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

Optimal. Leaf size=594 \[ \frac {x \left (a \left (-c^2 (2 a f+b e)+b c (3 a g+b f)+b^3 (-g)+2 c^3 d\right )+x^2 \left (-b^2 c (c e-4 a g)+b c^2 (c d-3 a f)+2 a c^2 (c e-a g)+b^4 (-g)+b^3 c f\right )\right )}{2 c^3 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right ) \left (-b^2 c (c e-24 a g)-\frac {-b^3 c (c e-34 a g)-b^2 c^2 (19 a f+c d)+4 a b c^2 (2 c e-13 a g)-4 a c^3 (c d-5 a f)-5 b^5 g+3 b^4 c f}{\sqrt {b^2-4 a c}}-b c^2 (13 a f+c d)+2 a c^2 (3 c e-7 a g)-5 b^4 g+3 b^3 c f\right )}{2 \sqrt {2} c^{7/2} \left (b^2-4 a c\right ) \sqrt {b-\sqrt {b^2-4 a c}}}-\frac {\tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {\sqrt {b^2-4 a c}+b}}\right ) \left (-b^2 c (c e-24 a g)+\frac {-b^3 c (c e-34 a g)-b^2 c^2 (19 a f+c d)+4 a b c^2 (2 c e-13 a g)-4 a c^3 (c d-5 a f)-5 b^5 g+3 b^4 c f}{\sqrt {b^2-4 a c}}-b c^2 (13 a f+c d)+2 a c^2 (3 c e-7 a g)-5 b^4 g+3 b^3 c f\right )}{2 \sqrt {2} c^{7/2} \left (b^2-4 a c\right ) \sqrt {\sqrt {b^2-4 a c}+b}}+\frac {x (c f-2 b g)}{c^3}+\frac {g x^3}{3 c^2} \]

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Rubi [A]  time = 14.11, antiderivative size = 594, 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} \begin {gather*} \frac {x \left (x^2 \left (-b^2 c (c e-4 a g)+b c^2 (c d-3 a f)+2 a c^2 (c e-a g)+b^3 c f+b^4 (-g)\right )+a \left (-c^2 (2 a f+b e)+b c (3 a g+b f)+b^3 (-g)+2 c^3 d\right )\right )}{2 c^3 \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^2 (19 a f+c d)-b^3 c (c e-34 a g)+4 a b c^2 (2 c e-13 a g)-4 a c^3 (c d-5 a f)+3 b^4 c f-5 b^5 g}{\sqrt {b^2-4 a c}}-b^2 c (c e-24 a g)-b c^2 (13 a f+c d)+2 a c^2 (3 c e-7 a g)+3 b^3 c f-5 b^4 g\right )}{2 \sqrt {2} c^{7/2} \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^2 (19 a f+c d)-b^3 c (c e-34 a g)+4 a b c^2 (2 c e-13 a g)-4 a c^3 (c d-5 a f)+3 b^4 c f-5 b^5 g}{\sqrt {b^2-4 a c}}-b^2 c (c e-24 a g)-b c^2 (13 a f+c d)+2 a c^2 (3 c e-7 a g)+3 b^3 c f-5 b^4 g\right )}{2 \sqrt {2} c^{7/2} \left (b^2-4 a c\right ) \sqrt {\sqrt {b^2-4 a c}+b}}+\frac {x (c f-2 b g)}{c^3}+\frac {g x^3}{3 c^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

((c*f - 2*b*g)*x)/c^3 + (g*x^3)/(3*c^2) + (x*(a*(2*c^3*d - c^2*(b*e + 2*a*f) - b^3*g + b*c*(b*f + 3*a*g)) + (b
^3*c*f + b*c^2*(c*d - 3*a*f) - b^4*g - b^2*c*(c*e - 4*a*g) + 2*a*c^2*(c*e - a*g))*x^2))/(2*c^3*(b^2 - 4*a*c)*(
a + b*x^2 + c*x^4)) - ((3*b^3*c*f - b*c^2*(c*d + 13*a*f) - 5*b^4*g - b^2*c*(c*e - 24*a*g) + 2*a*c^2*(3*c*e - 7
*a*g) - (3*b^4*c*f - 4*a*c^3*(c*d - 5*a*f) - b^2*c^2*(c*d + 19*a*f) - 5*b^5*g - b^3*c*(c*e - 34*a*g) + 4*a*b*c
^2*(2*c*e - 13*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^
(7/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((3*b^3*c*f - b*c^2*(c*d + 13*a*f) - 5*b^4*g - b^2*c*(c*e -
24*a*g) + 2*a*c^2*(3*c*e - 7*a*g) + (3*b^4*c*f - 4*a*c^3*(c*d - 5*a*f) - b^2*c^2*(c*d + 19*a*f) - 5*b^5*g - b
^3*c*(c*e - 34*a*g) + 4*a*b*c^2*(2*c*e - 13*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^(7/2)*(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^4 \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 (a \left (2 c^3 d-c^2 (b e+2 a f)-b^3 g+b c (b f+3 a g)\right )+\left (b^3 c f+b c^2 (c d-3 a f)-b^4 g-b^2 c (c e-4 a g)+2 a c^2 (c e-a g)\right ) x^2\right )}{2 c^3 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\int \frac {\frac {a^2 \left (2 c^3 d-c^2 (b e+2 a f)-b^3 g+b c (b f+3 a g)\right )}{c^3}+\frac {a \left (b^3 c f-b c^2 (c d+5 a f)-b^4 g-b^2 c (c e-6 a g)+6 a c^2 (c e-a g)\right ) x^2}{c^3}-\frac {2 a \left (b^2-4 a c\right ) (c f-b g) x^4}{c^2}+2 a \left (4 a-\frac {b^2}{c}\right ) g x^6}{a+b x^2+c x^4} \, dx}{2 a \left (b^2-4 a c\right )}\\ &=\frac {x \left (a \left (2 c^3 d-c^2 (b e+2 a f)-b^3 g+b c (b f+3 a g)\right )+\left (b^3 c f+b c^2 (c d-3 a f)-b^4 g-b^2 c (c e-4 a g)+2 a c^2 (c e-a g)\right ) x^2\right )}{2 c^3 \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 ) (c f-2 b g)}{c^3}-\frac {2 a \left (b^2-4 a c\right ) g x^2}{c^2}+\frac {a^2 \left (2 c^3 d-c^2 (b e+10 a f)-5 b^3 g+b c (3 b f+19 a g)\right )+a \left (3 b^3 c f-b c^2 (c d+13 a f)-5 b^4 g-b^2 c (c e-24 a g)+2 a c^2 (3 c e-7 a g)\right ) x^2}{c^3 \left (a+b x^2+c x^4\right )}\right ) \, dx}{2 a \left (b^2-4 a c\right )}\\ &=\frac {(c f-2 b g) x}{c^3}+\frac {g x^3}{3 c^2}+\frac {x \left (a \left (2 c^3 d-c^2 (b e+2 a f)-b^3 g+b c (b f+3 a g)\right )+\left (b^3 c f+b c^2 (c d-3 a f)-b^4 g-b^2 c (c e-4 a g)+2 a c^2 (c e-a g)\right ) x^2\right )}{2 c^3 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\int \frac {a^2 \left (2 c^3 d-c^2 (b e+10 a f)-5 b^3 g+b c (3 b f+19 a g)\right )+a \left (3 b^3 c f-b c^2 (c d+13 a f)-5 b^4 g-b^2 c (c e-24 a g)+2 a c^2 (3 c e-7 a g)\right ) x^2}{a+b x^2+c x^4} \, dx}{2 a c^3 \left (b^2-4 a c\right )}\\ &=\frac {(c f-2 b g) x}{c^3}+\frac {g x^3}{3 c^2}+\frac {x \left (a \left (2 c^3 d-c^2 (b e+2 a f)-b^3 g+b c (b f+3 a g)\right )+\left (b^3 c f+b c^2 (c d-3 a f)-b^4 g-b^2 c (c e-4 a g)+2 a c^2 (c e-a g)\right ) x^2\right )}{2 c^3 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\left (3 b^3 c f-b c^2 (c d+13 a f)-5 b^4 g-b^2 c (c e-24 a g)+2 a c^2 (3 c e-7 a g)-\frac {3 b^4 c f-4 a c^3 (c d-5 a f)-b^2 c^2 (c d+19 a f)-5 b^5 g-b^3 c (c e-34 a g)+4 a b c^2 (2 c e-13 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^3 \left (b^2-4 a c\right )}-\frac {\left (3 b^3 c f-b c^2 (c d+13 a f)-5 b^4 g-b^2 c (c e-24 a g)+2 a c^2 (3 c e-7 a g)+\frac {3 b^4 c f-4 a c^3 (c d-5 a f)-b^2 c^2 (c d+19 a f)-5 b^5 g-b^3 c (c e-34 a g)+4 a b c^2 (2 c e-13 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^3 \left (b^2-4 a c\right )}\\ &=\frac {(c f-2 b g) x}{c^3}+\frac {g x^3}{3 c^2}+\frac {x \left (a \left (2 c^3 d-c^2 (b e+2 a f)-b^3 g+b c (b f+3 a g)\right )+\left (b^3 c f+b c^2 (c d-3 a f)-b^4 g-b^2 c (c e-4 a g)+2 a c^2 (c e-a g)\right ) x^2\right )}{2 c^3 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\left (3 b^3 c f-b c^2 (c d+13 a f)-5 b^4 g-b^2 c (c e-24 a g)+2 a c^2 (3 c e-7 a g)-\frac {3 b^4 c f-4 a c^3 (c d-5 a f)-b^2 c^2 (c d+19 a f)-5 b^5 g-b^3 c (c e-34 a g)+4 a b c^2 (2 c e-13 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^{7/2} \left (b^2-4 a c\right ) \sqrt {b-\sqrt {b^2-4 a c}}}-\frac {\left (3 b^3 c f-b c^2 (c d+13 a f)-5 b^4 g-b^2 c (c e-24 a g)+2 a c^2 (3 c e-7 a g)+\frac {3 b^4 c f-4 a c^3 (c d-5 a f)-b^2 c^2 (c d+19 a f)-5 b^5 g-b^3 c (c e-34 a g)+4 a b c^2 (2 c e-13 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^{7/2} \left (b^2-4 a c\right ) \sqrt {b+\sqrt {b^2-4 a c}}}\\ \end {align*}

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Mathematica [A]  time = 2.64, size = 721, normalized size = 1.21 \begin {gather*} \frac {\frac {6 \sqrt {c} x \left (a^2 c \left (3 b g-2 c \left (f+g x^2\right )\right )+a \left (b^3 (-g)+b^2 c \left (f+4 g x^2\right )-b c^2 \left (e+3 f x^2\right )+2 c^3 \left (d+e x^2\right )\right )+b x^2 \left (b^3 (-g)+b^2 c f-b c^2 e+c^3 d\right )\right )}{\left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {3 \sqrt {2} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right ) \left (-b^2 c \left (-c e \sqrt {b^2-4 a c}+24 a g \sqrt {b^2-4 a c}+19 a c f+c^2 d\right )+b c^2 \left (c \left (d \sqrt {b^2-4 a c}+8 a e\right )+13 a \left (f \sqrt {b^2-4 a c}-4 a g\right )\right )+2 a c^2 \left (-3 c e \sqrt {b^2-4 a c}+7 a g \sqrt {b^2-4 a c}+10 a c f-2 c^2 d\right )+b^4 \left (5 g \sqrt {b^2-4 a c}+3 c f\right )-b^3 c \left (3 f \sqrt {b^2-4 a c}-34 a g+c e\right )-5 b^5 g\right )}{\left (b^2-4 a c\right )^{3/2} \sqrt {b-\sqrt {b^2-4 a c}}}+\frac {3 \sqrt {2} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {\sqrt {b^2-4 a c}+b}}\right ) \left (b^2 c \left (c e \sqrt {b^2-4 a c}-24 a g \sqrt {b^2-4 a c}+19 a c f+c^2 d\right )+b c^2 \left (c \left (d \sqrt {b^2-4 a c}-8 a e\right )+13 a \left (f \sqrt {b^2-4 a c}+4 a g\right )\right )+2 a c^2 \left (-3 c e \sqrt {b^2-4 a c}+7 a g \sqrt {b^2-4 a c}-10 a c f+2 c^2 d\right )+b^4 \left (5 g \sqrt {b^2-4 a c}-3 c f\right )+b^3 c \left (-3 f \sqrt {b^2-4 a c}-34 a g+c e\right )+5 b^5 g\right )}{\left (b^2-4 a c\right )^{3/2} \sqrt {\sqrt {b^2-4 a c}+b}}+12 \sqrt {c} x (c f-2 b g)+4 c^{3/2} g x^3}{12 c^{7/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(12*Sqrt[c]*(c*f - 2*b*g)*x + 4*c^(3/2)*g*x^3 + (6*Sqrt[c]*x*(b*(c^3*d - b*c^2*e + b^2*c*f - b^3*g)*x^2 + a^2*
c*(3*b*g - 2*c*(f + g*x^2)) + a*(-(b^3*g) + 2*c^3*(d + e*x^2) - b*c^2*(e + 3*f*x^2) + b^2*c*(f + 4*g*x^2))))/(
(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (3*Sqrt[2]*(-5*b^5*g - b^3*c*(c*e + 3*Sqrt[b^2 - 4*a*c]*f - 34*a*g) + b^4
*(3*c*f + 5*Sqrt[b^2 - 4*a*c]*g) + 2*a*c^2*(-2*c^2*d - 3*c*Sqrt[b^2 - 4*a*c]*e + 10*a*c*f + 7*a*Sqrt[b^2 - 4*a
*c]*g) - b^2*c*(c^2*d - c*Sqrt[b^2 - 4*a*c]*e + 19*a*c*f + 24*a*Sqrt[b^2 - 4*a*c]*g) + b*c^2*(c*(Sqrt[b^2 - 4*
a*c]*d + 8*a*e) + 13*a*(Sqrt[b^2 - 4*a*c]*f - 4*a*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]]) + (3*Sqrt[2]*(5*b^5*g + b^3*c*(c*e - 3*Sqrt[b^2 - 4*a*c]*f
- 34*a*g) + b^4*(-3*c*f + 5*Sqrt[b^2 - 4*a*c]*g) + b^2*c*(c^2*d + c*Sqrt[b^2 - 4*a*c]*e + 19*a*c*f - 24*a*Sqr
t[b^2 - 4*a*c]*g) + 2*a*c^2*(2*c^2*d - 3*c*Sqrt[b^2 - 4*a*c]*e - 10*a*c*f + 7*a*Sqrt[b^2 - 4*a*c]*g) + b*c^2*(
c*(Sqrt[b^2 - 4*a*c]*d - 8*a*e) + 13*a*(Sqrt[b^2 - 4*a*c]*f + 4*a*g)))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqr
t[b^2 - 4*a*c]]])/((b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]))/(12*c^(7/2))

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^4 \left (d+e x^2+f x^4+g x^6\right )}{\left (a+b x^2+c x^4\right )^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^4*(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 = 9.95, size = 10761, normalized size = 18.12

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*(b*c^3*d*x^3 + b^3*c*f*x^3 - 3*a*b*c^2*f*x^3 - b^4*g*x^3 + 4*a*b^2*c*g*x^3 - 2*a^2*c^2*g*x^3 - b^2*c^2*x^3
*e + 2*a*c^3*x^3*e + 2*a*c^3*d*x + a*b^2*c*f*x - 2*a^2*c^2*f*x - a*b^3*g*x + 3*a^2*b*c*g*x - a*b*c^2*x*e)/((b^
2*c^3 - 4*a*c^4)*(c*x^4 + b*x^2 + a)) + 1/16*((2*b^3*c^5 - 8*a*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sq
rt(b^2 - 4*a*c)*c)*b^3*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 + 2*sqrt(2)*s
qrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a
*c)*c)*b*c^5 - 2*(b^2 - 4*a*c)*b*c^5)*(b^2*c^3 - 4*a*c^4)^2*d - (6*b^5*c^3 - 50*a*b^3*c^4 + 104*a^2*b*c^5 - 3*
sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c + 25*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt
(b^2 - 4*a*c)*c)*a*b^3*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 52*sqrt(2)*
sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2
- 4*a*c)*c)*a*b^2*c^3 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 13*sqrt(2)*sqrt
(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 6*(b^2 - 4*a*c)*b^3*c^3 + 26*(b^2 - 4*a*c)*a*b*c^4)*(b
^2*c^3 - 4*a*c^4)^2*f + (10*b^6*c^2 - 88*a*b^4*c^3 + 220*a^2*b^2*c^4 - 112*a^3*c^5 - 5*sqrt(2)*sqrt(b^2 - 4*a*
c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 + 44*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c
+ 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 110*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
+ sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 -
5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c +
sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 24*sqr
t(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqr
t(b^2 - 4*a*c)*c)*a^2*c^4 - 10*(b^2 - 4*a*c)*b^4*c^2 + 48*(b^2 - 4*a*c)*a*b^2*c^3 - 28*(b^2 - 4*a*c)*a^2*c^4)*
(b^2*c^3 - 4*a*c^4)^2*g + (2*b^4*c^4 - 20*a*b^2*c^5 + 48*a^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b
^2 - 4*a*c)*c)*b^4*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 2*sqrt(2)*sq
rt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4
*a*c)*c)*a^2*c^4 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - sqrt(2)*sqrt(b^2 - 4
*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^4 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*
c^5 - 2*(b^2 - 4*a*c)*b^2*c^4 + 12*(b^2 - 4*a*c)*a*c^5)*(b^2*c^3 - 4*a*c^4)^2*e - 4*(sqrt(2)*sqrt(b*c + sqrt(b
^2 - 4*a*c)*c)*a*b^4*c^7 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^8 - 2*sqrt(2)*sqrt(b*c + sqrt(b
^2 - 4*a*c)*c)*a*b^3*c^8 - 2*a*b^4*c^8 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^9 + 8*sqrt(2)*sqrt(b
*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^9 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^9 + 16*a^2*b^2*c^9 - 4*s
qrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^10 - 32*a^3*c^10 + 2*(b^2 - 4*a*c)*a*b^2*c^8 - 8*(b^2 - 4*a*c)*a^
2*c^9)*d*abs(b^2*c^3 - 4*a*c^4) - 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^5 - 34*sqrt(2)*sqrt(b*c
+ sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^6 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^6 - 6*a*b^6*c^6 + 128*
sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^7 + 44*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 +
3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^7 + 68*a^2*b^4*c^7 - 160*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*
c)*c)*a^4*c^8 - 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 - 22*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)
*c)*a^2*b^2*c^8 - 256*a^3*b^2*c^8 + 40*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^9 + 320*a^4*c^9 + 6*(b^2
- 4*a*c)*a*b^4*c^6 - 44*(b^2 - 4*a*c)*a^2*b^2*c^7 + 80*(b^2 - 4*a*c)*a^3*c^8)*f*abs(b^2*c^3 - 4*a*c^4) + 2*(5*
sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^4 - 59*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^5 - 1
0*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^5 - 10*a*b^7*c^5 + 232*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*
c)*a^3*b^3*c^6 + 78*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^6 + 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*
c)*c)*a*b^5*c^6 + 118*a^2*b^5*c^6 - 304*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^7 - 152*sqrt(2)*sqrt(b
*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^7 - 39*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 - 464*a^3*b^3*c
^7 + 76*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 + 608*a^4*b*c^8 + 10*(b^2 - 4*a*c)*a*b^5*c^5 - 78*(b
^2 - 4*a*c)*a^2*b^3*c^6 + 152*(b^2 - 4*a*c)*a^3*b*c^7)*g*abs(b^2*c^3 - 4*a*c^4) + 2*(sqrt(2)*sqrt(b*c + sqrt(b
^2 - 4*a*c)*c)*a*b^5*c^6 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 - 2*sqrt(2)*sqrt(b*c + sqrt(b
^2 - 4*a*c)*c)*a*b^4*c^7 - 2*a*b^5*c^7 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 + 8*sqrt(2)*sqrt
(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^8 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^8 + 16*a^2*b^3*c^8 -
4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^9 - 32*a^3*b*c^9 + 2*(b^2 - 4*a*c)*a*b^3*c^7 - 8*(b^2 - 4*a
*c)*a^2*b*c^8)*abs(b^2*c^3 - 4*a*c^4)*e - (2*b^7*c^11 - 8*a*b^5*c^12 - 32*a^2*b^3*c^13 + 128*a^3*b*c^14 - sqrt
(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^9 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^
2 - 4*a*c)*c)*a*b^5*c^10 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^10 + 16*sqrt(2)*s
qrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^11 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2
- 4*a*c)*c)*b^5*c^11 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^12 - 32*sqrt(2)*sq
rt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^12 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^
2 - 4*a*c)*c)*a^2*b*c^13 - 2*(b^2 - 4*a*c)*b^5*c^11 + 32*(b^2 - 4*a*c)*a^2*b*c^13)*d + (6*b^9*c^9 - 86*a*b^7*c
^10 + 440*a^2*b^5*c^11 - 928*a^3*b^3*c^12 + 640*a^4*b*c^13 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 -
4*a*c)*c)*b^9*c^7 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^8 + 6*sqrt(2)*sqrt(b
^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^8 - 220*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*
c)*c)*a^2*b^5*c^9 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^9 - 3*sqrt(2)*sqrt(b^
2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^9 + 464*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c
)*c)*a^3*b^3*c^10 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 + 31*sqrt(2)*sq
rt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^10 - 320*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2
- 4*a*c)*c)*a^4*b*c^11 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 - 96*sqrt
(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^11 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + s
qrt(b^2 - 4*a*c)*c)*a^3*b*c^12 - 6*(b^2 - 4*a*c)*b^7*c^9 + 62*(b^2 - 4*a*c)*a*b^5*c^10 - 192*(b^2 - 4*a*c)*a^2
*b^3*c^11 + 160*(b^2 - 4*a*c)*a^3*b*c^12)*f - (10*b^10*c^8 - 148*a*b^8*c^9 + 808*a^2*b^6*c^10 - 1920*a^3*b^4*c
^11 + 1664*a^4*b^2*c^12 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^10*c^6 + 74*sqrt(2)*sq
rt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^8*c^7 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 -
4*a*c)*c)*b^9*c^7 - 404*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^8 - 108*sqrt(2)*s
qrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^8 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 -
4*a*c)*c)*b^8*c^8 + 960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^9 + 376*sqrt(2)*s
qrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^9 + 54*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^
2 - 4*a*c)*c)*a*b^6*c^9 - 832*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^10 - 416*sqr
t(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^10 - 188*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c +
sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 + 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^1
1 - 10*(b^2 - 4*a*c)*b^8*c^8 + 108*(b^2 - 4*a*c)*a*b^6*c^9 - 376*(b^2 - 4*a*c)*a^2*b^4*c^10 + 416*(b^2 - 4*a*c
)*a^3*b^2*c^11)*g - (2*b^8*c^10 - 32*a*b^6*c^11 + 160*a^2*b^4*c^12 - 256*a^3*b^2*c^13 - sqrt(2)*sqrt(b^2 - 4*a
*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^8 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b
^6*c^9 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^9 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sq
rt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^
5*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^10 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sq
rt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*
b^3*c^11 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^11 - 32*sqrt(2)*sqrt(b^2 - 4*a
*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^12 - 2*(b^2 - 4*a*c)*b^6*c^10 + 24*(b^2 - 4*a*c)*a*b^4*c^11 - 64
*(b^2 - 4*a*c)*a^2*b^2*c^12)*e)*arctan(2*sqrt(1/2)*x/sqrt((b^3*c^3 - 4*a*b*c^4 + sqrt((b^3*c^3 - 4*a*b*c^4)^2
- 4*(a*b^2*c^3 - 4*a^2*c^4)*(b^2*c^4 - 4*a*c^5)))/(b^2*c^4 - 4*a*c^5)))/((a*b^6*c^7 - 12*a^2*b^4*c^8 - 2*a*b^5
*c^8 + 48*a^3*b^2*c^9 + 16*a^2*b^3*c^9 + a*b^4*c^9 - 64*a^4*c^10 - 32*a^3*b*c^10 - 8*a^2*b^2*c^10 + 16*a^3*c^1
1)*abs(b^2*c^3 - 4*a*c^4)*abs(c)) + 1/16*((2*b^3*c^5 - 8*a*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b
^2 - 4*a*c)*c)*b^3*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 + 2*sqrt(2)*sqrt(
b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*
c)*b*c^5 - 2*(b^2 - 4*a*c)*b*c^5)*(b^2*c^3 - 4*a*c^4)^2*d - (6*b^5*c^3 - 50*a*b^3*c^4 + 104*a^2*b*c^5 - 3*sqrt
(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c + 25*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2
- 4*a*c)*c)*a*b^3*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 52*sqrt(2)*sqrt
(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4
*a*c)*c)*a*b^2*c^3 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 13*sqrt(2)*sqrt(b^2
- 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 6*(b^2 - 4*a*c)*b^3*c^3 + 26*(b^2 - 4*a*c)*a*b*c^4)*(b^2*c
^3 - 4*a*c^4)^2*f + (10*b^6*c^2 - 88*a*b^4*c^3 + 220*a^2*b^2*c^4 - 112*a^3*c^5 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*s
qrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 + 44*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 10
*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 110*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sq
rt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 5*sq
rt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt
(b^2 - 4*a*c)*c)*a^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 24*sqrt(2)
*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^
2 - 4*a*c)*c)*a^2*c^4 - 10*(b^2 - 4*a*c)*b^4*c^2 + 48*(b^2 - 4*a*c)*a*b^2*c^3 - 28*(b^2 - 4*a*c)*a^2*c^4)*(b^2
*c^3 - 4*a*c^4)^2*g + (2*b^4*c^4 - 20*a*b^2*c^5 + 48*a^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*b^4*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 2*sqrt(2)*sqrt(b
^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c
)*c)*a^2*c^4 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c
)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^4 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^5
- 2*(b^2 - 4*a*c)*b^2*c^4 + 12*(b^2 - 4*a*c)*a*c^5)*(b^2*c^3 - 4*a*c^4)^2*e - 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*a*b^4*c^7 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^8 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*a*b^3*c^8 + 2*a*b^4*c^8 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^9 + 8*sqrt(2)*sqrt(b*c -
sqrt(b^2 - 4*a*c)*c)*a^2*b*c^9 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^9 - 16*a^2*b^2*c^9 - 4*sqrt(
2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^10 + 32*a^3*c^10 - 2*(b^2 - 4*a*c)*a*b^2*c^8 + 8*(b^2 - 4*a*c)*a^2*c^
9)*d*abs(b^2*c^3 - 4*a*c^4) - 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^5 - 34*sqrt(2)*sqrt(b*c - s
qrt(b^2 - 4*a*c)*c)*a^2*b^4*c^6 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^6 + 6*a*b^6*c^6 + 128*sqrt
(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^7 + 44*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 + 3*s
qrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^7 - 68*a^2*b^4*c^7 - 160*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c
)*a^4*c^8 - 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 - 22*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*
a^2*b^2*c^8 + 256*a^3*b^2*c^8 + 40*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^9 - 320*a^4*c^9 - 6*(b^2 - 4*
