∫ 1_______√ d+ex (a+bx+cx2)2 dx

3.2299 \(\int \frac {1}{\sqrt {d+e x} (a+b x+c x^2)^2} \, dx\)

Optimal. Leaf size=428 \[ \frac {\sqrt {c} \left (-2 c e \left (-d \sqrt {b^2-4 a c}-6 a e+4 b d\right )-b e^2 \left (\sqrt {b^2-4 a c}+b\right )+8 c^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )}}\right )}{\sqrt {2} \left (b^2-4 a c\right )^{3/2} \sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )} \left (a e^2-b d e+c d^2\right )}-\frac {\sqrt {c} \left (-2 c e \left (d \sqrt {b^2-4 a c}-6 a e+4 b d\right )-b e^2 \left (b-\sqrt {b^2-4 a c}\right )+8 c^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}\right )}{\sqrt {2} \left (b^2-4 a c\right )^{3/2} \sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )} \left (a e^2-b d e+c d^2\right )}-\frac {\sqrt {d+e x} \left (2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right )}{\left (b^2-4 a c\right ) \left (a+b x+c x^2\right ) \left (a e^2-b d e+c d^2\right )} \]

[Out]

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

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

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

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

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

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

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Rubi [A] time = 1.47, antiderivative size = 428, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 4, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {740, 826, 1166, 208} \[ \frac {\sqrt {c} \left (-2 c e \left (-d \sqrt {b^2-4 a c}-6 a e+4 b d\right )-b e^2 \left (\sqrt {b^2-4 a c}+b\right )+8 c^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )}}\right )}{\sqrt {2} \left (b^2-4 a c\right )^{3/2} \sqrt {2 c d-e \left (b-\sqrt {b^2-4 a c}\right )} \left (a e^2-b d e+c d^2\right )}-\frac {\sqrt {c} \left (-2 c e \left (d \sqrt {b^2-4 a c}-6 a e+4 b d\right )-b e^2 \left (b-\sqrt {b^2-4 a c}\right )+8 c^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}\right )}{\sqrt {2} \left (b^2-4 a c\right )^{3/2} \sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )} \left (a e^2-b d e+c d^2\right )}-\frac {\sqrt {d+e x} \left (2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right )}{\left (b^2-4 a c\right ) \left (a+b x+c x^2\right ) \left (a e^2-b d e+c d^2\right )} \]

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

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

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

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

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

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 740

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((d + e*x)^(m + 1)*(

b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*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*Simp[b*c*d*e*(2*p - m

+ 2) + b^2*e^2*(m + p + 2) - 2*c^2*d^2*(2*p + 3) - 2*a*c*e^2*(m + 2*p + 3) - c*e*(2*c*d - b*e)*(m + 2*p + 4)*x

, x]*(a + b*x + c*x^2)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e, m}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b

*d*e + a*e^2, 0] && NeQ[2*c*d - b*e, 0] && LtQ[p, -1] && IntQuadraticQ[a, b, c, d, e, m, p, x]

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 {1}{\sqrt {d+e x} \left (a+b x+c x^2\right )^2} \, dx &=-\frac {\sqrt {d+e x} \left (b c d-b^2 e+2 a c e+c (2 c d-b e) x\right )}{\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 )}-\frac {\int \frac {\frac {1}{2} \left (4 c^2 d^2-b^2 e^2-3 c e (b d-2 a e)\right )+\frac {1}{2} c e (2 c d-b e) x}{\sqrt {d+e x} \left (a+b x+c x^2\right )} \, dx}{\left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )}\\ &=-\frac {\sqrt {d+e x} \left (b c d-b^2 e+2 a c e+c (2 c d-b e) x\right )}{\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 )}-\frac {2 \operatorname {Subst}\left (\int \frac {-\frac {1}{2} c d e (2 c d-b e)+\frac {1}{2} e \left (4 c^2 d^2-b^2 e^2-3 c e (b d-2 a e)\right )+\frac {1}{2} c e (2 c d-b e) x^2}{c d^2-b d e+a e^2+(-2 c d+b e) x^2+c x^4} \, dx,x,\sqrt {d+e x}\right )}{\left (b^2-4 a c\right ) \left (c d^2-b d e+a e^2\right )}\\ &=-\frac {\sqrt {d+e x} \left (b c d-b^2 e+2 a c e+c (2 c d-b e) x\right )}{\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 )}-\frac {\left (c \left (8 c^2 d^2-b \left (b+\sqrt {b^2-4 a c}\right ) e^2-2 c e \left (4 b d-\sqrt {b^2-4 a c} d-6 a e\right )\right )\right ) \operatorname {Subst}\left (\int \frac {1}{-\frac {1}{2} \sqrt {b^2-4 a c} e+\frac {1}{2} (-2 c d+b e)+c x^2} \, dx,x,\sqrt {d+e x}\right )}{2 \left (b^2-4 a c\right )^{3/2} \left (c d^2-b d e+a e^2\right )}+\frac {\left (c \left (8 c^2 d^2-b \left (b-\sqrt {b^2-4 a c}\right ) e^2-2 c e \left (4 b d+\sqrt {b^2-4 a c} d-6 a e\right )\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {1}{2} \sqrt {b^2-4 a c} e+\frac {1}{2} (-2 c d+b e)+c x^2} \, dx,x,\sqrt {d+e x}\right )}{2 \left (b^2-4 a c\right )^{3/2} \left (c d^2-b d e+a e^2\right )}\\ &=-\frac {\sqrt {d+e x} \left (b c d-b^2 e+2 a c e+c (2 c d-b e) x\right )}{\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 )}+\frac {\sqrt {c} \left (8 c^2 d^2-b \left (b+\sqrt {b^2-4 a c}\right ) e^2-2 c e \left (4 b d-\sqrt {b^2-4 a c} d-6 a e\right )\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e}}\right )}{\sqrt {2} \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 )}-\frac {\sqrt {c} \left (8 c^2 d^2-b \left (b-\sqrt {b^2-4 a c}\right ) e^2-2 c e \left (4 b d+\sqrt {b^2-4 a c} d-6 a e\right )\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e}}\right )}{\sqrt {2} \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 )}\\ \end {align*}

