3.309 \(\int \frac {1}{x^4 (d+e x^2) (a+b x^2+c x^4)} \, dx\)

Optimal. Leaf size=348 \[ \frac {\sqrt {c} \left (\frac {3 a b c e-2 a c^2 d+b^3 (-e)+b^2 c d}{\sqrt {b^2-4 a c}}+a c e+b^2 (-e)+b c d\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{\sqrt {2} a^2 \sqrt {b-\sqrt {b^2-4 a c}} \left (a e^2-b d e+c d^2\right )}+\frac {\sqrt {c} \left (-\frac {3 a b c e-2 a c^2 d+b^3 (-e)+b^2 c d}{\sqrt {b^2-4 a c}}+a c e+b^2 (-e)+b c d\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {\sqrt {b^2-4 a c}+b}}\right )}{\sqrt {2} a^2 \sqrt {\sqrt {b^2-4 a c}+b} \left (a e^2-b d e+c d^2\right )}+\frac {a e+b d}{a^2 d^2 x}+\frac {e^{7/2} \tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right )}{d^{5/2} \left (a e^2-b d e+c d^2\right )}-\frac {1}{3 a d x^3} \]

[Out]

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

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Rubi [A]  time = 1.55, antiderivative size = 348, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 3, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {1287, 205, 1166} \[ \frac {\sqrt {c} \left (\frac {3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt {b^2-4 a c}}+a c e+b^2 (-e)+b c d\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{\sqrt {2} a^2 \sqrt {b-\sqrt {b^2-4 a c}} \left (a e^2-b d e+c d^2\right )}+\frac {\sqrt {c} \left (-\frac {3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt {b^2-4 a c}}+a c e+b^2 (-e)+b c d\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {\sqrt {b^2-4 a c}+b}}\right )}{\sqrt {2} a^2 \sqrt {\sqrt {b^2-4 a c}+b} \left (a e^2-b d e+c d^2\right )}+\frac {a e+b d}{a^2 d^2 x}+\frac {e^{7/2} \tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right )}{d^{5/2} \left (a e^2-b d e+c d^2\right )}-\frac {1}{3 a d x^3} \]

Antiderivative was successfully verified.

[In]

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

[Out]

-1/(3*a*d*x^3) + (b*d + a*e)/(a^2*d^2*x) + (Sqrt[c]*(b*c*d - b^2*e + a*c*e + (b^2*c*d - 2*a*c^2*d - b^3*e + 3*
a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b - Sqr
t[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)) + (Sqrt[c]*(b*c*d - b^2*e + a*c*e - (b^2*c*d - 2*a*c^2*d - b^3*e + 3*
a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b + Sqr
t[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)) + (e^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(d^(5/2)*(c*d^2 - b*d*e + a*e
^2))

Rule 205

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(Rt[a/b, 2]*ArcTan[x/Rt[a/b, 2]])/a, x] /; FreeQ[{a, b}, x]
&& PosQ[a/b]

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]

Rule 1287

Int[(((f_.)*(x_))^(m_.)*((d_) + (e_.)*(x_)^2)^(q_.))/((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4), x_Symbol] :> Int[Ex
pandIntegrand[((f*x)^m*(d + e*x^2)^q)/(a + b*x^2 + c*x^4), x], x] /; FreeQ[{a, b, c, d, e, f, m}, x] && NeQ[b^
2 - 4*a*c, 0] && IntegerQ[q] && IntegerQ[m]

Rubi steps

\begin {align*} \int \frac {1}{x^4 \left (d+e x^2\right ) \left (a+b x^2+c x^4\right )} \, dx &=\int \left (\frac {1}{a d x^4}+\frac {-b d-a e}{a^2 d^2 x^2}+\frac {e^4}{d^2 \left (c d^2-b d e+a e^2\right ) \left (d+e x^2\right )}+\frac {b^2 c d-a c^2 d-b^3 e+2 a b c e+c \left (b c d-b^2 e+a c e\right ) x^2}{a^2 \left (c d^2-b d e+a e^2\right ) \left (a+b x^2+c x^4\right )}\right ) \, dx\\ &=-\frac {1}{3 a d x^3}+\frac {b d+a e}{a^2 d^2 x}+\frac {\int \frac {b^2 c d-a c^2 d-b^3 e+2 a b c e+c \left (b c d-b^2 e+a c e\right ) x^2}{a+b x^2+c x^4} \, dx}{a^2 \left (c d^2-b d e+a e^2\right )}+\frac {e^4 \int \frac {1}{d+e x^2} \, dx}{d^2 \left (c d^2-b d e+a e^2\right )}\\ &=-\frac {1}{3 a d x^3}+\frac {b d+a e}{a^2 d^2 x}+\frac {e^{7/2} \tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right )}{d^{5/2} \left (c d^2-b d e+a e^2\right )}+\frac {\left (c \left (b c d-b^2 e+a c e-\frac {b^2 c d-2 a c^2 d-b^3 e+3 a b c e}{\sqrt {b^2-4 a c}}\right )\right ) \int \frac {1}{\frac {b}{2}+\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx}{2 a^2 \left (c d^2-b d e+a e^2\right )}+\frac {\left (c \left (b c d-b^2 e+a c e+\frac {b^2 c d-2 a c^2 d-b^3 e+3 a b c e}{\sqrt {b^2-4 a c}}\right )\right ) \int \frac {1}{\frac {b}{2}-\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx}{2 a^2 \left (c d^2-b d e+a e^2\right )}\\ &=-\frac {1}{3 a d x^3}+\frac {b d+a e}{a^2 d^2 x}+\frac {\sqrt {c} \left (b c d-b^2 e+a c e+\frac {b^2 c d-2 a c^2 d-b^3 e+3 a b c e}{\sqrt {b^2-4 a c}}\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{\sqrt {2} a^2 \sqrt {b-\sqrt {b^2-4 a c}} \left (c d^2-b d e+a e^2\right )}+\frac {\sqrt {c} \left (b c d-b^2 e+a c e-\frac {b^2 c d-2 a c^2 d-b^3 e+3 a b c e}{\sqrt {b^2-4 a c}}\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b+\sqrt {b^2-4 a c}}}\right )}{\sqrt {2} a^2 \sqrt {b+\sqrt {b^2-4 a c}} \left (c d^2-b d e+a e^2\right )}+\frac {e^{7/2} \tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right )}{d^{5/2} \left (c d^2-b d e+a e^2\right )}\\ \end {align*}

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Mathematica [A]  time = 0.52, size = 410, normalized size = 1.18 \[ \frac {\sqrt {c} \left (b^2 \left (c d-e \sqrt {b^2-4 a c}\right )+b c \left (d \sqrt {b^2-4 a c}+3 a e\right )+a c \left (e \sqrt {b^2-4 a c}-2 c d\right )+b^3 (-e)\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{\sqrt {2} a^2 \sqrt {b^2-4 a c} \sqrt {b-\sqrt {b^2-4 a c}} \left (e (a e-b d)+c d^2\right )}+\frac {\sqrt {c} \left (-b^2 \left (e \sqrt {b^2-4 a c}+c d\right )+b c \left (d \sqrt {b^2-4 a c}-3 a e\right )+a c \left (e \sqrt {b^2-4 a c}+2 c d\right )+b^3 e\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {\sqrt {b^2-4 a c}+b}}\right )}{\sqrt {2} a^2 \sqrt {b^2-4 a c} \sqrt {\sqrt {b^2-4 a c}+b} \left (e (a e-b d)+c d^2\right )}+\frac {a e+b d}{a^2 d^2 x}+\frac {e^{7/2} \tan ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d}}\right )}{d^{5/2} \left (a e^2-b d e+c d^2\right )}-\frac {1}{3 a d x^3} \]

Antiderivative was successfully verified.

[In]

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

[Out]

-1/3*1/(a*d*x^3) + (b*d + a*e)/(a^2*d^2*x) + (Sqrt[c]*(-(b^3*e) + b*c*(Sqrt[b^2 - 4*a*c]*d + 3*a*e) + b^2*(c*d
- Sqrt[b^2 - 4*a*c]*e) + a*c*(-2*c*d + Sqrt[b^2 - 4*a*c]*e))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4
*a*c]]])/(Sqrt[2]*a^2*Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]*(c*d^2 + e*(-(b*d) + a*e))) + (Sqrt[c]*(b^
3*e + b*c*(Sqrt[b^2 - 4*a*c]*d - 3*a*e) - b^2*(c*d + Sqrt[b^2 - 4*a*c]*e) + a*c*(2*c*d + Sqrt[b^2 - 4*a*c]*e))
*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4
*a*c]]*(c*d^2 + e*(-(b*d) + a*e))) + (e^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(d^(5/2)*(c*d^2 - b*d*e + a*e^2))

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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/x^4/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm="fricas")

[Out]

Timed out

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giac [B]  time = 12.00, size = 12268, normalized size = 35.25 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^4/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm="giac")

[Out]