a*c)*a*b^4*c^6 + 44*(b^2 - 4*a*c)*a^2*b^2*c^7 - 80*(b^2 - 4*a*c)*a^3*c^8)*f*abs(b^2*c^3 - 4*a*c^4) + 2*(5*sqrt
(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^4 - 59*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^5 - 10*sq
rt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^5 + 10*a*b^7*c^5 + 232*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a
^3*b^3*c^6 + 78*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^6 + 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c
)*a*b^5*c^6 - 118*a^2*b^5*c^6 - 304*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^7 - 152*sqrt(2)*sqrt(b*c -
sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^7 - 39*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 + 464*a^3*b^3*c^7 +
76*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 - 608*a^4*b*c^8 - 10*(b^2 - 4*a*c)*a*b^5*c^5 + 78*(b^2 -
4*a*c)*a^2*b^3*c^6 - 152*(b^2 - 4*a*c)*a^3*b*c^7)*g*abs(b^2*c^3 - 4*a*c^4) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*a*b^5*c^6 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*a*b^4*c^7 + 2*a*b^5*c^7 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 + 8*sqrt(2)*sqrt(b*c
- sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^8 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^8 - 16*a^2*b^3*c^8 - 4*s
qrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^9 + 32*a^3*b*c^9 - 2*(b^2 - 4*a*c)*a*b^3*c^7 + 8*(b^2 - 4*a*c)*
a^2*b*c^8)*abs(b^2*c^3 - 4*a*c^4)*e - (2*b^7*c^11 - 8*a*b^5*c^12 - 32*a^2*b^3*c^13 + 128*a^3*b*c^14 - sqrt(2)*
sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^9 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*a*b^5*c^10 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^10 + 16*sqrt(2)*sqrt(
b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^11 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*
a*c)*c)*b^5*c^11 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^12 - 32*sqrt(2)*sqrt(b
^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^12 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*a^2*b*c^13 - 2*(b^2 - 4*a*c)*b^5*c^11 + 32*(b^2 - 4*a*c)*a^2*b*c^13)*d + (6*b^9*c^9 - 86*a*b^7*c^10
+ 440*a^2*b^5*c^11 - 928*a^3*b^3*c^12 + 640*a^4*b*c^13 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a
*c)*c)*b^9*c^7 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^8 + 6*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^8 - 220*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c
)*a^2*b^5*c^9 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^9 - 3*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^9 + 464*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)
*a^3*b^3*c^10 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 + 31*sqrt(2)*sqrt(b
^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^10 - 320*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4
*a*c)*c)*a^4*b*c^11 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 - 96*sqrt(2)*
sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^11 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(
b^2 - 4*a*c)*c)*a^3*b*c^12 - 6*(b^2 - 4*a*c)*b^7*c^9 + 62*(b^2 - 4*a*c)*a*b^5*c^10 - 192*(b^2 - 4*a*c)*a^2*b^3
*c^11 + 160*(b^2 - 4*a*c)*a^3*b*c^12)*f - (10*b^10*c^8 - 148*a*b^8*c^9 + 808*a^2*b^6*c^10 - 1920*a^3*b^4*c^11
+ 1664*a^4*b^2*c^12 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^10*c^6 + 74*sqrt(2)*sqrt(b
^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^8*c^7 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a
*c)*c)*b^9*c^7 - 404*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^8 - 108*sqrt(2)*sqrt(
b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^8 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a
*c)*c)*b^8*c^8 + 960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^9 + 376*sqrt(2)*sqrt(
b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^9 + 54*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*a*b^6*c^9 - 832*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^10 - 416*sqrt(2)
*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^10 - 188*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqr
t(b^2 - 4*a*c)*c)*a^2*b^4*c^10 + 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 -
10*(b^2 - 4*a*c)*b^8*c^8 + 108*(b^2 - 4*a*c)*a*b^6*c^9 - 376*(b^2 - 4*a*c)*a^2*b^4*c^10 + 416*(b^2 - 4*a*c)*a^
3*b^2*c^11)*g - (2*b^8*c^10 - 32*a*b^6*c^11 + 160*a^2*b^4*c^12 - 256*a^3*b^2*c^13 - sqrt(2)*sqrt(b^2 - 4*a*c)*
sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^8 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c
^9 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^9 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b
*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^
10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^10 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b
*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*
c^11 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^11 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*
sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^12 - 2*(b^2 - 4*a*c)*b^6*c^10 + 24*(b^2 - 4*a*c)*a*b^4*c^11 - 64*(b^
2 - 4*a*c)*a^2*b^2*c^12)*e)*arctan(2*sqrt(1/2)*x/sqrt((b^3*c^3 - 4*a*b*c^4 - sqrt((b^3*c^3 - 4*a*b*c^4)^2 - 4*
(a*b^2*c^3 - 4*a^2*c^4)*(b^2*c^4 - 4*a*c^5)))/(b^2*c^4 - 4*a*c^5)))/((a*b^6*c^7 - 12*a^2*b^4*c^8 - 2*a*b^5*c^8
+ 48*a^3*b^2*c^9 + 16*a^2*b^3*c^9 + a*b^4*c^9 - 64*a^4*c^10 - 32*a^3*b*c^10 - 8*a^2*b^2*c^10 + 16*a^3*c^11)*a
bs(b^2*c^3 - 4*a*c^4)*abs(c)) + 1/3*(c^4*g*x^3 + 3*c^4*f*x - 6*b*c^3*g*x)/c^6

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maple [B]  time = 0.06, size = 3028, normalized size = 5.10 \begin {gather*} \text {output too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-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*e*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*f-13/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a*b/c*f*arct
an(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/3*g*x^3/c^2-5/4/c^3/(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^5*g+6/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)*a*b^2*g-5/4/c
^3/(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^5*g-6/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)*a*b^2*g-2/c^3*x*b*g+1/c^2*f*x-2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a*b^2*g-13/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^2*b*g+17/2/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)*arc
tan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^3*g-13/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^2*b*g+17/2/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)*a*b^3*g+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a*b/c*e*x+3/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a*b/c*f*x^3-1/2/(c*x^4+b*
x^2+a)/(4*a*c-b^2)*a*b^2/c^2*f*x-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*f+1/4/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arct
anh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+3/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1
/2)*b^3/c^2*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^2/c*e*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)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d-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*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/
2))*c)^(1/2)*c*x)+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*f+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*f-1/4/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)*b^3*e+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*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1
/2))*c)^(1/2)*c*x)-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a*d*x-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a*e*x^3-1/2/(c*x^4+b*x^2+
a)/(4*a*c-b^2)*b*d*x^3-3/2/c^2/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*x*b*g+1/2/c^3/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*b
^3*g-5/4/c^3/(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^4*g+7/2/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^2*g+5/4/c^3/(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^4*g-7/2/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^2*g-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*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+3/4/(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^4/c^2*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+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*e-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*d-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*f-19/4/(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)*a*b^2/c*f*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)*b^3/c^2*f*x^3+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b^2/c*e*x^3+1/(c*x^4+b*x^2+a)/(4*a*c-b^2
)*a^2/c*f*x-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*e+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*d+3/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a*e*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*d*arctan(2^(1/2)/((b+
(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+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)*a^
2*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a^2*g+1/2/c^3/(c*
x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b^4*g

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {{\left (b c^{3} d - {\left (b^{2} c^{2} - 2 \, a c^{3}\right )} e + {\left (b^{3} c - 3 \, a b c^{2}\right )} f - {\left (b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right )} g\right )} x^{3} + {\left (2 \, a c^{3} d - a b c^{2} e + {\left (a b^{2} c - 2 \, a^{2} c^{2}\right )} f - {\left (a b^{3} - 3 \, a^{2} b c\right )} g\right )} x}{2 \, {\left (a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left (b^{2} c^{4} - 4 \, a c^{5}\right )} x^{4} + {\left (b^{3} c^{3} - 4 \, a b c^{4}\right )} x^{2}\right )}} + \frac {-\int \frac {2 \, a c^{3} d - a b c^{2} e - {\left (b c^{3} d + {\left (b^{2} c^{2} - 6 \, a c^{3}\right )} e - {\left (3 \, b^{3} c - 13 \, a b c^{2}\right )} f + {\left (5 \, b^{4} - 24 \, a b^{2} c + 14 \, a^{2} c^{2}\right )} g\right )} x^{2} + {\left (3 \, a b^{2} c - 10 \, a^{2} c^{2}\right )} f - {\left (5 \, a b^{3} - 19 \, a^{2} b c\right )} g}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left (b^{2} c^{3} - 4 \, a c^{4}\right )}} + \frac {c g x^{3} + 3 \, {\left (c f - 2 \, b g\right )} x}{3 \, c^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*((b*c^3*d - (b^2*c^2 - 2*a*c^3)*e + (b^3*c - 3*a*b*c^2)*f - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*g)*x^3 + (2*a*c^
3*d - a*b*c^2*e + (a*b^2*c - 2*a^2*c^2)*f - (a*b^3 - 3*a^2*b*c)*g)*x)/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*
c^5)*x^4 + (b^3*c^3 - 4*a*b*c^4)*x^2) + 1/2*integrate(-(2*a*c^3*d - a*b*c^2*e - (b*c^3*d + (b^2*c^2 - 6*a*c^3)
*e - (3*b^3*c - 13*a*b*c^2)*f + (5*b^4 - 24*a*b^2*c + 14*a^2*c^2)*g)*x^2 + (3*a*b^2*c - 10*a^2*c^2)*f - (5*a*b
^3 - 19*a^2*b*c)*g)/(c*x^4 + b*x^2 + a), x)/(b^2*c^3 - 4*a*c^4) + 1/3*(c*g*x^3 + 3*(c*f - 2*b*g)*x)/c^3

