3.127 \(\int \frac {x^2 (d+e x^2+f x^4+g x^6)}{(a+b x^2+c x^4)^2} \, dx\)

Optimal. Leaf size=471 \[ -\frac {x \left (x^2 \left (-c^2 (2 a f+b e)+b c (3 a g+b f)+b^3 (-g)+2 c^3 d\right )-a b^2 g+b c (a f+c d)-2 a c (c e-a g)\right )}{2 c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right ) \left (\frac {b^2 c (19 a g+c e)-4 b c^2 (2 a f+c d)+4 a c^2 (c e-5 a g)-3 b^4 g+b^3 c f}{\sqrt {b^2-4 a c}}-c^2 (b e-6 a f)-b c (13 a g+b f)+3 b^3 g+2 c^3 d\right )}{2 \sqrt {2} c^{5/2} \left (b^2-4 a c\right ) \sqrt {b-\sqrt {b^2-4 a c}}}-\frac {\tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {\sqrt {b^2-4 a c}+b}}\right ) \left (-\frac {b^2 c (19 a g+c e)-4 b c^2 (2 a f+c d)+4 a c^2 (c e-5 a g)-3 b^4 g+b^3 c f}{\sqrt {b^2-4 a c}}-c^2 (b e-6 a f)-b c (13 a g+b f)+3 b^3 g+2 c^3 d\right )}{2 \sqrt {2} c^{5/2} \left (b^2-4 a c\right ) \sqrt {\sqrt {b^2-4 a c}+b}}+\frac {g x}{c^2} \]

[Out]

g*x/c^2-1/2*x*(b*c*(a*f+c*d)-a*b^2*g-2*a*c*(-a*g+c*e)+(2*c^3*d-c^2*(2*a*f+b*e)-b^3*g+b*c*(3*a*g+b*f))*x^2)/c^2
/(-4*a*c+b^2)/(c*x^4+b*x^2+a)-1/4*arctan(x*2^(1/2)*c^(1/2)/(b-(-4*a*c+b^2)^(1/2))^(1/2))*(2*c^3*d-c^2*(-6*a*f+
b*e)+3*b^3*g-b*c*(13*a*g+b*f)+(b^3*c*f-4*b*c^2*(2*a*f+c*d)-3*b^4*g+4*a*c^2*(-5*a*g+c*e)+b^2*c*(19*a*g+c*e))/(-
4*a*c+b^2)^(1/2))/c^(5/2)/(-4*a*c+b^2)*2^(1/2)/(b-(-4*a*c+b^2)^(1/2))^(1/2)-1/4*arctan(x*2^(1/2)*c^(1/2)/(b+(-
4*a*c+b^2)^(1/2))^(1/2))*(2*c^3*d-c^2*(-6*a*f+b*e)+3*b^3*g-b*c*(13*a*g+b*f)+(-b^3*c*f+4*b*c^2*(2*a*f+c*d)+3*b^
4*g-4*a*c^2*(-5*a*g+c*e)-b^2*c*(19*a*g+c*e))/(-4*a*c+b^2)^(1/2))/c^(5/2)/(-4*a*c+b^2)*2^(1/2)/(b+(-4*a*c+b^2)^
(1/2))^(1/2)

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Rubi [A]  time = 6.66, antiderivative size = 471, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 4, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.114, Rules used = {1668, 1676, 1166, 205} \[ -\frac {x \left (x^2 \left (-c^2 (2 a f+b e)+b c (3 a g+b f)+b^3 (-g)+2 c^3 d\right )-a b^2 g+b c (a f+c d)-2 a c (c e-a g)\right )}{2 c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right ) \left (\frac {b^2 c (19 a g+c e)-4 b c^2 (2 a f+c d)+4 a c^2 (c e-5 a g)+b^3 c f-3 b^4 g}{\sqrt {b^2-4 a c}}-c^2 (b e-6 a f)-b c (13 a g+b f)+3 b^3 g+2 c^3 d\right )}{2 \sqrt {2} c^{5/2} \left (b^2-4 a c\right ) \sqrt {b-\sqrt {b^2-4 a c}}}-\frac {\tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {\sqrt {b^2-4 a c}+b}}\right ) \left (-\frac {b^2 c (19 a g+c e)-4 b c^2 (2 a f+c d)+4 a c^2 (c e-5 a g)+b^3 c f-3 b^4 g}{\sqrt {b^2-4 a c}}-c^2 (b e-6 a f)-b c (13 a g+b f)+3 b^3 g+2 c^3 d\right )}{2 \sqrt {2} c^{5/2} \left (b^2-4 a c\right ) \sqrt {\sqrt {b^2-4 a c}+b}}+\frac {g x}{c^2} \]

Antiderivative was successfully verified.

[In]

Int[(x^2*(d + e*x^2 + f*x^4 + g*x^6))/(a + b*x^2 + c*x^4)^2,x]

[Out]

(g*x)/c^2 - (x*(b*c*(c*d + a*f) - a*b^2*g - 2*a*c*(c*e - a*g) + (2*c^3*d - c^2*(b*e + 2*a*f) - b^3*g + b*c*(b*
f + 3*a*g))*x^2))/(2*c^2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((2*c^3*d - c^2*(b*e - 6*a*f) + 3*b^3*g - b*c*(b
*f + 13*a*g) + (b^3*c*f - 4*b*c^2*(c*d + 2*a*f) - 3*b^4*g + 4*a*c^2*(c*e - 5*a*g) + b^2*c*(c*e + 19*a*g))/Sqrt
[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)*Sqrt[
b - Sqrt[b^2 - 4*a*c]]) - ((2*c^3*d - c^2*(b*e - 6*a*f) + 3*b^3*g - b*c*(b*f + 13*a*g) - (b^3*c*f - 4*b*c^2*(c
*d + 2*a*f) - 3*b^4*g + 4*a*c^2*(c*e - 5*a*g) + b^2*c*(c*e + 19*a*g))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[
c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])

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 1668

Int[(Pq_)*(x_)^(m_)*((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4)^(p_), x_Symbol] :> With[{d = Coeff[PolynomialRemainde
r[x^m*Pq, a + b*x^2 + c*x^4, x], x, 0], e = Coeff[PolynomialRemainder[x^m*Pq, a + b*x^2 + c*x^4, x], x, 2]}, S
imp[(x*(a + b*x^2 + c*x^4)^(p + 1)*(a*b*e - d*(b^2 - 2*a*c) - c*(b*d - 2*a*e)*x^2))/(2*a*(p + 1)*(b^2 - 4*a*c)
), x] + Dist[1/(2*a*(p + 1)*(b^2 - 4*a*c)), Int[(a + b*x^2 + c*x^4)^(p + 1)*ExpandToSum[2*a*(p + 1)*(b^2 - 4*a
*c)*PolynomialQuotient[x^m*Pq, a + b*x^2 + c*x^4, x] + b^2*d*(2*p + 3) - 2*a*c*d*(4*p + 5) - a*b*e + c*(4*p +
7)*(b*d - 2*a*e)*x^2, x], x], x]] /; FreeQ[{a, b, c}, x] && PolyQ[Pq, x^2] && GtQ[Expon[Pq, x^2], 1] && NeQ[b^
2 - 4*a*c, 0] && LtQ[p, -1] && IGtQ[m/2, 0]

Rule 1676

Int[(Pq_)/((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4), x_Symbol] :> Int[ExpandIntegrand[Pq/(a + b*x^2 + c*x^4), x], x
] /; FreeQ[{a, b, c}, x] && PolyQ[Pq, x^2] && Expon[Pq, x^2] > 1

