*b^11*c*e^9 - 21*b^12*c*d*e^8 - 1536*a^2*b^2*c^9*d^7*e^2 + 5376*a^2*b^3*c^8*d^6*e^3 - 1344*a^2*b^4*c^7*d^5*
e^4 - 10080*a^2*b^5*c^6*d^4*e^5 + 7840*a^2*b^6*c^5*d^3*e^6 + 1008*a^2*b^7*c^4*d^2*e^7 - 7168*a^3*b^2*c^8*d^5*e
^4 + 35840*a^3*b^3*c^7*d^4*e^5 - 17920*a^3*b^4*c^6*d^3*e^6 - 12544*a^3*b^5*c^5*d^2*e^7 + 44800*a^4*b^3*c^6*d^2
*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) + 532*a*b^10*c^2*
d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7*e^2 - 1344*a*b^5*c^7*d^6*e^3 + 896*a*b^6*c
^6*d^5*e^4 + 1120*a*b^7*c^5*d^4*e^5 - 1260*a*b^8*c^4*d^3*e^6 + 98*a*b^9*c^3*d^2*e^7 - 5418*a^2*b^8*c^3*d*e^8 -
7168*a^3*b*c^9*d^6*e^3 + 28224*a^3*b^6*c^4*d*e^8 - 44800*a^4*b*c^8*d^4*e^5 - 78400*a^4*b^4*c^5*d*e^8 - 53760*
a^5*b*c^7*d^2*e^7 + 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(
-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10
+ 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*
e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 +
3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c
^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*
a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 +
2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 -
11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 +
490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4
+ 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2
- 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e
^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*
e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^
3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^
6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*
c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^
5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^
13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9
*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 120
0*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*
b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2) + ((d + e*x)^(1/2)*(9*b^6*c^3*e^10
- 200*a^3*c^6*e^10 + 32*c^9*d^6*e^4 - 96*a*b^4*c^4*e^10 + 248*a*c^8*d^4*e^6 - 96*b*c^8*d^5*e^5 - 12*b^5*c^4*d*
e^9 + 298*a^2*b^2*c^5*e^10 + 592*a^2*c^7*d^2*e^8 + 58*b^2*c^7*d^4*e^6 + 44*b^3*c^6*d^3*e^7 - 26*b^4*c^5*d^2*e^
8 - 496*a*b*c^7*d^3*e^7 + 172*a*b^3*c^5*d*e^9 - 592*a^2*b*c^6*d*e^9 + 76*a*b^2*c^6*d^2*e^8))/(8*(16*a^2*c^6*d^
8 + a^4*b^4*e^8 + 16*a^6*c^2*e^8 + b^4*c^4*d^8 + b^8*d^4*e^4 - 8*a*b^2*c^5*d^8 - 8*a^5*b^2*c*e^8 - 4*a*b^7*d^3
*e^5 - 4*a^3*b^5*d*e^7 - 4*b^5*c^3*d^7*e - 4*b^7*c*d^5*e^3 + 6*a^2*b^6*d^2*e^6 + 64*a^3*c^5*d^6*e^2 + 96*a^4*c
^4*d^4*e^4 + 64*a^5*c^3*d^2*e^6 + 6*b^6*c^2*d^6*e^2 + 64*a^2*b^2*c^4*d^6*e^2 + 32*a^2*b^3*c^3*d^5*e^3 - 74*a^2
*b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^3*d^4*e^4 + 32*a^3*b^3*c^2*d^3*e^5 + 64*a^4*b^2*c^2*d^2*e^6 + 32*a*b^3*c^4*d^
7*e + 4*a*b^6*c*d^4*e^4 - 64*a^2*b*c^5*d^7*e + 32*a^4*b^3*c*d*e^7 - 64*a^5*b*c^2*d*e^7 - 44*a*b^4*c^3*d^6*e^2
+ 20*a*b^5*c^2*d^5*e^3 + 20*a^2*b^5*c*d^3*e^5 - 192*a^3*b*c^4*d^5*e^3 - 44*a^3*b^4*c*d^2*e^6 - 192*a^4*b*c^3*d
^3*e^5)))*(-(9*b^13*e^9 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) + 26880*a^6*b*c^6*e^9 - 53760*a^6*c^7*d*e^8 + 207
7*a^2*b^9*c^2*e^9 - 10656*a^3*b^7*c^3*e^9 + 30240*a^4*b^5*c^4*e^9 - 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(
4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^10*d^7*e^2 + 17920*a^4*c^9*d^5*e^4 + 35840*a^5*c^8*d^3*e^6 - 32*b^6*c^7*d^7
*e^2 + 112*b^7*c^6*d^6*e^3 - 98*b^8*c^5*d^5*e^4 - 35*b^9*c^4*d^4*e^5 + 70*b^10*c^3*d^3*e^6 - 14*b^11*c^2*d^2*e
^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^9 - 21*b^12*c*d*e^8 - 1536*a^2*b^2*c^9*d^7*e^2 +
5376*a^2*b^3*c^8*d^6*e^3 - 1344*a^2*b^4*c^7*d^5*e^4 - 10080*a^2*b^5*c^6*d^4*e^5 + 7840*a^2*b^6*c^5*d^3*e^6 +
1008*a^2*b^7*c^4*d^2*e^7 - 7168*a^3*b^2*c^8*d^5*e^4 + 35840*a^3*b^3*c^7*d^4*e^5 - 17920*a^3*b^4*c^6*d^3*e^6 -
12544*a^3*b^5*c^5*d^2*e^7 + 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2
*c*e^9*(-(4*a*c - b^2)^9)^(1/2) + 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c
^8*d^7*e^2 - 1344*a*b^5*c^7*d^6*e^3 + 896*a*b^6*c^6*d^5*e^4 + 1120*a*b^7*c^5*d^4*e^5 - 1260*a*b^8*c^4*d^3*e^6
+ 98*a*b^9*c^3*d^2*e^7 - 5418*a^2*b^8*c^3*d*e^8 - 7168*a^3*b*c^9*d^6*e^3 + 28224*a^3*b^6*c^4*d*e^8 - 44800*a^4
*b*c^8*d^4*e^5 - 78400*a^4*b^4*c^5*d*e^8 - 53760*a^5*b*c^7*d^2*e^7 + 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*