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Mathematica [A] time = 1.26, size = 366, normalized size = 0.86 \[ \frac {\frac {\sqrt {c} \left (\frac {\left (2 c e \left (d \sqrt {b^2-4 a c}+6 a e-4 b d\right )-b e^2 \left (\sqrt {b^2-4 a c}+b\right )+8 c^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {e \sqrt {b^2-4 a c}-b e+2 c d}}\right )}{\sqrt {e \left (\sqrt {b^2-4 a c}-b\right )+2 c d}}-\frac {\left (-2 c e \left (d \sqrt {b^2-4 a c}-6 a e+4 b d\right )+b e^2 \left (\sqrt {b^2-4 a c}-b\right )+8 c^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {c} \sqrt {d+e x}}{\sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}\right )}{\sqrt {2 c d-e \left (\sqrt {b^2-4 a c}+b\right )}}\right )}{\sqrt {2} \sqrt {b^2-4 a c}}+\frac {\sqrt {d+e x} \left (-2 c (a e+c d x)+b^2 e+b c (e x-d)\right )}{a+x (b+c x)}}{\left (b^2-4 a c\right ) \left (e (a e-b d)+c d^2\right )} \]

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

((Sqrt[d + e*x]*(b^2*e - 2*c*(a*e + c*d*x) + b*c*(-d + e*x)))/(a + x*(b + c*x)) + (Sqrt[c]*(((8*c^2*d^2 - b*(b

+ Sqrt[b^2 - 4*a*c])*e^2 + 2*c*e*(-4*b*d + Sqrt[b^2 - 4*a*c]*d + 6*a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*

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

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

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

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

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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giac [B] time = 2.02, size = 2822, normalized size = 6.59 \[ \text {result too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

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

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

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

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

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

4*a*b*c*d*e^2 + a*b^2*e^3 - 4*a^2*c*e^3) - (16*(b^2*c^5 - 4*a*c^6)*d^7*e - 56*(b^3*c^4 - 4*a*b*c^5)*d^6*e^2 +

14*(5*b^4*c^3 - 16*a*b^2*c^4 - 16*a^2*c^5)*d^5*e^3 - 35*(b^5*c^2 - 16*a^2*b*c^4)*d^4*e^4 + 4*(b^6*c + 23*a*b^4

*c^2 - 92*a^2*b^2*c^3 - 64*a^3*c^4)*d^3*e^5 + (b^7 - 26*a*b^5*c - 8*a^2*b^3*c^2 + 384*a^3*b*c^3)*d^2*e^6 - 2*(

a*b^6 - 19*a^2*b^4*c + 48*a^3*b^2*c^2 + 48*a^4*c^3)*d*e^7 + (a^2*b^5 - 16*a^3*b^3*c + 48*a^4*b*c^2)*e^8)*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^2*d^3 - 8*a*c^3*d

^3 - 3*b^3*c*d^2*e + 12*a*b*c^2*d^2*e + b^4*d*e^2 - 2*a*b^2*c*d*e^2 - 8*a^2*c^2*d*e^2 - a*b^3*e^3 + 4*a^2*b*c*

e^3 + sqrt((2*b^2*c^2*d^3 - 8*a*c^3*d^3 - 3*b^3*c*d^2*e + 12*a*b*c^2*d^2*e + b^4*d*e^2 - 2*a*b^2*c*d*e^2 - 8*a

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

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

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

)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*sqrt(b^2 - 4*a*c)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*s