Rubi steps

\begin {align*} \int \frac {x^2 \left (d+e x^2+f x^4+g x^6\right )}{\left (a+b x^2+c x^4\right )^2} \, dx &=-\frac {x \left (b c (c d+a f)-a b^2 g-2 a c (c e-a g)+\left (2 c^3 d-c^2 (b e+2 a f)-b^3 g+b c (b f+3 a g)\right ) x^2\right )}{2 c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\int \frac {-\frac {a \left (b c (c d+a f)-a b^2 g-2 a c (c e-a g)\right )}{c^2}+\frac {a \left (2 c^3 d-c^2 (b e-6 a f)+b^3 g-b c (b f+5 a g)\right ) x^2}{c^2}+2 a \left (4 a-\frac {b^2}{c}\right ) g x^4}{a+b x^2+c x^4} \, dx}{2 a \left (b^2-4 a c\right )}\\ &=-\frac {x \left (b c (c d+a f)-a b^2 g-2 a c (c e-a g)+\left (2 c^3 d-c^2 (b e+2 a f)-b^3 g+b c (b f+3 a g)\right ) x^2\right )}{2 c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\int \left (-\frac {2 a \left (b^2-4 a c\right ) g}{c^2}-\frac {a \left (b c (c d+a f)-3 a b^2 g-2 a c (c e-5 a g)\right )-a \left (2 c^3 d-c^2 (b e-6 a f)+3 b^3 g-b c (b f+13 a g)\right ) x^2}{c^2 \left (a+b x^2+c x^4\right )}\right ) \, dx}{2 a \left (b^2-4 a c\right )}\\ &=\frac {g x}{c^2}-\frac {x \left (b c (c d+a f)-a b^2 g-2 a c (c e-a g)+\left (2 c^3 d-c^2 (b e+2 a f)-b^3 g+b c (b f+3 a g)\right ) x^2\right )}{2 c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {\int \frac {a \left (b c (c d+a f)-3 a b^2 g-2 a c (c e-5 a g)\right )-a \left (2 c^3 d-c^2 (b e-6 a f)+3 b^3 g-b c (b f+13 a g)\right ) x^2}{a+b x^2+c x^4} \, dx}{2 a c^2 \left (b^2-4 a c\right )}\\ &=\frac {g x}{c^2}-\frac {x \left (b c (c d+a f)-a b^2 g-2 a c (c e-a g)+\left (2 c^3 d-c^2 (b e+2 a f)-b^3 g+b c (b f+3 a g)\right ) x^2\right )}{2 c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\left (2 c^3 d-c^2 (b e-6 a f)+3 b^3 g-b c (b f+13 a g)-\frac {b^3 c f-4 b c^2 (c d+2 a f)-3 b^4 g+4 a c^2 (c e-5 a g)+b^2 c (c e+19 a g)}{\sqrt {b^2-4 a c}}\right ) \int \frac {1}{\frac {b}{2}+\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx}{4 c^2 \left (b^2-4 a c\right )}-\frac {\left (2 c^3 d-c^2 (b e-6 a f)+3 b^3 g-b c (b f+13 a g)+\frac {b^3 c f-4 b c^2 (c d+2 a f)-3 b^4 g+4 a c^2 (c e-5 a g)+b^2 c (c e+19 a g)}{\sqrt {b^2-4 a c}}\right ) \int \frac {1}{\frac {b}{2}-\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx}{4 c^2 \left (b^2-4 a c\right )}\\ &=\frac {g x}{c^2}-\frac {x \left (b c (c d+a f)-a b^2 g-2 a c (c e-a g)+\left (2 c^3 d-c^2 (b e+2 a f)-b^3 g+b c (b f+3 a g)\right ) x^2\right )}{2 c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\left (2 c^3 d-c^2 (b e-6 a f)+3 b^3 g-b c (b f+13 a g)+\frac {b^3 c f-4 b c^2 (c d+2 a f)-3 b^4 g+4 a c^2 (c e-5 a g)+b^2 c (c e+19 a g)}{\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 )}{2 \sqrt {2} c^{5/2} \left (b^2-4 a c\right ) \sqrt {b-\sqrt {b^2-4 a c}}}-\frac {\left (2 c^3 d-c^2 (b e-6 a f)+3 b^3 g-b c (b f+13 a g)-\frac {b^3 c f-4 b c^2 (c d+2 a f)-3 b^4 g+4 a c^2 (c e-5 a g)+b^2 c (c e+19 a g)}{\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 )}{2 \sqrt {2} c^{5/2} \left (b^2-4 a c\right ) \sqrt {b+\sqrt {b^2-4 a c}}}\\ \end {align*}

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Mathematica [A]  time = 1.95, size = 575, normalized size = 1.22 \[ \frac {-\frac {2 \sqrt {c} x \left (2 c \left (a^2 g-a c \left (e+f x^2\right )+c^2 d x^2\right )+b^2 \left (c f x^2-a g\right )+b c \left (a \left (f+3 g x^2\right )+c \left (d-e x^2\right )\right )+b^3 (-g) x^2\right )}{\left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\sqrt {2} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right ) \left (2 c^2 \left (-10 a^2 g+c d \sqrt {b^2-4 a c}+3 a f \sqrt {b^2-4 a c}+2 a c e\right )-b c \left (c e \sqrt {b^2-4 a c}+13 a g \sqrt {b^2-4 a c}+8 a c f+4 c^2 d\right )+b^2 c \left (-f \sqrt {b^2-4 a c}+19 a g+c e\right )+b^3 \left (3 g \sqrt {b^2-4 a c}+c f\right )-3 b^4 g\right )}{\left (b^2-4 a c\right )^{3/2} \sqrt {b-\sqrt {b^2-4 a c}}}-\frac {\sqrt {2} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {\sqrt {b^2-4 a c}+b}}\right ) \left (2 c^2 \left (10 a^2 g+c d \sqrt {b^2-4 a c}+3 a f \sqrt {b^2-4 a c}-2 a c e\right )+b c \left (-c e \sqrt {b^2-4 a c}-13 a g \sqrt {b^2-4 a c}+8 a c f+4 c^2 d\right )-b^2 c \left (f \sqrt {b^2-4 a c}+19 a g+c e\right )+b^3 \left (3 g \sqrt {b^2-4 a c}-c f\right )+3 b^4 g\right )}{\left (b^2-4 a c\right )^{3/2} \sqrt {\sqrt {b^2-4 a c}+b}}+4 \sqrt {c} g x}{4 c^{5/2}} \]

Antiderivative was successfully verified.

[In]

Integrate[(x^2*(d + e*x^2 + f*x^4 + g*x^6))/(a + b*x^2 + c*x^4)^2,x]

[Out]

(4*Sqrt[c]*g*x - (2*Sqrt[c]*x*(-(b^3*g*x^2) + b^2*(-(a*g) + c*f*x^2) + 2*c*(a^2*g + c^2*d*x^2 - a*c*(e + f*x^2
)) + b*c*(c*(d - e*x^2) + a*(f + 3*g*x^2))))/((b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (Sqrt[2]*(-3*b^4*g + b^2*c*
(c*e - Sqrt[b^2 - 4*a*c]*f + 19*a*g) + 2*c^2*(c*Sqrt[b^2 - 4*a*c]*d + 2*a*c*e + 3*a*Sqrt[b^2 - 4*a*c]*f - 10*a
^2*g) + b^3*(c*f + 3*Sqrt[b^2 - 4*a*c]*g) - b*c*(4*c^2*d + c*Sqrt[b^2 - 4*a*c]*e + 8*a*c*f + 13*a*Sqrt[b^2 - 4
*a*c]*g))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/((b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*
a*c]]) - (Sqrt[2]*(3*b^4*g - b^2*c*(c*e + Sqrt[b^2 - 4*a*c]*f + 19*a*g) + 2*c^2*(c*Sqrt[b^2 - 4*a*c]*d - 2*a*c
*e + 3*a*Sqrt[b^2 - 4*a*c]*f + 10*a^2*g) + b^3*(-(c*f) + 3*Sqrt[b^2 - 4*a*c]*g) + b*c*(4*c^2*d - c*Sqrt[b^2 -
4*a*c]*e + 8*a*c*f - 13*a*Sqrt[b^2 - 4*a*c]*g))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/((b^2
- 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]))/(4*c^(5/2))

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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(x^2*(g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm="fricas")

[Out]

Timed out

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giac [B]  time = 8.92, size = 9170, normalized size = 19.47 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2*(g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm="giac")

[Out]