1/8*((2*a^4*b^5*c^5 - 12*a^5*b^3*c^6 + 16*a^6*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c
)*a^4*b^5*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)
*c)*a^6*b*c^5 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4
*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c
)*a^5*b*c^6 - 2*(b^2 - 4*a*c)*a^4*b^3*c^5 + 4*(b^2 - 4*a*c)*a^5*b*c^6)*d^5 - (6*a^4*b^6*c^4 - 38*a^5*b^4*c^5 +
56*a^6*b^2*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 + 19*sqrt(2)*sqrt(b^
2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a
*c)*c)*a^4*b^5*c^3 - 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4 - 14*sqrt(2)*sqr
t(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 -
4*a*c)*c)*a^4*b^4*c^4 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^5 - 6*(b^2 - 4*
a*c)*a^4*b^4*c^4 + 14*(b^2 - 4*a*c)*a^5*b^2*c^5)*d^4*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^
2 - 9*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*
c^3 - 2*a^2*b^6*c^3 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 10*sqrt(2)*sqrt(b*c + sqrt(b^2
- 4*a*c)*c)*a^3*b^3*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 + 18*a^3*b^4*c^4 - 16*sqrt(2)*sq
rt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 5*sqrt(2)*sqrt(b
*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 - 48*a^4*b^2*c^5 + 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^6 + 3
2*a^5*c^6 + 2*(b^2 - 4*a*c)*a^2*b^4*c^3 - 10*(b^2 - 4*a*c)*a^3*b^2*c^4 + 8*(b^2 - 4*a*c)*a^4*c^5)*d^3*abs(a^2*
c*d^2 - a^2*b*d*e + a^3*e^2) + (6*a^4*b^7*c^3 - 36*a^5*b^5*c^4 + 40*a^6*b^3*c^5 + 32*a^7*b*c^6 - 3*sqrt(2)*sqr
t(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c + 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 -
4*a*c)*c)*a^5*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 - 20*sqrt(2)*s
qrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^
2 - 4*a*c)*c)*a^5*b^4*c^3 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^3 - 16*sqrt(
2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b
^2 - 4*a*c)*c)*a^6*b^2*c^4 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^4 + 4*sqrt(
2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^5 - 6*(b^2 - 4*a*c)*a^4*b^5*c^3 + 12*(b^2 - 4*a*c
)*a^5*b^3*c^4 + 8*(b^2 - 4*a*c)*a^6*b*c^5)*d^3*e^2 - 2*(2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c -
19*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2
- 4*a^2*b^7*c^2 + 56*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 + 22*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4
*a*c)*c)*a^3*b^4*c^3 + 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 + 38*a^3*b^5*c^3 - 48*sqrt(2)*sqr
t(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 11*sqrt(2)*s
qrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 112*a^4*b^3*c^4 + 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*
b*c^5 + 96*a^5*b*c^5 + 4*(b^2 - 4*a*c)*a^2*b^5*c^2 - 22*(b^2 - 4*a*c)*a^3*b^3*c^3 + 24*(b^2 - 4*a*c)*a^4*b*c^4
)*d^2*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*e + (2*b^5*c^3 - 16*a*b^3*c^4 + 32*a^2*b*c^5 - sqrt(2)*sqrt(b^2 - 4
*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^
3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqr
t(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3
- sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c +
sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 2*(b^2 - 4*a*c)*b^3*c^3 + 8*(b^2 - 4*a*c)*a*b*c^4)*(a^2*c*d^2 - a^2*b*d*e + a^3
*e^2)^2*d - (2*a^4*b^8*c^2 - 6*a^5*b^6*c^3 - 28*a^6*b^4*c^4 + 80*a^7*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(
b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c + 2
*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c +
sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 -
sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
+ sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3
- sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*
c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4 - 2*(b^2 - 4*a*c)*a^4*b^6*c^2 - 2*(b^2 - 4*a*c)*a^5*b^4*c^3 + 20*(b^2 - 4
*a*c)*a^6*b^2*c^4)*d^2*e^3 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^8 - 9*sqrt(2)*sqrt(b*c + sqrt(b^
2 - 4*a*c)*c)*a^3*b^6*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 2*a^2*b^8*c + 23*sqrt(2)*sqrt(
b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 + 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + sqrt(2)*sqrt
(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + 18*a^3*b^6*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c
^3 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4
*c^3 - 46*a^4*b^4*c^3 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*c^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4
*a*c)*c)*a^5*b*c^4 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 16*a^5*b^2*c^4 + 4*sqrt(2)*sqrt(b
*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^5 + 32*a^6*c^5 + 2*(b^2 - 4*a*c)*a^2*b^6*c - 10*(b^2 - 4*a*c)*a^3*b^4*c^2 + 6*
(b^2 - 4*a*c)*a^4*b^2*c^3 + 8*(b^2 - 4*a*c)*a^5*c^4)*d*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*e^2 - (2*b^6*c^2 -
18*a*b^4*c^3 + 48*a^2*b^2*c^4 - 32*a^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 +
9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + s
qrt(b^2 - 4*a*c)*c)*b^5*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 10*sqrt
(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^
2 - 4*a*c)*c)*b^4*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(
b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a
*c)*c)*a*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 2*(b^2 - 4*a*c)*b^4*c
^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)^2*e + (4*a^5*b^7*
c^2 - 26*a^6*b^5*c^3 + 36*a^7*b^3*c^4 + 16*a^8*b*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c
)*c)*a^5*b^7 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c + 4*sqrt(2)*sqrt(b^2 - 4
*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)
*a^7*b^3*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 - 2*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)
*c)*a^8*b*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 + 5*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)
*c)*a^7*b*c^4 - 4*(b^2 - 4*a*c)*a^5*b^5*c^2 + 10*(b^2 - 4*a*c)*a^6*b^3*c^3 + 4*(b^2 - 4*a*c)*a^7*b*c^4)*d*e^4
- 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c -
2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c - 2*a^3*b^7*c + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)
*a^5*b^3*c^2 + 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c
)*a^3*b^5*c^2 + 20*a^4*b^5*c^2 - 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^3 - 16*sqrt(2)*sqrt(b*c +
sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 64*a^5*b^3*c^3 + 8*
sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 64*a^6*b*c^4 + 2*(b^2 - 4*a*c)*a^3*b^5*c - 12*(b^2 - 4*a*c
)*a^4*b^3*c^2 + 16*(b^2 - 4*a*c)*a^5*b*c^3)*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*e^3 - (2*a^6*b^6*c^2 - 14*a^7
*b^4*c^3 + 24*a^8*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^6 + 7*sqrt(2)*sqrt
(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*
a*c)*c)*a^6*b^5*c - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^2*c^2 - 6*sqrt(2)*sqrt(
b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a
*c)*c)*a^6*b^4*c^2 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 - 2*(b^2 - 4*a*c)
*a^6*b^4*c^2 + 6*(b^2 - 4*a*c)*a^7*b^2*c^3)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b*c*d^2 - a^2*b^2*d*e + a^3*b*
e^2 + sqrt((a^2*b*c*d^2 - a^2*b^2*d*e + a^3*b*e^2)^2 - 4*(a^3*c*d^2 - a^3*b*d*e + a^4*e^2)*(a^2*c^2*d^2 - a^2*
b*c*d*e + a^3*c*e^2)))/(a^2*c^2*d^2 - a^2*b*c*d*e + a^3*c*e^2)))/((a^5*b^4*c^2 - 8*a^6*b^2*c^3 - 2*a^5*b^3*c^3
+ 16*a^7*c^4 + 8*a^6*b*c^4 + a^5*b^2*c^4 - 4*a^6*c^5)*d^4*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c) - 2*(a^
5*b^5*c - 8*a^6*b^3*c^2 - 2*a^5*b^4*c^2 + 16*a^7*b*c^3 + 8*a^6*b^2*c^3 + a^5*b^3*c^3 - 4*a^6*b*c^4)*d^3*abs(a^
2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)*e + (a^5*b^6 - 6*a^6*b^4*c - 2*a^5*b^5*c + 4*a^6*b^3*c^2 + a^5*b^4*c^2 +
32*a^8*c^3 + 16*a^7*b*c^3 - 2*a^6*b^2*c^3 - 8*a^7*c^4)*d^2*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)*e^2 -
2*(a^6*b^5 - 8*a^7*b^3*c - 2*a^6*b^4*c + 16*a^8*b*c^2 + 8*a^7*b^2*c^2 + a^6*b^3*c^2 - 4*a^7*b*c^3)*d*abs(a^2*c
*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)*e^3 + (a^7*b^4 - 8*a^8*b^2*c - 2*a^7*b^3*c + 16*a^9*c^2 + 8*a^8*b*c^2 + a^7
*b^2*c^2 - 4*a^8*c^3)*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)*e^4) - 1/8*((2*a^4*b^5*c^5 - 12*a^5*b^3*c^6
+ 16*a^6*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^3 + 6*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*
c)*a^4*b^4*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^5 - 4*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)
*a^4*b^3*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^6 - 2*(b^2 - 4*a*c)*a^4*b^3
*c^5 + 4*(b^2 - 4*a*c)*a^5*b*c^6)*d^5 - (6*a^4*b^6*c^4 - 38*a^5*b^4*c^5 + 56*a^6*b^2*c^6 - 3*sqrt(2)*sqrt(b^2
- 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*
c)*c)*a^5*b^4*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^3 - 28*sqrt(2)*sqrt(
b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4 - 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*a^5*b^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^4 + 7*sqrt(2)*sq
rt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^5 - 6*(b^2 - 4*a*c)*a^4*b^4*c^4 + 14*(b^2 - 4*a*c)*a
^5*b^2*c^5)*d^4*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 - 9*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4
*a*c)*c)*a^3*b^4*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 + 2*a^2*b^6*c^3 + 24*sqrt(2)*sqrt
(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 + sqrt(2)*sqr
t(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 18*a^3*b^4*c^4 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^5
- 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5
+ 48*a^4*b^2*c^5 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 32*a^5*c^6 - 2*(b^2 - 4*a*c)*a^2*b^4*c
^3 + 10*(b^2 - 4*a*c)*a^3*b^2*c^4 - 8*(b^2 - 4*a*c)*a^4*c^5)*d^3*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2) + (6*a^4
*b^7*c^3 - 36*a^5*b^5*c^4 + 40*a^6*b^3*c^5 + 32*a^7*b*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*a^4*b^7*c + 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 + 6*sqrt(2)*sqr
t(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2
- 4*a*c)*c)*a^6*b^3*c^3 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 - 3*sqrt(2)
*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^3 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(
b^2 - 4*a*c)*c)*a^7*b*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4 + 6*sqrt(2
)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(
b^2 - 4*a*c)*c)*a^6*b*c^5 - 6*(b^2 - 4*a*c)*a^4*b^5*c^3 + 12*(b^2 - 4*a*c)*a^5*b^3*c^4 + 8*(b^2 - 4*a*c)*a^6*b
*c^5)*d^3*e^2 + 2*(2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 19*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*
c)*c)*a^3*b^5*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + 4*a^2*b^7*c^2 + 56*sqrt(2)*sqrt(b*
c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 + 22*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 2*sqrt(2)*sqrt
(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 - 38*a^3*b^5*c^3 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^
4 - 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 11*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^
3*c^4 + 112*a^4*b^3*c^4 + 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 96*a^5*b*c^5 - 4*(b^2 - 4*a*c
)*a^2*b^5*c^2 + 22*(b^2 - 4*a*c)*a^3*b^3*c^3 - 24*(b^2 - 4*a*c)*a^4*b*c^4)*d^2*abs(a^2*c*d^2 - a^2*b*d*e + a^3
*e^2)*e + (2*b^5*c^3 - 16*a*b^3*c^4 + 32*a^2*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)
*b^5*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*s
qrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^
3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
- sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 2*(b^2
- 4*a*c)*b^3*c^3 + 8*(b^2 - 4*a*c)*a*b*c^4)*(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)^2*d - (2*a^4*b^8*c^2 - 6*a^5*b^
6*c^3 - 28*a^6*b^4*c^4 + 80*a^7*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8 +
3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c -
sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 + 2
*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c -
sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 -
20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
- sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4
- 2*(b^2 - 4*a*c)*a^4*b^6*c^2 - 2*(b^2 - 4*a*c)*a^5*b^4*c^3 + 20*(b^2 - 4*a*c)*a^6*b^2*c^4)*d^2*e^3 - 2*(sqrt(
2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^8 - 9*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c - 2*sqrt(2)*s
qrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c + 2*a^2*b^8*c + 23*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^
2 + 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c
^2 - 18*a^3*b^6*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*a^4*b^3*c^3 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 46*a^4*b^4*c^3 - 16*sqrt(2)*sq
rt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*c^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 3*sqrt(2)*sqrt(b
*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 16*a^5*b^2*c^4 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^5 - 3
2*a^6*c^5 - 2*(b^2 - 4*a*c)*a^2*b^6*c + 10*(b^2 - 4*a*c)*a^3*b^4*c^2 - 6*(b^2 - 4*a*c)*a^4*b^2*c^3 - 8*(b^2 -
4*a*c)*a^5*c^4)*d*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*e^2 - (2*b^6*c^2 - 18*a*b^4*c^3 + 48*a^2*b^2*c^4 - 32*a
^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
- sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 24*sqrt(2
)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt
(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 16*sqrt(2)*sq
rt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*
a*c)*c)*a^2*b*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 4*sqrt(2)*sqrt(b^2
- 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 2*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(
b^2 - 4*a*c)*a^2*c^4)*(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)^2*e + (4*a^5*b^7*c^2 - 26*a^6*b^5*c^3 + 36*a^7*b^3*c^4
+ 16*a^8*b*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^7 + 13*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)
*a^5*b^6*c - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^2 - 10*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*
c)*a^5*b^5*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*c^3 - 4*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*
c)*a^6*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^4 - 4*(b^2 - 4*a*c)*a^5*b
^5*c^2 + 10*(b^2 - 4*a*c)*a^6*b^3*c^3 + 4*(b^2 - 4*a*c)*a^7*b*c^4)*d*e^4 + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*
a*c)*c)*a^3*b^7 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c
)*c)*a^3*b^6*c + 2*a^3*b^7*c + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^2 + 12*sqrt(2)*sqrt(b*c -
sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 20*a^4*b^5*c^2 - 32*s
qrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^3 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 - 6*
sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 + 64*a^5*b^3*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*
c)*a^5*b*c^4 - 64*a^6*b*c^4 - 2*(b^2 - 4*a*c)*a^3*b^5*c + 12*(b^2 - 4*a*c)*a^4*b^3*c^2 - 16*(b^2 - 4*a*c)*a^5*
b*c^3)*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*e^3 - (2*a^6*b^6*c^2 - 14*a^7*b^4*c^3 + 24*a^8*b^2*c^4 - sqrt(2)*s
qrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^6 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4
*a*c)*c)*a^7*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c - 12*sqrt(2)*sqrt(b
^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^2*c^2 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*
a*c)*c)*a^7*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 + 3*sqrt(2)*sqrt(b
^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 - 2*(b^2 - 4*a*c)*a^6*b^4*c^2 + 6*(b^2 - 4*a*c)*a^7*b^
2*c^3)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b*c*d^2 - a^2*b^2*d*e + a^3*b*e^2 - sqrt((a^2*b*c*d^2 - a^2*b^2*d*e
+ a^3*b*e^2)^2 - 4*(a^3*c*d^2 - a^3*b*d*e + a^4*e^2)*(a^2*c^2*d^2 - a^2*b*c*d*e + a^3*c*e^2)))/(a^2*c^2*d^2 -
a^2*b*c*d*e + a^3*c*e^2)))/((a^5*b^4*c^2 - 8*a^6*b^2*c^3 - 2*a^5*b^3*c^3 + 16*a^7*c^4 + 8*a^6*b*c^4 + a^5*b^2
*c^4 - 4*a^6*c^5)*d^4*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c) - 2*(a^5*b^5*c - 8*a^6*b^3*c^2 - 2*a^5*b^4*c
^2 + 16*a^7*b*c^3 + 8*a^6*b^2*c^3 + a^5*b^3*c^3 - 4*a^6*b*c^4)*d^3*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)
*e + (a^5*b^6 - 6*a^6*b^4*c - 2*a^5*b^5*c + 4*a^6*b^3*c^2 + a^5*b^4*c^2 + 32*a^8*c^3 + 16*a^7*b*c^3 - 2*a^6*b^
2*c^3 - 8*a^7*c^4)*d^2*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)*e^2 - 2*(a^6*b^5 - 8*a^7*b^3*c - 2*a^6*b^4*
c + 16*a^8*b*c^2 + 8*a^7*b^2*c^2 + a^6*b^3*c^2 - 4*a^7*b*c^3)*d*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)*e^
3 + (a^7*b^4 - 8*a^8*b^2*c - 2*a^7*b^3*c + 16*a^9*c^2 + 8*a^8*b*c^2 + a^7*b^2*c^2 - 4*a^8*c^3)*abs(a^2*c*d^2 -
a^2*b*d*e + a^3*e^2)*abs(c)*e^4) + arctan(x*e^(1/2)/sqrt(d))*e^(7/2)/((c*d^4 - b*d^3*e + a*d^2*e^2)*sqrt(d))
+ 1/3*(3*b*d*x^2 + 3*a*x^2*e - a*d)/(a^2*d^2*x^3)