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

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

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

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

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

*c)*sqrt(b^2 - 4*a*c)*e^5)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*c*d^2*e - 4*a*c^2*d^2*e -

b^3*d*e^2 + 4*a*b*c*d*e^2 + a*b^2*e^3 - 4*a^2*c*e^3) - (16*(b^2*c^5 - 4*a*c^6)*d^7*e - 56*(b^3*c^4 - 4*a*b*c^5

)*d^6*e^2 + 14*(5*b^4*c^3 - 16*a*b^2*c^4 - 16*a^2*c^5)*d^5*e^3 - 35*(b^5*c^2 - 16*a^2*b*c^4)*d^4*e^4 + 4*(b^6*

c + 23*a*b^4*c^2 - 92*a^2*b^2*c^3 - 64*a^3*c^4)*d^3*e^5 + (b^7 - 26*a*b^5*c - 8*a^2*b^3*c^2 + 384*a^3*b*c^3)*d

^2*e^6 - 2*(a*b^6 - 19*a^2*b^4*c + 48*a^3*b^2*c^2 + 48*a^4*c^3)*d*e^7 + (a^2*b^5 - 16*a^3*b^3*c + 48*a^4*b*c^2

)*e^8)*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^2*d^3

- 8*a*c^3*d^3 - 3*b^3*c*d^2*e + 12*a*b*c^2*d^2*e + b^4*d*e^2 - 2*a*b^2*c*d*e^2 - 8*a^2*c^2*d*e^2 - a*b^3*e^3

+ 4*a^2*b*c*e^3 - sqrt((2*b^2*c^2*d^3 - 8*a*c^3*d^3 - 3*b^3*c*d^2*e + 12*a*b*c^2*d^2*e + b^4*d*e^2 - 2*a*b^2*c

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

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

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

(b^2 - 4*a*c)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*sqrt(b^2 - 4*a*c)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c -

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

qrt(b^2 - 4*a*c)*e^6)*abs(b^2*c*d^2*e - 4*a*c^2*d^2*e - b^3*d*e^2 + 4*a*b*c*d*e^2 + a*b^2*e^3 - 4*a^2*c*e^3)*a

bs(c))

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maple [B] time = 0.44, size = 1120, normalized size = 2.62 \[ \frac {8 \sqrt {2}\, b \,c^{2} e^{2} \arctanh \left (\frac {\sqrt {e x +d}\, \sqrt {2}\, c}{\sqrt {\left (-b e +2 c d +\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\right ) c}}\right )}{\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\, \left (4 a c -b^{2}\right ) \left (-2 b e +4 c d +2 \sqrt {-4 a c \,e^{2}+b^{2} e^{2}}\right ) \sqrt {\left (-b e +2 c d +\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\right ) c}}-\frac {8 \sqrt {2}\, b \,c^{2} e^{2} \arctan \left (\frac {\sqrt {e x +d}\, \sqrt {2}\, c}{\sqrt {\left (b e -2 c d +\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\right ) c}}\right )}{\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\, \left (4 a c -b^{2}\right ) \left (2 b e -4 c d +2 \sqrt {-4 a c \,e^{2}+b^{2} e^{2}}\right ) \sqrt {\left (b e -2 c d +\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\right ) c}}-\frac {16 \sqrt {2}\, c^{3} d e \arctanh \left (\frac {\sqrt {e x +d}\, \sqrt {2}\, c}{\sqrt {\left (-b e +2 c d +\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\right ) c}}\right )}{\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\, \left (4 a c -b^{2}\right ) \left (-2 b e +4 c d +2 \sqrt {-4 a c \,e^{2}+b^{2} e^{2}}\right ) \sqrt {\left (-b e +2 c d +\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\right ) c}}+\frac {16 \sqrt {2}\, c^{3} d e \arctan \left (\frac {\sqrt {e x +d}\, \sqrt {2}\, c}{\sqrt {\left (b e -2 c d +\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\right ) c}}\right )}{\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\, \left (4 a c -b^{2}\right ) \left (2 b e -4 c d +2 \sqrt {-4 a c \,e^{2}+b^{2} e^{2}}\right ) \sqrt {\left (b e -2 c d +\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\right ) c}}-\frac {12 \sqrt {2}\, \sqrt {-4 a c \,e^{2}+b^{2} e^{2}}\, c^{2} e \arctanh \left (\frac {\sqrt {e x +d}\, \sqrt {2}\, c}{\sqrt {\left (-b e +2 c d +\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\right ) c}}\right )}{\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\, \left (4 a c -b^{2}\right ) \left (-2 b e +4 c d +2 \sqrt {-4 a c \,e^{2}+b^{2} e^{2}}\right ) \sqrt {\left (-b e +2 c d +\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\right ) c}}-\frac {12 \sqrt {2}\, \sqrt {-4 a c \,e^{2}+b^{2} e^{2}}\, c^{2} e \arctan \left (\frac {\sqrt {e x +d}\, \sqrt {2}\, c}{\sqrt {\left (b e -2 c d +\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\right ) c}}\right )}{\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\, \left (4 a c -b^{2}\right ) \left (2 b e -4 c d +2 \sqrt {-4 a c \,e^{2}+b^{2} e^{2}}\right ) \sqrt {\left (b e -2 c d +\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\right ) c}}+\frac {2 \sqrt {-4 a c \,e^{2}+b^{2} e^{2}}\, \sqrt {e x +d}\, c e}{\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\, \left (4 a c -b^{2}\right ) \left (-b e +2 c d +\sqrt {-4 a c \,e^{2}+b^{2} e^{2}}\right ) \left (e x +\frac {b e}{2 c}-\frac {\sqrt {\left (-4 a c +b^{2}\right ) e^{2}}}{2 c}\right )}+\frac {2 \sqrt {-4 a c \,e^{2}+b^{2} e^{2}}\, \sqrt {e x +d}\, c e}{\sqrt {-\left (4 a c -b^{2}\right ) e^{2}}\, \left (4 a c -b^{2}\right ) \left (-b e +2 c d -\sqrt {-4 a c \,e^{2}+b^{2} e^{2}}\right ) \left (e x +\frac {b e}{2 c}+\frac {\sqrt {\left (-4 a c +b^{2}\right ) e^{2}}}{2 c}\right )} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