g*x/c^2 - 1/2*(2*c^3*d*x^3 + b^2*c*f*x^3 - 2*a*c^2*f*x^3 - b^3*g*x^3 + 3*a*b*c*g*x^3 - b*c^2*x^3*e + b*c^2*d*x
+ a*b*c*f*x - a*b^2*g*x + 2*a^2*c*g*x - 2*a*c^2*x*e)/((c*x^4 + b*x^2 + a)*(b^2*c^2 - 4*a*c^3)) - 1/16*(2*(2*b
^2*c^5 - 8*a*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*
a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^4
- sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*c^5 - 2*(b^2 - 4*a*c)*c^5)*(b^2*c^2 - 4*a*c^3)^2*
d - (2*b^4*c^3 - 20*a*b^2*c^4 + 48*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c +
10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
- sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 12*sq
rt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^
2 - 4*a*c)*c)*b^2*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^
2*c^3 + 12*(b^2 - 4*a*c)*a*c^4)*(b^2*c^2 - 4*a*c^3)^2*f + (6*b^5*c^2 - 50*a*b^3*c^3 + 104*a^2*b*c^4 - 3*sqrt(2
)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 25*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4
*a*c)*c)*a*b^3*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 52*sqrt(2)*sqrt(b^2 - 4
*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)
*a*b^2*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 13*sqrt(2)*sqrt(b^2 - 4*a*c
)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 6*(b^2 - 4*a*c)*b^3*c^2 + 26*(b^2 - 4*a*c)*a*b*c^3)*(b^2*c^2 - 4*a
*c^3)^2*g - (2*b^3*c^4 - 8*a*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqr
t(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b
^2 - 4*a*c)*c)*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^4 - 2*(b^2 - 4*a*c)*b*c
^4)*(b^2*c^2 - 4*a*c^3)^2*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b
^2 - 4*a*c)*c)*a*b^3*c^6 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^6 + 2*b^5*c^6 + 16*sqrt(2)*sqrt(b*c
- sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^7 + sqrt(2)*sqrt(b*c - s
qrt(b^2 - 4*a*c)*c)*b^3*c^7 - 16*a*b^3*c^7 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^8 + 32*a^2*b*c^8
- 2*(b^2 - 4*a*c)*b^3*c^6 + 8*(b^2 - 4*a*c)*a*b*c^7)*d*abs(-b^2*c^2 + 4*a*c^3) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^
2 - 4*a*c)*c)*a*b^5*c^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - 2*sqrt(2)*sqrt(b*c - sqrt(b^
2 - 4*a*c)*c)*a*b^4*c^5 + 2*a*b^5*c^5 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 + 8*sqrt(2)*sqrt(
b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 - 16*a^2*b^3*c^6 -
4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 + 32*a^3*b*c^7 - 2*(b^2 - 4*a*c)*a*b^3*c^5 + 8*(b^2 - 4*a*
c)*a^2*b*c^6)*f*abs(-b^2*c^2 + 4*a*c^3) + 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 - 34*sqrt(2)*
sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 6*a*b^6*c^
4 + 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 44*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b
^3*c^5 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 68*a^2*b^4*c^5 - 160*sqrt(2)*sqrt(b*c - sqrt(b^
2 - 4*a*c)*c)*a^4*c^6 - 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 22*sqrt(2)*sqrt(b*c - sqrt(b^2
- 4*a*c)*c)*a^2*b^2*c^6 + 256*a^3*b^2*c^6 + 40*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^7 - 320*a^4*c^7 -
6*(b^2 - 4*a*c)*a*b^4*c^4 + 44*(b^2 - 4*a*c)*a^2*b^2*c^5 - 80*(b^2 - 4*a*c)*a^3*c^6)*g*abs(-b^2*c^2 + 4*a*c^3
) + 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c
^6 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 + 2*a*b^4*c^6 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*
c)*c)*a^3*c^7 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*
a*b^2*c^7 - 16*a^2*b^2*c^7 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^8 + 32*a^3*c^8 - 2*(b^2 - 4*a*c)*
a*b^2*c^6 + 8*(b^2 - 4*a*c)*a^2*c^7)*abs(-b^2*c^2 + 4*a*c^3)*e - 4*(2*b^6*c^9 - 16*a*b^4*c^10 + 32*a^2*b^2*c^1
1 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c -
sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^8 - 16*sqr
t(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sq
rt(b^2 - 4*a*c)*c)*a*b^3*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^9 + 4*sqrt(2)*s
qrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^10 - 2*(b^2 - 4*a*c)*b^4*c^9 + 8*(b^2 - 4*a*c)*a*b^2*
c^10)*d + (2*b^8*c^7 - 32*a*b^6*c^8 + 160*a^2*b^4*c^9 - 256*a^3*b^2*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
- sqrt(b^2 - 4*a*c)*c)*b^8*c^5 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 + 2*sq
rt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^6 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt
(b^2 - 4*a*c)*c)*a^2*b^4*c^7 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - sqrt(2
)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^
2 - 4*a*c)*c)*a^3*b^2*c^8 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 12*sqrt
(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt
(b^2 - 4*a*c)*c)*a^2*b^2*c^9 - 2*(b^2 - 4*a*c)*b^6*c^7 + 24*(b^2 - 4*a*c)*a*b^4*c^8 - 64*(b^2 - 4*a*c)*a^2*b^2
*c^9)*f - (6*b^9*c^6 - 86*a*b^7*c^7 + 440*a^2*b^5*c^8 - 928*a^3*b^3*c^9 + 640*a^4*b*c^10 - 3*sqrt(2)*sqrt(b^2
- 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^9*c^4 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c
)*a*b^7*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^5 - 220*sqrt(2)*sqrt(b^2 - 4*a
*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)
*a*b^6*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 464*sqrt(2)*sqrt(b^2 - 4*a*
c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)
*a^2*b^4*c^7 + 31*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - 320*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)
*c)*a^3*b^2*c^8 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 80*sqrt(2)*sqrt(b
^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 6*(b^2 - 4*a*c)*b^7*c^6 + 62*(b^2 - 4*a*c)*a*b^5*c^7 -
192*(b^2 - 4*a*c)*a^2*b^3*c^8 + 160*(b^2 - 4*a*c)*a^3*b*c^9)*g + (2*b^7*c^8 - 8*a*b^5*c^9 - 32*a^2*b^3*c^10 +
128*a^3*b*c^11 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a
*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^
6*c^7 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*s
qrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^8 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^
9 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sq
rt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^10 - 2*(b^2 - 4*a*c)*b^5*c^8 + 32*(b^2 - 4*a*c)*a^2*b*c^10)*e)*arctan(2*
sqrt(1/2)*x/sqrt((b^3*c^2 - 4*a*b*c^3 + sqrt((b^3*c^2 - 4*a*b*c^3)^2 - 4*(a*b^2*c^2 - 4*a^2*c^3)*(b^2*c^3 - 4*
a*c^4)))/(b^2*c^3 - 4*a*c^4)))/((a*b^6*c^5 - 12*a^2*b^4*c^6 - 2*a*b^5*c^6 + 48*a^3*b^2*c^7 + 16*a^2*b^3*c^7 +
a*b^4*c^7 - 64*a^4*c^8 - 32*a^3*b*c^8 - 8*a^2*b^2*c^8 + 16*a^3*c^9)*abs(-b^2*c^2 + 4*a*c^3)*abs(c)) + 1/16*(2*
(2*b^2*c^5 - 8*a*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 4*sqrt(2)*sqrt(b^2
- 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b
*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*c^5 - 2*(b^2 - 4*a*c)*c^5)*(b^2*c^2 - 4*a*c^3
)^2*d - (2*b^4*c^3 - 20*a*b^2*c^4 + 48*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4
*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt
(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 1
2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqr
t(b^2 - 4*a*c)*c)*b^2*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c
)*b^2*c^3 + 12*(b^2 - 4*a*c)*a*c^4)*(b^2*c^2 - 4*a*c^3)^2*f + (6*b^5*c^2 - 50*a*b^3*c^3 + 104*a^2*b*c^4 - 3*sq
rt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 25*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2
- 4*a*c)*c)*a*b^3*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 52*sqrt(2)*sqrt(b^2
- 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c
)*c)*a*b^2*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 13*sqrt(2)*sqrt(b^2 - 4
*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 6*(b^2 - 4*a*c)*b^3*c^2 + 26*(b^2 - 4*a*c)*a*b*c^3)*(b^2*c^2 -
4*a*c^3)^2*g - (2*b^3*c^4 - 8*a*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4
*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sq
rt(b^2 - 4*a*c)*c)*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^4 - 2*(b^2 - 4*a*c)
*b*c^4)*(b^2*c^2 - 4*a*c^3)^2*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^5 - 8*sqrt(2)*sqrt(b*c + sq
rt(b^2 - 4*a*c)*c)*a*b^3*c^6 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^6 - 2*b^5*c^6 + 16*sqrt(2)*sqrt
(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^7 + sqrt(2)*sqrt(b*c
+ sqrt(b^2 - 4*a*c)*c)*b^3*c^7 + 16*a*b^3*c^7 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^8 - 32*a^2*b*
c^8 + 2*(b^2 - 4*a*c)*b^3*c^6 - 8*(b^2 - 4*a*c)*a*b*c^7)*d*abs(-b^2*c^2 + 4*a*c^3) + 2*(sqrt(2)*sqrt(b*c + sqr
t(b^2 - 4*a*c)*c)*a*b^5*c^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - 2*sqrt(2)*sqrt(b*c + sqr
t(b^2 - 4*a*c)*c)*a*b^4*c^5 - 2*a*b^5*c^5 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 + 8*sqrt(2)*s
qrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 + 16*a^2*b^3*c^
6 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 - 32*a^3*b*c^7 + 2*(b^2 - 4*a*c)*a*b^3*c^5 - 8*(b^2 -
4*a*c)*a^2*b*c^6)*f*abs(-b^2*c^2 + 4*a*c^3) - 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 - 34*sqrt
(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - 6*a*b^
6*c^4 + 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 44*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a
^2*b^3*c^5 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 + 68*a^2*b^4*c^5 - 160*sqrt(2)*sqrt(b*c + sqr
t(b^2 - 4*a*c)*c)*a^4*c^6 - 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 22*sqrt(2)*sqrt(b*c + sqrt(
b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 256*a^3*b^2*c^6 + 40*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^7 + 320*a^4*c
^7 + 6*(b^2 - 4*a*c)*a*b^4*c^4 - 44*(b^2 - 4*a*c)*a^2*b^2*c^5 + 80*(b^2 - 4*a*c)*a^3*c^6)*g*abs(-b^2*c^2 + 4*a
*c^3) - 4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b
^2*c^6 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 - 2*a*b^4*c^6 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 -
4*a*c)*c)*a^3*c^7 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)
*c)*a*b^2*c^7 + 16*a^2*b^2*c^7 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^8 - 32*a^3*c^8 + 2*(b^2 - 4*a
*c)*a*b^2*c^6 - 8*(b^2 - 4*a*c)*a^2*c^7)*abs(-b^2*c^2 + 4*a*c^3)*e - 4*(2*b^6*c^9 - 16*a*b^4*c^10 + 32*a^2*b^2
*c^11 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b
*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^8 - 16
*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
+ sqrt(b^2 - 4*a*c)*c)*a*b^3*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^9 + 4*sqrt(
2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^10 - 2*(b^2 - 4*a*c)*b^4*c^9 + 8*(b^2 - 4*a*c)*a*
b^2*c^10)*d + (2*b^8*c^7 - 32*a*b^6*c^8 + 160*a^2*b^4*c^9 - 256*a^3*b^2*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(
b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^5 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 +
2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^6 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c +
sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - sq
rt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqr
t(b^2 - 4*a*c)*c)*a^3*b^2*c^8 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 12*
sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c +
sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 - 2*(b^2 - 4*a*c)*b^6*c^7 + 24*(b^2 - 4*a*c)*a*b^4*c^8 - 64*(b^2 - 4*a*c)*a^2
*b^2*c^9)*f - (6*b^9*c^6 - 86*a*b^7*c^7 + 440*a^2*b^5*c^8 - 928*a^3*b^3*c^9 + 640*a^4*b*c^10 - 3*sqrt(2)*sqrt(
b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^9*c^4 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*
c)*c)*a*b^7*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^5 - 220*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c
)*c)*a*b^6*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 464*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c
)*c)*a^2*b^4*c^7 + 31*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - 320*sqrt(2)*sqrt(b
^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*
a*c)*c)*a^3*b^2*c^8 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 80*sqrt(2)*sq
rt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 6*(b^2 - 4*a*c)*b^7*c^6 + 62*(b^2 - 4*a*c)*a*b^5*c
^7 - 192*(b^2 - 4*a*c)*a^2*b^3*c^8 + 160*(b^2 - 4*a*c)*a^3*b*c^9)*g + (2*b^7*c^8 - 8*a*b^5*c^9 - 32*a^2*b^3*c^
10 + 128*a^3*b*c^11 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 4*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c
)*b^6*c^7 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 - sqrt(2)*sqrt(b^2 - 4*a*
c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^8 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*
b*c^9 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 + 16*sqrt(2)*sqrt(b^2 - 4*a*c
)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^10 - 2*(b^2 - 4*a*c)*b^5*c^8 + 32*(b^2 - 4*a*c)*a^2*b*c^10)*e)*arcta
n(2*sqrt(1/2)*x/sqrt((b^3*c^2 - 4*a*b*c^3 - sqrt((b^3*c^2 - 4*a*b*c^3)^2 - 4*(a*b^2*c^2 - 4*a^2*c^3)*(b^2*c^3
- 4*a*c^4)))/(b^2*c^3 - 4*a*c^4)))/((a*b^6*c^5 - 12*a^2*b^4*c^6 - 2*a*b^5*c^6 + 48*a^3*b^2*c^7 + 16*a^2*b^3*c^
7 + a*b^4*c^7 - 64*a^4*c^8 - 32*a^3*b*c^8 - 8*a^2*b^2*c^8 + 16*a^3*c^9)*abs(-b^2*c^2 + 4*a*c^3)*abs(c))