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maple [B]  time = 0.04, size = 1160, normalized size = 3.33 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^4/(e*x^2+d)/(c*x^4+b*x^2+a),x)

[Out]

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

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^4/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 6.73, size = 42882, normalized size = 123.22 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^4*(d + e*x^2)*(a + b*x^2 + c*x^4)),x)

[Out]

(log(c^9*d^27*e^6 - b^9*d^18*e^15 + 2*a*c^8*d^25*e^8 - 2*b*c^8*d^26*e^7 + 2*b^8*c*d^19*e^14 + a^5*b^4*d^13*e^2
0 + a^2*c^7*d^23*e^10 + 16*a^4*c^5*d^19*e^14 + 16*a^7*c^2*d^13*e^20 + b^2*c^7*d^25*e^8 - b^7*c^2*d^20*e^13 - 2
5*a^2*b^3*c^4*d^20*e^13 + 66*a^2*b^4*c^3*d^19*e^14 - 42*a^2*b^5*c^2*d^18*e^15 - 76*a^3*b^2*c^4*d^19*e^14 + 63*
a^3*b^3*c^3*d^18*e^15 - a^5*b^4*e^3*x*(-d^5*e^7)^(5/2) + a^2*c^7*d^15*x*(-d^5*e^7)^(3/2) - 16*a^7*c^2*e^3*x*(-
d^5*e^7)^(5/2) - b^9*d^10*e^5*x*(-d^5*e^7)^(3/2) - c^9*d^24*e^3*x*(-d^5*e^7)^(1/2) - 2*a*b*c^7*d^24*e^9 + 11*a
*b^7*c*d^18*e^15 + 9*a*b^5*c^3*d^20*e^13 - 20*a*b^6*c^2*d^19*e^14 + 20*a^3*b*c^5*d^20*e^13 - 28*a^4*b*c^4*d^18
*e^15 - 8*a^6*b^2*c*d^13*e^20 + 16*a^4*c^5*d^11*e^4*x*(-d^5*e^7)^(3/2) - b^7*c^2*d^12*e^3*x*(-d^5*e^7)^(3/2) -
b^2*c^7*d^22*e^5*x*(-d^5*e^7)^(1/2) + 8*a^6*b^2*c*e^3*x*(-d^5*e^7)^(5/2) - 2*a*c^8*d^22*e^5*x*(-d^5*e^7)^(1/2
) + 2*b^8*c*d^11*e^4*x*(-d^5*e^7)^(3/2) + 2*b*c^8*d^23*e^4*x*(-d^5*e^7)^(1/2) + 11*a*b^7*c*d^10*e^5*x*(-d^5*e^
7)^(3/2) + 2*a*b*c^7*d^21*e^6*x*(-d^5*e^7)^(1/2) + 9*a*b^5*c^3*d^12*e^3*x*(-d^5*e^7)^(3/2) - 20*a*b^6*c^2*d^11
*e^4*x*(-d^5*e^7)^(3/2) + 20*a^3*b*c^5*d^12*e^3*x*(-d^5*e^7)^(3/2) - 28*a^4*b*c^4*d^10*e^5*x*(-d^5*e^7)^(3/2)
- 25*a^2*b^3*c^4*d^12*e^3*x*(-d^5*e^7)^(3/2) + 66*a^2*b^4*c^3*d^11*e^4*x*(-d^5*e^7)^(3/2) - 42*a^2*b^5*c^2*d^1
0*e^5*x*(-d^5*e^7)^(3/2) - 76*a^3*b^2*c^4*d^11*e^4*x*(-d^5*e^7)^(3/2) + 63*a^3*b^3*c^3*d^10*e^5*x*(-d^5*e^7)^(
3/2))*(-d^5*e^7)^(1/2))/(2*c*d^7 + 2*a*d^5*e^2 - 2*b*d^6*e) - atan((((-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a
*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2
- a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)
^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*
c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)
^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*
(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9
*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*
c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^
2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(((-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5
*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2
)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4
*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/
2) - 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e
+ 76*a^3*b^2*c^4*d*e + 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6
*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 -
2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^
3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^
2)))^(1/2)*(x*(-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2
+ 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2
*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a
*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4
*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*
b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b
^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*
c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e +
16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(512*a^20*c^7*d^
24*e^3 + 512*a^21*c^6*d^22*e^5 - 512*a^22*c^5*d^20*e^7 - 512*a^23*c^4*d^18*e^9 - 32*a^18*b^3*c^6*d^25*e^2 + 12
8*a^18*b^4*c^5*d^24*e^3 - 192*a^18*b^5*c^4*d^23*e^4 + 128*a^18*b^6*c^3*d^22*e^5 - 32*a^18*b^7*c^2*d^21*e^6 - 6
40*a^19*b^2*c^6*d^24*e^3 + 1056*a^19*b^3*c^5*d^23*e^4 - 672*a^19*b^4*c^4*d^22*e^5 + 96*a^19*b^5*c^3*d^21*e^6 +
32*a^19*b^6*c^2*d^20*e^7 + 512*a^20*b^2*c^5*d^22*e^5 + 288*a^20*b^3*c^4*d^21*e^6 - 192*a^20*b^4*c^3*d^20*e^7
+ 32*a^20*b^5*c^2*d^19*e^8 + 384*a^21*b^2*c^4*d^20*e^7 - 288*a^21*b^3*c^3*d^19*e^8 - 32*a^21*b^4*c^2*d^18*e^9
+ 256*a^22*b^2*c^3*d^18*e^9 + 128*a^19*b*c^7*d^25*e^2 - 1152*a^20*b*c^6*d^23*e^4 - 640*a^21*b*c^5*d^21*e^6 + 6
40*a^22*b*c^4*d^19*e^8) - 64*a^18*c^8*d^24*e^2 + 128*a^19*c^7*d^22*e^4 + 192*a^20*c^6*d^20*e^6 - 256*a^21*c^5*
d^18*e^8 - 256*a^22*c^4*d^16*e^10 - 16*a^16*b^4*c^6*d^24*e^2 + 64*a^16*b^5*c^5*d^23*e^3 - 96*a^16*b^6*c^4*d^22
*e^4 + 64*a^16*b^7*c^3*d^21*e^5 - 16*a^16*b^8*c^2*d^20*e^6 + 80*a^17*b^2*c^7*d^24*e^2 - 368*a^17*b^3*c^6*d^23*
e^3 + 608*a^17*b^4*c^5*d^22*e^4 - 416*a^17*b^5*c^4*d^21*e^5 + 80*a^17*b^6*c^3*d^20*e^6 + 16*a^17*b^7*c^2*d^19*
e^7 - 928*a^18*b^2*c^6*d^22*e^4 + 640*a^18*b^3*c^5*d^21*e^5 + 32*a^18*b^4*c^4*d^20*e^6 - 128*a^18*b^5*c^3*d^19
*e^7 - 432*a^19*b^2*c^5*d^20*e^6 + 304*a^19*b^3*c^4*d^19*e^7 - 16*a^19*b^4*c^3*d^18*e^8 + 16*a^19*b^5*c^2*d^17
*e^9 + 128*a^20*b^2*c^4*d^18*e^8 - 128*a^20*b^3*c^3*d^17*e^9 - 16*a^20*b^4*c^2*d^16*e^10 + 128*a^21*b^2*c^3*d^
16*e^10 + 448*a^18*b*c^7*d^23*e^3 - 192*a^20*b*c^5*d^19*e^7 + 256*a^21*b*c^4*d^17*e^9) - x*(16*a^16*c^9*d^23*e
^2 + 32*a^17*c^8*d^21*e^4 - 112*a^18*c^7*d^19*e^6 - 128*a^20*c^5*d^15*e^10 + 8*a^14*b^4*c^7*d^23*e^2 - 16*a^14
*b^5*c^6*d^22*e^3 + 8*a^14*b^6*c^5*d^21*e^4 + 8*a^14*b^7*c^4*d^20*e^5 - 16*a^14*b^8*c^3*d^19*e^6 + 8*a^14*b^9*
c^2*d^18*e^7 - 32*a^15*b^2*c^8*d^23*e^2 + 64*a^15*b^3*c^7*d^22*e^3 - 16*a^15*b^4*c^6*d^21*e^4 - 88*a^15*b^5*c^
5*d^20*e^5 + 160*a^15*b^6*c^4*d^19*e^6 - 88*a^15*b^7*c^3*d^18*e^7 - 48*a^16*b^2*c^7*d^21*e^4 + 264*a^16*b^3*c^
6*d^20*e^5 - 520*a^16*b^4*c^5*d^19*e^6 + 336*a^16*b^5*c^4*d^18*e^7 + 576*a^17*b^2*c^6*d^19*e^6 - 504*a^17*b^3*
c^5*d^18*e^7 + 8*a^18*b^3*c^4*d^16*e^9 - 16*a^18*b^4*c^3*d^15*e^10 + 8*a^18*b^5*c^2*d^14*e^11 + 96*a^19*b^2*c^
4*d^15*e^10 - 56*a^19*b^3*c^3*d^14*e^11 - 32*a^16*b*c^8*d^22*e^3 - 192*a^17*b*c^7*d^20*e^5 + 224*a^18*b*c^6*d^
18*e^7 - 32*a^19*b*c^5*d^16*e^9 + 96*a^20*b*c^4*d^14*e^11))*(-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)
^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4
*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2)
- b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(
4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) -
66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c
- b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4
- 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e
^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e -
6*a^6*b^4*c*d^2*e^2)))^(1/2) - 4*a^15*c^9*d^21*e^3 - 4*a^16*c^8*d^19*e^5 + 48*a^18*c^6*d^15*e^9 - 4*a^14*b^2*
c^8*d^21*e^3 - 4*a^14*b^7*c^3*d^16*e^8 + 4*a^14*b^8*c^2*d^15*e^9 + 36*a^15*b^5*c^4*d^16*e^8 - 44*a^15*b^6*c^3*
d^15*e^9 + 4*a^15*b^7*c^2*d^14*e^10 - 100*a^16*b^3*c^5*d^16*e^8 + 160*a^16*b^4*c^4*d^15*e^9 - 32*a^16*b^5*c^3*
d^14*e^10 - 204*a^17*b^2*c^5*d^15*e^9 + 76*a^17*b^3*c^4*d^14*e^10 + 4*a^14*b*c^9*d^22*e^2 + 8*a^15*b*c^8*d^20*
e^4 + 80*a^17*b*c^6*d^16*e^8 - 48*a^18*b*c^5*d^14*e^10) - x*(2*a^14*c^9*d^18*e^5 + 4*a^16*c^7*d^14*e^9 + 2*a^1
4*b^4*c^5*d^14*e^9 - 8*a^15*b^2*c^6*d^14*e^9))*(-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9
*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c
- b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^
2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^
3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^
3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/
2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c
*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^
5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*
d^2*e^2)))^(1/2)*1i + ((-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*
b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^
2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/
2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2
*e^2*(-(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d
*e + 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(
4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 +
a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3
*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(((-(b^
9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2
- 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c
^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4
*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2
) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*b^2*c^3*d^2*(-(4*a*