e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9
)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b
^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4
+ 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*
c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a
^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*
e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*
a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a
^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800
*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920
*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32
256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 1
0240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 +
71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4
+ 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2
*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d
^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^1
0*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9
*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a
^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*
c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d
*e^9)))^(1/2)*1i)/((((106496*a^6*c^7*d*e^10 - 53248*a^6*b*c^6*e^11 - 192*a^2*b^9*c^2*e^11 + 3136*a^3*b^7*c^3*e
^11 - 19200*a^4*b^5*c^4*e^11 + 52224*a^5*b^3*c^5*e^11 + 8192*a^3*c^10*d^7*e^4 + 122880*a^4*c^9*d^5*e^6 + 22118
4*a^5*c^8*d^3*e^8 - 128*b^6*c^7*d^7*e^4 + 448*b^7*c^6*d^6*e^5 - 192*b^8*c^5*d^5*e^6 - 640*b^9*c^4*d^4*e^7 + 70
4*b^10*c^3*d^3*e^8 - 192*b^11*c^2*d^2*e^9 - 6144*a^2*b^2*c^9*d^7*e^4 + 21504*a^2*b^3*c^8*d^6*e^5 + 13824*a^2*b
^4*c^7*d^5*e^6 - 88320*a^2*b^5*c^6*d^4*e^7 + 67200*a^2*b^6*c^5*d^3*e^8 - 1728*a^2*b^7*c^4*d^2*e^9 - 79872*a^3*
b^2*c^8*d^5*e^6 + 271360*a^3*b^3*c^7*d^4*e^7 - 151040*a^3*b^4*c^6*d^3*e^8 - 59136*a^3*b^5*c^5*d^2*e^9 + 30720*
a^4*b^2*c^7*d^3*e^8 + 261120*a^4*b^3*c^6*d^2*e^9 + 384*a*b^10*c^2*d*e^10 + 1536*a*b^4*c^8*d^7*e^4 - 5376*a*b^5
*c^7*d^6*e^5 + 384*a*b^6*c^6*d^5*e^6 + 12480*a*b^7*c^5*d^4*e^7 - 11520*a*b^8*c^4*d^3*e^8 + 2112*a*b^9*c^3*d^2*
e^9 - 5952*a^2*b^8*c^3*d*e^10 - 28672*a^3*b*c^9*d^6*e^5 + 32896*a^3*b^6*c^4*d*e^10 - 307200*a^4*b*c^8*d^4*e^7
- 69120*a^4*b^4*c^5*d*e^10 - 331776*a^5*b*c^7*d^2*e^9 + 6144*a^5*b^2*c^6*d*e^10)/(64*(64*a^3*c^7*d^8 - a^4*b^6
*e^8 + 64*a^7*c^3*e^8 - b^6*c^4*d^8 - b^10*d^4*e^4 + 12*a*b^4*c^5*d^8 + 12*a^5*b^4*c*e^8 + 4*a*b^9*d^3*e^5 + 4
*a^3*b^7*d*e^7 + 4*b^7*c^3*d^7*e + 4*b^9*c*d^5*e^3 - 48*a^2*b^2*c^6*d^8 - 48*a^6*b^2*c^2*e^8 - 6*a^2*b^8*d^2*e
^6 + 256*a^4*c^6*d^6*e^2 + 384*a^5*c^5*d^4*e^4 + 256*a^6*c^4*d^2*e^6 - 6*b^8*c^2*d^6*e^2 - 240*a^2*b^4*c^4*d^6
*e^2 + 48*a^2*b^5*c^3*d^5*e^3 + 90*a^2*b^6*c^2*d^4*e^4 + 192*a^3*b^2*c^5*d^6*e^2 + 320*a^3*b^3*c^4*d^5*e^3 - 4
40*a^3*b^4*c^3*d^4*e^4 + 48*a^3*b^5*c^2*d^3*e^5 + 480*a^4*b^2*c^4*d^4*e^4 + 320*a^4*b^3*c^3*d^3*e^5 - 240*a^4*
b^4*c^2*d^2*e^6 + 192*a^5*b^2*c^3*d^2*e^6 - 48*a*b^5*c^4*d^7*e - 256*a^3*b*c^6*d^7*e - 48*a^4*b^5*c*d*e^7 - 25
6*a^6*b*c^3*d*e^7 + 68*a*b^6*c^3*d^6*e^2 - 36*a*b^7*c^2*d^5*e^3 + 192*a^2*b^3*c^5*d^7*e - 36*a^2*b^7*c*d^3*e^5
+ 68*a^3*b^6*c*d^2*e^6 - 768*a^4*b*c^5*d^5*e^3 - 768*a^5*b*c^4*d^3*e^5 + 192*a^5*b^3*c^2*d*e^7)) - ((d + e*x)
^(1/2)*(-(9*b^13*e^9 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) + 26880*a^6*b*c^6*e^9 - 53760*a^6*c^7*d*e^8 + 2077*a
^2*b^9*c^2*e^9 - 10656*a^3*b^7*c^3*e^9 + 30240*a^4*b^5*c^4*e^9 - 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a
*c - b^2)^9)^(1/2) + 2048*a^3*c^10*d^7*e^2 + 17920*a^4*c^9*d^5*e^4 + 35840*a^5*c^8*d^3*e^6 - 32*b^6*c^7*d^7*e^
2 + 112*b^7*c^6*d^6*e^3 - 98*b^8*c^5*d^5*e^4 - 35*b^9*c^4*d^4*e^5 + 70*b^10*c^3*d^3*e^6 - 14*b^11*c^2*d^2*e^7
+ 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^9 - 21*b^12*c*d*e^8 - 1536*a^2*b^2*c^9*d^7*e^2 + 53
76*a^2*b^3*c^8*d^6*e^3 - 1344*a^2*b^4*c^7*d^5*e^4 - 10080*a^2*b^5*c^6*d^4*e^5 + 7840*a^2*b^6*c^5*d^3*e^6 + 100
8*a^2*b^7*c^4*d^2*e^7 - 7168*a^3*b^2*c^8*d^5*e^4 + 35840*a^3*b^3*c^7*d^4*e^5 - 17920*a^3*b^4*c^6*d^3*e^6 - 125
44*a^3*b^5*c^5*d^2*e^7 + 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*
e^9*(-(4*a*c - b^2)^9)^(1/2) + 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*
d^7*e^2 - 1344*a*b^5*c^7*d^6*e^3 + 896*a*b^6*c^6*d^5*e^4 + 1120*a*b^7*c^5*d^4*e^5 - 1260*a*b^8*c^4*d^3*e^6 + 9