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maple [B]  time = 0.05, size = 2300, normalized size = 4.88 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2*(g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x)

[Out]

-19/4/c/(4*a*c-b^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)*a*b^2*g-19/4/c/(4*a*c-b^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)*a*b^2*g+g*x/c^2+3/4/c^2/(4*a*c-b^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*g+5/(4*a*c-b^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)*a^2*g-3/4/c
^2/(4*a*c-b^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*g+5/(4*a*c-b^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)*a^2*g+1/4/(4*a*c-b^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*f-1/4/(4*a*c-b^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*e-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b
^2)^(1/2))*c)^(1/2)*b^2/c*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^
(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b^2*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/
(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b*e-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*a*e+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b*d+
1/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2
)^(1/2))*c)^(1/2)*c*x)+13/4/c/(4*a*c-b^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)*a*b*g+3/4/c^2/(4*a*c-b^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^4*g+3/4/c^2/(4*a*c-b^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^4*g-13/4/c/(4*a*c-
b^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)*a*b*g-1/2/c
^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*a*b^2*g+2/(4*a*c-b^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)*a*b*f-1/(4*a*c-b^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)*a*e-1/4/(4*a*c-b^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*f+1/(4*a*c-b^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*d+2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/
2)*a*b*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4
*a*c+b^2)^(1/2))*c)^(1/2)*a*c*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/c^2/(c*x^4+b*x^2+a)/(
4*a*c-b^2)*x^3*b^3*g+1/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b^2*f+1/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*a^2*g+3/2/c
/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a*b*g+1/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*a*b*f-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^
(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b^3/c*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+c/
(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*d-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a*f-3/2/(4*a*c-b^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)*a*f+1/4/(4*a*c-b^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-1/2/(4*a*c-b^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)*d+3/2/(4*a*c-b^2)*2
^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/4/(4*a*c-b^
2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/2/(4*a*
c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*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(x^2*(g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm="maxima")

[Out]

-1/2*((2*c^3*d - b*c^2*e + (b^2*c - 2*a*c^2)*f - (b^3 - 3*a*b*c)*g)*x^3 + (b*c^2*d - 2*a*c^2*e + a*b*c*f - (a*
b^2 - 2*a^2*c)*g)*x)/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^4 + (b^3*c^2 - 4*a*b*c^3)*x^2) + g*x/c^2 +
1/2*integrate((b*c^2*d - 2*a*c^2*e + a*b*c*f - (2*c^3*d - b*c^2*e - (b^2*c - 6*a*c^2)*f + (3*b^3 - 13*a*b*c)*
g)*x^2 - (3*a*b^2 - 10*a^2*c)*g)/(c*x^4 + b*x^2 + a), x)/(b^2*c^2 - 4*a*c^3)

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mupad [B]  time = 4.22, size = 36589, normalized size = 77.68 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x^2*(d + e*x^2 + f*x^4 + g*x^6))/(a + b*x^2 + c*x^4)^2,x)

[Out]