c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a
^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2
*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3
- 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(x*(-(b^9*e^2 + b^7*c^2*d^2 - b^6*e
^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3
*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a
*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e
+ 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c
- b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3
*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4
+ 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2
+ 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a
^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(512*a^20*c^7*d^24*e^3 + 512*a^21*c^6*d^22*e^5 - 512*a^22*c^5*
d^20*e^7 - 512*a^23*c^4*d^18*e^9 - 32*a^18*b^3*c^6*d^25*e^2 + 128*a^18*b^4*c^5*d^24*e^3 - 192*a^18*b^5*c^4*d^2
3*e^4 + 128*a^18*b^6*c^3*d^22*e^5 - 32*a^18*b^7*c^2*d^21*e^6 - 640*a^19*b^2*c^6*d^24*e^3 + 1056*a^19*b^3*c^5*d
^23*e^4 - 672*a^19*b^4*c^4*d^22*e^5 + 96*a^19*b^5*c^3*d^21*e^6 + 32*a^19*b^6*c^2*d^20*e^7 + 512*a^20*b^2*c^5*d
^22*e^5 + 288*a^20*b^3*c^4*d^21*e^6 - 192*a^20*b^4*c^3*d^20*e^7 + 32*a^20*b^5*c^2*d^19*e^8 + 384*a^21*b^2*c^4*
d^20*e^7 - 288*a^21*b^3*c^3*d^19*e^8 - 32*a^21*b^4*c^2*d^18*e^9 + 256*a^22*b^2*c^3*d^18*e^9 + 128*a^19*b*c^7*d
^25*e^2 - 1152*a^20*b*c^6*d^23*e^4 - 640*a^21*b*c^5*d^21*e^6 + 640*a^22*b*c^4*d^19*e^8) + 64*a^18*c^8*d^24*e^2
- 128*a^19*c^7*d^22*e^4 - 192*a^20*c^6*d^20*e^6 + 256*a^21*c^5*d^18*e^8 + 256*a^22*c^4*d^16*e^10 + 16*a^16*b^
4*c^6*d^24*e^2 - 64*a^16*b^5*c^5*d^23*e^3 + 96*a^16*b^6*c^4*d^22*e^4 - 64*a^16*b^7*c^3*d^21*e^5 + 16*a^16*b^8*
c^2*d^20*e^6 - 80*a^17*b^2*c^7*d^24*e^2 + 368*a^17*b^3*c^6*d^23*e^3 - 608*a^17*b^4*c^5*d^22*e^4 + 416*a^17*b^5
*c^4*d^21*e^5 - 80*a^17*b^6*c^3*d^20*e^6 - 16*a^17*b^7*c^2*d^19*e^7 + 928*a^18*b^2*c^6*d^22*e^4 - 640*a^18*b^3
*c^5*d^21*e^5 - 32*a^18*b^4*c^4*d^20*e^6 + 128*a^18*b^5*c^3*d^19*e^7 + 432*a^19*b^2*c^5*d^20*e^6 - 304*a^19*b^
3*c^4*d^19*e^7 + 16*a^19*b^4*c^3*d^18*e^8 - 16*a^19*b^5*c^2*d^17*e^9 - 128*a^20*b^2*c^4*d^18*e^8 + 128*a^20*b^
3*c^3*d^17*e^9 + 16*a^20*b^4*c^2*d^16*e^10 - 128*a^21*b^2*c^3*d^16*e^10 - 448*a^18*b*c^7*d^23*e^3 + 192*a^20*b
*c^5*d^19*e^7 - 256*a^21*b*c^4*d^17*e^9) - x*(16*a^16*c^9*d^23*e^2 + 32*a^17*c^8*d^21*e^4 - 112*a^18*c^7*d^19*
e^6 - 128*a^20*c^5*d^15*e^10 + 8*a^14*b^4*c^7*d^23*e^2 - 16*a^14*b^5*c^6*d^22*e^3 + 8*a^14*b^6*c^5*d^21*e^4 +
8*a^14*b^7*c^4*d^20*e^5 - 16*a^14*b^8*c^3*d^19*e^6 + 8*a^14*b^9*c^2*d^18*e^7 - 32*a^15*b^2*c^8*d^23*e^2 + 64*a
^15*b^3*c^7*d^22*e^3 - 16*a^15*b^4*c^6*d^21*e^4 - 88*a^15*b^5*c^5*d^20*e^5 + 160*a^15*b^6*c^4*d^19*e^6 - 88*a^
15*b^7*c^3*d^18*e^7 - 48*a^16*b^2*c^7*d^21*e^4 + 264*a^16*b^3*c^6*d^20*e^5 - 520*a^16*b^4*c^5*d^19*e^6 + 336*a
^16*b^5*c^4*d^18*e^7 + 576*a^17*b^2*c^6*d^19*e^6 - 504*a^17*b^3*c^5*d^18*e^7 + 8*a^18*b^3*c^4*d^16*e^9 - 16*a^
18*b^4*c^3*d^15*e^10 + 8*a^18*b^5*c^2*d^14*e^11 + 96*a^19*b^2*c^4*d^15*e^10 - 56*a^19*b^3*c^3*d^14*e^11 - 32*a
^16*b*c^8*d^22*e^3 - 192*a^17*b*c^7*d^20*e^5 + 224*a^18*b*c^6*d^18*e^7 - 32*a^19*b*c^5*d^16*e^9 + 96*a^20*b*c^
4*d^14*e^11))*(-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2
+ 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2
*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a
*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4
*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*
b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b
^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*
c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e +
16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2) + 4*a^15*c^9*d^2
1*e^3 + 4*a^16*c^8*d^19*e^5 - 48*a^18*c^6*d^15*e^9 + 4*a^14*b^2*c^8*d^21*e^3 + 4*a^14*b^7*c^3*d^16*e^8 - 4*a^1
4*b^8*c^2*d^15*e^9 - 36*a^15*b^5*c^4*d^16*e^8 + 44*a^15*b^6*c^3*d^15*e^9 - 4*a^15*b^7*c^2*d^14*e^10 + 100*a^16
*b^3*c^5*d^16*e^8 - 160*a^16*b^4*c^4*d^15*e^9 + 32*a^16*b^5*c^3*d^14*e^10 + 204*a^17*b^2*c^5*d^15*e^9 - 76*a^1
7*b^3*c^4*d^14*e^10 - 4*a^14*b*c^9*d^22*e^2 - 8*a^15*b*c^8*d^20*e^4 - 80*a^17*b*c^6*d^16*e^8 + 48*a^18*b*c^5*d
^14*e^10) - x*(2*a^14*c^9*d^18*e^5 + 4*a^16*c^7*d^14*e^9 + 2*a^14*b^4*c^5*d^14*e^9 - 8*a^15*b^2*c^6*d^14*e^9))
*(-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c
^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3
*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 -
16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3
)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*b^2*c^3*d^2*(
-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))
/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a
^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*
d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*1i)/(((-(b^9*e^2 + b^7*c^2*d^
2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 2
5*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e
^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^
6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*
(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2)
- 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^
7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6
*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e
^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(((-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^
3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*
d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2)
- b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4
*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 6
6*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c -
b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 -
8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^
2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e -
6*a^6*b^4*c*d^2*e^2)))^(1/2)*(x*(-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2
- 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2
) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^
2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^
2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*
b^2*c^4*d*e + 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^
3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^
5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*
a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2
)*(512*a^20*c^7*d^24*e^3 + 512*a^21*c^6*d^22*e^5 - 512*a^22*c^5*d^20*e^7 - 512*a^23*c^4*d^18*e^9 - 32*a^18*b^3
*c^6*d^25*e^2 + 128*a^18*b^4*c^5*d^24*e^3 - 192*a^18*b^5*c^4*d^23*e^4 + 128*a^18*b^6*c^3*d^22*e^5 - 32*a^18*b^
7*c^2*d^21*e^6 - 640*a^19*b^2*c^6*d^24*e^3 + 1056*a^19*b^3*c^5*d^23*e^4 - 672*a^19*b^4*c^4*d^22*e^5 + 96*a^19*
b^5*c^3*d^21*e^6 + 32*a^19*b^6*c^2*d^20*e^7 + 512*a^20*b^2*c^5*d^22*e^5 + 288*a^20*b^3*c^4*d^21*e^6 - 192*a^20
*b^4*c^3*d^20*e^7 + 32*a^20*b^5*c^2*d^19*e^8 + 384*a^21*b^2*c^4*d^20*e^7 - 288*a^21*b^3*c^3*d^19*e^8 - 32*a^21
*b^4*c^2*d^18*e^9 + 256*a^22*b^2*c^3*d^18*e^9 + 128*a^19*b*c^7*d^25*e^2 - 1152*a^20*b*c^6*d^23*e^4 - 640*a^21*
b*c^5*d^21*e^6 + 640*a^22*b*c^4*d^19*e^8) + 64*a^18*c^8*d^24*e^2 - 128*a^19*c^7*d^22*e^4 - 192*a^20*c^6*d^20*e
^6 + 256*a^21*c^5*d^18*e^8 + 256*a^22*c^4*d^16*e^10 + 16*a^16*b^4*c^6*d^24*e^2 - 64*a^16*b^5*c^5*d^23*e^3 + 96
*a^16*b^6*c^4*d^22*e^4 - 64*a^16*b^7*c^3*d^21*e^5 + 16*a^16*b^8*c^2*d^20*e^6 - 80*a^17*b^2*c^7*d^24*e^2 + 368*
a^17*b^3*c^6*d^23*e^3 - 608*a^17*b^4*c^5*d^22*e^4 + 416*a^17*b^5*c^4*d^21*e^5 - 80*a^17*b^6*c^3*d^20*e^6 - 16*
a^17*b^7*c^2*d^19*e^7 + 928*a^18*b^2*c^6*d^22*e^4 - 640*a^18*b^3*c^5*d^21*e^5 - 32*a^18*b^4*c^4*d^20*e^6 + 128
*a^18*b^5*c^3*d^19*e^7 + 432*a^19*b^2*c^5*d^20*e^6 - 304*a^19*b^3*c^4*d^19*e^7 + 16*a^19*b^4*c^3*d^18*e^8 - 16
*a^19*b^5*c^2*d^17*e^9 - 128*a^20*b^2*c^4*d^18*e^8 + 128*a^20*b^3*c^3*d^17*e^9 + 16*a^20*b^4*c^2*d^16*e^10 - 1
28*a^21*b^2*c^3*d^16*e^10 - 448*a^18*b*c^7*d^23*e^3 + 192*a^20*b*c^5*d^19*e^7 - 256*a^21*b*c^4*d^17*e^9) - x*(
16*a^16*c^9*d^23*e^2 + 32*a^17*c^8*d^21*e^4 - 112*a^18*c^7*d^19*e^6 - 128*a^20*c^5*d^15*e^10 + 8*a^14*b^4*c^7*
d^23*e^2 - 16*a^14*b^5*c^6*d^22*e^3 + 8*a^14*b^6*c^5*d^21*e^4 + 8*a^14*b^7*c^4*d^20*e^5 - 16*a^14*b^8*c^3*d^19
*e^6 + 8*a^14*b^9*c^2*d^18*e^7 - 32*a^15*b^2*c^8*d^23*e^2 + 64*a^15*b^3*c^7*d^22*e^3 - 16*a^15*b^4*c^6*d^21*e^
4 - 88*a^15*b^5*c^5*d^20*e^5 + 160*a^15*b^6*c^4*d^19*e^6 - 88*a^15*b^7*c^3*d^18*e^7 - 48*a^16*b^2*c^7*d^21*e^4
+ 264*a^16*b^3*c^6*d^20*e^5 - 520*a^16*b^4*c^5*d^19*e^6 + 336*a^16*b^5*c^4*d^18*e^7 + 576*a^17*b^2*c^6*d^19*e