8*a*b^9*c^3*d^2*e^7 - 5418*a^2*b^8*c^3*d*e^8 - 7168*a^3*b*c^9*d^6*e^3 + 28224*a^3*b^6*c^4*d*e^8 - 44800*a^4*b*
c^8*d^4*e^5 - 78400*a^4*b^4*c^5*d*e^8 - 53760*a^5*b*c^7*d^2*e^7 + 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7
*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(
1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10
*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 2
40*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2
*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*
b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8
+ 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2
*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*
b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^
4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^
4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256
*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 1024
0*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71
680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 +
102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^
8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*
e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b
*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e
- 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*
b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3
*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^
9)))^(1/2)*(8192*a^7*c^6*d*e^10 - 4096*a^7*b*c^5*e^11 + 64*a^4*b^7*c^2*e^11 - 768*a^5*b^5*c^3*e^11 + 3072*a^6*
b^3*c^4*e^11 + 8192*a^3*c^10*d^9*e^2 + 32768*a^4*c^9*d^7*e^4 + 49152*a^5*c^8*d^5*e^6 + 32768*a^6*c^7*d^3*e^8 -
128*b^6*c^7*d^9*e^2 + 576*b^7*c^6*d^8*e^3 - 1024*b^8*c^5*d^7*e^4 + 896*b^9*c^4*d^6*e^5 - 384*b^10*c^3*d^5*e^6
+ 64*b^11*c^2*d^4*e^7 - 6144*a^2*b^2*c^9*d^9*e^2 + 27648*a^2*b^3*c^8*d^8*e^3 - 43008*a^2*b^4*c^7*d^7*e^4 + 21
504*a^2*b^5*c^6*d^6*e^5 + 8448*a^2*b^6*c^5*d^5*e^6 - 10368*a^2*b^7*c^4*d^4*e^7 + 1536*a^2*b^8*c^3*d^3*e^8 + 38
4*a^2*b^9*c^2*d^2*e^9 + 40960*a^3*b^2*c^8*d^7*e^4 + 28672*a^3*b^3*c^7*d^6*e^5 - 76800*a^3*b^4*c^6*d^5*e^6 + 34
304*a^3*b^5*c^5*d^4*e^7 + 5632*a^3*b^6*c^4*d^3*e^8 - 3840*a^3*b^7*c^3*d^2*e^9 + 110592*a^4*b^2*c^7*d^5*e^6 + 1
0240*a^4*b^3*c^6*d^4*e^7 - 51200*a^4*b^4*c^5*d^3*e^8 + 9216*a^4*b^5*c^4*d^2*e^9 + 73728*a^5*b^2*c^6*d^3*e^8 +
12288*a^5*b^3*c^5*d^2*e^9 + 1536*a*b^4*c^8*d^9*e^2 - 6912*a*b^5*c^7*d^8*e^3 + 11776*a*b^6*c^6*d^7*e^4 - 8960*a
*b^7*c^5*d^6*e^5 + 2304*a*b^8*c^4*d^5*e^6 + 512*a*b^9*c^3*d^4*e^7 - 256*a*b^10*c^2*d^3*e^8 - 36864*a^3*b*c^9*d
^8*e^3 - 256*a^3*b^8*c^2*d*e^10 - 114688*a^4*b*c^8*d^6*e^5 + 2944*a^4*b^6*c^3*d*e^10 - 122880*a^5*b*c^7*d^4*e^
7 - 10752*a^5*b^4*c^4*d*e^10 - 49152*a^6*b*c^6*d^2*e^9 + 10240*a^6*b^2*c^5*d*e^10))/(8*(16*a^2*c^6*d^8 + a^4*b
^4*e^8 + 16*a^6*c^2*e^8 + b^4*c^4*d^8 + b^8*d^4*e^4 - 8*a*b^2*c^5*d^8 - 8*a^5*b^2*c*e^8 - 4*a*b^7*d^3*e^5 - 4*
a^3*b^5*d*e^7 - 4*b^5*c^3*d^7*e - 4*b^7*c*d^5*e^3 + 6*a^2*b^6*d^2*e^6 + 64*a^3*c^5*d^6*e^2 + 96*a^4*c^4*d^4*e^
4 + 64*a^5*c^3*d^2*e^6 + 6*b^6*c^2*d^6*e^2 + 64*a^2*b^2*c^4*d^6*e^2 + 32*a^2*b^3*c^3*d^5*e^3 - 74*a^2*b^4*c^2*
d^4*e^4 + 144*a^3*b^2*c^3*d^4*e^4 + 32*a^3*b^3*c^2*d^3*e^5 + 64*a^4*b^2*c^2*d^2*e^6 + 32*a*b^3*c^4*d^7*e + 4*a
*b^6*c*d^4*e^4 - 64*a^2*b*c^5*d^7*e + 32*a^4*b^3*c*d*e^7 - 64*a^5*b*c^2*d*e^7 - 44*a*b^4*c^3*d^6*e^2 + 20*a*b^
5*c^2*d^5*e^3 + 20*a^2*b^5*c*d^3*e^5 - 192*a^3*b*c^4*d^5*e^3 - 44*a^3*b^4*c*d^2*e^6 - 192*a^4*b*c^3*d^3*e^5)))
*(-(9*b^13*e^9 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) + 26880*a^6*b*c^6*e^9 - 53760*a^6*c^7*d*e^8 + 2077*a^2*b^9
*c^2*e^9 - 10656*a^3*b^7*c^3*e^9 + 30240*a^4*b^5*c^4*e^9 - 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b
^2)^9)^(1/2) + 2048*a^3*c^10*d^7*e^2 + 17920*a^4*c^9*d^5*e^4 + 35840*a^5*c^8*d^3*e^6 - 32*b^6*c^7*d^7*e^2 + 11
2*b^7*c^6*d^6*e^3 - 98*b^8*c^5*d^5*e^4 - 35*b^9*c^4*d^4*e^5 + 70*b^10*c^3*d^3*e^6 - 14*b^11*c^2*d^2*e^7 + 35*c
^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^9 - 21*b^12*c*d*e^8 - 1536*a^2*b^2*c^9*d^7*e^2 + 5376*a^2
*b^3*c^8*d^6*e^3 - 1344*a^2*b^4*c^7*d^5*e^4 - 10080*a^2*b^5*c^6*d^4*e^5 + 7840*a^2*b^6*c^5*d^3*e^6 + 1008*a^2*
b^7*c^4*d^2*e^7 - 7168*a^3*b^2*c^8*d^5*e^4 + 35840*a^3*b^3*c^7*d^4*e^5 - 17920*a^3*b^4*c^6*d^3*e^6 - 12544*a^3
*b^5*c^5*d^2*e^7 + 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-
(4*a*c - b^2)^9)^(1/2) + 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7*e^