((x^3*(2*c^3*d - b^3*g - 2*a*c^2*f - b*c^2*e + b^2*c*f + 3*a*b*c*g))/(2*(4*a*c - b^2)) + (x*(b*c^2*d - 2*a*c^2
*e - a*b^2*g + 2*a^2*c*g + a*b*c*f))/(2*(4*a*c - b^2)))/(a*c^2 + c^3*x^4 + b*c^2*x^2) - atan(((((10240*a^5*c^7
*g - 16*b^7*c^5*d - 2048*a^4*c^8*e - 768*a^2*b^3*c^7*d - 384*a^2*b^4*c^6*e + 1536*a^3*b^2*c^7*e + 192*a^2*b^5*
c^5*f - 768*a^3*b^3*c^6*f - 736*a^2*b^6*c^4*g + 4224*a^3*b^4*c^5*g - 10752*a^4*b^2*c^6*g + 192*a*b^5*c^6*d + 1
024*a^3*b*c^8*d + 32*a*b^6*c^5*e - 16*a*b^7*c^4*f + 1024*a^4*b*c^7*f + 48*a*b^8*c^3*g)/(8*(64*a^3*c^6 - b^6*c^
3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5)) - (x*((c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^5*d^2 - 9*a*b^13*g^2 + 768
*a^4*b*c^9*d^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 - a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 384
0*a^6*b*c^7*f^2 - 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5
*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c
^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 + 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c
^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 - 25*a^3*c^2*g^2*(-(4*a*c - b^2
)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6
*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f + 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*
e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f
+ 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g
- 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7
*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g + 10*a^2*c^3*e*g*
(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*
c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g - a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 51*a^2*b^2*c*g^2*(
-(4*a*c - b^2)^9)^(1/2) - 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 6
*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 44*a^2*b*c^2*f*g*(-(4*a*c -
b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*
a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2)*(16*b^7*c^5 - 192*a*b^5*c^6 - 1024*a^3*b*c^8 + 768*a^2*b^3*c^7))/(2*(
16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))*((c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^5*d^2 - 9*a*b^13*g^2 + 768*a^
4*b*c^9*d^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 - a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a
^6*b*c^7*f^2 - 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^
7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*
f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 + 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*
g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 - 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9
)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*
b^9*c^4*d*f + 3584*a^5*b*c^8*d*f + 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f
+ 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 9
60*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g -
192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*
f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g + 10*a^2*c^3*e*g*(-(
4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5
*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g - a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 51*a^2*b^2*c*g^2*(-(4
*a*c - b^2)^9)^(1/2) - 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 6*a*
b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 44*a^2*b*c^2*f*g*(-(4*a*c - b^
2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5
*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2) - (x*(9*b^8*g^2 - 8*a*c^7*d^2 + 8*a^2*c^6*e^2 + 10*b^2*c^6*d^2 - 72*a^3*
c^5*f^2 + b^4*c^4*e^2 + 200*a^4*c^4*g^2 + b^6*c^2*f^2 + 2*a*b^2*c^5*e^2 - 16*a*b^4*c^3*f^2 - 6*b^7*c*f*g + 74*
a^2*b^2*c^4*f^2 + 481*a^2*b^4*c^2*g^2 - 718*a^3*b^2*c^3*g^2 - 114*a*b^6*c*g^2 - 48*a^2*c^6*d*f - 6*b^3*c^5*d*e
- 6*b^4*c^4*d*f - 80*a^3*c^5*e*g + 18*b^5*c^3*d*g + 2*b^5*c^3*e*f - 6*b^6*c^2*e*g + 52*a*b^2*c^5*d*f - 126*a*
b^3*c^4*d*g - 14*a*b^3*c^4*e*f + 184*a^2*b*c^5*d*g - 8*a^2*b*c^5*e*f + 32*a*b^4*c^3*e*g + 86*a*b^5*c^2*f*g + 4
72*a^3*b*c^4*f*g + 4*a^2*b^2*c^4*e*g - 374*a^2*b^3*c^3*f*g - 8*a*b*c^6*d*e))/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^
2*c^4)))*((c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^5*d^2 - 9*a*b^13*g^2 + 768*a^4*b*c^9*d^2 - a*b^9*c^4*e^2 +
768*a^5*b*c^8*e^2 - a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 - 9*a*b^4*g^2*(-
(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 +
96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 -
3840*a^5*b^3*c^6*f^2 + 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 -
30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 - 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e +
5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*
d*f + 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^
6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4
*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^
4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*
a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g + 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a
^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g
+ 6*a*b^12*c*f*g - a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b
*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^
(1/2) + 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^
11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)
))^(1/2)*1i - (((10240*a^5*c^7*g - 16*b^7*c^5*d - 2048*a^4*c^8*e - 768*a^2*b^3*c^7*d - 384*a^2*b^4*c^6*e + 153
6*a^3*b^2*c^7*e + 192*a^2*b^5*c^5*f - 768*a^3*b^3*c^6*f - 736*a^2*b^6*c^4*g + 4224*a^3*b^4*c^5*g - 10752*a^4*b
^2*c^6*g + 192*a*b^5*c^6*d + 1024*a^3*b*c^8*d + 32*a*b^6*c^5*e - 16*a*b^7*c^4*f + 1024*a^4*b*c^7*f + 48*a*b^8*
c^3*g)/(8*(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5)) + (x*((c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^
9*c^5*d^2 - 9*a*b^13*g^2 + 768*a^4*b*c^9*d^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 - a*c^4*e^2*(-(4*a*c - b^2)^9
)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 - 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26
880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a
^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 + 9*a^2*c^3*f^2*(-(4*a*c -
b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 -
25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*
c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f + 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*
a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*
c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*
c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*
b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5
*b^3*c^6*e*g + 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^
4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g - a*b^2*c^2*f^2*(-(4*a*c - b^2)
^9)^(1/2) + 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 2*a*b*c^3*e*
f*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2)
- 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*
c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2)*(16*b^7*c^5 - 192*a*b^5*c^6 - 1024*a^3*
b*c^8 + 768*a^2*b^3*c^7))/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))*((c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c
^5*d^2 - 9*a*b^13*g^2 + 768*a^4*b*c^9*d^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 - a*c^4*e^2*(-(4*a*c - b^2)^9)^(
1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 - 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880
*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*
b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 + 9*a^2*c^3*f^2*(-(4*a*c - b^2
)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 - 25
*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7
*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f + 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b
^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7
*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4
*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2
*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^
3*c^6*e*g + 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b
^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g - a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)
^(1/2) + 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 2*a*b*c^3*e*f*(
-(4*a*c - b^2)^9)^(1/2) + 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) -
44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7
- 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2) + (x*(9*b^8*g^2 - 8*a*c^7*d^2 + 8*a^2*c^6*
e^2 + 10*b^2*c^6*d^2 - 72*a^3*c^5*f^2 + b^4*c^4*e^2 + 200*a^4*c^4*g^2 + b^6*c^2*f^2 + 2*a*b^2*c^5*e^2 - 16*a*b
^4*c^3*f^2 - 6*b^7*c*f*g + 74*a^2*b^2*c^4*f^2 + 481*a^2*b^4*c^2*g^2 - 718*a^3*b^2*c^3*g^2 - 114*a*b^6*c*g^2 -
48*a^2*c^6*d*f - 6*b^3*c^5*d*e - 6*b^4*c^4*d*f - 80*a^3*c^5*e*g + 18*b^5*c^3*d*g + 2*b^5*c^3*e*f - 6*b^6*c^2*e
*g + 52*a*b^2*c^5*d*f - 126*a*b^3*c^4*d*g - 14*a*b^3*c^4*e*f + 184*a^2*b*c^5*d*g - 8*a^2*b*c^5*e*f + 32*a*b^4*
c^3*e*g + 86*a*b^5*c^2*f*g + 472*a^3*b*c^4*f*g + 4*a^2*b^2*c^4*e*g - 374*a^2*b^3*c^3*f*g - 8*a*b*c^6*d*e))/(2*
(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))*((c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^5*d^2 - 9*a*b^13*g^2 + 768*a
^4*b*c^9*d^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 - a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*
a^6*b*c^7*f^2 - 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c
^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4
*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 + 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2
*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 - 25*a^3*c^2*g^2*(-(4*a*c - b^2)^
9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a
*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f + 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*
f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f +
960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g -
192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e
*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g + 10*a^2*c^3*e*g*(-
(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^
5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g - a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 51*a^2*b^2*c*g^2*(-(
4*a*c - b^2)^9)^(1/2) - 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 6*a
*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 44*a^2*b*c^2*f*g*(-(4*a*c - b
^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^
5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2)*1i)/((((10240*a^5*c^7*g - 16*b^7*c^5*d - 2048*a^4*c^8*e - 768*a^2*b^3*c
^7*d - 384*a^2*b^4*c^6*e + 1536*a^3*b^2*c^7*e + 192*a^2*b^5*c^5*f - 768*a^3*b^3*c^6*f - 736*a^2*b^6*c^4*g + 42
24*a^3*b^4*c^5*g - 10752*a^4*b^2*c^6*g + 192*a*b^5*c^6*d + 1024*a^3*b*c^8*d + 32*a*b^6*c^5*e - 16*a*b^7*c^4*f
+ 1024*a^4*b*c^7*f + 48*a*b^8*c^3*g)/(8*(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5)) - (x*((c^5*d^2
*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^5*d^2 - 9*a*b^13*g^2 + 768*a^4*b*c^9*d^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2
- a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 - 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(
1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^
2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f
^2 + 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4
*g^2 + 44800*a^6*b^3*c^5*g^2 - 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g -
3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f + 6*a*c^4*d*f*
(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*
a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324
*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 12
8*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g -
1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g + 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g +