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mupad [B]  time = 4.73, size = 47339, normalized size = 79.70

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((x^3*(b^4*g + b^2*c^2*e + 2*a^2*c^2*g - 2*a*c^3*e - b*c^3*d - b^3*c*f + 3*a*b*c^2*f - 4*a*b^2*c*g))/(2*(4*a*c
- b^2)) + (x*(2*a^2*c^2*f - 2*a*c^3*d + a*b^3*g + a*b*c^2*e - a*b^2*c*f - 3*a^2*b*c*g))/(2*(4*a*c - b^2)))/(a
*c^3 + c^4*x^4 + b*c^3*x^2) + x*(f/c^2 - (2*b*g)/c^3) + atan(((((2048*a^4*c^10*d - 10240*a^5*c^9*f + 384*a^2*b
^4*c^8*d - 1536*a^3*b^2*c^9*d - 192*a^2*b^5*c^7*e + 768*a^3*b^3*c^8*e + 736*a^2*b^6*c^6*f - 4224*a^3*b^4*c^7*f
+ 10752*a^4*b^2*c^8*f - 1264*a^2*b^7*c^5*g + 7488*a^3*b^5*c^6*g - 19712*a^4*b^3*c^7*g - 32*a*b^6*c^7*d + 16*a
*b^7*c^6*e - 1024*a^4*b*c^9*e - 48*a*b^8*c^5*f + 80*a*b^9*c^4*g + 19456*a^5*b*c^8*g)/(8*(64*a^3*c^8 - b^6*c^5
+ 12*a*b^4*c^6 - 48*a^2*b^2*c^7)) - (x*(-(25*b^15*g^2 + b^9*c^6*d^2 + c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + b^11*
c^4*e^2 + 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^4*b*c^10*d^2 - 27*a*b^9*c^5*e^2 - 3840*
a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c^3*f^2 + 26880*a^6*b*c^8*f^2 - 80640*a^7*b*
c^7*g^2 - 30*b^14*c*f*g - 96*a^2*b^5*c^8*d^2 + 512*a^3*b^3*c^9*d^2 + 288*a^2*b^7*c^6*e^2 - 1504*a^3*b^5*c^7*e^
2 + 3840*a^4*b^3*c^8*e^2 + 2077*a^2*b^9*c^4*f^2 - 10656*a^3*b^7*c^5*f^2 + 30240*a^4*b^5*c^6*f^2 - 44800*a^5*b^
3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) + 6366*a^2*b^11*c^2
*g^2 - 35767*a^3*b^9*c^3*g^2 + 116928*a^4*b^7*c^4*g^2 - 219744*a^5*b^5*c^5*g^2 + 215040*a^6*b^3*c^6*g^2 - 49*a
^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c*g^2 + 3072*a^5*c^1
0*d*e + 2*b^10*c^5*d*e - 7168*a^6*c^9*d*g - 15360*a^6*c^9*e*f - 6*b^11*c^4*d*f + 10*b^12*c^3*d*g - 6*b^12*c^3*
e*f + 35840*a^7*c^8*f*g + 10*b^13*c^2*e*g - 36*a*b^8*c^6*d*e + 98*a*b^9*c^5*d*f - 1536*a^5*b*c^9*d*f - 10*a*c^
5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 168*a*b^10*c^4*d*g + 152*a*b^10*c^4*e*
f - 258*a*b^11*c^3*e*g + 43520*a^6*b*c^8*e*g + 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 24
6*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) + 192*a^2*b^6*c^7*d*e - 128*a^3*b^4*c^8*d*e - 1536*a^4*b^2*c^9*d*e
- 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 576*a^2*b^7*c^6*d*f + 1344*a^3*b^5*c^7*d*f - 512*a^4*b^3*c^8*d*f
+ 1044*a^2*b^8*c^5*d*g - 1548*a^2*b^8*c^5*e*f - 2688*a^3*b^6*c^6*d*g + 8064*a^3*b^6*c^6*e*f + 1152*a^4*b^4*c^7
*d*g - 22400*a^4*b^4*c^7*e*f + 6144*a^5*b^2*c^8*d*g + 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)
^(1/2) + 2706*a^2*b^9*c^4*e*g - 14784*a^3*b^7*c^5*e*g + 44352*a^4*b^5*c^6*e*g - 69120*a^5*b^3*c^7*e*g + 42*a^2
*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)
^(1/2) - 7278*a^2*b^10*c^3*f*g + 39132*a^3*b^8*c^4*f*g - 119616*a^4*b^6*c^5*f*g + 201600*a^5*b^4*c^6*f*g - 161
280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12
*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c -
b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(
4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*
b^2*c^12)))^(1/2)*(16*b^7*c^7 - 192*a*b^5*c^8 - 1024*a^3*b*c^10 + 768*a^2*b^3*c^9))/(2*(16*a^2*c^7 + b^4*c^5 -
8*a*b^2*c^6)))*(-(25*b^15*g^2 + b^9*c^6*d^2 + c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + b^11*c^4*e^2 + 9*b^13*c^2*f^
2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^4*b*c^10*d^2 - 27*a*b^9*c^5*e^2 - 3840*a^5*b*c^9*e^2 - 9*a*c^5
*e^2*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c^3*f^2 + 26880*a^6*b*c^8*f^2 - 80640*a^7*b*c^7*g^2 - 30*b^14*c*f*g
- 96*a^2*b^5*c^8*d^2 + 512*a^3*b^3*c^9*d^2 + 288*a^2*b^7*c^6*e^2 - 1504*a^3*b^5*c^7*e^2 + 3840*a^4*b^3*c^8*e^
2 + 2077*a^2*b^9*c^4*f^2 - 10656*a^3*b^7*c^5*f^2 + 30240*a^4*b^5*c^6*f^2 - 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*
f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) + 6366*a^2*b^11*c^2*g^2 - 35767*a^3*b^9*c^
3*g^2 + 116928*a^4*b^7*c^4*g^2 - 219744*a^5*b^5*c^5*g^2 + 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b
^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c*g^2 + 3072*a^5*c^10*d*e + 2*b^10*c^5*d*e
- 7168*a^6*c^9*d*g - 15360*a^6*c^9*e*f - 6*b^11*c^4*d*f + 10*b^12*c^3*d*g - 6*b^12*c^3*e*f + 35840*a^7*c^8*f*g
+ 10*b^13*c^2*e*g - 36*a*b^8*c^6*d*e + 98*a*b^9*c^5*d*f - 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9
)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 168*a*b^10*c^4*d*g + 152*a*b^10*c^4*e*f - 258*a*b^11*c^3*e*g
+ 43520*a^6*b*c^8*e*g + 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*
a*c - b^2)^9)^(1/2) + 192*a^2*b^6*c^7*d*e - 128*a^3*b^4*c^8*d*e - 1536*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*
a*c - b^2)^9)^(1/2) - 576*a^2*b^7*c^6*d*f + 1344*a^3*b^5*c^7*d*f - 512*a^4*b^3*c^8*d*f + 1044*a^2*b^8*c^5*d*g
- 1548*a^2*b^8*c^5*e*f - 2688*a^3*b^6*c^6*d*g + 8064*a^3*b^6*c^6*e*f + 1152*a^4*b^4*c^7*d*g - 22400*a^4*b^4*c^
7*e*f + 6144*a^5*b^2*c^8*d*g + 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^2*b^9*c
^4*e*g - 14784*a^3*b^7*c^5*e*g + 44352*a^4*b^5*c^6*e*g - 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2
)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^2*b^10*
c^3*f*g + 39132*a^3*b^8*c^4*f*g - 119616*a^4*b^6*c^5*f*g + 201600*a^5*b^4*c^6*f*g - 161280*a^6*b^2*c^7*f*g + 1
0*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c -
b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b
^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*c^
7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^(1/2) - (x*
(25*b^10*g^2 + 8*a^2*c^8*d^2 - 72*a^3*c^7*e^2 + b^4*c^6*d^2 + 200*a^4*c^6*f^2 + b^6*c^4*e^2 - 392*a^5*c^5*g^2
+ 9*b^8*c^2*f^2 + 2*a*b^2*c^7*d^2 - 16*a*b^4*c^5*e^2 - 114*a*b^6*c^3*f^2 - 30*b^9*c*f*g + 74*a^2*b^2*c^6*e^2 +
481*a^2*b^4*c^4*f^2 - 718*a^3*b^2*c^5*f^2 + 1676*a^2*b^6*c^2*g^2 - 3536*a^3*b^4*c^3*g^2 + 2794*a^4*b^2*c^4*g^
2 - 340*a*b^8*c*g^2 - 80*a^3*c^7*d*f + 2*b^5*c^5*d*e - 6*b^6*c^4*d*f + 336*a^4*c^6*e*g + 10*b^7*c^3*d*g - 6*b^
7*c^3*e*f + 10*b^8*c^2*e*g - 14*a*b^3*c^6*d*e - 8*a^2*b*c^7*d*e + 32*a*b^4*c^5*d*f - 58*a*b^5*c^4*d*g + 86*a*b
^5*c^4*e*f + 152*a^3*b*c^6*d*g + 472*a^3*b*c^6*e*f - 148*a*b^6*c^3*e*g + 394*a*b^7*c^2*f*g - 1768*a^4*b*c^5*f*
g + 4*a^2*b^2*c^6*d*f + 26*a^2*b^3*c^5*d*g - 374*a^2*b^3*c^5*e*f + 698*a^2*b^4*c^4*e*g - 1132*a^3*b^2*c^5*e*g
- 1804*a^2*b^5*c^3*f*g + 3266*a^3*b^3*c^4*f*g))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))*(-(25*b^15*g^2 + b^9
*c^6*d^2 + c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + b^11*c^4*e^2 + 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1
/2) - 768*a^4*b*c^10*d^2 - 27*a*b^9*c^5*e^2 - 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) - 213*
a*b^11*c^3*f^2 + 26880*a^6*b*c^8*f^2 - 80640*a^7*b*c^7*g^2 - 30*b^14*c*f*g - 96*a^2*b^5*c^8*d^2 + 512*a^3*b^3*
c^9*d^2 + 288*a^2*b^7*c^6*e^2 - 1504*a^3*b^5*c^7*e^2 + 3840*a^4*b^3*c^8*e^2 + 2077*a^2*b^9*c^4*f^2 - 10656*a^3
*b^7*c^5*f^2 + 30240*a^4*b^5*c^6*f^2 - 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c
^4*e^2*(-(4*a*c - b^2)^9)^(1/2) + 6366*a^2*b^11*c^2*g^2 - 35767*a^3*b^9*c^3*g^2 + 116928*a^4*b^7*c^4*g^2 - 219
744*a^5*b^5*c^5*g^2 + 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*
c - b^2)^9)^(1/2) - 615*a*b^13*c*g^2 + 3072*a^5*c^10*d*e + 2*b^10*c^5*d*e - 7168*a^6*c^9*d*g - 15360*a^6*c^9*e
*f - 6*b^11*c^4*d*f + 10*b^12*c^3*d*g - 6*b^12*c^3*e*f + 35840*a^7*c^8*f*g + 10*b^13*c^2*e*g - 36*a*b^8*c^6*d*
e + 98*a*b^9*c^5*d*f - 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2
)^9)^(1/2) - 168*a*b^10*c^4*d*g + 152*a*b^10*c^4*e*f - 258*a*b^11*c^3*e*g + 43520*a^6*b*c^8*e*g + 724*a*b^12*c
^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) + 192*a^2*b^6*c^
7*d*e - 128*a^3*b^4*c^8*d*e - 1536*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 576*a^2*b^7*c^
6*d*f + 1344*a^3*b^5*c^7*d*f - 512*a^4*b^3*c^8*d*f + 1044*a^2*b^8*c^5*d*g - 1548*a^2*b^8*c^5*e*f - 2688*a^3*b^
6*c^6*d*g + 8064*a^3*b^6*c^6*e*f + 1152*a^4*b^4*c^7*d*g - 22400*a^4*b^4*c^7*e*f + 6144*a^5*b^2*c^8*d*g + 30720
*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^2*b^9*c^4*e*g - 14784*a^3*b^7*c^5*e*g + 443
52*a^4*b^5*c^6*e*g - 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c
- b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^2*b^10*c^3*f*g + 39132*a^3*b^8*c^4*f*g - 11
9616*a^4*b^6*c^5*f*g + 201600*a^5*b^4*c^6*f*g - 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/
2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4
*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2)
- 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9
- 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^(1/2)*1i - (((2048*a^4*c^10*d - 10240*a^5*c^9*f
+ 384*a^2*b^4*c^8*d - 1536*a^3*b^2*c^9*d - 192*a^2*b^5*c^7*e + 768*a^3*b^3*c^8*e + 736*a^2*b^6*c^6*f - 4224*a
^3*b^4*c^7*f + 10752*a^4*b^2*c^8*f - 1264*a^2*b^7*c^5*g + 7488*a^3*b^5*c^6*g - 19712*a^4*b^3*c^7*g - 32*a*b^6*
c^7*d + 16*a*b^7*c^6*e - 1024*a^4*b*c^9*e - 48*a*b^8*c^5*f + 80*a*b^9*c^4*g + 19456*a^5*b*c^8*g)/(8*(64*a^3*c^
8 - b^6*c^5 + 12*a*b^4*c^6 - 48*a^2*b^2*c^7)) + (x*(-(25*b^15*g^2 + b^9*c^6*d^2 + c^6*d^2*(-(4*a*c - b^2)^9)^(
1/2) + b^11*c^4*e^2 + 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^4*b*c^10*d^2 - 27*a*b^9*c^5
*e^2 - 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c^3*f^2 + 26880*a^6*b*c^8*f^2 -
80640*a^7*b*c^7*g^2 - 30*b^14*c*f*g - 96*a^2*b^5*c^8*d^2 + 512*a^3*b^3*c^9*d^2 + 288*a^2*b^7*c^6*e^2 - 1504*a^
3*b^5*c^7*e^2 + 3840*a^4*b^3*c^8*e^2 + 2077*a^2*b^9*c^4*f^2 - 10656*a^3*b^7*c^5*f^2 + 30240*a^4*b^5*c^6*f^2 -
44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) + 6366*
a^2*b^11*c^2*g^2 - 35767*a^3*b^9*c^3*g^2 + 116928*a^4*b^7*c^4*g^2 - 219744*a^5*b^5*c^5*g^2 + 215040*a^6*b^3*c^
6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c*g^2 +
3072*a^5*c^10*d*e + 2*b^10*c^5*d*e - 7168*a^6*c^9*d*g - 15360*a^6*c^9*e*f - 6*b^11*c^4*d*f + 10*b^12*c^3*d*g -
6*b^12*c^3*e*f + 35840*a^7*c^8*f*g + 10*b^13*c^2*e*g - 36*a*b^8*c^6*d*e + 98*a*b^9*c^5*d*f - 1536*a^5*b*c^9*d
*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 168*a*b^10*c^4*d*g + 152*a
*b^10*c^4*e*f - 258*a*b^11*c^3*e*g + 43520*a^6*b*c^8*e*g + 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9
)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) + 192*a^2*b^6*c^7*d*e - 128*a^3*b^4*c^8*d*e - 1536*a^4*
b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 576*a^2*b^7*c^6*d*f + 1344*a^3*b^5*c^7*d*f - 512*a^4*
b^3*c^8*d*f + 1044*a^2*b^8*c^5*d*g - 1548*a^2*b^8*c^5*e*f - 2688*a^3*b^6*c^6*d*g + 8064*a^3*b^6*c^6*e*f + 1152
*a^4*b^4*c^7*d*g - 22400*a^4*b^4*c^7*e*f + 6144*a^5*b^2*c^8*d*g + 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a
*c - b^2)^9)^(1/2) + 2706*a^2*b^9*c^4*e*g - 14784*a^3*b^7*c^5*e*g + 44352*a^4*b^5*c^6*e*g - 69120*a^5*b^3*c^7*
e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a
*c - b^2)^9)^(1/2) - 7278*a^2*b^10*c^3*f*g + 39132*a^3*b^8*c^4*f*g - 119616*a^4*b^6*c^5*f*g + 201600*a^5*b^4*c
^6*f*g - 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9
)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g
*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^
(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11
- 6144*a^5*b^2*c^12)))^(1/2)*(16*b^7*c^7 - 192*a*b^5*c^8 - 1024*a^3*b*c^10 + 768*a^2*b^3*c^9))/(2*(16*a^2*c^7