2 - 1344*a*b^5*c^7*d^6*e^3 + 896*a*b^6*c^6*d^5*e^4 + 1120*a*b^7*c^5*d^4*e^5 - 1260*a*b^8*c^4*d^3*e^6 + 98*a*b^
9*c^3*d^2*e^7 - 5418*a^2*b^8*c^3*d*e^8 - 7168*a^3*b*c^9*d^6*e^3 + 28224*a^3*b^6*c^4*d*e^8 - 44800*a^4*b*c^8*d^
4*e^5 - 78400*a^4*b^4*c^5*d*e^8 - 53760*a^5*b*c^7*d^2*e^7 + 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*
a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/
(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d
^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2
*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10
- 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d
^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*
b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*
c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c
^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*
c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11
*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b
^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*
b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^
6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400
*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61
440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 +
120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d
*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a
^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c
*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9
- 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(
1/2) - ((d + e*x)^(1/2)*(9*b^6*c^3*e^10 - 200*a^3*c^6*e^10 + 32*c^9*d^6*e^4 - 96*a*b^4*c^4*e^10 + 248*a*c^8*d^
4*e^6 - 96*b*c^8*d^5*e^5 - 12*b^5*c^4*d*e^9 + 298*a^2*b^2*c^5*e^10 + 592*a^2*c^7*d^2*e^8 + 58*b^2*c^7*d^4*e^6
+ 44*b^3*c^6*d^3*e^7 - 26*b^4*c^5*d^2*e^8 - 496*a*b*c^7*d^3*e^7 + 172*a*b^3*c^5*d*e^9 - 592*a^2*b*c^6*d*e^9 +
76*a*b^2*c^6*d^2*e^8))/(8*(16*a^2*c^6*d^8 + a^4*b^4*e^8 + 16*a^6*c^2*e^8 + b^4*c^4*d^8 + b^8*d^4*e^4 - 8*a*b^2
*c^5*d^8 - 8*a^5*b^2*c*e^8 - 4*a*b^7*d^3*e^5 - 4*a^3*b^5*d*e^7 - 4*b^5*c^3*d^7*e - 4*b^7*c*d^5*e^3 + 6*a^2*b^6
*d^2*e^6 + 64*a^3*c^5*d^6*e^2 + 96*a^4*c^4*d^4*e^4 + 64*a^5*c^3*d^2*e^6 + 6*b^6*c^2*d^6*e^2 + 64*a^2*b^2*c^4*d
^6*e^2 + 32*a^2*b^3*c^3*d^5*e^3 - 74*a^2*b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^3*d^4*e^4 + 32*a^3*b^3*c^2*d^3*e^5 +
64*a^4*b^2*c^2*d^2*e^6 + 32*a*b^3*c^4*d^7*e + 4*a*b^6*c*d^4*e^4 - 64*a^2*b*c^5*d^7*e + 32*a^4*b^3*c*d*e^7 - 64
*a^5*b*c^2*d*e^7 - 44*a*b^4*c^3*d^6*e^2 + 20*a*b^5*c^2*d^5*e^3 + 20*a^2*b^5*c*d^3*e^5 - 192*a^3*b*c^4*d^5*e^3
- 44*a^3*b^4*c*d^2*e^6 - 192*a^4*b*c^3*d^3*e^5)))*(-(9*b^13*e^9 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) + 26880*a
^6*b*c^6*e^9 - 53760*a^6*c^7*d*e^8 + 2077*a^2*b^9*c^2*e^9 - 10656*a^3*b^7*c^3*e^9 + 30240*a^4*b^5*c^4*e^9 - 44
800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^10*d^7*e^2 + 17920*a^4*c^9*d^5*e^4
+ 35840*a^5*c^8*d^3*e^6 - 32*b^6*c^7*d^7*e^2 + 112*b^7*c^6*d^6*e^3 - 98*b^8*c^5*d^5*e^4 - 35*b^9*c^4*d^4*e^5 +
70*b^10*c^3*d^3*e^6 - 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^9 - 21*b
^12*c*d*e^8 - 1536*a^2*b^2*c^9*d^7*e^2 + 5376*a^2*b^3*c^8*d^6*e^3 - 1344*a^2*b^4*c^7*d^5*e^4 - 10080*a^2*b^5*c
^6*d^4*e^5 + 7840*a^2*b^6*c^5*d^3*e^6 + 1008*a^2*b^7*c^4*d^2*e^7 - 7168*a^3*b^2*c^8*d^5*e^4 + 35840*a^3*b^3*c^
7*d^4*e^5 - 17920*a^3*b^4*c^6*d^3*e^6 - 12544*a^3*b^5*c^5*d^2*e^7 + 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2
*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) + 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^
8*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7*e^2 - 1344*a*b^5*c^7*d^6*e^3 + 896*a*b^6*c^6*d^5*e^4 + 1120*a*b
^7*c^5*d^4*e^5 - 1260*a*b^8*c^4*d^3*e^6 + 98*a*b^9*c^3*d^2*e^7 - 5418*a^2*b^8*c^3*d*e^8 - 7168*a^3*b*c^9*d^6*e
^3 + 28224*a^3*b^6*c^4*d*e^8 - 44800*a^4*b*c^8*d^4*e^5 - 78400*a^4*b^4*c^5*d*e^8 - 53760*a^5*b*c^7*d^2*e^7 + 1
07520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/
2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10
+ b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^
9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10
- 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b
^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 409
60*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^
8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^