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

+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b-16*e*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*

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

tanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-12*e*c^2/(-(4*a*c-b^2)*e^2)^(1

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

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

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

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

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

x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b+16*e*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*

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

n((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-12*e*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/

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

arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*(-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 \[ \int \frac {1}{{\left (c x^{2} + b x + a\right )}^{2} \sqrt {e x + d}}\,{d x} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [B] time = 7.89, size = 45676, normalized size = 106.72 \[ \text {result too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

*(d + e*x)^2 + a*e^2 + c*d^2 - b*d*e) - atan(((((1536*a^5*c^6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6 - 72*a^2

*b^6*c^3*e^7 + 480*a^3*b^4*c^4*e^7 - 1408*a^4*b^2*c^5*e^7 + 512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^5 - 8*b^6

*c^5*d^4*e^3 + 16*b^7*c^4*d^3*e^4 - 4*b^8*c^3*d^2*e^5 - 384*a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3*e^4 + 19

2*a^2*b^4*c^5*d^2*e^5 - 1280*a^3*b^2*c^6*d^2*e^5 + 80*a*b^7*c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b^4*c^6*d^

4*e^3 - 192*a*b^5*c^5*d^3*e^4 + 16*a*b^6*c^4*d^2*e^5 - 576*a^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4 + 1792*a

^3*b^3*c^5*d*e^6)/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^

4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c

*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^

5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) - (2*(d +

e*x)^(1/2)*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6

*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5

+ 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3

- 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e

^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*

c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480

*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*

d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e

^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5

+ 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6

144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6

- 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a

^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*

b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b

^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^

2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 1228

8*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d

^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11

520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*(512*a^5*c^6*d*e^6 - 256*a^

5*b*c^5*e^7 + 4*a^2*b^7*c^2*e^7 - 48*a^3*b^5*c^3*e^7 + 192*a^4*b^3*c^4*e^7 + 512*a^3*c^8*d^5*e^2 + 1024*a^4*c^

7*d^3*e^4 - 8*b^6*c^5*d^5*e^2 + 20*b^7*c^4*d^4*e^3 - 16*b^8*c^3*d^3*e^4 + 4*b^9*c^2*d^2*e^5 - 384*a^2*b^2*c^7*

d^5*e^2 + 960*a^2*b^3*c^6*d^4*e^3 - 576*a^2*b^4*c^5*d^3*e^4 - 96*a^2*b^5*c^4*d^2*e^5 + 256*a^3*b^2*c^6*d^3*e^4

+ 896*a^3*b^3*c^5*d^2*e^5 - 8*a*b^8*c^2*d*e^6 + 96*a*b^4*c^6*d^5*e^2 - 240*a*b^5*c^5*d^4*e^3 + 176*a*b^6*c^4*

d^3*e^4 - 24*a*b^7*c^3*d^2*e^5 + 88*a^2*b^6*c^3*d*e^6 - 1280*a^3*b*c^7*d^4*e^3 - 288*a^3*b^4*c^4*d*e^6 - 1536*

a^4*b*c^6*d^2*e^5 + 128*a^4*b^2*c^5*d*e^6))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6

*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c

^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^

5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 -

7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 38

40*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c -

b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c -

b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c

^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b

^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*

e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12

*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14

*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^

5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 1

2288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3

*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b

^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^

2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^

3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^1

2*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5

*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 2457

6*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) - (2*(d + e*x)^(1/2)*(72*a^2*c^5*e^6 + b^4*c^3*e^6 + 32