+ b^4*c^5 - 8*a*b^2*c^6)))*(-(25*b^15*g^2 + b^9*c^6*d^2 + c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + b^11*c^4*e^2 + 9
*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^4*b*c^10*d^2 - 27*a*b^9*c^5*e^2 - 3840*a^5*b*c^9*e
^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c^3*f^2 + 26880*a^6*b*c^8*f^2 - 80640*a^7*b*c^7*g^2 - 3
0*b^14*c*f*g - 96*a^2*b^5*c^8*d^2 + 512*a^3*b^3*c^9*d^2 + 288*a^2*b^7*c^6*e^2 - 1504*a^3*b^5*c^7*e^2 + 3840*a^
4*b^3*c^8*e^2 + 2077*a^2*b^9*c^4*f^2 - 10656*a^3*b^7*c^5*f^2 + 30240*a^4*b^5*c^6*f^2 - 44800*a^5*b^3*c^7*f^2 +
25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) + 6366*a^2*b^11*c^2*g^2 - 3576
7*a^3*b^9*c^3*g^2 + 116928*a^4*b^7*c^4*g^2 - 219744*a^5*b^5*c^5*g^2 + 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*
(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c*g^2 + 3072*a^5*c^10*d*e + 2*b
^10*c^5*d*e - 7168*a^6*c^9*d*g - 15360*a^6*c^9*e*f - 6*b^11*c^4*d*f + 10*b^12*c^3*d*g - 6*b^12*c^3*e*f + 35840
*a^7*c^8*f*g + 10*b^13*c^2*e*g - 36*a*b^8*c^6*d*e + 98*a*b^9*c^5*d*f - 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*
a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 168*a*b^10*c^4*d*g + 152*a*b^10*c^4*e*f - 258*a*b
^11*c^3*e*g + 43520*a^6*b*c^8*e*g + 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c
^2*g^2*(-(4*a*c - b^2)^9)^(1/2) + 192*a^2*b^6*c^7*d*e - 128*a^3*b^4*c^8*d*e - 1536*a^4*b^2*c^9*d*e - 165*a*b^4
*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 576*a^2*b^7*c^6*d*f + 1344*a^3*b^5*c^7*d*f - 512*a^4*b^3*c^8*d*f + 1044*a^2*
b^8*c^5*d*g - 1548*a^2*b^8*c^5*e*f - 2688*a^3*b^6*c^6*d*g + 8064*a^3*b^6*c^6*e*f + 1152*a^4*b^4*c^7*d*g - 2240
0*a^4*b^4*c^7*e*f + 6144*a^5*b^2*c^8*d*g + 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 27
06*a^2*b^9*c^4*e*g - 14784*a^3*b^7*c^5*e*g + 44352*a^4*b^5*c^6*e*g - 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-
(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 72
78*a^2*b^10*c^3*f*g + 39132*a^3*b^8*c^4*f*g - 119616*a^4*b^6*c^5*f*g + 201600*a^5*b^4*c^6*f*g - 161280*a^6*b^2
*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*
g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/
2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^
13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))
^(1/2) + (x*(25*b^10*g^2 + 8*a^2*c^8*d^2 - 72*a^3*c^7*e^2 + b^4*c^6*d^2 + 200*a^4*c^6*f^2 + b^6*c^4*e^2 - 392*
a^5*c^5*g^2 + 9*b^8*c^2*f^2 + 2*a*b^2*c^7*d^2 - 16*a*b^4*c^5*e^2 - 114*a*b^6*c^3*f^2 - 30*b^9*c*f*g + 74*a^2*b
^2*c^6*e^2 + 481*a^2*b^4*c^4*f^2 - 718*a^3*b^2*c^5*f^2 + 1676*a^2*b^6*c^2*g^2 - 3536*a^3*b^4*c^3*g^2 + 2794*a^
4*b^2*c^4*g^2 - 340*a*b^8*c*g^2 - 80*a^3*c^7*d*f + 2*b^5*c^5*d*e - 6*b^6*c^4*d*f + 336*a^4*c^6*e*g + 10*b^7*c^
3*d*g - 6*b^7*c^3*e*f + 10*b^8*c^2*e*g - 14*a*b^3*c^6*d*e - 8*a^2*b*c^7*d*e + 32*a*b^4*c^5*d*f - 58*a*b^5*c^4*
d*g + 86*a*b^5*c^4*e*f + 152*a^3*b*c^6*d*g + 472*a^3*b*c^6*e*f - 148*a*b^6*c^3*e*g + 394*a*b^7*c^2*f*g - 1768*
a^4*b*c^5*f*g + 4*a^2*b^2*c^6*d*f + 26*a^2*b^3*c^5*d*g - 374*a^2*b^3*c^5*e*f + 698*a^2*b^4*c^4*e*g - 1132*a^3*
b^2*c^5*e*g - 1804*a^2*b^5*c^3*f*g + 3266*a^3*b^3*c^4*f*g))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))*(-(25*b^
15*g^2 + b^9*c^6*d^2 + c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + b^11*c^4*e^2 + 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c
- b^2)^9)^(1/2) - 768*a^4*b*c^10*d^2 - 27*a*b^9*c^5*e^2 - 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^
(1/2) - 213*a*b^11*c^3*f^2 + 26880*a^6*b*c^8*f^2 - 80640*a^7*b*c^7*g^2 - 30*b^14*c*f*g - 96*a^2*b^5*c^8*d^2 +
512*a^3*b^3*c^9*d^2 + 288*a^2*b^7*c^6*e^2 - 1504*a^3*b^5*c^7*e^2 + 3840*a^4*b^3*c^8*e^2 + 2077*a^2*b^9*c^4*f^2
- 10656*a^3*b^7*c^5*f^2 + 30240*a^4*b^5*c^6*f^2 - 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(
1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) + 6366*a^2*b^11*c^2*g^2 - 35767*a^3*b^9*c^3*g^2 + 116928*a^4*b^7*c
^4*g^2 - 219744*a^5*b^5*c^5*g^2 + 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2
*f^2*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c*g^2 + 3072*a^5*c^10*d*e + 2*b^10*c^5*d*e - 7168*a^6*c^9*d*g - 153
60*a^6*c^9*e*f - 6*b^11*c^4*d*f + 10*b^12*c^3*d*g - 6*b^12*c^3*e*f + 35840*a^7*c^8*f*g + 10*b^13*c^2*e*g - 36*
a*b^8*c^6*d*e + 98*a*b^9*c^5*d*f - 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-
(4*a*c - b^2)^9)^(1/2) - 168*a*b^10*c^4*d*g + 152*a*b^10*c^4*e*f - 258*a*b^11*c^3*e*g + 43520*a^6*b*c^8*e*g +
724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) + 19
2*a^2*b^6*c^7*d*e - 128*a^3*b^4*c^8*d*e - 1536*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 57
6*a^2*b^7*c^6*d*f + 1344*a^3*b^5*c^7*d*f - 512*a^4*b^3*c^8*d*f + 1044*a^2*b^8*c^5*d*g - 1548*a^2*b^8*c^5*e*f -
2688*a^3*b^6*c^6*d*g + 8064*a^3*b^6*c^6*e*f + 1152*a^4*b^4*c^7*d*g - 22400*a^4*b^4*c^7*e*f + 6144*a^5*b^2*c^8
*d*g + 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^2*b^9*c^4*e*g - 14784*a^3*b^7*c
^5*e*g + 44352*a^4*b^5*c^6*e*g - 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*
d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^2*b^10*c^3*f*g + 39132*a^3*b^8*
c^4*f*g - 119616*a^4*b^6*c^5*f*g + 201600*a^5*b^4*c^6*f*g - 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c -
b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*
c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^
2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*
a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^(1/2)*1i)/((((2048*a^4*c^10*d - 102
40*a^5*c^9*f + 384*a^2*b^4*c^8*d - 1536*a^3*b^2*c^9*d - 192*a^2*b^5*c^7*e + 768*a^3*b^3*c^8*e + 736*a^2*b^6*c^
6*f - 4224*a^3*b^4*c^7*f + 10752*a^4*b^2*c^8*f - 1264*a^2*b^7*c^5*g + 7488*a^3*b^5*c^6*g - 19712*a^4*b^3*c^7*g
- 32*a*b^6*c^7*d + 16*a*b^7*c^6*e - 1024*a^4*b*c^9*e - 48*a*b^8*c^5*f + 80*a*b^9*c^4*g + 19456*a^5*b*c^8*g)/(
8*(64*a^3*c^8 - b^6*c^5 + 12*a*b^4*c^6 - 48*a^2*b^2*c^7)) - (x*(-(25*b^15*g^2 + b^9*c^6*d^2 + c^6*d^2*(-(4*a*c
- b^2)^9)^(1/2) + b^11*c^4*e^2 + 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^4*b*c^10*d^2 -
27*a*b^9*c^5*e^2 - 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c^3*f^2 + 26880*a^6*
b*c^8*f^2 - 80640*a^7*b*c^7*g^2 - 30*b^14*c*f*g - 96*a^2*b^5*c^8*d^2 + 512*a^3*b^3*c^9*d^2 + 288*a^2*b^7*c^6*e
^2 - 1504*a^3*b^5*c^7*e^2 + 3840*a^4*b^3*c^8*e^2 + 2077*a^2*b^9*c^4*f^2 - 10656*a^3*b^7*c^5*f^2 + 30240*a^4*b^
5*c^6*f^2 - 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(
1/2) + 6366*a^2*b^11*c^2*g^2 - 35767*a^3*b^9*c^3*g^2 + 116928*a^4*b^7*c^4*g^2 - 219744*a^5*b^5*c^5*g^2 + 21504
0*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b
^13*c*g^2 + 3072*a^5*c^10*d*e + 2*b^10*c^5*d*e - 7168*a^6*c^9*d*g - 15360*a^6*c^9*e*f - 6*b^11*c^4*d*f + 10*b^
12*c^3*d*g - 6*b^12*c^3*e*f + 35840*a^7*c^8*f*g + 10*b^13*c^2*e*g - 36*a*b^8*c^6*d*e + 98*a*b^9*c^5*d*f - 1536
*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 168*a*b^10*c^4
*d*g + 152*a*b^10*c^4*e*f - 258*a*b^11*c^3*e*g + 43520*a^6*b*c^8*e*g + 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*
a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) + 192*a^2*b^6*c^7*d*e - 128*a^3*b^4*c^8*d*e
- 1536*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 576*a^2*b^7*c^6*d*f + 1344*a^3*b^5*c^7*d*
f - 512*a^4*b^3*c^8*d*f + 1044*a^2*b^8*c^5*d*g - 1548*a^2*b^8*c^5*e*f - 2688*a^3*b^6*c^6*d*g + 8064*a^3*b^6*c^
6*e*f + 1152*a^4*b^4*c^7*d*g - 22400*a^4*b^4*c^7*e*f + 6144*a^5*b^2*c^8*d*g + 30720*a^5*b^2*c^8*e*f - 6*b^2*c^
4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^2*b^9*c^4*e*g - 14784*a^3*b^7*c^5*e*g + 44352*a^4*b^5*c^6*e*g - 69120*
a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^
3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^2*b^10*c^3*f*g + 39132*a^3*b^8*c^4*f*g - 119616*a^4*b^6*c^5*f*g + 2016
00*a^5*b^4*c^6*f*g - 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*
a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a
*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*
c - b^2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*
a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^(1/2)*(16*b^7*c^7 - 192*a*b^5*c^8 - 1024*a^3*b*c^10 + 768*a^2*b^3*c^9))/(2
*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))*(-(25*b^15*g^2 + b^9*c^6*d^2 + c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + b^11
*c^4*e^2 + 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^4*b*c^10*d^2 - 27*a*b^9*c^5*e^2 - 3840
*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c^3*f^2 + 26880*a^6*b*c^8*f^2 - 80640*a^7*b
*c^7*g^2 - 30*b^14*c*f*g - 96*a^2*b^5*c^8*d^2 + 512*a^3*b^3*c^9*d^2 + 288*a^2*b^7*c^6*e^2 - 1504*a^3*b^5*c^7*e
^2 + 3840*a^4*b^3*c^8*e^2 + 2077*a^2*b^9*c^4*f^2 - 10656*a^3*b^7*c^5*f^2 + 30240*a^4*b^5*c^6*f^2 - 44800*a^5*b
^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) + 6366*a^2*b^11*c^
2*g^2 - 35767*a^3*b^9*c^3*g^2 + 116928*a^4*b^7*c^4*g^2 - 219744*a^5*b^5*c^5*g^2 + 215040*a^6*b^3*c^6*g^2 - 49*
a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c*g^2 + 3072*a^5*c^
10*d*e + 2*b^10*c^5*d*e - 7168*a^6*c^9*d*g - 15360*a^6*c^9*e*f - 6*b^11*c^4*d*f + 10*b^12*c^3*d*g - 6*b^12*c^3
*e*f + 35840*a^7*c^8*f*g + 10*b^13*c^2*e*g - 36*a*b^8*c^6*d*e + 98*a*b^9*c^5*d*f - 1536*a^5*b*c^9*d*f - 10*a*c
^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 168*a*b^10*c^4*d*g + 152*a*b^10*c^4*e
*f - 258*a*b^11*c^3*e*g + 43520*a^6*b*c^8*e*g + 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 2
46*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) + 192*a^2*b^6*c^7*d*e - 128*a^3*b^4*c^8*d*e - 1536*a^4*b^2*c^9*d*e
- 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 576*a^2*b^7*c^6*d*f + 1344*a^3*b^5*c^7*d*f - 512*a^4*b^3*c^8*d*f
+ 1044*a^2*b^8*c^5*d*g - 1548*a^2*b^8*c^5*e*f - 2688*a^3*b^6*c^6*d*g + 8064*a^3*b^6*c^6*e*f + 1152*a^4*b^4*c^
7*d*g - 22400*a^4*b^4*c^7*e*f + 6144*a^5*b^2*c^8*d*g + 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9
)^(1/2) + 2706*a^2*b^9*c^4*e*g - 14784*a^3*b^7*c^5*e*g + 44352*a^4*b^5*c^6*e*g - 69120*a^5*b^3*c^7*e*g + 42*a^
2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9
)^(1/2) - 7278*a^2*b^10*c^3*f*g + 39132*a^3*b^8*c^4*f*g - 119616*a^4*b^6*c^5*f*g + 201600*a^5*b^4*c^6*f*g - 16
1280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 1
2*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c -
b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*
(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5
*b^2*c^12)))^(1/2) - (x*(25*b^10*g^2 + 8*a^2*c^8*d^2 - 72*a^3*c^7*e^2 + b^4*c^6*d^2 + 200*a^4*c^6*f^2 + b^6*c^
4*e^2 - 392*a^5*c^5*g^2 + 9*b^8*c^2*f^2 + 2*a*b^2*c^7*d^2 - 16*a*b^4*c^5*e^2 - 114*a*b^6*c^3*f^2 - 30*b^9*c*f*
g + 74*a^2*b^2*c^6*e^2 + 481*a^2*b^4*c^4*f^2 - 718*a^3*b^2*c^5*f^2 + 1676*a^2*b^6*c^2*g^2 - 3536*a^3*b^4*c^3*g
^2 + 2794*a^4*b^2*c^4*g^2 - 340*a*b^8*c*g^2 - 80*a^3*c^7*d*f + 2*b^5*c^5*d*e - 6*b^6*c^4*d*f + 336*a^4*c^6*e*g
+ 10*b^7*c^3*d*g - 6*b^7*c^3*e*f + 10*b^8*c^2*e*g - 14*a*b^3*c^6*d*e - 8*a^2*b*c^7*d*e + 32*a*b^4*c^5*d*f - 5
8*a*b^5*c^4*d*g + 86*a*b^5*c^4*e*f + 152*a^3*b*c^6*d*g + 472*a^3*b*c^6*e*f - 148*a*b^6*c^3*e*g + 394*a*b^7*c^2
*f*g - 1768*a^4*b*c^5*f*g + 4*a^2*b^2*c^6*d*f + 26*a^2*b^3*c^5*d*g - 374*a^2*b^3*c^5*e*f + 698*a^2*b^4*c^4*e*g