^6 - 504*a^17*b^3*c^5*d^18*e^7 + 8*a^18*b^3*c^4*d^16*e^9 - 16*a^18*b^4*c^3*d^15*e^10 + 8*a^18*b^5*c^2*d^14*e^1
1 + 96*a^19*b^2*c^4*d^15*e^10 - 56*a^19*b^3*c^3*d^14*e^11 - 32*a^16*b*c^8*d^22*e^3 - 192*a^17*b*c^7*d^20*e^5 +
224*a^18*b*c^6*d^18*e^7 - 32*a^19*b*c^5*d^16*e^9 + 96*a^20*b*c^4*d^14*e^11))*(-(b^9*e^2 + b^7*c^2*d^2 - b^6*e
^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3
*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a
*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e
+ 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c
- b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3
*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4
+ 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2
+ 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a
^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2) + 4*a^15*c^9*d^21*e^3 + 4*a^16*c^8*d^19*e^5 - 48*a^18*c^6*d^15
*e^9 + 4*a^14*b^2*c^8*d^21*e^3 + 4*a^14*b^7*c^3*d^16*e^8 - 4*a^14*b^8*c^2*d^15*e^9 - 36*a^15*b^5*c^4*d^16*e^8
+ 44*a^15*b^6*c^3*d^15*e^9 - 4*a^15*b^7*c^2*d^14*e^10 + 100*a^16*b^3*c^5*d^16*e^8 - 160*a^16*b^4*c^4*d^15*e^9
+ 32*a^16*b^5*c^3*d^14*e^10 + 204*a^17*b^2*c^5*d^15*e^9 - 76*a^17*b^3*c^4*d^14*e^10 - 4*a^14*b*c^9*d^22*e^2 -
8*a^15*b*c^8*d^20*e^4 - 80*a^17*b*c^6*d^16*e^8 + 48*a^18*b*c^5*d^14*e^10) - x*(2*a^14*c^9*d^18*e^5 + 4*a^16*c^
7*d^14*e^9 + 2*a^14*b^4*c^5*d^14*e^9 - 8*a^15*b^2*c^6*d^14*e^9))*(-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c -
b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^
2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^
(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*
e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/
2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4
*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2
*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*
d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^
3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2) - ((-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^
3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3
)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*
c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2)
- 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 7
6*a^3*b^2*c^4*d*e + 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^
2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*
a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e
- 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2))
)^(1/2)*(((-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 2
8*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2
- 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7
*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4*a*c
- b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*b^2*
c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^
3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*
d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a
^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(x*(-(b^9*e^2 + b^7*
c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d
*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3
*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 2
0*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*
c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^
(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 +
16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a
^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c
^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(512*a^20*c^7*d^24*e^3 + 512*a^21*c^6*d^22*e^5
- 512*a^22*c^5*d^20*e^7 - 512*a^23*c^4*d^18*e^9 - 32*a^18*b^3*c^6*d^25*e^2 + 128*a^18*b^4*c^5*d^24*e^3 - 192*a
^18*b^5*c^4*d^23*e^4 + 128*a^18*b^6*c^3*d^22*e^5 - 32*a^18*b^7*c^2*d^21*e^6 - 640*a^19*b^2*c^6*d^24*e^3 + 1056
*a^19*b^3*c^5*d^23*e^4 - 672*a^19*b^4*c^4*d^22*e^5 + 96*a^19*b^5*c^3*d^21*e^6 + 32*a^19*b^6*c^2*d^20*e^7 + 512
*a^20*b^2*c^5*d^22*e^5 + 288*a^20*b^3*c^4*d^21*e^6 - 192*a^20*b^4*c^3*d^20*e^7 + 32*a^20*b^5*c^2*d^19*e^8 + 38
4*a^21*b^2*c^4*d^20*e^7 - 288*a^21*b^3*c^3*d^19*e^8 - 32*a^21*b^4*c^2*d^18*e^9 + 256*a^22*b^2*c^3*d^18*e^9 + 1
28*a^19*b*c^7*d^25*e^2 - 1152*a^20*b*c^6*d^23*e^4 - 640*a^21*b*c^5*d^21*e^6 + 640*a^22*b*c^4*d^19*e^8) - 64*a^
18*c^8*d^24*e^2 + 128*a^19*c^7*d^22*e^4 + 192*a^20*c^6*d^20*e^6 - 256*a^21*c^5*d^18*e^8 - 256*a^22*c^4*d^16*e^
10 - 16*a^16*b^4*c^6*d^24*e^2 + 64*a^16*b^5*c^5*d^23*e^3 - 96*a^16*b^6*c^4*d^22*e^4 + 64*a^16*b^7*c^3*d^21*e^5
- 16*a^16*b^8*c^2*d^20*e^6 + 80*a^17*b^2*c^7*d^24*e^2 - 368*a^17*b^3*c^6*d^23*e^3 + 608*a^17*b^4*c^5*d^22*e^4
- 416*a^17*b^5*c^4*d^21*e^5 + 80*a^17*b^6*c^3*d^20*e^6 + 16*a^17*b^7*c^2*d^19*e^7 - 928*a^18*b^2*c^6*d^22*e^4
+ 640*a^18*b^3*c^5*d^21*e^5 + 32*a^18*b^4*c^4*d^20*e^6 - 128*a^18*b^5*c^3*d^19*e^7 - 432*a^19*b^2*c^5*d^20*e^
6 + 304*a^19*b^3*c^4*d^19*e^7 - 16*a^19*b^4*c^3*d^18*e^8 + 16*a^19*b^5*c^2*d^17*e^9 + 128*a^20*b^2*c^4*d^18*e^
8 - 128*a^20*b^3*c^3*d^17*e^9 - 16*a^20*b^4*c^2*d^16*e^10 + 128*a^21*b^2*c^3*d^16*e^10 + 448*a^18*b*c^7*d^23*e
^3 - 192*a^20*b*c^5*d^19*e^7 + 256*a^21*b*c^4*d^17*e^9) - x*(16*a^16*c^9*d^23*e^2 + 32*a^17*c^8*d^21*e^4 - 112
*a^18*c^7*d^19*e^6 - 128*a^20*c^5*d^15*e^10 + 8*a^14*b^4*c^7*d^23*e^2 - 16*a^14*b^5*c^6*d^22*e^3 + 8*a^14*b^6*
c^5*d^21*e^4 + 8*a^14*b^7*c^4*d^20*e^5 - 16*a^14*b^8*c^3*d^19*e^6 + 8*a^14*b^9*c^2*d^18*e^7 - 32*a^15*b^2*c^8*
d^23*e^2 + 64*a^15*b^3*c^7*d^22*e^3 - 16*a^15*b^4*c^6*d^21*e^4 - 88*a^15*b^5*c^5*d^20*e^5 + 160*a^15*b^6*c^4*d
^19*e^6 - 88*a^15*b^7*c^3*d^18*e^7 - 48*a^16*b^2*c^7*d^21*e^4 + 264*a^16*b^3*c^6*d^20*e^5 - 520*a^16*b^4*c^5*d
^19*e^6 + 336*a^16*b^5*c^4*d^18*e^7 + 576*a^17*b^2*c^6*d^19*e^6 - 504*a^17*b^3*c^5*d^18*e^7 + 8*a^18*b^3*c^4*d
^16*e^9 - 16*a^18*b^4*c^3*d^15*e^10 + 8*a^18*b^5*c^2*d^14*e^11 + 96*a^19*b^2*c^4*d^15*e^10 - 56*a^19*b^3*c^3*d
^14*e^11 - 32*a^16*b*c^8*d^22*e^3 - 192*a^17*b*c^7*d^20*e^5 + 224*a^18*b*c^6*d^18*e^7 - 32*a^19*b*c^5*d^16*e^9
+ 96*a^20*b*c^4*d^14*e^11))*(-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 2
0*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) +
42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^
3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b
^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2
*c^4*d*e + 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d
*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d
*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7
*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2) -
4*a^15*c^9*d^21*e^3 - 4*a^16*c^8*d^19*e^5 + 48*a^18*c^6*d^15*e^9 - 4*a^14*b^2*c^8*d^21*e^3 - 4*a^14*b^7*c^3*d
^16*e^8 + 4*a^14*b^8*c^2*d^15*e^9 + 36*a^15*b^5*c^4*d^16*e^8 - 44*a^15*b^6*c^3*d^15*e^9 + 4*a^15*b^7*c^2*d^14*
e^10 - 100*a^16*b^3*c^5*d^16*e^8 + 160*a^16*b^4*c^4*d^15*e^9 - 32*a^16*b^5*c^3*d^14*e^10 - 204*a^17*b^2*c^5*d^
15*e^9 + 76*a^17*b^3*c^4*d^14*e^10 + 4*a^14*b*c^9*d^22*e^2 + 8*a^15*b*c^8*d^20*e^4 + 80*a^17*b*c^6*d^16*e^8 -
48*a^18*b*c^5*d^14*e^10) - x*(2*a^14*c^9*d^18*e^5 + 4*a^16*c^7*d^14*e^9 + 2*a^14*b^4*c^5*d^14*e^9 - 8*a^15*b^2
*c^6*d^14*e^9))*(-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d
^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c
^2*e^2 - 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11
*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-
(4*a*c - b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*
a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c -
b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^
4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e
+ 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2) + 2*a^14*c^8*d
^14*e^8))*(-(b^9*e^2 + b^7*c^2*d^2 - b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 2
8*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 - a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2
- 63*a^3*b^3*c^3*e^2 + a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7
*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e + 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b^2*c^2*e^2*(-(4*a*c
- b^2)^3)^(1/2) + 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e + 3*a*b^2*
c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) - 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^
3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*
d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a
^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*2i - (1/(3*a*d) - (x
^2*(a*e + b*d))/(a^2*d^2))/x^3 - (log(c^9*d^27*e^6 - b^9*d^18*e^15 + 2*a*c^8*d^25*e^8 - 2*b*c^8*d^26*e^7 + 2*b