8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4
*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d
^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*
d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3
*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*
c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8
*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7
*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a
^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*
e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a
*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d
^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 -
81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920
*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2) - (1000*a^2*c^7*e^10 + 63*b^4*c^5*e^10 - 32*c^9*d^4*e^6
- 510*a*b^2*c^6*e^10 - 40*a*c^8*d^2*e^8 + 64*b*c^8*d^3*e^7 + 6*b^3*c^6*d*e^9 - 38*b^2*c^7*d^2*e^8 + 40*a*b*c^7
*d*e^9)/(32*(64*a^3*c^7*d^8 - a^4*b^6*e^8 + 64*a^7*c^3*e^8 - b^6*c^4*d^8 - b^10*d^4*e^4 + 12*a*b^4*c^5*d^8 + 1
2*a^5*b^4*c*e^8 + 4*a*b^9*d^3*e^5 + 4*a^3*b^7*d*e^7 + 4*b^7*c^3*d^7*e + 4*b^9*c*d^5*e^3 - 48*a^2*b^2*c^6*d^8 -
48*a^6*b^2*c^2*e^8 - 6*a^2*b^8*d^2*e^6 + 256*a^4*c^6*d^6*e^2 + 384*a^5*c^5*d^4*e^4 + 256*a^6*c^4*d^2*e^6 - 6*
b^8*c^2*d^6*e^2 - 240*a^2*b^4*c^4*d^6*e^2 + 48*a^2*b^5*c^3*d^5*e^3 + 90*a^2*b^6*c^2*d^4*e^4 + 192*a^3*b^2*c^5*
d^6*e^2 + 320*a^3*b^3*c^4*d^5*e^3 - 440*a^3*b^4*c^3*d^4*e^4 + 48*a^3*b^5*c^2*d^3*e^5 + 480*a^4*b^2*c^4*d^4*e^4
+ 320*a^4*b^3*c^3*d^3*e^5 - 240*a^4*b^4*c^2*d^2*e^6 + 192*a^5*b^2*c^3*d^2*e^6 - 48*a*b^5*c^4*d^7*e - 256*a^3*
b*c^6*d^7*e - 48*a^4*b^5*c*d*e^7 - 256*a^6*b*c^3*d*e^7 + 68*a*b^6*c^3*d^6*e^2 - 36*a*b^7*c^2*d^5*e^3 + 192*a^2
*b^3*c^5*d^7*e - 36*a^2*b^7*c*d^3*e^5 + 68*a^3*b^6*c*d^2*e^6 - 768*a^4*b*c^5*d^5*e^3 - 768*a^5*b*c^4*d^3*e^5 +
192*a^5*b^3*c^2*d*e^7)) + (((106496*a^6*c^7*d*e^10 - 53248*a^6*b*c^6*e^11 - 192*a^2*b^9*c^2*e^11 + 3136*a^3*b
^7*c^3*e^11 - 19200*a^4*b^5*c^4*e^11 + 52224*a^5*b^3*c^5*e^11 + 8192*a^3*c^10*d^7*e^4 + 122880*a^4*c^9*d^5*e^6
+ 221184*a^5*c^8*d^3*e^8 - 128*b^6*c^7*d^7*e^4 + 448*b^7*c^6*d^6*e^5 - 192*b^8*c^5*d^5*e^6 - 640*b^9*c^4*d^4*
e^7 + 704*b^10*c^3*d^3*e^8 - 192*b^11*c^2*d^2*e^9 - 6144*a^2*b^2*c^9*d^7*e^4 + 21504*a^2*b^3*c^8*d^6*e^5 + 138
24*a^2*b^4*c^7*d^5*e^6 - 88320*a^2*b^5*c^6*d^4*e^7 + 67200*a^2*b^6*c^5*d^3*e^8 - 1728*a^2*b^7*c^4*d^2*e^9 - 79
872*a^3*b^2*c^8*d^5*e^6 + 271360*a^3*b^3*c^7*d^4*e^7 - 151040*a^3*b^4*c^6*d^3*e^8 - 59136*a^3*b^5*c^5*d^2*e^9
+ 30720*a^4*b^2*c^7*d^3*e^8 + 261120*a^4*b^3*c^6*d^2*e^9 + 384*a*b^10*c^2*d*e^10 + 1536*a*b^4*c^8*d^7*e^4 - 53
76*a*b^5*c^7*d^6*e^5 + 384*a*b^6*c^6*d^5*e^6 + 12480*a*b^7*c^5*d^4*e^7 - 11520*a*b^8*c^4*d^3*e^8 + 2112*a*b^9*
c^3*d^2*e^9 - 5952*a^2*b^8*c^3*d*e^10 - 28672*a^3*b*c^9*d^6*e^5 + 32896*a^3*b^6*c^4*d*e^10 - 307200*a^4*b*c^8*
d^4*e^7 - 69120*a^4*b^4*c^5*d*e^10 - 331776*a^5*b*c^7*d^2*e^9 + 6144*a^5*b^2*c^6*d*e^10)/(64*(64*a^3*c^7*d^8 -
a^4*b^6*e^8 + 64*a^7*c^3*e^8 - b^6*c^4*d^8 - b^10*d^4*e^4 + 12*a*b^4*c^5*d^8 + 12*a^5*b^4*c*e^8 + 4*a*b^9*d^3
*e^5 + 4*a^3*b^7*d*e^7 + 4*b^7*c^3*d^7*e + 4*b^9*c*d^5*e^3 - 48*a^2*b^2*c^6*d^8 - 48*a^6*b^2*c^2*e^8 - 6*a^2*b
^8*d^2*e^6 + 256*a^4*c^6*d^6*e^2 + 384*a^5*c^5*d^4*e^4 + 256*a^6*c^4*d^2*e^6 - 6*b^8*c^2*d^6*e^2 - 240*a^2*b^4
*c^4*d^6*e^2 + 48*a^2*b^5*c^3*d^5*e^3 + 90*a^2*b^6*c^2*d^4*e^4 + 192*a^3*b^2*c^5*d^6*e^2 + 320*a^3*b^3*c^4*d^5
*e^3 - 440*a^3*b^4*c^3*d^4*e^4 + 48*a^3*b^5*c^2*d^3*e^5 + 480*a^4*b^2*c^4*d^4*e^4 + 320*a^4*b^3*c^3*d^3*e^5 -
240*a^4*b^4*c^2*d^2*e^6 + 192*a^5*b^2*c^3*d^2*e^6 - 48*a*b^5*c^4*d^7*e - 256*a^3*b*c^6*d^7*e - 48*a^4*b^5*c*d*
e^7 - 256*a^6*b*c^3*d*e^7 + 68*a*b^6*c^3*d^6*e^2 - 36*a*b^7*c^2*d^5*e^3 + 192*a^2*b^3*c^5*d^7*e - 36*a^2*b^7*c
*d^3*e^5 + 68*a^3*b^6*c*d^2*e^6 - 768*a^4*b*c^5*d^5*e^3 - 768*a^5*b*c^4*d^3*e^5 + 192*a^5*b^3*c^2*d*e^7)) + ((
d + e*x)^(1/2)*(-(9*b^13*e^9 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) + 26880*a^6*b*c^6*e^9 - 53760*a^6*c^7*d*e^8
+ 2077*a^2*b^9*c^2*e^9 - 10656*a^3*b^7*c^3*e^9 + 30240*a^4*b^5*c^4*e^9 - 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^
9*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^10*d^7*e^2 + 17920*a^4*c^9*d^5*e^4 + 35840*a^5*c^8*d^3*e^6 - 32*b^6*c^
7*d^7*e^2 + 112*b^7*c^6*d^6*e^3 - 98*b^8*c^5*d^5*e^4 - 35*b^9*c^4*d^4*e^5 + 70*b^10*c^3*d^3*e^6 - 14*b^11*c^2*