- 1132*a^3*b^2*c^5*e*g - 1804*a^2*b^5*c^3*f*g + 3266*a^3*b^3*c^4*f*g))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6
)))*(-(25*b^15*g^2 + b^9*c^6*d^2 + c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + b^11*c^4*e^2 + 9*b^13*c^2*f^2 + 25*b^6*g
^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^4*b*c^10*d^2 - 27*a*b^9*c^5*e^2 - 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*
c - b^2)^9)^(1/2) - 213*a*b^11*c^3*f^2 + 26880*a^6*b*c^8*f^2 - 80640*a^7*b*c^7*g^2 - 30*b^14*c*f*g - 96*a^2*b^
5*c^8*d^2 + 512*a^3*b^3*c^9*d^2 + 288*a^2*b^7*c^6*e^2 - 1504*a^3*b^5*c^7*e^2 + 3840*a^4*b^3*c^8*e^2 + 2077*a^2
*b^9*c^4*f^2 - 10656*a^3*b^7*c^5*f^2 + 30240*a^4*b^5*c^6*f^2 - 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c
- b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) + 6366*a^2*b^11*c^2*g^2 - 35767*a^3*b^9*c^3*g^2 + 1169
28*a^4*b^7*c^4*g^2 - 219744*a^5*b^5*c^5*g^2 + 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2)
+ 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c*g^2 + 3072*a^5*c^10*d*e + 2*b^10*c^5*d*e - 7168*a^6*c
^9*d*g - 15360*a^6*c^9*e*f - 6*b^11*c^4*d*f + 10*b^12*c^3*d*g - 6*b^12*c^3*e*f + 35840*a^7*c^8*f*g + 10*b^13*c
^2*e*g - 36*a*b^8*c^6*d*e + 98*a*b^9*c^5*d*f - 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*
b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 168*a*b^10*c^4*d*g + 152*a*b^10*c^4*e*f - 258*a*b^11*c^3*e*g + 43520*a^6*
b*c^8*e*g + 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9
)^(1/2) + 192*a^2*b^6*c^7*d*e - 128*a^3*b^4*c^8*d*e - 1536*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9
)^(1/2) - 576*a^2*b^7*c^6*d*f + 1344*a^3*b^5*c^7*d*f - 512*a^4*b^3*c^8*d*f + 1044*a^2*b^8*c^5*d*g - 1548*a^2*b
^8*c^5*e*f - 2688*a^3*b^6*c^6*d*g + 8064*a^3*b^6*c^6*e*f + 1152*a^4*b^4*c^7*d*g - 22400*a^4*b^4*c^7*e*f + 6144
*a^5*b^2*c^8*d*g + 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^2*b^9*c^4*e*g - 147
84*a^3*b^7*c^5*e*g + 44352*a^4*b^5*c^6*e*g - 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) +
10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^2*b^10*c^3*f*g + 39
132*a^3*b^8*c^4*f*g - 119616*a^4*b^6*c^5*f*g + 201600*a^5*b^4*c^6*f*g - 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*
g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/
2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(
-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^1
0*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^(1/2) + (((2048*a^4*c^1
0*d - 10240*a^5*c^9*f + 384*a^2*b^4*c^8*d - 1536*a^3*b^2*c^9*d - 192*a^2*b^5*c^7*e + 768*a^3*b^3*c^8*e + 736*a
^2*b^6*c^6*f - 4224*a^3*b^4*c^7*f + 10752*a^4*b^2*c^8*f - 1264*a^2*b^7*c^5*g + 7488*a^3*b^5*c^6*g - 19712*a^4*
b^3*c^7*g - 32*a*b^6*c^7*d + 16*a*b^7*c^6*e - 1024*a^4*b*c^9*e - 48*a*b^8*c^5*f + 80*a*b^9*c^4*g + 19456*a^5*b
*c^8*g)/(8*(64*a^3*c^8 - b^6*c^5 + 12*a*b^4*c^6 - 48*a^2*b^2*c^7)) + (x*(-(25*b^15*g^2 + b^9*c^6*d^2 + c^6*d^2
*(-(4*a*c - b^2)^9)^(1/2) + b^11*c^4*e^2 + 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^4*b*c^
10*d^2 - 27*a*b^9*c^5*e^2 - 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c^3*f^2 + 2
6880*a^6*b*c^8*f^2 - 80640*a^7*b*c^7*g^2 - 30*b^14*c*f*g - 96*a^2*b^5*c^8*d^2 + 512*a^3*b^3*c^9*d^2 + 288*a^2*
b^7*c^6*e^2 - 1504*a^3*b^5*c^7*e^2 + 3840*a^4*b^3*c^8*e^2 + 2077*a^2*b^9*c^4*f^2 - 10656*a^3*b^7*c^5*f^2 + 302
40*a^4*b^5*c^6*f^2 - 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c -
b^2)^9)^(1/2) + 6366*a^2*b^11*c^2*g^2 - 35767*a^3*b^9*c^3*g^2 + 116928*a^4*b^7*c^4*g^2 - 219744*a^5*b^5*c^5*g^
2 + 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2)
- 615*a*b^13*c*g^2 + 3072*a^5*c^10*d*e + 2*b^10*c^5*d*e - 7168*a^6*c^9*d*g - 15360*a^6*c^9*e*f - 6*b^11*c^4*d*
f + 10*b^12*c^3*d*g - 6*b^12*c^3*e*f + 35840*a^7*c^8*f*g + 10*b^13*c^2*e*g - 36*a*b^8*c^6*d*e + 98*a*b^9*c^5*d
*f - 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 168*a
*b^10*c^4*d*g + 152*a*b^10*c^4*e*f - 258*a*b^11*c^3*e*g + 43520*a^6*b*c^8*e*g + 724*a*b^12*c^2*f*g - 30*b^5*c*
f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) + 192*a^2*b^6*c^7*d*e - 128*a^3*b^
4*c^8*d*e - 1536*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 576*a^2*b^7*c^6*d*f + 1344*a^3*b
^5*c^7*d*f - 512*a^4*b^3*c^8*d*f + 1044*a^2*b^8*c^5*d*g - 1548*a^2*b^8*c^5*e*f - 2688*a^3*b^6*c^6*d*g + 8064*a
^3*b^6*c^6*e*f + 1152*a^4*b^4*c^7*d*g - 22400*a^4*b^4*c^7*e*f + 6144*a^5*b^2*c^8*d*g + 30720*a^5*b^2*c^8*e*f -
6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^2*b^9*c^4*e*g - 14784*a^3*b^7*c^5*e*g + 44352*a^4*b^5*c^6*e*g
- 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) -
6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^2*b^10*c^3*f*g + 39132*a^3*b^8*c^4*f*g - 119616*a^4*b^6*c^5*f
*g + 201600*a^5*b^4*c^6*f*g - 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*
f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/
2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*
g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^1
0 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^(1/2)*(16*b^7*c^7 - 192*a*b^5*c^8 - 1024*a^3*b*c^10 + 768*a^2*b^3
*c^9))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))*(-(25*b^15*g^2 + b^9*c^6*d^2 + c^6*d^2*(-(4*a*c - b^2)^9)^(1/
2) + b^11*c^4*e^2 + 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^4*b*c^10*d^2 - 27*a*b^9*c^5*e
^2 - 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c^3*f^2 + 26880*a^6*b*c^8*f^2 - 80
640*a^7*b*c^7*g^2 - 30*b^14*c*f*g - 96*a^2*b^5*c^8*d^2 + 512*a^3*b^3*c^9*d^2 + 288*a^2*b^7*c^6*e^2 - 1504*a^3*
b^5*c^7*e^2 + 3840*a^4*b^3*c^8*e^2 + 2077*a^2*b^9*c^4*f^2 - 10656*a^3*b^7*c^5*f^2 + 30240*a^4*b^5*c^6*f^2 - 44
800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) + 6366*a^
2*b^11*c^2*g^2 - 35767*a^3*b^9*c^3*g^2 + 116928*a^4*b^7*c^4*g^2 - 219744*a^5*b^5*c^5*g^2 + 215040*a^6*b^3*c^6*
g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c*g^2 + 30
72*a^5*c^10*d*e + 2*b^10*c^5*d*e - 7168*a^6*c^9*d*g - 15360*a^6*c^9*e*f - 6*b^11*c^4*d*f + 10*b^12*c^3*d*g - 6
*b^12*c^3*e*f + 35840*a^7*c^8*f*g + 10*b^13*c^2*e*g - 36*a*b^8*c^6*d*e + 98*a*b^9*c^5*d*f - 1536*a^5*b*c^9*d*f
- 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 168*a*b^10*c^4*d*g + 152*a*b
^10*c^4*e*f - 258*a*b^11*c^3*e*g + 43520*a^6*b*c^8*e*g + 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^
(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) + 192*a^2*b^6*c^7*d*e - 128*a^3*b^4*c^8*d*e - 1536*a^4*b^
2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 576*a^2*b^7*c^6*d*f + 1344*a^3*b^5*c^7*d*f - 512*a^4*b^
3*c^8*d*f + 1044*a^2*b^8*c^5*d*g - 1548*a^2*b^8*c^5*e*f - 2688*a^3*b^6*c^6*d*g + 8064*a^3*b^6*c^6*e*f + 1152*a
^4*b^4*c^7*d*g - 22400*a^4*b^4*c^7*e*f + 6144*a^5*b^2*c^8*d*g + 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c
- b^2)^9)^(1/2) + 2706*a^2*b^9*c^4*e*g - 14784*a^3*b^7*c^5*e*g + 44352*a^4*b^5*c^6*e*g - 69120*a^5*b^3*c^7*e*
g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c
- b^2)^9)^(1/2) - 7278*a^2*b^10*c^3*f*g + 39132*a^3*b^8*c^4*f*g - 119616*a^4*b^6*c^5*f*g + 201600*a^5*b^4*c^6
*f*g - 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^
(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(
-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1
/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 -
6144*a^5*b^2*c^12)))^(1/2) + (x*(25*b^10*g^2 + 8*a^2*c^8*d^2 - 72*a^3*c^7*e^2 + b^4*c^6*d^2 + 200*a^4*c^6*f^2
+ b^6*c^4*e^2 - 392*a^5*c^5*g^2 + 9*b^8*c^2*f^2 + 2*a*b^2*c^7*d^2 - 16*a*b^4*c^5*e^2 - 114*a*b^6*c^3*f^2 - 30
*b^9*c*f*g + 74*a^2*b^2*c^6*e^2 + 481*a^2*b^4*c^4*f^2 - 718*a^3*b^2*c^5*f^2 + 1676*a^2*b^6*c^2*g^2 - 3536*a^3*
b^4*c^3*g^2 + 2794*a^4*b^2*c^4*g^2 - 340*a*b^8*c*g^2 - 80*a^3*c^7*d*f + 2*b^5*c^5*d*e - 6*b^6*c^4*d*f + 336*a^
4*c^6*e*g + 10*b^7*c^3*d*g - 6*b^7*c^3*e*f + 10*b^8*c^2*e*g - 14*a*b^3*c^6*d*e - 8*a^2*b*c^7*d*e + 32*a*b^4*c^
5*d*f - 58*a*b^5*c^4*d*g + 86*a*b^5*c^4*e*f + 152*a^3*b*c^6*d*g + 472*a^3*b*c^6*e*f - 148*a*b^6*c^3*e*g + 394*
a*b^7*c^2*f*g - 1768*a^4*b*c^5*f*g + 4*a^2*b^2*c^6*d*f + 26*a^2*b^3*c^5*d*g - 374*a^2*b^3*c^5*e*f + 698*a^2*b^
4*c^4*e*g - 1132*a^3*b^2*c^5*e*g - 1804*a^2*b^5*c^3*f*g + 3266*a^3*b^3*c^4*f*g))/(2*(16*a^2*c^7 + b^4*c^5 - 8*
a*b^2*c^6)))*(-(25*b^15*g^2 + b^9*c^6*d^2 + c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + b^11*c^4*e^2 + 9*b^13*c^2*f^2 +
25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^4*b*c^10*d^2 - 27*a*b^9*c^5*e^2 - 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^
2*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c^3*f^2 + 26880*a^6*b*c^8*f^2 - 80640*a^7*b*c^7*g^2 - 30*b^14*c*f*g -
96*a^2*b^5*c^8*d^2 + 512*a^3*b^3*c^9*d^2 + 288*a^2*b^7*c^6*e^2 - 1504*a^3*b^5*c^7*e^2 + 3840*a^4*b^3*c^8*e^2 +
2077*a^2*b^9*c^4*f^2 - 10656*a^3*b^7*c^5*f^2 + 30240*a^4*b^5*c^6*f^2 - 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2
*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) + 6366*a^2*b^11*c^2*g^2 - 35767*a^3*b^9*c^3*g
^2 + 116928*a^4*b^7*c^4*g^2 - 219744*a^5*b^5*c^5*g^2 + 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)
^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c*g^2 + 3072*a^5*c^10*d*e + 2*b^10*c^5*d*e - 7
168*a^6*c^9*d*g - 15360*a^6*c^9*e*f - 6*b^11*c^4*d*f + 10*b^12*c^3*d*g - 6*b^12*c^3*e*f + 35840*a^7*c^8*f*g +
10*b^13*c^2*e*g - 36*a*b^8*c^6*d*e + 98*a*b^9*c^5*d*f - 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(
1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 168*a*b^10*c^4*d*g + 152*a*b^10*c^4*e*f - 258*a*b^11*c^3*e*g + 4
3520*a^6*b*c^8*e*g + 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c
- b^2)^9)^(1/2) + 192*a^2*b^6*c^7*d*e - 128*a^3*b^4*c^8*d*e - 1536*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c
- b^2)^9)^(1/2) - 576*a^2*b^7*c^6*d*f + 1344*a^3*b^5*c^7*d*f - 512*a^4*b^3*c^8*d*f + 1044*a^2*b^8*c^5*d*g - 1
548*a^2*b^8*c^5*e*f - 2688*a^3*b^6*c^6*d*g + 8064*a^3*b^6*c^6*e*f + 1152*a^4*b^4*c^7*d*g - 22400*a^4*b^4*c^7*e
*f + 6144*a^5*b^2*c^8*d*g + 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^2*b^9*c^4*
e*g - 14784*a^3*b^7*c^5*e*g + 44352*a^4*b^5*c^6*e*g - 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9
)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^2*b^10*c^3
*f*g + 39132*a^3*b^8*c^4*f*g - 119616*a^4*b^6*c^5*f*g + 201600*a^5*b^4*c^6*f*g - 161280*a^6*b^2*c^7*f*g + 10*b
^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^
2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*
c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 -
24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^(1/2) - (2744*
a^7*c^3*g^3 - 225*a^4*b^6*g^3 - 216*a^4*c^6*e^3 + 3*a*b^3*c^6*d^3 + 4*a^2*b*c^7*d^3 + 1300*a^5*b*c^4*f^3 - 24*
a^3*c^7*d^2*e + 2060*a^5*b^4*c*g^3 - 125*a^2*b^8*e*g^2 + 56*a^4*c^6*d^2*g - 600*a^5*c^5*e*f^2 + 175*a^3*b^7*f*
g^2 + 1512*a^5*c^5*e^2*g - 3528*a^6*c^4*e*g^2 + 1400*a^6*c^4*f^2*g - 5*a^2*b^4*c^4*e^3 + 66*a^3*b^2*c^5*e^3 +
63*a^3*b^5*c^2*f^3 - 573*a^4*b^3*c^3*f^3 - 5334*a^6*b^2*c^2*g^3 + 75*a*b^9*d*g^2 + 240*a^4*c^6*d*e*f - 560*a^5
*c^5*d*f*g + 6*a*b^4*c^5*d^2*e + 3*a*b^5*c^4*d*e^2 + 204*a^3*b*c^6*d*e^2 - 18*a*b^5*c^4*d^2*f + 27*a*b^7*c^2*d
*f^2 + 12*a^3*b*c^6*d^2*f - 420*a^4*b*c^5*d*f^2 + 30*a*b^6*c^3*d^2*g - 845*a^2*b^7*c*d*g^2 + 924*a^4*b*c^5*e^2