1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g -
a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b*c^3*d*g*(-(4*a*c
- b^2)^9)^(1/2) - 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^2*c^
2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 -
24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2)*(16*b^7*c
^5 - 192*a*b^5*c^6 - 1024*a^3*b*c^8 + 768*a^2*b^3*c^7))/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))*((c^5*d^2*(-
(4*a*c - b^2)^9)^(1/2) - b^9*c^5*d^2 - 9*a*b^13*g^2 + 768*a^4*b*c^9*d^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 -
a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 - 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2
) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 -
512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2
+ 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^
2 + 44800*a^6*b^3*c^5*g^2 - 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 30
72*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f + 6*a*c^4*d*f*(-(
4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2
*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^
2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a
^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 134
4*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g + 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 154
8*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g - a*
b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b*c^3*d*g*(-(4*a*c - b
^2)^9)^(1/2) - 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^2*c^2*e
*g*(-(4*a*c - b^2)^9)^(1/2) - 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*
a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2) - (x*(9*b^8*
g^2 - 8*a*c^7*d^2 + 8*a^2*c^6*e^2 + 10*b^2*c^6*d^2 - 72*a^3*c^5*f^2 + b^4*c^4*e^2 + 200*a^4*c^4*g^2 + b^6*c^2*
f^2 + 2*a*b^2*c^5*e^2 - 16*a*b^4*c^3*f^2 - 6*b^7*c*f*g + 74*a^2*b^2*c^4*f^2 + 481*a^2*b^4*c^2*g^2 - 718*a^3*b^
2*c^3*g^2 - 114*a*b^6*c*g^2 - 48*a^2*c^6*d*f - 6*b^3*c^5*d*e - 6*b^4*c^4*d*f - 80*a^3*c^5*e*g + 18*b^5*c^3*d*g
+ 2*b^5*c^3*e*f - 6*b^6*c^2*e*g + 52*a*b^2*c^5*d*f - 126*a*b^3*c^4*d*g - 14*a*b^3*c^4*e*f + 184*a^2*b*c^5*d*g
- 8*a^2*b*c^5*e*f + 32*a*b^4*c^3*e*g + 86*a*b^5*c^2*f*g + 472*a^3*b*c^4*f*g + 4*a^2*b^2*c^4*e*g - 374*a^2*b^3
*c^3*f*g - 8*a*b*c^6*d*e))/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))*((c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*
c^5*d^2 - 9*a*b^13*g^2 + 768*a^4*b*c^9*d^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 - a*c^4*e^2*(-(4*a*c - b^2)^9)^
(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 - 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 2688
0*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2
*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 + 9*a^2*c^3*f^2*(-(4*a*c - b^
2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 - 2
5*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^
7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f + 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*
b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^
7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^
4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^
2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b
^3*c^6*e*g + 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*
b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g - a*b^2*c^2*f^2*(-(4*a*c - b^2)^9
)^(1/2) + 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 2*a*b*c^3*e*f*
(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) -
44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^
7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2) + (((10240*a^5*c^7*g - 16*b^7*c^5*d - 204
8*a^4*c^8*e - 768*a^2*b^3*c^7*d - 384*a^2*b^4*c^6*e + 1536*a^3*b^2*c^7*e + 192*a^2*b^5*c^5*f - 768*a^3*b^3*c^6
*f - 736*a^2*b^6*c^4*g + 4224*a^3*b^4*c^5*g - 10752*a^4*b^2*c^6*g + 192*a*b^5*c^6*d + 1024*a^3*b*c^8*d + 32*a*
b^6*c^5*e - 16*a*b^7*c^4*f + 1024*a^4*b*c^7*f + 48*a*b^8*c^3*g)/(8*(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a
^2*b^2*c^5)) + (x*((c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^5*d^2 - 9*a*b^13*g^2 + 768*a^4*b*c^9*d^2 - a*b^9*
c^4*e^2 + 768*a^5*b*c^8*e^2 - a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 - 9*a*b
^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*
c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c
^5*f^2 - 3840*a^5*b^3*c^6*f^2 + 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*
c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 - 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c
^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a
^5*b*c^8*d*f + 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g
+ 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f -
3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f
+ 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e
*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g + 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2
) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2
*c^6*f*g + 6*a*b^12*c*f*g - a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2)
- 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^3*c*f*g*(-(4*a*c -
b^2)^9)^(1/2) + 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(40
96*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*
b^2*c^10)))^(1/2)*(16*b^7*c^5 - 192*a*b^5*c^6 - 1024*a^3*b*c^8 + 768*a^2*b^3*c^7))/(2*(16*a^2*c^5 + b^4*c^3 -
8*a*b^2*c^4)))*((c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^5*d^2 - 9*a*b^13*g^2 + 768*a^4*b*c^9*d^2 - a*b^9*c^4
*e^2 + 768*a^5*b*c^8*e^2 - a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 - 9*a*b^4*
g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8
*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*
f^2 - 3840*a^5*b^3*c^6*f^2 + 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3
*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 - 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*
d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*
b*c^8*d*f + 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1
536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 30
72*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7
296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g
+ 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g + 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) -
152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^
6*f*g + 6*a*b^12*c*f*g - a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) -
18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^3*c*f*g*(-(4*a*c - b^
2)^9)^(1/2) + 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*
a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2
*c^10)))^(1/2) + (x*(9*b^8*g^2 - 8*a*c^7*d^2 + 8*a^2*c^6*e^2 + 10*b^2*c^6*d^2 - 72*a^3*c^5*f^2 + b^4*c^4*e^2 +
200*a^4*c^4*g^2 + b^6*c^2*f^2 + 2*a*b^2*c^5*e^2 - 16*a*b^4*c^3*f^2 - 6*b^7*c*f*g + 74*a^2*b^2*c^4*f^2 + 481*a
^2*b^4*c^2*g^2 - 718*a^3*b^2*c^3*g^2 - 114*a*b^6*c*g^2 - 48*a^2*c^6*d*f - 6*b^3*c^5*d*e - 6*b^4*c^4*d*f - 80*a
^3*c^5*e*g + 18*b^5*c^3*d*g + 2*b^5*c^3*e*f - 6*b^6*c^2*e*g + 52*a*b^2*c^5*d*f - 126*a*b^3*c^4*d*g - 14*a*b^3*
c^4*e*f + 184*a^2*b*c^5*d*g - 8*a^2*b*c^5*e*f + 32*a*b^4*c^3*e*g + 86*a*b^5*c^2*f*g + 472*a^3*b*c^4*f*g + 4*a^
2*b^2*c^4*e*g - 374*a^2*b^3*c^3*f*g - 8*a*b*c^6*d*e))/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))*((c^5*d^2*(-(4
*a*c - b^2)^9)^(1/2) - b^9*c^5*d^2 - 9*a*b^13*g^2 + 768*a^4*b*c^9*d^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 - a*
c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 - 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2)
+ 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 5
12*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 +
9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2
+ 44800*a^6*b^3*c^5*g^2 - 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072
*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f + 6*a*c^4*d*f*(-(4*
a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b
^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*
b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4
*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*
a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g + 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*
a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g - a*b^
2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b*c^3*d*g*(-(4*a*c - b^2
)^9)^(1/2) - 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^2*c^2*e*g
*(-(4*a*c - b^2)^9)^(1/2) - 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^
2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2) - (8*a*c^7*d^3
+ 9*b^8*d*g^2 + 6*b^2*c^6*d^3 - 63*a^3*b^5*g^3 + 216*a^4*c^4*f^3 - 3*a*b^3*c^4*e^3 - 4*a^2*b*c^5*e^3 + 8*a^2*
c^6*d*e^2 + 573*a^4*b^3*c*g^3 - 1300*a^5*b*c^2*g^3 + 72*a^2*c^6*d^2*f + 216*a^3*c^5*d*f^2 - 5*b^3*c^5*d^2*e +
b^4*c^4*d*e^2 + 24*a^3*c^5*e^2*f + 200*a^4*c^4*d*g^2 - 5*b^4*c^4*d^2*f + b^6*c^2*d*f^2 + 45*a^2*b^6*f*g^2 + 15
*b^5*c^3*d^2*g + 600*a^5*c^3*f*g^2 + 5*a^2*b^4*c^2*f^3 - 66*a^3*b^2*c^3*f^3 - 27*a*b^7*e*g^2 - 28*a*b*c^6*d^2*
e - 78*a*b^6*c*d*g^2 - 80*a^3*c^5*d*e*g + 2*b^5*c^3*d*e*f - 6*b^6*c^2*d*e*g - 240*a^4*c^4*e*f*g + 18*a*b^2*c^5
*d*e^2 + 26*a*b^2*c^5*d^2*f - 12*a*b^4*c^3*d*f^2 - 53*a*b^3*c^4*d^2*g - 6*a*b^4*c^3*e^2*f - 3*a*b^5*c^2*e*f^2
- 76*a^2*b*c^5*d^2*g - 204*a^3*b*c^4*e*f^2 + 18*a*b^5*c^2*e^2*g + 279*a^2*b^5*c*e*g^2 - 12*a^3*b*c^4*e^2*g + 4
20*a^4*b*c^3*e*g^2 - 30*a^2*b^5*c*f^2*g - 402*a^3*b^4*c*f*g^2 - 924*a^4*b*c^3*f^2*g - 6*b^7*c*d*f*g + 2*a^2*b^
2*c^4*d*f^2 + 42*a^2*b^2*c^4*e^2*f + 51*a^2*b^3*c^3*e*f^2 + 133*a^2*b^4*c^2*d*g^2 + 114*a^3*b^2*c^3*d*g^2 - 81
*a^2*b^3*c^3*e^2*g - 801*a^3*b^3*c^2*e*g^2 + 339*a^3*b^3*c^2*f^2*g + 762*a^4*b^2*c^2*f*g^2 + 18*a*b^6*c*e*f*g
+ 6*a*b^3*c^4*d*e*f - 152*a^2*b*c^5*d*e*f - 28*a*b^4*c^3*d*e*g + 62*a*b^5*c^2*d*f*g - 536*a^3*b*c^4*d*f*g + 27
6*a^2*b^2*c^4*d*e*g - 42*a^2*b^3*c^3*d*f*g - 246*a^2*b^4*c^2*e*f*g + 804*a^3*b^2*c^3*e*f*g)/(4*(64*a^3*c^6 - b
^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5))))*((c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^5*d^2 - 9*a*b^13*g^2 + 7
68*a^4*b*c^9*d^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 - a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3
840*a^6*b*c^7*f^2 - 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b
^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7
*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 + 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9
*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 - 25*a^3*c^2*g^2*(-(4*a*c - b
^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e +
6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f + 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^
3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*
f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d
*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c
^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g + 10*a^2*c^3*e*
g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^
4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g - a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 51*a^2*b^2*c*g^2
*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) +
6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 44*a^2*b*c^2*f*g*(-(4*a*c
- b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 384
0*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2)*2i - atan(((((10240*a^5*c^7*g - 16*b^7*c^5*d - 2048*a^4*c^8*e - 768
*a^2*b^3*c^7*d - 384*a^2*b^4*c^6*e + 1536*a^3*b^2*c^7*e + 192*a^2*b^5*c^5*f - 768*a^3*b^3*c^6*f - 736*a^2*b^6*
c^4*g + 4224*a^3*b^4*c^5*g - 10752*a^4*b^2*c^6*g + 192*a*b^5*c^6*d + 1024*a^3*b*c^8*d + 32*a*b^6*c^5*e - 16*a*
b^7*c^4*f + 1024*a^4*b*c^7*f + 48*a*b^8*c^3*g)/(8*(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5)) - (x
*((768*a^4*b*c^9*d^2 - b^9*c^5*d^2 - c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a*b^13*g^2 - a*b^9*c^4*e^2 + 768*a^5