d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^9 - 21*b^12*c*d*e^8 - 1536*a^2*b^2*c^9*d^7*
e^2 + 5376*a^2*b^3*c^8*d^6*e^3 - 1344*a^2*b^4*c^7*d^5*e^4 - 10080*a^2*b^5*c^6*d^4*e^5 + 7840*a^2*b^6*c^5*d^3*e
^6 + 1008*a^2*b^7*c^4*d^2*e^7 - 7168*a^3*b^2*c^8*d^5*e^4 + 35840*a^3*b^3*c^7*d^4*e^5 - 17920*a^3*b^4*c^6*d^3*e
^6 - 12544*a^3*b^5*c^5*d^2*e^7 + 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*
a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) + 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) + 384*a*
b^4*c^8*d^7*e^2 - 1344*a*b^5*c^7*d^6*e^3 + 896*a*b^6*c^6*d^5*e^4 + 1120*a*b^7*c^5*d^4*e^5 - 1260*a*b^8*c^4*d^3
*e^6 + 98*a*b^9*c^3*d^2*e^7 - 5418*a^2*b^8*c^3*d*e^8 - 7168*a^3*b*c^9*d^6*e^3 + 28224*a^3*b^6*c^4*d*e^8 - 4480
0*a^4*b*c^8*d^4*e^5 - 78400*a^4*b^4*c^5*d*e^8 - 53760*a^5*b*c^7*d^2*e^7 + 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3
*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b
^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 2
4*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6
*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7
*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 +
10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7
*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 +
490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 +
560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 -
12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 -
1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4
- 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^
8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*
e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^
6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^
4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*
c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 2048
0*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^
6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e -
235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7
*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*
c^5*d*e^9)))^(1/2)*(8192*a^7*c^6*d*e^10 - 4096*a^7*b*c^5*e^11 + 64*a^4*b^7*c^2*e^11 - 768*a^5*b^5*c^3*e^11 + 3
072*a^6*b^3*c^4*e^11 + 8192*a^3*c^10*d^9*e^2 + 32768*a^4*c^9*d^7*e^4 + 49152*a^5*c^8*d^5*e^6 + 32768*a^6*c^7*d
^3*e^8 - 128*b^6*c^7*d^9*e^2 + 576*b^7*c^6*d^8*e^3 - 1024*b^8*c^5*d^7*e^4 + 896*b^9*c^4*d^6*e^5 - 384*b^10*c^3
*d^5*e^6 + 64*b^11*c^2*d^4*e^7 - 6144*a^2*b^2*c^9*d^9*e^2 + 27648*a^2*b^3*c^8*d^8*e^3 - 43008*a^2*b^4*c^7*d^7*
e^4 + 21504*a^2*b^5*c^6*d^6*e^5 + 8448*a^2*b^6*c^5*d^5*e^6 - 10368*a^2*b^7*c^4*d^4*e^7 + 1536*a^2*b^8*c^3*d^3*
e^8 + 384*a^2*b^9*c^2*d^2*e^9 + 40960*a^3*b^2*c^8*d^7*e^4 + 28672*a^3*b^3*c^7*d^6*e^5 - 76800*a^3*b^4*c^6*d^5*
e^6 + 34304*a^3*b^5*c^5*d^4*e^7 + 5632*a^3*b^6*c^4*d^3*e^8 - 3840*a^3*b^7*c^3*d^2*e^9 + 110592*a^4*b^2*c^7*d^5
*e^6 + 10240*a^4*b^3*c^6*d^4*e^7 - 51200*a^4*b^4*c^5*d^3*e^8 + 9216*a^4*b^5*c^4*d^2*e^9 + 73728*a^5*b^2*c^6*d^
3*e^8 + 12288*a^5*b^3*c^5*d^2*e^9 + 1536*a*b^4*c^8*d^9*e^2 - 6912*a*b^5*c^7*d^8*e^3 + 11776*a*b^6*c^6*d^7*e^4
- 8960*a*b^7*c^5*d^6*e^5 + 2304*a*b^8*c^4*d^5*e^6 + 512*a*b^9*c^3*d^4*e^7 - 256*a*b^10*c^2*d^3*e^8 - 36864*a^3
*b*c^9*d^8*e^3 - 256*a^3*b^8*c^2*d*e^10 - 114688*a^4*b*c^8*d^6*e^5 + 2944*a^4*b^6*c^3*d*e^10 - 122880*a^5*b*c^
7*d^4*e^7 - 10752*a^5*b^4*c^4*d*e^10 - 49152*a^6*b*c^6*d^2*e^9 + 10240*a^6*b^2*c^5*d*e^10))/(8*(16*a^2*c^6*d^8
+ a^4*b^4*e^8 + 16*a^6*c^2*e^8 + b^4*c^4*d^8 + b^8*d^4*e^4 - 8*a*b^2*c^5*d^8 - 8*a^5*b^2*c*e^8 - 4*a*b^7*d^3*
e^5 - 4*a^3*b^5*d*e^7 - 4*b^5*c^3*d^7*e - 4*b^7*c*d^5*e^3 + 6*a^2*b^6*d^2*e^6 + 64*a^3*c^5*d^6*e^2 + 96*a^4*c^
4*d^4*e^4 + 64*a^5*c^3*d^2*e^6 + 6*b^6*c^2*d^6*e^2 + 64*a^2*b^2*c^4*d^6*e^2 + 32*a^2*b^3*c^3*d^5*e^3 - 74*a^2*
b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^3*d^4*e^4 + 32*a^3*b^3*c^2*d^3*e^5 + 64*a^4*b^2*c^2*d^2*e^6 + 32*a*b^3*c^4*d^7
*e + 4*a*b^6*c*d^4*e^4 - 64*a^2*b*c^5*d^7*e + 32*a^4*b^3*c*d*e^7 - 64*a^5*b*c^2*d*e^7 - 44*a*b^4*c^3*d^6*e^2 +
20*a*b^5*c^2*d^5*e^3 + 20*a^2*b^5*c*d^3*e^5 - 192*a^3*b*c^4*d^5*e^3 - 44*a^3*b^4*c*d^2*e^6 - 192*a^4*b*c^3*d^
3*e^5)))*(-(9*b^13*e^9 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) + 26880*a^6*b*c^6*e^9 - 53760*a^6*c^7*d*e^8 + 2077
*a^2*b^9*c^2*e^9 - 10656*a^3*b^7*c^3*e^9 + 30240*a^4*b^5*c^4*e^9 - 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4