^8*c*d^19*e^14 + a^5*b^4*d^13*e^20 + a^2*c^7*d^23*e^10 + 16*a^4*c^5*d^19*e^14 + 16*a^7*c^2*d^13*e^20 + b^2*c^7
*d^25*e^8 - b^7*c^2*d^20*e^13 - 25*a^2*b^3*c^4*d^20*e^13 + 66*a^2*b^4*c^3*d^19*e^14 - 42*a^2*b^5*c^2*d^18*e^15
- 76*a^3*b^2*c^4*d^19*e^14 + 63*a^3*b^3*c^3*d^18*e^15 + a^5*b^4*e^3*x*(-d^5*e^7)^(5/2) - a^2*c^7*d^15*x*(-d^5
*e^7)^(3/2) + 16*a^7*c^2*e^3*x*(-d^5*e^7)^(5/2) + b^9*d^10*e^5*x*(-d^5*e^7)^(3/2) + c^9*d^24*e^3*x*(-d^5*e^7)^
(1/2) - 2*a*b*c^7*d^24*e^9 + 11*a*b^7*c*d^18*e^15 + 9*a*b^5*c^3*d^20*e^13 - 20*a*b^6*c^2*d^19*e^14 + 20*a^3*b*
c^5*d^20*e^13 - 28*a^4*b*c^4*d^18*e^15 - 8*a^6*b^2*c*d^13*e^20 - 16*a^4*c^5*d^11*e^4*x*(-d^5*e^7)^(3/2) + b^7*
c^2*d^12*e^3*x*(-d^5*e^7)^(3/2) + b^2*c^7*d^22*e^5*x*(-d^5*e^7)^(1/2) - 8*a^6*b^2*c*e^3*x*(-d^5*e^7)^(5/2) + 2
*a*c^8*d^22*e^5*x*(-d^5*e^7)^(1/2) - 2*b^8*c*d^11*e^4*x*(-d^5*e^7)^(3/2) - 2*b*c^8*d^23*e^4*x*(-d^5*e^7)^(1/2)
- 11*a*b^7*c*d^10*e^5*x*(-d^5*e^7)^(3/2) - 2*a*b*c^7*d^21*e^6*x*(-d^5*e^7)^(1/2) - 9*a*b^5*c^3*d^12*e^3*x*(-d
^5*e^7)^(3/2) + 20*a*b^6*c^2*d^11*e^4*x*(-d^5*e^7)^(3/2) - 20*a^3*b*c^5*d^12*e^3*x*(-d^5*e^7)^(3/2) + 28*a^4*b
*c^4*d^10*e^5*x*(-d^5*e^7)^(3/2) + 25*a^2*b^3*c^4*d^12*e^3*x*(-d^5*e^7)^(3/2) - 66*a^2*b^4*c^3*d^11*e^4*x*(-d^
5*e^7)^(3/2) + 42*a^2*b^5*c^2*d^10*e^5*x*(-d^5*e^7)^(3/2) + 76*a^3*b^2*c^4*d^11*e^4*x*(-d^5*e^7)^(3/2) - 63*a^
3*b^3*c^3*d^10*e^5*x*(-d^5*e^7)^(3/2))*(-d^5*e^7)^(1/2))/(2*(c*d^7 + a*d^5*e^2 - b*d^6*e)) - atan((((-(b^9*e^2
+ b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*
b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^
2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*
d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5
*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b
^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^
4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*
d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*
a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(((-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(
4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d
^2 + a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b
^2)^3)^(1/2) + b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b
^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)
^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d
*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*
a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a
^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3
*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(x*(-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a
*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c -
b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^2*
(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^3)
^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*
d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2)
- 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e
^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*
c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^
2*e^2)))^(1/2)*(512*a^20*c^7*d^24*e^3 + 512*a^21*c^6*d^22*e^5 - 512*a^22*c^5*d^20*e^7 - 512*a^23*c^4*d^18*e^9
- 32*a^18*b^3*c^6*d^25*e^2 + 128*a^18*b^4*c^5*d^24*e^3 - 192*a^18*b^5*c^4*d^23*e^4 + 128*a^18*b^6*c^3*d^22*e^5
- 32*a^18*b^7*c^2*d^21*e^6 - 640*a^19*b^2*c^6*d^24*e^3 + 1056*a^19*b^3*c^5*d^23*e^4 - 672*a^19*b^4*c^4*d^22*e
^5 + 96*a^19*b^5*c^3*d^21*e^6 + 32*a^19*b^6*c^2*d^20*e^7 + 512*a^20*b^2*c^5*d^22*e^5 + 288*a^20*b^3*c^4*d^21*e
^6 - 192*a^20*b^4*c^3*d^20*e^7 + 32*a^20*b^5*c^2*d^19*e^8 + 384*a^21*b^2*c^4*d^20*e^7 - 288*a^21*b^3*c^3*d^19*
e^8 - 32*a^21*b^4*c^2*d^18*e^9 + 256*a^22*b^2*c^3*d^18*e^9 + 128*a^19*b*c^7*d^25*e^2 - 1152*a^20*b*c^6*d^23*e^
4 - 640*a^21*b*c^5*d^21*e^6 + 640*a^22*b*c^4*d^19*e^8) - 64*a^18*c^8*d^24*e^2 + 128*a^19*c^7*d^22*e^4 + 192*a^
20*c^6*d^20*e^6 - 256*a^21*c^5*d^18*e^8 - 256*a^22*c^4*d^16*e^10 - 16*a^16*b^4*c^6*d^24*e^2 + 64*a^16*b^5*c^5*
d^23*e^3 - 96*a^16*b^6*c^4*d^22*e^4 + 64*a^16*b^7*c^3*d^21*e^5 - 16*a^16*b^8*c^2*d^20*e^6 + 80*a^17*b^2*c^7*d^
24*e^2 - 368*a^17*b^3*c^6*d^23*e^3 + 608*a^17*b^4*c^5*d^22*e^4 - 416*a^17*b^5*c^4*d^21*e^5 + 80*a^17*b^6*c^3*d
^20*e^6 + 16*a^17*b^7*c^2*d^19*e^7 - 928*a^18*b^2*c^6*d^22*e^4 + 640*a^18*b^3*c^5*d^21*e^5 + 32*a^18*b^4*c^4*d
^20*e^6 - 128*a^18*b^5*c^3*d^19*e^7 - 432*a^19*b^2*c^5*d^20*e^6 + 304*a^19*b^3*c^4*d^19*e^7 - 16*a^19*b^4*c^3*
d^18*e^8 + 16*a^19*b^5*c^2*d^17*e^9 + 128*a^20*b^2*c^4*d^18*e^8 - 128*a^20*b^3*c^3*d^17*e^9 - 16*a^20*b^4*c^2*
d^16*e^10 + 128*a^21*b^2*c^3*d^16*e^10 + 448*a^18*b*c^7*d^23*e^3 - 192*a^20*b*c^5*d^19*e^7 + 256*a^21*b*c^4*d^
17*e^9) - x*(16*a^16*c^9*d^23*e^2 + 32*a^17*c^8*d^21*e^4 - 112*a^18*c^7*d^19*e^6 - 128*a^20*c^5*d^15*e^10 + 8*
a^14*b^4*c^7*d^23*e^2 - 16*a^14*b^5*c^6*d^22*e^3 + 8*a^14*b^6*c^5*d^21*e^4 + 8*a^14*b^7*c^4*d^20*e^5 - 16*a^14
*b^8*c^3*d^19*e^6 + 8*a^14*b^9*c^2*d^18*e^7 - 32*a^15*b^2*c^8*d^23*e^2 + 64*a^15*b^3*c^7*d^22*e^3 - 16*a^15*b^
4*c^6*d^21*e^4 - 88*a^15*b^5*c^5*d^20*e^5 + 160*a^15*b^6*c^4*d^19*e^6 - 88*a^15*b^7*c^3*d^18*e^7 - 48*a^16*b^2
*c^7*d^21*e^4 + 264*a^16*b^3*c^6*d^20*e^5 - 520*a^16*b^4*c^5*d^19*e^6 + 336*a^16*b^5*c^4*d^18*e^7 + 576*a^17*b
^2*c^6*d^19*e^6 - 504*a^17*b^3*c^5*d^18*e^7 + 8*a^18*b^3*c^4*d^16*e^9 - 16*a^18*b^4*c^3*d^15*e^10 + 8*a^18*b^5
*c^2*d^14*e^11 + 96*a^19*b^2*c^4*d^15*e^10 - 56*a^19*b^3*c^3*d^14*e^11 - 32*a^16*b*c^8*d^22*e^3 - 192*a^17*b*c
^7*d^20*e^5 + 224*a^18*b*c^6*d^18*e^7 - 32*a^19*b*c^5*d^16*e^9 + 96*a^20*b*c^4*d^14*e^11))*(-(b^9*e^2 + b^7*c^
2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e
+ 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c
^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*
a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*
e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1
/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 1
6*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5
*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2
*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2) - 4*a^15*c^9*d^21*e^3 - 4*a^16*c^8*d^19*e^5 + 48*
a^18*c^6*d^15*e^9 - 4*a^14*b^2*c^8*d^21*e^3 - 4*a^14*b^7*c^3*d^16*e^8 + 4*a^14*b^8*c^2*d^15*e^9 + 36*a^15*b^5*
c^4*d^16*e^8 - 44*a^15*b^6*c^3*d^15*e^9 + 4*a^15*b^7*c^2*d^14*e^10 - 100*a^16*b^3*c^5*d^16*e^8 + 160*a^16*b^4*
c^4*d^15*e^9 - 32*a^16*b^5*c^3*d^14*e^10 - 204*a^17*b^2*c^5*d^15*e^9 + 76*a^17*b^3*c^4*d^14*e^10 + 4*a^14*b*c^
9*d^22*e^2 + 8*a^15*b*c^8*d^20*e^4 + 80*a^17*b*c^6*d^16*e^8 - 48*a^18*b*c^5*d^14*e^10) - x*(2*a^14*c^9*d^18*e^
5 + 4*a^16*c^7*d^14*e^9 + 2*a^14*b^4*c^5*d^14*e^9 - 8*a^15*b^2*c^6*d^14*e^9))*(-(b^9*e^2 + b^7*c^2*d^2 + b^6*e
^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3
*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a
*c - b^2)^3)^(1/2) + b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e
- 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c
- b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3
*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4
+ 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2
+ 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a
^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*1i + ((-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1
/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(
-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4
*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c
- b^2)^3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2
*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)
^3)^(1/2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^
8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2
*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6
*b^4*c*d^2*e^2)))^(1/2)*(((-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a
^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42
*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^2*(-(4*a*c - b^2)^3)^
(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b^2*
c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^
4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b*c^3*d*e*
(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^
3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*
c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(x*(
-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4
*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b
^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16
*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^