*c^7*d^4*e^2 - 14*a*b^2*c^4*e^6 + 88*a*c^6*d^2*e^4 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4 -

88*a*b*c^5*d*e^5))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d

^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2

*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b

^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*

b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 768

0*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9

*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*

b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c

^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^

2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d

*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6

+ 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8

*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6

*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 6

48*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a

^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^

5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^

6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^

3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*

b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e

^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18

432*a^7*b^3*c^5*d*e^5)))^(1/2)*1i - (((1536*a^5*c^6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6 - 72*a^2*b^6*c^3*e

^7 + 480*a^3*b^4*c^4*e^7 - 1408*a^4*b^2*c^5*e^7 + 512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^5 - 8*b^6*c^5*d^4*e

^3 + 16*b^7*c^4*d^3*e^4 - 4*b^8*c^3*d^2*e^5 - 384*a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3*e^4 + 192*a^2*b^4*

c^5*d^2*e^5 - 1280*a^3*b^2*c^6*d^2*e^5 + 80*a*b^7*c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b^4*c^6*d^4*e^3 - 19

2*a*b^5*c^5*d^3*e^4 + 16*a*b^6*c^4*d^2*e^5 - 576*a^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4 + 1792*a^3*b^3*c^5

*d*e^6)/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3

*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 2

4*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3

+ 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) + (2*(d + e*x)^(1/2

)*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 384

0*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^

3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d

^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c

*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^

2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4

*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11

520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*

c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*

c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^

2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a

^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4

*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^

3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2

*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*

e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^

6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 115

20*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^

5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*(512*a^5*c^6*d*e^6 - 256*a^5*b*c^5*e^

7 + 4*a^2*b^7*c^2*e^7 - 48*a^3*b^5*c^3*e^7 + 192*a^4*b^3*c^4*e^7 + 512*a^3*c^8*d^5*e^2 + 1024*a^4*c^7*d^3*e^4

- 8*b^6*c^5*d^5*e^2 + 20*b^7*c^4*d^4*e^3 - 16*b^8*c^3*d^3*e^4 + 4*b^9*c^2*d^2*e^5 - 384*a^2*b^2*c^7*d^5*e^2 +

960*a^2*b^3*c^6*d^4*e^3 - 576*a^2*b^4*c^5*d^3*e^4 - 96*a^2*b^5*c^4*d^2*e^5 + 256*a^3*b^2*c^6*d^3*e^4 + 896*a^3

*b^3*c^5*d^2*e^5 - 8*a*b^8*c^2*d*e^6 + 96*a*b^4*c^6*d^5*e^2 - 240*a*b^5*c^5*d^4*e^3 + 176*a*b^6*c^4*d^3*e^4 -

24*a*b^7*c^3*d^2*e^5 + 88*a^2*b^6*c^3*d*e^6 - 1280*a^3*b*c^7*d^4*e^3 - 288*a^3*b^4*c^4*d*e^6 - 1536*a^4*b*c^6*

d^2*e^5 + 128*a^4*b^2*c^5*d*e^6))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 -

8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e -

6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a

^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c

^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3

*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1

/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1

/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3

+ 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2

*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840

*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*

a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2

- 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*

e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c

^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d

^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2

*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*

e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e -

18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*

e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a

^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^

7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) + (2*(d + e*x)^(1/2)*(72*a^2*c^5*e^6 + b^4*c^3*e^6 + 32*c^7*d^4*e

^2 - 14*a*b^2*c^4*e^6 + 88*a*c^6*d^2*e^4 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4 - 88*a*b*c^

5*d*e^5))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3

*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*

a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 +

b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^

4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*

d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9

*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^

3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e +

90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*

d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(

b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*

b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 +

1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e

^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^1

0*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^

2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*

d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*

d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72

*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^

5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432

*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^

3*c^5*d*e^5)))^(1/2)*1i)/((2*(5*b^3*c^4*e^6 + 32*c^7*d^3*e^3 - 48*b*c^6*d^2*e^4 + 6*b^2*c^5*d*e^5 - 36*a*b*c^5

*e^6 + 72*a*c^6*d*e^5))/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*

c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2

*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*

a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) + (

((1536*a^5*c^6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6 - 72*a^2*b^6*c^3*e^7 + 480*a^3*b^4*c^4*e^7 - 1408*a^4*b

^2*c^5*e^7 + 512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^5 - 8*b^6*c^5*d^4*e^3 + 16*b^7*c^4*d^3*e^4 - 4*b^8*c^3*d

^2*e^5 - 384*a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3*e^4 + 192*a^2*b^4*c^5*d^2*e^5 - 1280*a^3*b^2*c^6*d^2*e^

5 + 80*a*b^7*c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b^4*c^6*d^4*e^3 - 192*a*b^5*c^5*d^3*e^4 + 16*a*b^6*c^4*d^