*a*c - b^2)^9)^(1/2) + 2048*a^3*c^10*d^7*e^2 + 17920*a^4*c^9*d^5*e^4 + 35840*a^5*c^8*d^3*e^6 - 32*b^6*c^7*d^7*
e^2 + 112*b^7*c^6*d^6*e^3 - 98*b^8*c^5*d^5*e^4 - 35*b^9*c^4*d^4*e^5 + 70*b^10*c^3*d^3*e^6 - 14*b^11*c^2*d^2*e^
7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^9 - 21*b^12*c*d*e^8 - 1536*a^2*b^2*c^9*d^7*e^2 +
5376*a^2*b^3*c^8*d^6*e^3 - 1344*a^2*b^4*c^7*d^5*e^4 - 10080*a^2*b^5*c^6*d^4*e^5 + 7840*a^2*b^6*c^5*d^3*e^6 + 1
008*a^2*b^7*c^4*d^2*e^7 - 7168*a^3*b^2*c^8*d^5*e^4 + 35840*a^3*b^3*c^7*d^4*e^5 - 17920*a^3*b^4*c^6*d^3*e^6 - 1
2544*a^3*b^5*c^5*d^2*e^7 + 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*
c*e^9*(-(4*a*c - b^2)^9)^(1/2) + 532*a*b^10*c^2*d*e^8 + 21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^
8*d^7*e^2 - 1344*a*b^5*c^7*d^6*e^3 + 896*a*b^6*c^6*d^5*e^4 + 1120*a*b^7*c^5*d^4*e^5 - 1260*a*b^8*c^4*d^3*e^6 +
98*a*b^9*c^3*d^2*e^7 - 5418*a^2*b^8*c^3*d*e^8 - 7168*a^3*b*c^9*d^6*e^3 + 28224*a^3*b^6*c^4*d*e^8 - 44800*a^4*
b*c^8*d^4*e^5 - 78400*a^4*b^4*c^5*d*e^8 - 53760*a^5*b*c^7*d^2*e^7 + 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e
^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)
^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^
10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 +
240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c
^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^
3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e
^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a
^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^
3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*
a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*
a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 322
56*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10
240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 +
71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4
+ 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*
e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^
2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10
*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*
e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^
4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c
^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*
e^9)))^(1/2) + ((d + e*x)^(1/2)*(9*b^6*c^3*e^10 - 200*a^3*c^6*e^10 + 32*c^9*d^6*e^4 - 96*a*b^4*c^4*e^10 + 248*
a*c^8*d^4*e^6 - 96*b*c^8*d^5*e^5 - 12*b^5*c^4*d*e^9 + 298*a^2*b^2*c^5*e^10 + 592*a^2*c^7*d^2*e^8 + 58*b^2*c^7*
d^4*e^6 + 44*b^3*c^6*d^3*e^7 - 26*b^4*c^5*d^2*e^8 - 496*a*b*c^7*d^3*e^7 + 172*a*b^3*c^5*d*e^9 - 592*a^2*b*c^6*
d*e^9 + 76*a*b^2*c^6*d^2*e^8))/(8*(16*a^2*c^6*d^8 + a^4*b^4*e^8 + 16*a^6*c^2*e^8 + b^4*c^4*d^8 + b^8*d^4*e^4 -
8*a*b^2*c^5*d^8 - 8*a^5*b^2*c*e^8 - 4*a*b^7*d^3*e^5 - 4*a^3*b^5*d*e^7 - 4*b^5*c^3*d^7*e - 4*b^7*c*d^5*e^3 + 6
*a^2*b^6*d^2*e^6 + 64*a^3*c^5*d^6*e^2 + 96*a^4*c^4*d^4*e^4 + 64*a^5*c^3*d^2*e^6 + 6*b^6*c^2*d^6*e^2 + 64*a^2*b
^2*c^4*d^6*e^2 + 32*a^2*b^3*c^3*d^5*e^3 - 74*a^2*b^4*c^2*d^4*e^4 + 144*a^3*b^2*c^3*d^4*e^4 + 32*a^3*b^3*c^2*d^
3*e^5 + 64*a^4*b^2*c^2*d^2*e^6 + 32*a*b^3*c^4*d^7*e + 4*a*b^6*c*d^4*e^4 - 64*a^2*b*c^5*d^7*e + 32*a^4*b^3*c*d*
e^7 - 64*a^5*b*c^2*d*e^7 - 44*a*b^4*c^3*d^6*e^2 + 20*a*b^5*c^2*d^5*e^3 + 20*a^2*b^5*c*d^3*e^5 - 192*a^3*b*c^4*
d^5*e^3 - 44*a^3*b^4*c*d^2*e^6 - 192*a^4*b*c^3*d^3*e^5)))*(-(9*b^13*e^9 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(1/2) +
26880*a^6*b*c^6*e^9 - 53760*a^6*c^7*d*e^8 + 2077*a^2*b^9*c^2*e^9 - 10656*a^3*b^7*c^3*e^9 + 30240*a^4*b^5*c^4*
e^9 - 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^10*d^7*e^2 + 17920*a^4*c^9*
d^5*e^4 + 35840*a^5*c^8*d^3*e^6 - 32*b^6*c^7*d^7*e^2 + 112*b^7*c^6*d^6*e^3 - 98*b^8*c^5*d^5*e^4 - 35*b^9*c^4*d
^4*e^5 + 70*b^10*c^3*d^3*e^6 - 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^
9 - 21*b^12*c*d*e^8 - 1536*a^2*b^2*c^9*d^7*e^2 + 5376*a^2*b^3*c^8*d^6*e^3 - 1344*a^2*b^4*c^7*d^5*e^4 - 10080*a
^2*b^5*c^6*d^4*e^5 + 7840*a^2*b^6*c^5*d^3*e^6 + 1008*a^2*b^7*c^4*d^2*e^7 - 7168*a^3*b^2*c^8*d^5*e^4 + 35840*a^
3*b^3*c^7*d^4*e^5 - 17920*a^3*b^4*c^6*d^3*e^6 - 12544*a^3*b^5*c^5*d^2*e^7 + 44800*a^4*b^3*c^6*d^2*e^7 + 14*b^2
*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) + 532*a*b^10*c^2*d*e^8 + 21*b^
3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7*e^2 - 1344*a*b^5*c^7*d^6*e^3 + 896*a*b^6*c^6*d^5*e^4 +