(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(
4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(
8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6
*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*
e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(512*a^20*c^7*d^24*e^3 + 512*a^
21*c^6*d^22*e^5 - 512*a^22*c^5*d^20*e^7 - 512*a^23*c^4*d^18*e^9 - 32*a^18*b^3*c^6*d^25*e^2 + 128*a^18*b^4*c^5*
d^24*e^3 - 192*a^18*b^5*c^4*d^23*e^4 + 128*a^18*b^6*c^3*d^22*e^5 - 32*a^18*b^7*c^2*d^21*e^6 - 640*a^19*b^2*c^6
*d^24*e^3 + 1056*a^19*b^3*c^5*d^23*e^4 - 672*a^19*b^4*c^4*d^22*e^5 + 96*a^19*b^5*c^3*d^21*e^6 + 32*a^19*b^6*c^
2*d^20*e^7 + 512*a^20*b^2*c^5*d^22*e^5 + 288*a^20*b^3*c^4*d^21*e^6 - 192*a^20*b^4*c^3*d^20*e^7 + 32*a^20*b^5*c
^2*d^19*e^8 + 384*a^21*b^2*c^4*d^20*e^7 - 288*a^21*b^3*c^3*d^19*e^8 - 32*a^21*b^4*c^2*d^18*e^9 + 256*a^22*b^2*
c^3*d^18*e^9 + 128*a^19*b*c^7*d^25*e^2 - 1152*a^20*b*c^6*d^23*e^4 - 640*a^21*b*c^5*d^21*e^6 + 640*a^22*b*c^4*d
^19*e^8) + 64*a^18*c^8*d^24*e^2 - 128*a^19*c^7*d^22*e^4 - 192*a^20*c^6*d^20*e^6 + 256*a^21*c^5*d^18*e^8 + 256*
a^22*c^4*d^16*e^10 + 16*a^16*b^4*c^6*d^24*e^2 - 64*a^16*b^5*c^5*d^23*e^3 + 96*a^16*b^6*c^4*d^22*e^4 - 64*a^16*
b^7*c^3*d^21*e^5 + 16*a^16*b^8*c^2*d^20*e^6 - 80*a^17*b^2*c^7*d^24*e^2 + 368*a^17*b^3*c^6*d^23*e^3 - 608*a^17*
b^4*c^5*d^22*e^4 + 416*a^17*b^5*c^4*d^21*e^5 - 80*a^17*b^6*c^3*d^20*e^6 - 16*a^17*b^7*c^2*d^19*e^7 + 928*a^18*
b^2*c^6*d^22*e^4 - 640*a^18*b^3*c^5*d^21*e^5 - 32*a^18*b^4*c^4*d^20*e^6 + 128*a^18*b^5*c^3*d^19*e^7 + 432*a^19
*b^2*c^5*d^20*e^6 - 304*a^19*b^3*c^4*d^19*e^7 + 16*a^19*b^4*c^3*d^18*e^8 - 16*a^19*b^5*c^2*d^17*e^9 - 128*a^20
*b^2*c^4*d^18*e^8 + 128*a^20*b^3*c^3*d^17*e^9 + 16*a^20*b^4*c^2*d^16*e^10 - 128*a^21*b^2*c^3*d^16*e^10 - 448*a
^18*b*c^7*d^23*e^3 + 192*a^20*b*c^5*d^19*e^7 - 256*a^21*b*c^4*d^17*e^9) - x*(16*a^16*c^9*d^23*e^2 + 32*a^17*c^
8*d^21*e^4 - 112*a^18*c^7*d^19*e^6 - 128*a^20*c^5*d^15*e^10 + 8*a^14*b^4*c^7*d^23*e^2 - 16*a^14*b^5*c^6*d^22*e
^3 + 8*a^14*b^6*c^5*d^21*e^4 + 8*a^14*b^7*c^4*d^20*e^5 - 16*a^14*b^8*c^3*d^19*e^6 + 8*a^14*b^9*c^2*d^18*e^7 -
32*a^15*b^2*c^8*d^23*e^2 + 64*a^15*b^3*c^7*d^22*e^3 - 16*a^15*b^4*c^6*d^21*e^4 - 88*a^15*b^5*c^5*d^20*e^5 + 16
0*a^15*b^6*c^4*d^19*e^6 - 88*a^15*b^7*c^3*d^18*e^7 - 48*a^16*b^2*c^7*d^21*e^4 + 264*a^16*b^3*c^6*d^20*e^5 - 52
0*a^16*b^4*c^5*d^19*e^6 + 336*a^16*b^5*c^4*d^18*e^7 + 576*a^17*b^2*c^6*d^19*e^6 - 504*a^17*b^3*c^5*d^18*e^7 +
8*a^18*b^3*c^4*d^16*e^9 - 16*a^18*b^4*c^3*d^15*e^10 + 8*a^18*b^5*c^2*d^14*e^11 + 96*a^19*b^2*c^4*d^15*e^10 - 5
6*a^19*b^3*c^3*d^14*e^11 - 32*a^16*b*c^8*d^22*e^3 - 192*a^17*b*c^7*d^20*e^5 + 224*a^18*b*c^6*d^18*e^7 - 32*a^1
9*b*c^5*d^16*e^9 + 96*a^20*b*c^4*d^14*e^11))*(-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a
*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c -
b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^2*
(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^3)
^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*
d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2)
- 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e
^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*
c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^
2*e^2)))^(1/2) + 4*a^15*c^9*d^21*e^3 + 4*a^16*c^8*d^19*e^5 - 48*a^18*c^6*d^15*e^9 + 4*a^14*b^2*c^8*d^21*e^3 +
4*a^14*b^7*c^3*d^16*e^8 - 4*a^14*b^8*c^2*d^15*e^9 - 36*a^15*b^5*c^4*d^16*e^8 + 44*a^15*b^6*c^3*d^15*e^9 - 4*a^
15*b^7*c^2*d^14*e^10 + 100*a^16*b^3*c^5*d^16*e^8 - 160*a^16*b^4*c^4*d^15*e^9 + 32*a^16*b^5*c^3*d^14*e^10 + 204
*a^17*b^2*c^5*d^15*e^9 - 76*a^17*b^3*c^4*d^14*e^10 - 4*a^14*b*c^9*d^22*e^2 - 8*a^15*b*c^8*d^20*e^4 - 80*a^17*b
*c^6*d^16*e^8 + 48*a^18*b*c^5*d^14*e^10) - x*(2*a^14*c^9*d^18*e^5 + 4*a^16*c^7*d^14*e^9 + 2*a^14*b^4*c^5*d^14*
e^9 - 8*a^15*b^2*c^6*d^14*e^9))*(-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2
- 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2
) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^2*(-(4*a*c - b^
2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^
2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*
b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b*c^
3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^
5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*
a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2
)*1i)/(((-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*
a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 -
63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c
*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c -
b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^
3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)
^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^
4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7
*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(((-(b^9*e^2 + b^7*c^2
*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e
+ 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^
3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a
*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e
^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/
2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16
*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*
b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*
d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(x*(-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b
^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*
c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1
/2) + b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*
(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2)
- 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a
*c - b^2)^3)^(1/2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e
^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^
2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*
e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(512*a^20*c^7*d^24*e^3 + 512*a^21*c^6*d^22*e^5 - 512*a^22*c^5*d^20*e^7 - 512*
a^23*c^4*d^18*e^9 - 32*a^18*b^3*c^6*d^25*e^2 + 128*a^18*b^4*c^5*d^24*e^3 - 192*a^18*b^5*c^4*d^23*e^4 + 128*a^1
8*b^6*c^3*d^22*e^5 - 32*a^18*b^7*c^2*d^21*e^6 - 640*a^19*b^2*c^6*d^24*e^3 + 1056*a^19*b^3*c^5*d^23*e^4 - 672*a
^19*b^4*c^4*d^22*e^5 + 96*a^19*b^5*c^3*d^21*e^6 + 32*a^19*b^6*c^2*d^20*e^7 + 512*a^20*b^2*c^5*d^22*e^5 + 288*a
^20*b^3*c^4*d^21*e^6 - 192*a^20*b^4*c^3*d^20*e^7 + 32*a^20*b^5*c^2*d^19*e^8 + 384*a^21*b^2*c^4*d^20*e^7 - 288*
a^21*b^3*c^3*d^19*e^8 - 32*a^21*b^4*c^2*d^18*e^9 + 256*a^22*b^2*c^3*d^18*e^9 + 128*a^19*b*c^7*d^25*e^2 - 1152*
a^20*b*c^6*d^23*e^4 - 640*a^21*b*c^5*d^21*e^6 + 640*a^22*b*c^4*d^19*e^8) + 64*a^18*c^8*d^24*e^2 - 128*a^19*c^7
*d^22*e^4 - 192*a^20*c^6*d^20*e^6 + 256*a^21*c^5*d^18*e^8 + 256*a^22*c^4*d^16*e^10 + 16*a^16*b^4*c^6*d^24*e^2
- 64*a^16*b^5*c^5*d^23*e^3 + 96*a^16*b^6*c^4*d^22*e^4 - 64*a^16*b^7*c^3*d^21*e^5 + 16*a^16*b^8*c^2*d^20*e^6 -
80*a^17*b^2*c^7*d^24*e^2 + 368*a^17*b^3*c^6*d^23*e^3 - 608*a^17*b^4*c^5*d^22*e^4 + 416*a^17*b^5*c^4*d^21*e^5 -
80*a^17*b^6*c^3*d^20*e^6 - 16*a^17*b^7*c^2*d^19*e^7 + 928*a^18*b^2*c^6*d^22*e^4 - 640*a^18*b^3*c^5*d^21*e^5 -
32*a^18*b^4*c^4*d^20*e^6 + 128*a^18*b^5*c^3*d^19*e^7 + 432*a^19*b^2*c^5*d^20*e^6 - 304*a^19*b^3*c^4*d^19*e^7
+ 16*a^19*b^4*c^3*d^18*e^8 - 16*a^19*b^5*c^2*d^17*e^9 - 128*a^20*b^2*c^4*d^18*e^8 + 128*a^20*b^3*c^3*d^17*e^9
+ 16*a^20*b^4*c^2*d^16*e^10 - 128*a^21*b^2*c^3*d^16*e^10 - 448*a^18*b*c^7*d^23*e^3 + 192*a^20*b*c^5*d^19*e^7 -
256*a^21*b*c^4*d^17*e^9) - x*(16*a^16*c^9*d^23*e^2 + 32*a^17*c^8*d^21*e^4 - 112*a^18*c^7*d^19*e^6 - 128*a^20*
c^5*d^15*e^10 + 8*a^14*b^4*c^7*d^23*e^2 - 16*a^14*b^5*c^6*d^22*e^3 + 8*a^14*b^6*c^5*d^21*e^4 + 8*a^14*b^7*c^4*
d^20*e^5 - 16*a^14*b^8*c^3*d^19*e^6 + 8*a^14*b^9*c^2*d^18*e^7 - 32*a^15*b^2*c^8*d^23*e^2 + 64*a^15*b^3*c^7*d^2
2*e^3 - 16*a^15*b^4*c^6*d^21*e^4 - 88*a^15*b^5*c^5*d^20*e^5 + 160*a^15*b^6*c^4*d^19*e^6 - 88*a^15*b^7*c^3*d^18
*e^7 - 48*a^16*b^2*c^7*d^21*e^4 + 264*a^16*b^3*c^6*d^20*e^5 - 520*a^16*b^4*c^5*d^19*e^6 + 336*a^16*b^5*c^4*d^1
8*e^7 + 576*a^17*b^2*c^6*d^19*e^6 - 504*a^17*b^3*c^5*d^18*e^7 + 8*a^18*b^3*c^4*d^16*e^9 - 16*a^18*b^4*c^3*d^15
*e^10 + 8*a^18*b^5*c^2*d^14*e^11 + 96*a^19*b^2*c^4*d^15*e^10 - 56*a^19*b^3*c^3*d^14*e^11 - 32*a^16*b*c^8*d^22*
e^3 - 192*a^17*b*c^7*d^20*e^5 + 224*a^18*b*c^6*d^18*e^7 - 32*a^19*b*c^5*d^16*e^9 + 96*a^20*b*c^4*d^14*e^11))*(
-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4
*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b
^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16