*b*c^8*e^2 + a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 + 9*a*b^4*g^2*(-(4*a*c -
b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*
b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5
*b^3*c^6*f^2 - 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a
^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 + 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6
*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f - 6*
a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*
e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7
*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^
6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*
c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g - 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*
c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^
12*c*f*g + a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 18*a*b*c^3*d*g
*(-(4*a*c - b^2)^9)^(1/2) + 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) -
6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b
^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2)
*(16*b^7*c^5 - 192*a*b^5*c^6 - 1024*a^3*b*c^8 + 768*a^2*b^3*c^7))/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))*((
768*a^4*b*c^9*d^2 - b^9*c^5*d^2 - c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a*b^13*g^2 - a*b^9*c^4*e^2 + 768*a^5*b*
c^8*e^2 + a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 + 9*a*b^4*g^2*(-(4*a*c - b^
2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5
*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^
3*c^6*f^2 - 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*
b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 + 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^
8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f - 6*a*c
^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g
- 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*
f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d
*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4
*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g - 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2
*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*
c*f*g + a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 18*a*b*c^3*d*g*(-
(4*a*c - b^2)^9)^(1/2) + 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a
*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12
*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2) -
(x*(9*b^8*g^2 - 8*a*c^7*d^2 + 8*a^2*c^6*e^2 + 10*b^2*c^6*d^2 - 72*a^3*c^5*f^2 + b^4*c^4*e^2 + 200*a^4*c^4*g^2
+ b^6*c^2*f^2 + 2*a*b^2*c^5*e^2 - 16*a*b^4*c^3*f^2 - 6*b^7*c*f*g + 74*a^2*b^2*c^4*f^2 + 481*a^2*b^4*c^2*g^2 -
718*a^3*b^2*c^3*g^2 - 114*a*b^6*c*g^2 - 48*a^2*c^6*d*f - 6*b^3*c^5*d*e - 6*b^4*c^4*d*f - 80*a^3*c^5*e*g + 18*b
^5*c^3*d*g + 2*b^5*c^3*e*f - 6*b^6*c^2*e*g + 52*a*b^2*c^5*d*f - 126*a*b^3*c^4*d*g - 14*a*b^3*c^4*e*f + 184*a^2
*b*c^5*d*g - 8*a^2*b*c^5*e*f + 32*a*b^4*c^3*e*g + 86*a*b^5*c^2*f*g + 472*a^3*b*c^4*f*g + 4*a^2*b^2*c^4*e*g - 3
74*a^2*b^3*c^3*f*g - 8*a*b*c^6*d*e))/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))*((768*a^4*b*c^9*d^2 - b^9*c^5*d
^2 - c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a*b^13*g^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 + a*c^4*e^2*(-(4*a*c
- b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 + 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*
g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^
2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 - 9*a^2*c^3*f^2*(-(
4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c
^5*g^2 + 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15
360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f - 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/
2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*
a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*
a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10
752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g +
512*a^5*b^3*c^6*e*g - 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g -
8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g + a*b^2*c^2*f^2*(-(4*a*
c - b^2)^9)^(1/2) - 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) + 2*a*
b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^
9)^(1/2) + 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*
a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2)*1i - (((10240*a^5*c^7*g - 16*b^
7*c^5*d - 2048*a^4*c^8*e - 768*a^2*b^3*c^7*d - 384*a^2*b^4*c^6*e + 1536*a^3*b^2*c^7*e + 192*a^2*b^5*c^5*f - 76
8*a^3*b^3*c^6*f - 736*a^2*b^6*c^4*g + 4224*a^3*b^4*c^5*g - 10752*a^4*b^2*c^6*g + 192*a*b^5*c^6*d + 1024*a^3*b*
c^8*d + 32*a*b^6*c^5*e - 16*a*b^7*c^4*f + 1024*a^4*b*c^7*f + 48*a*b^8*c^3*g)/(8*(64*a^3*c^6 - b^6*c^3 + 12*a*b
^4*c^4 - 48*a^2*b^2*c^5)) + (x*((768*a^4*b*c^9*d^2 - b^9*c^5*d^2 - c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a*b^13
*g^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 + a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^
7*f^2 + 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 -
512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1
504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 - 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 1
0656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 + 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2)
- 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4
*d*f + 3584*a^5*b*c^8*d*f - 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*
b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*
b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3
*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*
a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g - 10*a^2*c^3*e*g*(-(4*a*c -
b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g -
30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g + a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 51*a^2*b^2*c*g^2*(-(4*a*c -
b^2)^9)^(1/2) + 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) + 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^3*c*f
*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(
1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^
9 - 6144*a^6*b^2*c^10)))^(1/2)*(16*b^7*c^5 - 192*a*b^5*c^6 - 1024*a^3*b*c^8 + 768*a^2*b^3*c^7))/(2*(16*a^2*c^5
+ b^4*c^3 - 8*a*b^2*c^4)))*((768*a^4*b*c^9*d^2 - b^9*c^5*d^2 - c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a*b^13*g^
2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 + a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f
^2 + 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 51
2*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504
*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 - 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 1065
6*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 + 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) -
1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*
f + 3584*a^5*b*c^8*d*f - 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^1
1*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5
*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^
6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2
*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g - 10*a^2*c^3*e*g*(-(4*a*c - b^
2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 307
20*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g + a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 51*a^2*b^2*c*g^2*(-(4*a*c - b^2
)^9)^(1/2) + 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) + 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^3*c*f*g*
(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2
))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 -
6144*a^6*b^2*c^10)))^(1/2) + (x*(9*b^8*g^2 - 8*a*c^7*d^2 + 8*a^2*c^6*e^2 + 10*b^2*c^6*d^2 - 72*a^3*c^5*f^2 +
b^4*c^4*e^2 + 200*a^4*c^4*g^2 + b^6*c^2*f^2 + 2*a*b^2*c^5*e^2 - 16*a*b^4*c^3*f^2 - 6*b^7*c*f*g + 74*a^2*b^2*c^
4*f^2 + 481*a^2*b^4*c^2*g^2 - 718*a^3*b^2*c^3*g^2 - 114*a*b^6*c*g^2 - 48*a^2*c^6*d*f - 6*b^3*c^5*d*e - 6*b^4*c
^4*d*f - 80*a^3*c^5*e*g + 18*b^5*c^3*d*g + 2*b^5*c^3*e*f - 6*b^6*c^2*e*g + 52*a*b^2*c^5*d*f - 126*a*b^3*c^4*d*
g - 14*a*b^3*c^4*e*f + 184*a^2*b*c^5*d*g - 8*a^2*b*c^5*e*f + 32*a*b^4*c^3*e*g + 86*a*b^5*c^2*f*g + 472*a^3*b*c
^4*f*g + 4*a^2*b^2*c^4*e*g - 374*a^2*b^3*c^3*f*g - 8*a*b*c^6*d*e))/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))*(
(768*a^4*b*c^9*d^2 - b^9*c^5*d^2 - c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a*b^13*g^2 - a*b^9*c^4*e^2 + 768*a^5*b
*c^8*e^2 + a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 + 9*a*b^4*g^2*(-(4*a*c - b
^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^
5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b
^3*c^6*f^2 - 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5
*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 + 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c
^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f - 6*a*
c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*
g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d
*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*
d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^
4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g - 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^
2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12
*c*f*g + a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 18*a*b*c^3*d*g*(
-(4*a*c - b^2)^9)^(1/2) + 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) - 6*
a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^1
2*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2)*1
i)/((((10240*a^5*c^7*g - 16*b^7*c^5*d - 2048*a^4*c^8*e - 768*a^2*b^3*c^7*d - 384*a^2*b^4*c^6*e + 1536*a^3*b^2*
c^7*e + 192*a^2*b^5*c^5*f - 768*a^3*b^3*c^6*f - 736*a^2*b^6*c^4*g + 4224*a^3*b^4*c^5*g - 10752*a^4*b^2*c^6*g +
192*a*b^5*c^6*d + 1024*a^3*b*c^8*d + 32*a*b^6*c^5*e - 16*a*b^7*c^4*f + 1024*a^4*b*c^7*f + 48*a*b^8*c^3*g)/(8*
(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5)) - (x*((768*a^4*b*c^9*d^2 - b^9*c^5*d^2 - c^5*d^2*(-(4*
a*c - b^2)^9)^(1/2) - 9*a*b^13*g^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 + a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) -
a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 + 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*
c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3
*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 - 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1
/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 + 25*a^3*c^
2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g +
12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f - 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3
*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e -
128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f -
2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*
g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e
*g - 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*
f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g + a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2)
- 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) + 2*a*b*c^3*e*f*(-(4*a*c
- b^2)^9)^(1/2) - 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^2*
b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280
*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2)*(16*b^7*c^5 - 192*a*b^5*c^6 - 1024*a^3*b*c^8 + 76
8*a^2*b^3*c^7))/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))*((768*a^4*b*c^9*d^2 - b^9*c^5*d^2 - c^5*d^2*(-(4*a*c
- b^2)^9)^(1/2) - 9*a*b^13*g^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 + a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b
^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 + 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6
*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^