2*e^5 - 576*a^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4 + 1792*a^3*b^3*c^5*d*e^6)/(a^2*b^6*e^4 - 64*a^3*c^5*d^4

- 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*

a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^

3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3

*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) - (2*(d + e*x)^(1/2)*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^

5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4

- 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5

- 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*

a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960

*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*

b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 38

40*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*

c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^

4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^

2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 128

0*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^

4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 -

648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 69

12*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 327

68*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13

*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720

*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^

2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3

- 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*(512*a^5*c^6*d*e^6 - 256*a^5*b*c^5*e^7 + 4*a^2*b^7*c^2*e^7 - 48*a^3*b^5*c^

3*e^7 + 192*a^4*b^3*c^4*e^7 + 512*a^3*c^8*d^5*e^2 + 1024*a^4*c^7*d^3*e^4 - 8*b^6*c^5*d^5*e^2 + 20*b^7*c^4*d^4*

e^3 - 16*b^8*c^3*d^3*e^4 + 4*b^9*c^2*d^2*e^5 - 384*a^2*b^2*c^7*d^5*e^2 + 960*a^2*b^3*c^6*d^4*e^3 - 576*a^2*b^4

*c^5*d^3*e^4 - 96*a^2*b^5*c^4*d^2*e^5 + 256*a^3*b^2*c^6*d^3*e^4 + 896*a^3*b^3*c^5*d^2*e^5 - 8*a*b^8*c^2*d*e^6

+ 96*a*b^4*c^6*d^5*e^2 - 240*a*b^5*c^5*d^4*e^3 + 176*a*b^6*c^4*d^3*e^4 - 24*a*b^7*c^3*d^2*e^5 + 88*a^2*b^6*c^3

*d*e^6 - 1280*a^3*b*c^7*d^4*e^3 - 288*a^3*b^4*c^4*d*e^6 - 1536*a^4*b*c^6*d^2*e^5 + 128*a^4*b^2*c^5*d*e^6))/(a^

2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 +

32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3

*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*

a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^

2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*

b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4

*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*

a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2

*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a

^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3

- 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 -

3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6

*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7

*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2

+ 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7

680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 168

96*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 691

2*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d

*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*

b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*

d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5))

)^(1/2) - (2*(d + e*x)^(1/2)*(72*a^2*c^5*e^6 + b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 14*a*b^2*c^4*e^6 + 88*a*c^6*d^2*

e^4 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4 - 88*a*b*c^5*d*e^5))/(a^2*b^4*e^4 + 16*a^2*c^4*d

^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a

*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3

- 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 38

4*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*

b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*

c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5

*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 25

60*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*

d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a

^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 409

6*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2

*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*

c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*

b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e

^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2

- 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 -

7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 +

6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d

^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^

3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3

*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) + (((1536*a^5*c^

6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6 - 72*a^2*b^6*c^3*e^7 + 480*a^3*b^4*c^4*e^7 - 1408*a^4*b^2*c^5*e^7 +

512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^5 - 8*b^6*c^5*d^4*e^3 + 16*b^7*c^4*d^3*e^4 - 4*b^8*c^3*d^2*e^5 - 384*

a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3*e^4 + 192*a^2*b^4*c^5*d^2*e^5 - 1280*a^3*b^2*c^6*d^2*e^5 + 80*a*b^7*

c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b^4*c^6*d^4*e^3 - 192*a*b^5*c^5*d^3*e^4 + 16*a*b^6*c^4*d^2*e^5 - 576*a

^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4 + 1792*a^3*b^3*c^5*d*e^6)/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3

*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e

^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 2

4*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a

^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) + (2*(d + e*x)^(1/2)*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5

+ b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*

d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^

7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 -

9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*

d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e

+ 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^

6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8

*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^

4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6

+ 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3

*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b

^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*

c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^

6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^

6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 -

72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*

d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 184

32*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*

b^3*c^5*d*e^5)))^(1/2)*(512*a^5*c^6*d*e^6 - 256*a^5*b*c^5*e^7 + 4*a^2*b^7*c^2*e^7 - 48*a^3*b^5*c^3*e^7 + 192*a

^4*b^3*c^4*e^7 + 512*a^3*c^8*d^5*e^2 + 1024*a^4*c^7*d^3*e^4 - 8*b^6*c^5*d^5*e^2 + 20*b^7*c^4*d^4*e^3 - 16*b^8*

c^3*d^3*e^4 + 4*b^9*c^2*d^2*e^5 - 384*a^2*b^2*c^7*d^5*e^2 + 960*a^2*b^3*c^6*d^4*e^3 - 576*a^2*b^4*c^5*d^3*e^4

- 96*a^2*b^5*c^4*d^2*e^5 + 256*a^3*b^2*c^6*d^3*e^4 + 896*a^3*b^3*c^5*d^2*e^5 - 8*a*b^8*c^2*d*e^6 + 96*a*b^4*c^