*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^
(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(
4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(
8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6
*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*
e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2) + 4*a^15*c^9*d^21*e^3 + 4*a^16*
c^8*d^19*e^5 - 48*a^18*c^6*d^15*e^9 + 4*a^14*b^2*c^8*d^21*e^3 + 4*a^14*b^7*c^3*d^16*e^8 - 4*a^14*b^8*c^2*d^15*
e^9 - 36*a^15*b^5*c^4*d^16*e^8 + 44*a^15*b^6*c^3*d^15*e^9 - 4*a^15*b^7*c^2*d^14*e^10 + 100*a^16*b^3*c^5*d^16*e
^8 - 160*a^16*b^4*c^4*d^15*e^9 + 32*a^16*b^5*c^3*d^14*e^10 + 204*a^17*b^2*c^5*d^15*e^9 - 76*a^17*b^3*c^4*d^14*
e^10 - 4*a^14*b*c^9*d^22*e^2 - 8*a^15*b*c^8*d^20*e^4 - 80*a^17*b*c^6*d^16*e^8 + 48*a^18*b*c^5*d^14*e^10) - x*(
2*a^14*c^9*d^18*e^5 + 4*a^16*c^7*d^14*e^9 + 2*a^14*b^4*c^5*d^14*e^9 - 8*a^15*b^2*c^6*d^14*e^9))*(-(b^9*e^2 + b
^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*
c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 -
a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e
+ 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b
^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^
3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^
4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4
+ a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*
b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2) - ((-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a
*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2
+ a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)
^3)^(1/2) + b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*
c*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)
^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*
(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9
*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*
c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^
2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(((-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5
*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c - b^2
)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^2*(-(4
*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/
2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e
+ 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6
*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 -
2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^
3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^
2)))^(1/2)*(x*(-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2
+ 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2
*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a
*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4
*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*
b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b
^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*
c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e +
16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^2)))^(1/2)*(512*a^20*c^7*d^
24*e^3 + 512*a^21*c^6*d^22*e^5 - 512*a^22*c^5*d^20*e^7 - 512*a^23*c^4*d^18*e^9 - 32*a^18*b^3*c^6*d^25*e^2 + 12
8*a^18*b^4*c^5*d^24*e^3 - 192*a^18*b^5*c^4*d^23*e^4 + 128*a^18*b^6*c^3*d^22*e^5 - 32*a^18*b^7*c^2*d^21*e^6 - 6
40*a^19*b^2*c^6*d^24*e^3 + 1056*a^19*b^3*c^5*d^23*e^4 - 672*a^19*b^4*c^4*d^22*e^5 + 96*a^19*b^5*c^3*d^21*e^6 +
32*a^19*b^6*c^2*d^20*e^7 + 512*a^20*b^2*c^5*d^22*e^5 + 288*a^20*b^3*c^4*d^21*e^6 - 192*a^20*b^4*c^3*d^20*e^7
+ 32*a^20*b^5*c^2*d^19*e^8 + 384*a^21*b^2*c^4*d^20*e^7 - 288*a^21*b^3*c^3*d^19*e^8 - 32*a^21*b^4*c^2*d^18*e^9
+ 256*a^22*b^2*c^3*d^18*e^9 + 128*a^19*b*c^7*d^25*e^2 - 1152*a^20*b*c^6*d^23*e^4 - 640*a^21*b*c^5*d^21*e^6 + 6
40*a^22*b*c^4*d^19*e^8) - 64*a^18*c^8*d^24*e^2 + 128*a^19*c^7*d^22*e^4 + 192*a^20*c^6*d^20*e^6 - 256*a^21*c^5*
d^18*e^8 - 256*a^22*c^4*d^16*e^10 - 16*a^16*b^4*c^6*d^24*e^2 + 64*a^16*b^5*c^5*d^23*e^3 - 96*a^16*b^6*c^4*d^22
*e^4 + 64*a^16*b^7*c^3*d^21*e^5 - 16*a^16*b^8*c^2*d^20*e^6 + 80*a^17*b^2*c^7*d^24*e^2 - 368*a^17*b^3*c^6*d^23*
e^3 + 608*a^17*b^4*c^5*d^22*e^4 - 416*a^17*b^5*c^4*d^21*e^5 + 80*a^17*b^6*c^3*d^20*e^6 + 16*a^17*b^7*c^2*d^19*
e^7 - 928*a^18*b^2*c^6*d^22*e^4 + 640*a^18*b^3*c^5*d^21*e^5 + 32*a^18*b^4*c^4*d^20*e^6 - 128*a^18*b^5*c^3*d^19
*e^7 - 432*a^19*b^2*c^5*d^20*e^6 + 304*a^19*b^3*c^4*d^19*e^7 - 16*a^19*b^4*c^3*d^18*e^8 + 16*a^19*b^5*c^2*d^17
*e^9 + 128*a^20*b^2*c^4*d^18*e^8 - 128*a^20*b^3*c^3*d^17*e^9 - 16*a^20*b^4*c^2*d^16*e^10 + 128*a^21*b^2*c^3*d^
16*e^10 + 448*a^18*b*c^7*d^23*e^3 - 192*a^20*b*c^5*d^19*e^7 + 256*a^21*b*c^4*d^17*e^9) - x*(16*a^16*c^9*d^23*e
^2 + 32*a^17*c^8*d^21*e^4 - 112*a^18*c^7*d^19*e^6 - 128*a^20*c^5*d^15*e^10 + 8*a^14*b^4*c^7*d^23*e^2 - 16*a^14
*b^5*c^6*d^22*e^3 + 8*a^14*b^6*c^5*d^21*e^4 + 8*a^14*b^7*c^4*d^20*e^5 - 16*a^14*b^8*c^3*d^19*e^6 + 8*a^14*b^9*
c^2*d^18*e^7 - 32*a^15*b^2*c^8*d^23*e^2 + 64*a^15*b^3*c^7*d^22*e^3 - 16*a^15*b^4*c^6*d^21*e^4 - 88*a^15*b^5*c^
5*d^20*e^5 + 160*a^15*b^6*c^4*d^19*e^6 - 88*a^15*b^7*c^3*d^18*e^7 - 48*a^16*b^2*c^7*d^21*e^4 + 264*a^16*b^3*c^
6*d^20*e^5 - 520*a^16*b^4*c^5*d^19*e^6 + 336*a^16*b^5*c^4*d^18*e^7 + 576*a^17*b^2*c^6*d^19*e^6 - 504*a^17*b^3*
c^5*d^18*e^7 + 8*a^18*b^3*c^4*d^16*e^9 - 16*a^18*b^4*c^3*d^15*e^10 + 8*a^18*b^5*c^2*d^14*e^11 + 96*a^19*b^2*c^
4*d^15*e^10 - 56*a^19*b^3*c^3*d^14*e^11 - 32*a^16*b*c^8*d^22*e^3 - 192*a^17*b*c^7*d^20*e^5 + 224*a^18*b*c^6*d^
18*e^7 - 32*a^19*b*c^5*d^16*e^9 + 96*a^20*b*c^4*d^14*e^11))*(-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)
^3)^(1/2) - 9*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4
*d^2*(-(4*a*c - b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2)
+ b^4*c^2*d^2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(
4*a*c - b^2)^3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) -
66*a^2*b^4*c^3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c
- b^2)^3)^(1/2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4
- 8*a^8*b^2*c*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e
^2 - 2*a^5*b^5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e -
6*a^6*b^4*c*d^2*e^2)))^(1/2) - 4*a^15*c^9*d^21*e^3 - 4*a^16*c^8*d^19*e^5 + 48*a^18*c^6*d^15*e^9 - 4*a^14*b^2*
c^8*d^21*e^3 - 4*a^14*b^7*c^3*d^16*e^8 + 4*a^14*b^8*c^2*d^15*e^9 + 36*a^15*b^5*c^4*d^16*e^8 - 44*a^15*b^6*c^3*
d^15*e^9 + 4*a^15*b^7*c^2*d^14*e^10 - 100*a^16*b^3*c^5*d^16*e^8 + 160*a^16*b^4*c^4*d^15*e^9 - 32*a^16*b^5*c^3*
d^14*e^10 - 204*a^17*b^2*c^5*d^15*e^9 + 76*a^17*b^3*c^4*d^14*e^10 + 4*a^14*b*c^9*d^22*e^2 + 8*a^15*b*c^8*d^20*
e^4 + 80*a^17*b*c^6*d^16*e^8 - 48*a^18*b*c^5*d^14*e^10) - x*(2*a^14*c^9*d^18*e^5 + 4*a^16*c^7*d^14*e^9 + 2*a^1
4*b^4*c^5*d^14*e^9 - 8*a^15*b^2*c^6*d^14*e^9))*(-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9
*a*b^5*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c
- b^2)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^
2*(-(4*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^
3)^(1/2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^
3*d*e + 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/
2) - 6*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c
*e^4 - 2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^
5*c*d^3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*
d^2*e^2)))^(1/2) + 2*a^14*c^8*d^14*e^8))*(-(b^9*e^2 + b^7*c^2*d^2 + b^6*e^2*(-(4*a*c - b^2)^3)^(1/2) - 9*a*b^5
*c^3*d^2 - 20*a^3*b*c^5*d^2 + 28*a^4*b*c^4*e^2 - 2*b^8*c*d*e + 25*a^2*b^3*c^4*d^2 + a^2*c^4*d^2*(-(4*a*c - b^2
)^3)^(1/2) + 42*a^2*b^5*c^2*e^2 - 63*a^3*b^3*c^3*e^2 - a^3*c^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + b^4*c^2*d^2*(-(4
*a*c - b^2)^3)^(1/2) - 11*a*b^7*c*e^2 - 16*a^4*c^5*d*e + 20*a*b^6*c^2*d*e - 2*b^5*c*d*e*(-(4*a*c - b^2)^3)^(1/
2) + 6*a^2*b^2*c^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 5*a*b^4*c*e^2*(-(4*a*c - b^2)^3)^(1/2) - 66*a^2*b^4*c^3*d*e
+ 76*a^3*b^2*c^4*d*e - 3*a*b^2*c^3*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^3*c^2*d*e*(-(4*a*c - b^2)^3)^(1/2) - 6
*a^2*b*c^3*d*e*(-(4*a*c - b^2)^3)^(1/2))/(8*(a^7*b^4*e^4 + 16*a^7*c^4*d^4 + 16*a^9*c^2*e^4 - 8*a^8*b^2*c*e^4 -
2*a^6*b^5*d*e^3 + a^5*b^4*c^2*d^4 - 8*a^6*b^2*c^3*d^4 + a^5*b^6*d^2*e^2 + 32*a^8*c^3*d^2*e^2 - 2*a^5*b^5*c*d^
3*e - 32*a^7*b*c^3*d^3*e + 16*a^7*b^3*c*d*e^3 - 32*a^8*b*c^2*d*e^3 + 16*a^6*b^3*c^2*d^3*e - 6*a^6*b^4*c*d^2*e^
2)))^(1/2)*2i

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**4/(e*x**2+d)/(c*x**4+b*x**2+a),x)

[Out]

Timed out

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