1120*a*b^7*c^5*d^4*e^5 - 1260*a*b^8*c^4*d^3*e^6 + 98*a*b^9*c^3*d^2*e^7 - 5418*a^2*b^8*c^3*d*e^8 - 7168*a^3*b*c
^9*d^6*e^3 + 28224*a^3*b^6*c^4*d*e^8 - 44800*a^4*b*c^8*d^4*e^5 - 78400*a^4*b^4*c^5*d*e^8 - 53760*a^5*b*c^7*d^2
*e^7 + 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c - b^2
)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*
c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b
^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*
c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 614
4*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e
^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^1
0*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^
8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12
*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b
^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*
b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5
*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*
a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600
*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 1
5360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 -
42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b
^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^
3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*
b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2
*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9
- 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)))*(-(9*b^13*e^9 - 9*b^4*e^9*(-(4*a*c - b^2)^9)^(
1/2) + 26880*a^6*b*c^6*e^9 - 53760*a^6*c^7*d*e^8 + 2077*a^2*b^9*c^2*e^9 - 10656*a^3*b^7*c^3*e^9 + 30240*a^4*b^
5*c^4*e^9 - 44800*a^5*b^3*c^5*e^9 - 25*a^2*c^2*e^9*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^10*d^7*e^2 + 17920*a^
4*c^9*d^5*e^4 + 35840*a^5*c^8*d^3*e^6 - 32*b^6*c^7*d^7*e^2 + 112*b^7*c^6*d^6*e^3 - 98*b^8*c^5*d^5*e^4 - 35*b^9
*c^4*d^4*e^5 + 70*b^10*c^3*d^3*e^6 - 14*b^11*c^2*d^2*e^7 + 35*c^4*d^4*e^5*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^1
1*c*e^9 - 21*b^12*c*d*e^8 - 1536*a^2*b^2*c^9*d^7*e^2 + 5376*a^2*b^3*c^8*d^6*e^3 - 1344*a^2*b^4*c^7*d^5*e^4 - 1
0080*a^2*b^5*c^6*d^4*e^5 + 7840*a^2*b^6*c^5*d^3*e^6 + 1008*a^2*b^7*c^4*d^2*e^7 - 7168*a^3*b^2*c^8*d^5*e^4 + 35
840*a^3*b^3*c^7*d^4*e^5 - 17920*a^3*b^4*c^6*d^3*e^6 - 12544*a^3*b^5*c^5*d^2*e^7 + 44800*a^4*b^3*c^6*d^2*e^7 +
14*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^9*(-(4*a*c - b^2)^9)^(1/2) + 532*a*b^10*c^2*d*e^8 +
21*b^3*c*d*e^8*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7*e^2 - 1344*a*b^5*c^7*d^6*e^3 + 896*a*b^6*c^6*d^5*
e^4 + 1120*a*b^7*c^5*d^4*e^5 - 1260*a*b^8*c^4*d^3*e^6 + 98*a*b^9*c^3*d^2*e^7 - 5418*a^2*b^8*c^3*d*e^8 - 7168*a
^3*b*c^9*d^6*e^3 + 28224*a^3*b^6*c^4*d*e^8 - 44800*a^4*b*c^8*d^4*e^5 - 78400*a^4*b^4*c^5*d*e^8 - 53760*a^5*b*c
^7*d^2*e^7 + 107520*a^5*b^2*c^6*d*e^8 + 154*a*c^3*d^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^6*(-(4*a*c
- b^2)^9)^(1/2) - 154*a*b*c^2*d*e^8*(-(4*a*c - b^2)^9)^(1/2))/(128*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096
*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5
*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^
4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10
- 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9
*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a
^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*
a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^
3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560
*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 1536
0*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 80
00*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 1
25440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 -
11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e
^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3
*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120
*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*
d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 22
0*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b
^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4
*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*2i

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*c*x+b)/(c*x**2+b*x+a)**3/(e*x+d)**(1/2),x)

[Out]

Timed out

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