6*d^5*e^2 - 240*a*b^5*c^5*d^4*e^3 + 176*a*b^6*c^4*d^3*e^4 - 24*a*b^7*c^3*d^2*e^5 + 88*a^2*b^6*c^3*d*e^6 - 1280

*a^3*b*c^7*d^4*e^3 - 288*a^3*b^4*c^4*d*e^6 - 1536*a^4*b*c^6*d^2*e^5 + 128*a^4*b^2*c^5*d*e^6))/(a^2*b^4*e^4 + 1

6*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^

2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b

^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)

^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5

- 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e

^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9

)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d

^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120

*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*

e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^

9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*

e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 38

40*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6

+ 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^1

1*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c

^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^

5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5

*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*

a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^

4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*

a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) + (2*

(d + e*x)^(1/2)*(72*a^2*c^5*e^6 + b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 14*a*b^2*c^4*e^6 + 88*a*c^6*d^2*e^4 - 64*b*c^

6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4 - 88*a*b*c^5*d*e^5))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c

^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 -

2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^

2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d

^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 +

1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 -

5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4

+ 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^

6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a

*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*

e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6

- b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 +

3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 614

4*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 -

12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3

*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^

7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6

*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*

c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*

a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5

*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 1152

0*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)))*(-(32*b^6*c^5*d^5 - 2048*a^

3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^

6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*

c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/

2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/

2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3

+ 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*

e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*

a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a

*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2

- 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e

^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^

7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^

3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*

e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e

^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 1

8*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e

^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^

4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7

*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*2i - atan(((((1536*a^5*c^6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6

- 72*a^2*b^6*c^3*e^7 + 480*a^3*b^4*c^4*e^7 - 1408*a^4*b^2*c^5*e^7 + 512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^

5 - 8*b^6*c^5*d^4*e^3 + 16*b^7*c^4*d^3*e^4 - 4*b^8*c^3*d^2*e^5 - 384*a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3

*e^4 + 192*a^2*b^4*c^5*d^2*e^5 - 1280*a^3*b^2*c^6*d^2*e^5 + 80*a*b^7*c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b

^4*c^6*d^4*e^3 - 192*a*b^5*c^5*d^3*e^4 + 16*a*b^6*c^4*d^2*e^5 - 576*a^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4

+ 1792*a^3*b^3*c^5*d*e^6)/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b

^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3

- 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 +

24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3)

- (2*(d + e*x)^(1/2)*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*

a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^

7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^

2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b

^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560

*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^

4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3

*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*

a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b

^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^

7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^

2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3

+ 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 -

3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7

680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 61

44*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5

*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*

b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d

*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*(512*a^5*c^6*d*e^6

- 256*a^5*b*c^5*e^7 + 4*a^2*b^7*c^2*e^7 - 48*a^3*b^5*c^3*e^7 + 192*a^4*b^3*c^4*e^7 + 512*a^3*c^8*d^5*e^2 + 10

24*a^4*c^7*d^3*e^4 - 8*b^6*c^5*d^5*e^2 + 20*b^7*c^4*d^4*e^3 - 16*b^8*c^3*d^3*e^4 + 4*b^9*c^2*d^2*e^5 - 384*a^2

*b^2*c^7*d^5*e^2 + 960*a^2*b^3*c^6*d^4*e^3 - 576*a^2*b^4*c^5*d^3*e^4 - 96*a^2*b^5*c^4*d^2*e^5 + 256*a^3*b^2*c^

6*d^3*e^4 + 896*a^3*b^3*c^5*d^2*e^5 - 8*a*b^8*c^2*d*e^6 + 96*a*b^4*c^6*d^5*e^2 - 240*a*b^5*c^5*d^4*e^3 + 176*a

*b^6*c^4*d^3*e^4 - 24*a*b^7*c^3*d^2*e^5 + 88*a^2*b^6*c^3*d*e^6 - 1280*a^3*b*c^7*d^4*e^3 - 288*a^3*b^4*c^4*d*e^

6 - 1536*a^4*b*c^6*d^2*e^5 + 128*a^4*b^2*c^5*d*e^6))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*

d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 1

6*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b

^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c

^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3

*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-

(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-

(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*

a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2

- 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b

*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 -

a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e

- 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6

- 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^

4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2

+ 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3

120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 61

44*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*

a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 +

69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^

5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e

^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) - (2*(d + e*x)^(1/2)*(72*a^2*c^5*e^6 + b^4*c^3