*f + 2044*a^5*b*c^4*d*g^2 + 1350*a^3*b^6*c*e*g^2 - 210*a^3*b^6*c*f^2*g - 1485*a^4*b^5*c*f*g^2 + 364*a^6*b*c^3*
f*g^2 - 42*a^2*b^2*c^6*d^2*e - 51*a^2*b^3*c^5*d*e^2 + 81*a^2*b^3*c^5*d^2*f - 279*a^2*b^5*c^3*d*f^2 + 801*a^3*b
^3*c^4*d*f^2 - 149*a^2*b^4*c^4*d^2*g + 30*a^2*b^5*c^3*e^2*f - 45*a^2*b^6*c^2*e*f^2 + 78*a^3*b^2*c^5*d^2*g - 33
9*a^3*b^3*c^4*e^2*f + 402*a^3*b^4*c^3*e*f^2 + 3198*a^3*b^5*c^2*d*g^2 - 762*a^4*b^2*c^4*e*f^2 - 4571*a^4*b^3*c^
3*d*g^2 - 50*a^2*b^6*c^2*e^2*g + 600*a^3*b^4*c^3*e^2*g - 2002*a^4*b^2*c^4*e^2*g - 4835*a^4*b^4*c^2*e*g^2 + 659
8*a^5*b^2*c^3*e*g^2 + 1927*a^4*b^4*c^2*f^2*g - 4722*a^5*b^2*c^3*f^2*g + 3061*a^5*b^3*c^2*f*g^2 - 90*a*b^8*c*d*
f*g - 18*a*b^6*c^3*d*e*f + 30*a*b^7*c^2*d*e*g - 1352*a^4*b*c^5*d*e*g + 150*a^2*b^7*c*e*f*g - 2312*a^5*b*c^4*e*
f*g + 246*a^2*b^4*c^4*d*e*f - 804*a^3*b^2*c^5*d*e*f - 424*a^2*b^5*c^3*d*e*g + 1578*a^3*b^3*c^4*d*e*g + 972*a^2
*b^6*c^2*d*f*g - 3244*a^3*b^4*c^3*d*f*g + 3276*a^4*b^2*c^4*d*f*g - 1480*a^3*b^5*c^2*e*f*g + 4122*a^4*b^3*c^3*e
*f*g)/(4*(64*a^3*c^8 - b^6*c^5 + 12*a*b^4*c^6 - 48*a^2*b^2*c^7))))*(-(25*b^15*g^2 + b^9*c^6*d^2 + c^6*d^2*(-(4
*a*c - b^2)^9)^(1/2) + b^11*c^4*e^2 + 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^4*b*c^10*d^
2 - 27*a*b^9*c^5*e^2 - 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c^3*f^2 + 26880*
a^6*b*c^8*f^2 - 80640*a^7*b*c^7*g^2 - 30*b^14*c*f*g - 96*a^2*b^5*c^8*d^2 + 512*a^3*b^3*c^9*d^2 + 288*a^2*b^7*c
^6*e^2 - 1504*a^3*b^5*c^7*e^2 + 3840*a^4*b^3*c^8*e^2 + 2077*a^2*b^9*c^4*f^2 - 10656*a^3*b^7*c^5*f^2 + 30240*a^
4*b^5*c^6*f^2 - 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^
9)^(1/2) + 6366*a^2*b^11*c^2*g^2 - 35767*a^3*b^9*c^3*g^2 + 116928*a^4*b^7*c^4*g^2 - 219744*a^5*b^5*c^5*g^2 + 2
15040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) - 615
*a*b^13*c*g^2 + 3072*a^5*c^10*d*e + 2*b^10*c^5*d*e - 7168*a^6*c^9*d*g - 15360*a^6*c^9*e*f - 6*b^11*c^4*d*f + 1
0*b^12*c^3*d*g - 6*b^12*c^3*e*f + 35840*a^7*c^8*f*g + 10*b^13*c^2*e*g - 36*a*b^8*c^6*d*e + 98*a*b^9*c^5*d*f -
1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 168*a*b^10
*c^4*d*g + 152*a*b^10*c^4*e*f - 258*a*b^11*c^3*e*g + 43520*a^6*b*c^8*e*g + 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(
-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) + 192*a^2*b^6*c^7*d*e - 128*a^3*b^4*c^8
*d*e - 1536*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) - 576*a^2*b^7*c^6*d*f + 1344*a^3*b^5*c^
7*d*f - 512*a^4*b^3*c^8*d*f + 1044*a^2*b^8*c^5*d*g - 1548*a^2*b^8*c^5*e*f - 2688*a^3*b^6*c^6*d*g + 8064*a^3*b^
6*c^6*e*f + 1152*a^4*b^4*c^7*d*g - 22400*a^4*b^4*c^7*e*f + 6144*a^5*b^2*c^8*d*g + 30720*a^5*b^2*c^8*e*f - 6*b^
2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^2*b^9*c^4*e*g - 14784*a^3*b^7*c^5*e*g + 44352*a^4*b^5*c^6*e*g - 69
120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^
3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^2*b^10*c^3*f*g + 39132*a^3*b^8*c^4*f*g - 119616*a^4*b^6*c^5*f*g +
201600*a^5*b^4*c^6*f*g - 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(
-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) -
78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(
4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3
840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^(1/2)*2i + atan(((((2048*a^4*c^10*d - 10240*a^5*c^9*f + 384*a^2*b^4*c^
8*d - 1536*a^3*b^2*c^9*d - 192*a^2*b^5*c^7*e + 768*a^3*b^3*c^8*e + 736*a^2*b^6*c^6*f - 4224*a^3*b^4*c^7*f + 10
752*a^4*b^2*c^8*f - 1264*a^2*b^7*c^5*g + 7488*a^3*b^5*c^6*g - 19712*a^4*b^3*c^7*g - 32*a*b^6*c^7*d + 16*a*b^7*
c^6*e - 1024*a^4*b*c^9*e - 48*a*b^8*c^5*f + 80*a*b^9*c^4*g + 19456*a^5*b*c^8*g)/(8*(64*a^3*c^8 - b^6*c^5 + 12*
a*b^4*c^6 - 48*a^2*b^2*c^7)) - (x*((c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^6*d^2 - 25*b^15*g^2 - b^11*c^4*e^
2 - 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^4*b*c^10*d^2 + 27*a*b^9*c^5*e^2 + 3840*a^5*b*
c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c^3*f^2 - 26880*a^6*b*c^8*f^2 + 80640*a^7*b*c^7*g^
2 + 30*b^14*c*f*g + 96*a^2*b^5*c^8*d^2 - 512*a^3*b^3*c^9*d^2 - 288*a^2*b^7*c^6*e^2 + 1504*a^3*b^5*c^7*e^2 - 38
40*a^4*b^3*c^8*e^2 - 2077*a^2*b^9*c^4*f^2 + 10656*a^3*b^7*c^5*f^2 - 30240*a^4*b^5*c^6*f^2 + 44800*a^5*b^3*c^7*
f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 6366*a^2*b^11*c^2*g^2 +
35767*a^3*b^9*c^3*g^2 - 116928*a^4*b^7*c^4*g^2 + 219744*a^5*b^5*c^5*g^2 - 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3
*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 615*a*b^13*c*g^2 - 3072*a^5*c^10*d*e
- 2*b^10*c^5*d*e + 7168*a^6*c^9*d*g + 15360*a^6*c^9*e*f + 6*b^11*c^4*d*f - 10*b^12*c^3*d*g + 6*b^12*c^3*e*f -
35840*a^7*c^8*f*g - 10*b^13*c^2*e*g + 36*a*b^8*c^6*d*e - 98*a*b^9*c^5*d*f + 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*
(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 168*a*b^10*c^4*d*g - 152*a*b^10*c^4*e*f + 25
8*a*b^11*c^3*e*g - 43520*a^6*b*c^8*e*g - 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*
b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 192*a^2*b^6*c^7*d*e + 128*a^3*b^4*c^8*d*e + 1536*a^4*b^2*c^9*d*e - 165*
a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 576*a^2*b^7*c^6*d*f - 1344*a^3*b^5*c^7*d*f + 512*a^4*b^3*c^8*d*f - 1044
*a^2*b^8*c^5*d*g + 1548*a^2*b^8*c^5*e*f + 2688*a^3*b^6*c^6*d*g - 8064*a^3*b^6*c^6*e*f - 1152*a^4*b^4*c^7*d*g +
22400*a^4*b^4*c^7*e*f - 6144*a^5*b^2*c^8*d*g - 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2)
- 2706*a^2*b^9*c^4*e*g + 14784*a^3*b^7*c^5*e*g - 44352*a^4*b^5*c^6*e*g + 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e
*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2)
+ 7278*a^2*b^10*c^3*f*g - 39132*a^3*b^8*c^4*f*g + 119616*a^4*b^6*c^5*f*g - 201600*a^5*b^4*c^6*f*g + 161280*a^
6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c
^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9
)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a
^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^
12)))^(1/2)*(16*b^7*c^7 - 192*a*b^5*c^8 - 1024*a^3*b*c^10 + 768*a^2*b^3*c^9))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b
^2*c^6)))*((c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^6*d^2 - 25*b^15*g^2 - b^11*c^4*e^2 - 9*b^13*c^2*f^2 + 25*
b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^4*b*c^10*d^2 + 27*a*b^9*c^5*e^2 + 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-
(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c^3*f^2 - 26880*a^6*b*c^8*f^2 + 80640*a^7*b*c^7*g^2 + 30*b^14*c*f*g + 96*a
^2*b^5*c^8*d^2 - 512*a^3*b^3*c^9*d^2 - 288*a^2*b^7*c^6*e^2 + 1504*a^3*b^5*c^7*e^2 - 3840*a^4*b^3*c^8*e^2 - 207
7*a^2*b^9*c^4*f^2 + 10656*a^3*b^7*c^5*f^2 - 30240*a^4*b^5*c^6*f^2 + 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(
4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 6366*a^2*b^11*c^2*g^2 + 35767*a^3*b^9*c^3*g^2 -
116928*a^4*b^7*c^4*g^2 + 219744*a^5*b^5*c^5*g^2 - 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^
(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 615*a*b^13*c*g^2 - 3072*a^5*c^10*d*e - 2*b^10*c^5*d*e + 7168*
a^6*c^9*d*g + 15360*a^6*c^9*e*f + 6*b^11*c^4*d*f - 10*b^12*c^3*d*g + 6*b^12*c^3*e*f - 35840*a^7*c^8*f*g - 10*b
^13*c^2*e*g + 36*a*b^8*c^6*d*e - 98*a*b^9*c^5*d*f + 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2)
+ 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 168*a*b^10*c^4*d*g - 152*a*b^10*c^4*e*f + 258*a*b^11*c^3*e*g - 43520
*a^6*b*c^8*e*g - 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b
^2)^9)^(1/2) - 192*a^2*b^6*c^7*d*e + 128*a^3*b^4*c^8*d*e + 1536*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b
^2)^9)^(1/2) + 576*a^2*b^7*c^6*d*f - 1344*a^3*b^5*c^7*d*f + 512*a^4*b^3*c^8*d*f - 1044*a^2*b^8*c^5*d*g + 1548*
a^2*b^8*c^5*e*f + 2688*a^3*b^6*c^6*d*g - 8064*a^3*b^6*c^6*e*f - 1152*a^4*b^4*c^7*d*g + 22400*a^4*b^4*c^7*e*f -
6144*a^5*b^2*c^8*d*g - 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^2*b^9*c^4*e*g
+ 14784*a^3*b^7*c^5*e*g - 44352*a^4*b^5*c^6*e*g + 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1
/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^2*b^10*c^3*f*g
- 39132*a^3*b^8*c^4*f*g + 119616*a^4*b^6*c^5*f*g - 201600*a^5*b^4*c^6*f*g + 161280*a^6*b^2*c^7*f*g + 10*b^4*c
^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9
)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*
f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*
a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^(1/2) - (x*(25*b^1
0*g^2 + 8*a^2*c^8*d^2 - 72*a^3*c^7*e^2 + b^4*c^6*d^2 + 200*a^4*c^6*f^2 + b^6*c^4*e^2 - 392*a^5*c^5*g^2 + 9*b^8
*c^2*f^2 + 2*a*b^2*c^7*d^2 - 16*a*b^4*c^5*e^2 - 114*a*b^6*c^3*f^2 - 30*b^9*c*f*g + 74*a^2*b^2*c^6*e^2 + 481*a^
2*b^4*c^4*f^2 - 718*a^3*b^2*c^5*f^2 + 1676*a^2*b^6*c^2*g^2 - 3536*a^3*b^4*c^3*g^2 + 2794*a^4*b^2*c^4*g^2 - 340
*a*b^8*c*g^2 - 80*a^3*c^7*d*f + 2*b^5*c^5*d*e - 6*b^6*c^4*d*f + 336*a^4*c^6*e*g + 10*b^7*c^3*d*g - 6*b^7*c^3*e
*f + 10*b^8*c^2*e*g - 14*a*b^3*c^6*d*e - 8*a^2*b*c^7*d*e + 32*a*b^4*c^5*d*f - 58*a*b^5*c^4*d*g + 86*a*b^5*c^4*
e*f + 152*a^3*b*c^6*d*g + 472*a^3*b*c^6*e*f - 148*a*b^6*c^3*e*g + 394*a*b^7*c^2*f*g - 1768*a^4*b*c^5*f*g + 4*a
^2*b^2*c^6*d*f + 26*a^2*b^3*c^5*d*g - 374*a^2*b^3*c^5*e*f + 698*a^2*b^4*c^4*e*g - 1132*a^3*b^2*c^5*e*g - 1804*
a^2*b^5*c^3*f*g + 3266*a^3*b^3*c^4*f*g))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))*((c^6*d^2*(-(4*a*c - b^2)^9
)^(1/2) - b^9*c^6*d^2 - 25*b^15*g^2 - b^11*c^4*e^2 - 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 76
8*a^4*b*c^10*d^2 + 27*a*b^9*c^5*e^2 + 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c
^3*f^2 - 26880*a^6*b*c^8*f^2 + 80640*a^7*b*c^7*g^2 + 30*b^14*c*f*g + 96*a^2*b^5*c^8*d^2 - 512*a^3*b^3*c^9*d^2
- 288*a^2*b^7*c^6*e^2 + 1504*a^3*b^5*c^7*e^2 - 3840*a^4*b^3*c^8*e^2 - 2077*a^2*b^9*c^4*f^2 + 10656*a^3*b^7*c^5
*f^2 - 30240*a^4*b^5*c^6*f^2 + 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(
-(4*a*c - b^2)^9)^(1/2) - 6366*a^2*b^11*c^2*g^2 + 35767*a^3*b^9*c^3*g^2 - 116928*a^4*b^7*c^4*g^2 + 219744*a^5*
b^5*c^5*g^2 - 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)
^9)^(1/2) + 615*a*b^13*c*g^2 - 3072*a^5*c^10*d*e - 2*b^10*c^5*d*e + 7168*a^6*c^9*d*g + 15360*a^6*c^9*e*f + 6*b
^11*c^4*d*f - 10*b^12*c^3*d*g + 6*b^12*c^3*e*f - 35840*a^7*c^8*f*g - 10*b^13*c^2*e*g + 36*a*b^8*c^6*d*e - 98*a
*b^9*c^5*d*f + 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/
2) + 168*a*b^10*c^4*d*g - 152*a*b^10*c^4*e*f + 258*a*b^11*c^3*e*g - 43520*a^6*b*c^8*e*g - 724*a*b^12*c^2*f*g -
30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 192*a^2*b^6*c^7*d*e +
128*a^3*b^4*c^8*d*e + 1536*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 576*a^2*b^7*c^6*d*f -
1344*a^3*b^5*c^7*d*f + 512*a^4*b^3*c^8*d*f - 1044*a^2*b^8*c^5*d*g + 1548*a^2*b^8*c^5*e*f + 2688*a^3*b^6*c^6*d*
g - 8064*a^3*b^6*c^6*e*f - 1152*a^4*b^4*c^7*d*g + 22400*a^4*b^4*c^7*e*f - 6144*a^5*b^2*c^8*d*g - 30720*a^5*b^2
*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^2*b^9*c^4*e*g + 14784*a^3*b^7*c^5*e*g - 44352*a^4*b
^5*c^6*e*g + 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^
9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^2*b^10*c^3*f*g - 39132*a^3*b^8*c^4*f*g + 119616*a^4