2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 - 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2)
- 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 + 25*a^3*c^2*g
^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*
a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f - 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*
g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128
*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 224
0*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g +
1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g
- 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g
+ 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g + a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 5
1*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) + 2*a*b*c^3*e*f*(-(4*a*c -
b^2)^9)^(1/2) - 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^2*b*c
^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^
4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2) - (x*(9*b^8*g^2 - 8*a*c^7*d^2 + 8*a^2*c^6*e^2 + 10*b
^2*c^6*d^2 - 72*a^3*c^5*f^2 + b^4*c^4*e^2 + 200*a^4*c^4*g^2 + b^6*c^2*f^2 + 2*a*b^2*c^5*e^2 - 16*a*b^4*c^3*f^2
- 6*b^7*c*f*g + 74*a^2*b^2*c^4*f^2 + 481*a^2*b^4*c^2*g^2 - 718*a^3*b^2*c^3*g^2 - 114*a*b^6*c*g^2 - 48*a^2*c^6
*d*f - 6*b^3*c^5*d*e - 6*b^4*c^4*d*f - 80*a^3*c^5*e*g + 18*b^5*c^3*d*g + 2*b^5*c^3*e*f - 6*b^6*c^2*e*g + 52*a*
b^2*c^5*d*f - 126*a*b^3*c^4*d*g - 14*a*b^3*c^4*e*f + 184*a^2*b*c^5*d*g - 8*a^2*b*c^5*e*f + 32*a*b^4*c^3*e*g +
86*a*b^5*c^2*f*g + 472*a^3*b*c^4*f*g + 4*a^2*b^2*c^4*e*g - 374*a^2*b^3*c^3*f*g - 8*a*b*c^6*d*e))/(2*(16*a^2*c^
5 + b^4*c^3 - 8*a*b^2*c^4)))*((768*a^4*b*c^9*d^2 - b^9*c^5*d^2 - c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a*b^13*g
^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 + a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*
f^2 + 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 5
12*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 150
4*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 - 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 106
56*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 + 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) -
1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d
*f + 3584*a^5*b*c^8*d*f - 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^
11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^
5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b
^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^
2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g - 10*a^2*c^3*e*g*(-(4*a*c - b
^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30
720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g + a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 51*a^2*b^2*c*g^2*(-(4*a*c - b^
2)^9)^(1/2) + 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) + 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^3*c*f*g
*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/
2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9
- 6144*a^6*b^2*c^10)))^(1/2) + (((10240*a^5*c^7*g - 16*b^7*c^5*d - 2048*a^4*c^8*e - 768*a^2*b^3*c^7*d - 384*a^
2*b^4*c^6*e + 1536*a^3*b^2*c^7*e + 192*a^2*b^5*c^5*f - 768*a^3*b^3*c^6*f - 736*a^2*b^6*c^4*g + 4224*a^3*b^4*c^
5*g - 10752*a^4*b^2*c^6*g + 192*a*b^5*c^6*d + 1024*a^3*b*c^8*d + 32*a*b^6*c^5*e - 16*a*b^7*c^4*f + 1024*a^4*b*
c^7*f + 48*a*b^8*c^3*g)/(8*(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5)) + (x*((768*a^4*b*c^9*d^2 -
b^9*c^5*d^2 - c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a*b^13*g^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 + a*c^4*e^2*
(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 + 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^
2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b
^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 - 9*a^2*c^
3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*
a^6*b^3*c^5*g^2 + 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8
*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f - 6*a*c^4*d*f*(-(4*a*c - b^
2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d
*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*
d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6
*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*
c^5*e*g + 512*a^5*b^3*c^6*e*g - 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*
c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g + a*b^2*c^2*f^
2*(-(4*a*c - b^2)^9)^(1/2) - 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/
2) + 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^2*c^2*e*g*(-(4*a*
c - b^2)^9)^(1/2) + 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c
^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2)*(16*b^7*c^5 - 192*a*b^
5*c^6 - 1024*a^3*b*c^8 + 768*a^2*b^3*c^7))/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))*((768*a^4*b*c^9*d^2 - b^9
*c^5*d^2 - c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a*b^13*g^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 + a*c^4*e^2*(-(
4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 + 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b
^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*
c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 - 9*a^2*c^3*f
^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6
*b^3*c^5*g^2 + 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*
f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f - 6*a*c^4*d*f*(-(4*a*c - b^2)^
9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e
+ 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g
+ 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*
f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5
*e*g + 512*a^5*b^3*c^6*e*g - 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3
*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g + a*b^2*c^2*f^2*(
-(4*a*c - b^2)^9)^(1/2) - 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2)
+ 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^2*c^2*e*g*(-(4*a*c -
b^2)^9)^(1/2) + 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6
+ 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2) + (x*(9*b^8*g^2 - 8*a*c^7
*d^2 + 8*a^2*c^6*e^2 + 10*b^2*c^6*d^2 - 72*a^3*c^5*f^2 + b^4*c^4*e^2 + 200*a^4*c^4*g^2 + b^6*c^2*f^2 + 2*a*b^2
*c^5*e^2 - 16*a*b^4*c^3*f^2 - 6*b^7*c*f*g + 74*a^2*b^2*c^4*f^2 + 481*a^2*b^4*c^2*g^2 - 718*a^3*b^2*c^3*g^2 - 1
14*a*b^6*c*g^2 - 48*a^2*c^6*d*f - 6*b^3*c^5*d*e - 6*b^4*c^4*d*f - 80*a^3*c^5*e*g + 18*b^5*c^3*d*g + 2*b^5*c^3*
e*f - 6*b^6*c^2*e*g + 52*a*b^2*c^5*d*f - 126*a*b^3*c^4*d*g - 14*a*b^3*c^4*e*f + 184*a^2*b*c^5*d*g - 8*a^2*b*c^
5*e*f + 32*a*b^4*c^3*e*g + 86*a*b^5*c^2*f*g + 472*a^3*b*c^4*f*g + 4*a^2*b^2*c^4*e*g - 374*a^2*b^3*c^3*f*g - 8*
a*b*c^6*d*e))/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))*((768*a^4*b*c^9*d^2 - b^9*c^5*d^2 - c^5*d^2*(-(4*a*c -
b^2)^9)^(1/2) - 9*a*b^13*g^2 - a*b^9*c^4*e^2 + 768*a^5*b*c^8*e^2 + a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^1
1*c^2*f^2 + 3840*a^6*b*c^7*f^2 + 9*a*b^4*g^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g
^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2
- 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a^5*b^3*c^6*f^2 - 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) -
2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 + 25*a^3*c^2*g^2
*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*
b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f - 6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g
- 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a
^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*
a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1
536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g -
10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^10*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g +
22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*b^12*c*f*g + a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 51*
a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 18*a*b*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) + 2*a*b*c^3*e*f*(-(4*a*c - b^
2)^9)^(1/2) - 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^2*b*c^2
*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*
b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/2) - (8*a*c^7*d^3 + 9*b^8*d*g^2 + 6*b^2*c^6*d^3 - 63*a^3*
b^5*g^3 + 216*a^4*c^4*f^3 - 3*a*b^3*c^4*e^3 - 4*a^2*b*c^5*e^3 + 8*a^2*c^6*d*e^2 + 573*a^4*b^3*c*g^3 - 1300*a^5
*b*c^2*g^3 + 72*a^2*c^6*d^2*f + 216*a^3*c^5*d*f^2 - 5*b^3*c^5*d^2*e + b^4*c^4*d*e^2 + 24*a^3*c^5*e^2*f + 200*a
^4*c^4*d*g^2 - 5*b^4*c^4*d^2*f + b^6*c^2*d*f^2 + 45*a^2*b^6*f*g^2 + 15*b^5*c^3*d^2*g + 600*a^5*c^3*f*g^2 + 5*a
^2*b^4*c^2*f^3 - 66*a^3*b^2*c^3*f^3 - 27*a*b^7*e*g^2 - 28*a*b*c^6*d^2*e - 78*a*b^6*c*d*g^2 - 80*a^3*c^5*d*e*g
+ 2*b^5*c^3*d*e*f - 6*b^6*c^2*d*e*g - 240*a^4*c^4*e*f*g + 18*a*b^2*c^5*d*e^2 + 26*a*b^2*c^5*d^2*f - 12*a*b^4*c
^3*d*f^2 - 53*a*b^3*c^4*d^2*g - 6*a*b^4*c^3*e^2*f - 3*a*b^5*c^2*e*f^2 - 76*a^2*b*c^5*d^2*g - 204*a^3*b*c^4*e*f
^2 + 18*a*b^5*c^2*e^2*g + 279*a^2*b^5*c*e*g^2 - 12*a^3*b*c^4*e^2*g + 420*a^4*b*c^3*e*g^2 - 30*a^2*b^5*c*f^2*g
- 402*a^3*b^4*c*f*g^2 - 924*a^4*b*c^3*f^2*g - 6*b^7*c*d*f*g + 2*a^2*b^2*c^4*d*f^2 + 42*a^2*b^2*c^4*e^2*f + 51*
a^2*b^3*c^3*e*f^2 + 133*a^2*b^4*c^2*d*g^2 + 114*a^3*b^2*c^3*d*g^2 - 81*a^2*b^3*c^3*e^2*g - 801*a^3*b^3*c^2*e*g
^2 + 339*a^3*b^3*c^2*f^2*g + 762*a^4*b^2*c^2*f*g^2 + 18*a*b^6*c*e*f*g + 6*a*b^3*c^4*d*e*f - 152*a^2*b*c^5*d*e*
f - 28*a*b^4*c^3*d*e*g + 62*a*b^5*c^2*d*f*g - 536*a^3*b*c^4*d*f*g + 276*a^2*b^2*c^4*d*e*g - 42*a^2*b^3*c^3*d*f
*g - 246*a^2*b^4*c^2*e*f*g + 804*a^3*b^2*c^3*e*f*g)/(4*(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5))
))*((768*a^4*b*c^9*d^2 - b^9*c^5*d^2 - c^5*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a*b^13*g^2 - a*b^9*c^4*e^2 + 768*a
^5*b*c^8*e^2 + a*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - a*b^11*c^2*f^2 + 3840*a^6*b*c^7*f^2 + 9*a*b^4*g^2*(-(4*a*c
- b^2)^9)^(1/2) + 213*a^2*b^11*c*g^2 - 26880*a^7*b*c^6*g^2 + 96*a^2*b^5*c^7*d^2 - 512*a^3*b^3*c^8*d^2 + 96*a^
3*b^5*c^6*e^2 - 512*a^4*b^3*c^7*e^2 + 27*a^2*b^9*c^3*f^2 - 288*a^3*b^7*c^4*f^2 + 1504*a^4*b^5*c^5*f^2 - 3840*a
^5*b^3*c^6*f^2 - 9*a^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^3*b^9*c^2*g^2 + 10656*a^4*b^7*c^3*g^2 - 30240
*a^5*b^5*c^4*g^2 + 44800*a^6*b^3*c^5*g^2 + 25*a^3*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 1024*a^5*c^9*d*e + 5120*a
^6*c^8*d*g - 3072*a^6*c^8*e*f + 15360*a^7*c^7*f*g + 12*a*b^8*c^5*d*e + 6*a*b^9*c^4*d*f + 3584*a^5*b*c^8*d*f -
6*a*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 18*a*b^10*c^3*d*g - 2*a*b^10*c^3*e*f + 6*a*b^11*c^2*e*g + 1536*a^6*b*c^
7*e*g - 128*a^2*b^6*c^6*d*e + 384*a^3*b^4*c^7*d*e - 128*a^2*b^7*c^5*d*f + 960*a^3*b^5*c^6*d*f - 3072*a^4*b^3*c
^7*d*f + 324*a^2*b^8*c^4*d*g + 36*a^2*b^8*c^4*e*f - 2240*a^3*b^6*c^5*d*g - 192*a^3*b^6*c^5*e*f + 7296*a^4*b^4*
c^6*d*g + 128*a^4*b^4*c^6*e*f - 10752*a^5*b^2*c^7*d*g + 1536*a^5*b^2*c^7*e*f - 98*a^2*b^9*c^3*e*g + 576*a^3*b^
7*c^4*e*g - 1344*a^4*b^5*c^5*e*g + 512*a^5*b^3*c^6*e*g - 10*a^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) - 152*a^2*b^1
0*c^2*f*g + 1548*a^3*b^8*c^3*f*g - 8064*a^4*b^6*c^4*f*g + 22400*a^5*b^4*c^5*f*g - 30720*a^6*b^2*c^6*f*g + 6*a*
b^12*c*f*g + a*b^2*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 51*a^2*b^2*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 18*a*b*c^3*d
*g*(-(4*a*c - b^2)^9)^(1/2) + 2*a*b*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 6*a*b^3*c*f*g*(-(4*a*c - b^2)^9)^(1/2)
- 6*a*b^2*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^2*b*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^7*c^11 + a
*b^12*c^5 - 24*a^2*b^10*c^6 + 240*a^3*b^8*c^7 - 1280*a^4*b^6*c^8 + 3840*a^5*b^4*c^9 - 6144*a^6*b^2*c^10)))^(1/
2)*2i + (g*x)/c^2

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**2*(g*x**6+f*x**4+e*x**2+d)/(c*x**4+b*x**2+a)**2,x)

[Out]

Timed out

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