*e^6 + 32*c^7*d^4*e^2 - 14*a*b^2*c^4*e^6 + 88*a*c^6*d^2*e^4 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*

d^2*e^4 - 88*a*b*c^5*d*e^5))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*

b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*

b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^

8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*

e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*

e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) +

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

960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 96

0*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3

- 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*

b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^1

0*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 24

0*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 +

1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^

2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^

3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4

+ 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 -

32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*

b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 +

720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^

9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3

*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*1i - (((1536*a^5*c^6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6 - 72*a^2*

b^6*c^3*e^7 + 480*a^3*b^4*c^4*e^7 - 1408*a^4*b^2*c^5*e^7 + 512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^5 - 8*b^6*

c^5*d^4*e^3 + 16*b^7*c^4*d^3*e^4 - 4*b^8*c^3*d^2*e^5 - 384*a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3*e^4 + 192

*a^2*b^4*c^5*d^2*e^5 - 1280*a^3*b^2*c^6*d^2*e^5 + 80*a*b^7*c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b^4*c^6*d^4

*e^3 - 192*a*b^5*c^5*d^3*e^4 + 16*a*b^6*c^4*d^2*e^5 - 576*a^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4 + 1792*a^

3*b^3*c^5*d*e^6)/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4

- 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*

d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5

*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) + (2*(d +

e*x)^(1/2)*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*

d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5

+ 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3

+ 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^

4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c

^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*

a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d

*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^

6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5

+ 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 61

44*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6

- 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^

3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b

^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^

6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2

*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288

*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^

5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 115

20*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*(512*a^5*c^6*d*e^6 - 256*a^5

*b*c^5*e^7 + 4*a^2*b^7*c^2*e^7 - 48*a^3*b^5*c^3*e^7 + 192*a^4*b^3*c^4*e^7 + 512*a^3*c^8*d^5*e^2 + 1024*a^4*c^7

*d^3*e^4 - 8*b^6*c^5*d^5*e^2 + 20*b^7*c^4*d^4*e^3 - 16*b^8*c^3*d^3*e^4 + 4*b^9*c^2*d^2*e^5 - 384*a^2*b^2*c^7*d

^5*e^2 + 960*a^2*b^3*c^6*d^4*e^3 - 576*a^2*b^4*c^5*d^3*e^4 - 96*a^2*b^5*c^4*d^2*e^5 + 256*a^3*b^2*c^6*d^3*e^4

+ 896*a^3*b^3*c^5*d^2*e^5 - 8*a*b^8*c^2*d*e^6 + 96*a*b^4*c^6*d^5*e^2 - 240*a*b^5*c^5*d^4*e^3 + 176*a*b^6*c^4*d

^3*e^4 - 24*a*b^7*c^3*d^2*e^5 + 88*a^2*b^6*c^3*d*e^6 - 1280*a^3*b*c^7*d^4*e^3 - 288*a^3*b^4*c^4*d*e^6 - 1536*a

^4*b*c^6*d^2*e^5 + 128*a^4*b^2*c^5*d*e^6))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*

d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^

2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5

- 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7

680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 384

0*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b

^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b

^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^

5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^

7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e

^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*

e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*

c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5

*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12

288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*

b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^

8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2

*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3

*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12

*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*

e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576

*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) + (2*(d + e*x)^(1/2)*(72*a^2*c^5*e^6 + b^4*c^3*e^6 + 32*

c^7*d^4*e^2 - 14*a*b^2*c^4*e^6 + 88*a*c^6*d^2*e^4 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4 -

88*a*b*c^5*d*e^5))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^

4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*

e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^

11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b

^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680

*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*

c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b

^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^

5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2

*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*

e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6

+ 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*

c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*

b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 64

8*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^

3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5

*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6

*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3

*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b

^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^

5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 184

32*a^7*b^3*c^5*d*e^5)))^(1/2)*1i)/((2*(5*b^3*c^4*e^6 + 32*c^7*d^3*e^3 - 48*b*c^6*d^2*e^4 + 6*b^2*c^5*d*e^5 - 3

6*a*b*c^5*e^6 + 72*a*c^6*d*e^5))/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 -

12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*

d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*

e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d

*e^3) + (((1536*a^5*c^6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6 - 72*a^2*b^6*c^3*e^7 + 480*a^3*b^4*c^4*e^7 - 1

408*a^4*b^2*c^5*e^7 + 512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^5 - 8*b^6*c^5*d^4*e^3 + 16*b^7*c^4*d^3*e^4 - 4*

b^8*c^3*d^2*e^5 - 384*a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3*e^4 + 192*a^2*b^4*c^5*d^2*e^5 - 1280*a^3*b^2*c

^6*d^2*e^5 + 80*a*b^7*c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b^4*c^6*d^4*e^3 - 192*a*b^5*c^5*d^3*e^4 + 16*a*b

^6*c^4*d^2*e^5 - 576*a^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4 + 1792*a^3*b^3*c^5*d*e^6)/(a^2*b^6*e^4 - 64*a^

3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*

d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a

^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*

a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) - (2*(d + e*x)^(1/2)*(-(32*b^6*c^5*d^5 - 2048*a

^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c

^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3

*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1

/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1