*b^6*c^5*f*g - 201600*a^5*b^4*c^6*f*g + 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*
a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b
^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^
2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a
^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^(1/2)*1i - (((2048*a^4*c^10*d - 10240*a^5*c^9*f + 384*a
^2*b^4*c^8*d - 1536*a^3*b^2*c^9*d - 192*a^2*b^5*c^7*e + 768*a^3*b^3*c^8*e + 736*a^2*b^6*c^6*f - 4224*a^3*b^4*c
^7*f + 10752*a^4*b^2*c^8*f - 1264*a^2*b^7*c^5*g + 7488*a^3*b^5*c^6*g - 19712*a^4*b^3*c^7*g - 32*a*b^6*c^7*d +
16*a*b^7*c^6*e - 1024*a^4*b*c^9*e - 48*a*b^8*c^5*f + 80*a*b^9*c^4*g + 19456*a^5*b*c^8*g)/(8*(64*a^3*c^8 - b^6*
c^5 + 12*a*b^4*c^6 - 48*a^2*b^2*c^7)) + (x*((c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^6*d^2 - 25*b^15*g^2 - b^
11*c^4*e^2 - 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^4*b*c^10*d^2 + 27*a*b^9*c^5*e^2 + 38
40*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c^3*f^2 - 26880*a^6*b*c^8*f^2 + 80640*a^7
*b*c^7*g^2 + 30*b^14*c*f*g + 96*a^2*b^5*c^8*d^2 - 512*a^3*b^3*c^9*d^2 - 288*a^2*b^7*c^6*e^2 + 1504*a^3*b^5*c^7
*e^2 - 3840*a^4*b^3*c^8*e^2 - 2077*a^2*b^9*c^4*f^2 + 10656*a^3*b^7*c^5*f^2 - 30240*a^4*b^5*c^6*f^2 + 44800*a^5
*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 6366*a^2*b^11*
c^2*g^2 + 35767*a^3*b^9*c^3*g^2 - 116928*a^4*b^7*c^4*g^2 + 219744*a^5*b^5*c^5*g^2 - 215040*a^6*b^3*c^6*g^2 - 4
9*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 615*a*b^13*c*g^2 - 3072*a^5*
c^10*d*e - 2*b^10*c^5*d*e + 7168*a^6*c^9*d*g + 15360*a^6*c^9*e*f + 6*b^11*c^4*d*f - 10*b^12*c^3*d*g + 6*b^12*c
^3*e*f - 35840*a^7*c^8*f*g - 10*b^13*c^2*e*g + 36*a*b^8*c^6*d*e - 98*a*b^9*c^5*d*f + 1536*a^5*b*c^9*d*f - 10*a
*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 168*a*b^10*c^4*d*g - 152*a*b^10*c^4
*e*f + 258*a*b^11*c^3*e*g - 43520*a^6*b*c^8*e*g - 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) +
246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 192*a^2*b^6*c^7*d*e + 128*a^3*b^4*c^8*d*e + 1536*a^4*b^2*c^9*d
*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 576*a^2*b^7*c^6*d*f - 1344*a^3*b^5*c^7*d*f + 512*a^4*b^3*c^8*d
*f - 1044*a^2*b^8*c^5*d*g + 1548*a^2*b^8*c^5*e*f + 2688*a^3*b^6*c^6*d*g - 8064*a^3*b^6*c^6*e*f - 1152*a^4*b^4*
c^7*d*g + 22400*a^4*b^4*c^7*e*f - 6144*a^5*b^2*c^8*d*g - 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)
^9)^(1/2) - 2706*a^2*b^9*c^4*e*g + 14784*a^3*b^7*c^5*e*g - 44352*a^4*b^5*c^6*e*g + 69120*a^5*b^3*c^7*e*g + 42*
a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)
^9)^(1/2) + 7278*a^2*b^10*c^3*f*g - 39132*a^3*b^8*c^4*f*g + 119616*a^4*b^6*c^5*f*g - 201600*a^5*b^4*c^6*f*g +
161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) +
12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c
- b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(3
2*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a
^5*b^2*c^12)))^(1/2)*(16*b^7*c^7 - 192*a*b^5*c^8 - 1024*a^3*b*c^10 + 768*a^2*b^3*c^9))/(2*(16*a^2*c^7 + b^4*c^
5 - 8*a*b^2*c^6)))*((c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^6*d^2 - 25*b^15*g^2 - b^11*c^4*e^2 - 9*b^13*c^2*
f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^4*b*c^10*d^2 + 27*a*b^9*c^5*e^2 + 3840*a^5*b*c^9*e^2 - 9*a*c
^5*e^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c^3*f^2 - 26880*a^6*b*c^8*f^2 + 80640*a^7*b*c^7*g^2 + 30*b^14*c*f
*g + 96*a^2*b^5*c^8*d^2 - 512*a^3*b^3*c^9*d^2 - 288*a^2*b^7*c^6*e^2 + 1504*a^3*b^5*c^7*e^2 - 3840*a^4*b^3*c^8*
e^2 - 2077*a^2*b^9*c^4*f^2 + 10656*a^3*b^7*c^5*f^2 - 30240*a^4*b^5*c^6*f^2 + 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^
4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 6366*a^2*b^11*c^2*g^2 + 35767*a^3*b^9*
c^3*g^2 - 116928*a^4*b^7*c^4*g^2 + 219744*a^5*b^5*c^5*g^2 - 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c -
b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 615*a*b^13*c*g^2 - 3072*a^5*c^10*d*e - 2*b^10*c^5*d*
e + 7168*a^6*c^9*d*g + 15360*a^6*c^9*e*f + 6*b^11*c^4*d*f - 10*b^12*c^3*d*g + 6*b^12*c^3*e*f - 35840*a^7*c^8*f
*g - 10*b^13*c^2*e*g + 36*a*b^8*c^6*d*e - 98*a*b^9*c^5*d*f + 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)
^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 168*a*b^10*c^4*d*g - 152*a*b^10*c^4*e*f + 258*a*b^11*c^3*e*
g - 43520*a^6*b*c^8*e*g - 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(
4*a*c - b^2)^9)^(1/2) - 192*a^2*b^6*c^7*d*e + 128*a^3*b^4*c^8*d*e + 1536*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(
4*a*c - b^2)^9)^(1/2) + 576*a^2*b^7*c^6*d*f - 1344*a^3*b^5*c^7*d*f + 512*a^4*b^3*c^8*d*f - 1044*a^2*b^8*c^5*d*
g + 1548*a^2*b^8*c^5*e*f + 2688*a^3*b^6*c^6*d*g - 8064*a^3*b^6*c^6*e*f - 1152*a^4*b^4*c^7*d*g + 22400*a^4*b^4*
c^7*e*f - 6144*a^5*b^2*c^8*d*g - 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^2*b^9
*c^4*e*g + 14784*a^3*b^7*c^5*e*g - 44352*a^4*b^5*c^6*e*g + 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b
^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^2*b^1
0*c^3*f*g - 39132*a^3*b^8*c^4*f*g + 119616*a^4*b^6*c^5*f*g - 201600*a^5*b^4*c^6*f*g + 161280*a^6*b^2*c^7*f*g +
10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c
- b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a
*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*
c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^(1/2) + (
x*(25*b^10*g^2 + 8*a^2*c^8*d^2 - 72*a^3*c^7*e^2 + b^4*c^6*d^2 + 200*a^4*c^6*f^2 + b^6*c^4*e^2 - 392*a^5*c^5*g^
2 + 9*b^8*c^2*f^2 + 2*a*b^2*c^7*d^2 - 16*a*b^4*c^5*e^2 - 114*a*b^6*c^3*f^2 - 30*b^9*c*f*g + 74*a^2*b^2*c^6*e^2
+ 481*a^2*b^4*c^4*f^2 - 718*a^3*b^2*c^5*f^2 + 1676*a^2*b^6*c^2*g^2 - 3536*a^3*b^4*c^3*g^2 + 2794*a^4*b^2*c^4*
g^2 - 340*a*b^8*c*g^2 - 80*a^3*c^7*d*f + 2*b^5*c^5*d*e - 6*b^6*c^4*d*f + 336*a^4*c^6*e*g + 10*b^7*c^3*d*g - 6*
b^7*c^3*e*f + 10*b^8*c^2*e*g - 14*a*b^3*c^6*d*e - 8*a^2*b*c^7*d*e + 32*a*b^4*c^5*d*f - 58*a*b^5*c^4*d*g + 86*a
*b^5*c^4*e*f + 152*a^3*b*c^6*d*g + 472*a^3*b*c^6*e*f - 148*a*b^6*c^3*e*g + 394*a*b^7*c^2*f*g - 1768*a^4*b*c^5*
f*g + 4*a^2*b^2*c^6*d*f + 26*a^2*b^3*c^5*d*g - 374*a^2*b^3*c^5*e*f + 698*a^2*b^4*c^4*e*g - 1132*a^3*b^2*c^5*e*
g - 1804*a^2*b^5*c^3*f*g + 3266*a^3*b^3*c^4*f*g))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))*((c^6*d^2*(-(4*a*c
- b^2)^9)^(1/2) - b^9*c^6*d^2 - 25*b^15*g^2 - b^11*c^4*e^2 - 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(
1/2) + 768*a^4*b*c^10*d^2 + 27*a*b^9*c^5*e^2 + 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) + 213
*a*b^11*c^3*f^2 - 26880*a^6*b*c^8*f^2 + 80640*a^7*b*c^7*g^2 + 30*b^14*c*f*g + 96*a^2*b^5*c^8*d^2 - 512*a^3*b^3
*c^9*d^2 - 288*a^2*b^7*c^6*e^2 + 1504*a^3*b^5*c^7*e^2 - 3840*a^4*b^3*c^8*e^2 - 2077*a^2*b^9*c^4*f^2 + 10656*a^
3*b^7*c^5*f^2 - 30240*a^4*b^5*c^6*f^2 + 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*
c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 6366*a^2*b^11*c^2*g^2 + 35767*a^3*b^9*c^3*g^2 - 116928*a^4*b^7*c^4*g^2 + 21
9744*a^5*b^5*c^5*g^2 - 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a
*c - b^2)^9)^(1/2) + 615*a*b^13*c*g^2 - 3072*a^5*c^10*d*e - 2*b^10*c^5*d*e + 7168*a^6*c^9*d*g + 15360*a^6*c^9*
e*f + 6*b^11*c^4*d*f - 10*b^12*c^3*d*g + 6*b^12*c^3*e*f - 35840*a^7*c^8*f*g - 10*b^13*c^2*e*g + 36*a*b^8*c^6*d
*e - 98*a*b^9*c^5*d*f + 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^
2)^9)^(1/2) + 168*a*b^10*c^4*d*g - 152*a*b^10*c^4*e*f + 258*a*b^11*c^3*e*g - 43520*a^6*b*c^8*e*g - 724*a*b^12*
c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 192*a^2*b^6*c
^7*d*e + 128*a^3*b^4*c^8*d*e + 1536*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 576*a^2*b^7*c
^6*d*f - 1344*a^3*b^5*c^7*d*f + 512*a^4*b^3*c^8*d*f - 1044*a^2*b^8*c^5*d*g + 1548*a^2*b^8*c^5*e*f + 2688*a^3*b
^6*c^6*d*g - 8064*a^3*b^6*c^6*e*f - 1152*a^4*b^4*c^7*d*g + 22400*a^4*b^4*c^7*e*f - 6144*a^5*b^2*c^8*d*g - 3072
0*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^2*b^9*c^4*e*g + 14784*a^3*b^7*c^5*e*g - 44
352*a^4*b^5*c^6*e*g + 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*
c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^2*b^10*c^3*f*g - 39132*a^3*b^8*c^4*f*g + 1
19616*a^4*b^6*c^5*f*g - 201600*a^5*b^4*c^6*f*g + 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1
/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(
4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2)
- 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9
- 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^(1/2)*1i)/((((2048*a^4*c^10*d - 10240*a^5*c^9*
f + 384*a^2*b^4*c^8*d - 1536*a^3*b^2*c^9*d - 192*a^2*b^5*c^7*e + 768*a^3*b^3*c^8*e + 736*a^2*b^6*c^6*f - 4224*
a^3*b^4*c^7*f + 10752*a^4*b^2*c^8*f - 1264*a^2*b^7*c^5*g + 7488*a^3*b^5*c^6*g - 19712*a^4*b^3*c^7*g - 32*a*b^6
*c^7*d + 16*a*b^7*c^6*e - 1024*a^4*b*c^9*e - 48*a*b^8*c^5*f + 80*a*b^9*c^4*g + 19456*a^5*b*c^8*g)/(8*(64*a^3*c
^8 - b^6*c^5 + 12*a*b^4*c^6 - 48*a^2*b^2*c^7)) - (x*((c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^6*d^2 - 25*b^15
*g^2 - b^11*c^4*e^2 - 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^4*b*c^10*d^2 + 27*a*b^9*c^5
*e^2 + 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c^3*f^2 - 26880*a^6*b*c^8*f^2 +
80640*a^7*b*c^7*g^2 + 30*b^14*c*f*g + 96*a^2*b^5*c^8*d^2 - 512*a^3*b^3*c^9*d^2 - 288*a^2*b^7*c^6*e^2 + 1504*a^
3*b^5*c^7*e^2 - 3840*a^4*b^3*c^8*e^2 - 2077*a^2*b^9*c^4*f^2 + 10656*a^3*b^7*c^5*f^2 - 30240*a^4*b^5*c^6*f^2 +
44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 6366*
a^2*b^11*c^2*g^2 + 35767*a^3*b^9*c^3*g^2 - 116928*a^4*b^7*c^4*g^2 + 219744*a^5*b^5*c^5*g^2 - 215040*a^6*b^3*c^
6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 615*a*b^13*c*g^2 -
3072*a^5*c^10*d*e - 2*b^10*c^5*d*e + 7168*a^6*c^9*d*g + 15360*a^6*c^9*e*f + 6*b^11*c^4*d*f - 10*b^12*c^3*d*g +
6*b^12*c^3*e*f - 35840*a^7*c^8*f*g - 10*b^13*c^2*e*g + 36*a*b^8*c^6*d*e - 98*a*b^9*c^5*d*f + 1536*a^5*b*c^9*d
*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 168*a*b^10*c^4*d*g - 152*a
*b^10*c^4*e*f + 258*a*b^11*c^3*e*g - 43520*a^6*b*c^8*e*g - 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9
)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 192*a^2*b^6*c^7*d*e + 128*a^3*b^4*c^8*d*e + 1536*a^4*
b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 576*a^2*b^7*c^6*d*f - 1344*a^3*b^5*c^7*d*f + 512*a^4*
b^3*c^8*d*f - 1044*a^2*b^8*c^5*d*g + 1548*a^2*b^8*c^5*e*f + 2688*a^3*b^6*c^6*d*g - 8064*a^3*b^6*c^6*e*f - 1152
*a^4*b^4*c^7*d*g + 22400*a^4*b^4*c^7*e*f - 6144*a^5*b^2*c^8*d*g - 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a
*c - b^2)^9)^(1/2) - 2706*a^2*b^9*c^4*e*g + 14784*a^3*b^7*c^5*e*g - 44352*a^4*b^5*c^6*e*g + 69120*a^5*b^3*c^7*
e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a
*c - b^2)^9)^(1/2) + 7278*a^2*b^10*c^3*f*g - 39132*a^3*b^8*c^4*f*g + 119616*a^4*b^6*c^5*f*g - 201600*a^5*b^4*c
^6*f*g + 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9
)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g
*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^
(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11
- 6144*a^5*b^2*c^12)))^(1/2)*(16*b^7*c^7 - 192*a*b^5*c^8 - 1024*a^3*b*c^10 + 768*a^2*b^3*c^9))/(2*(16*a^2*c^7
+ b^4*c^5 - 8*a*b^2*c^6)))*((c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^6*d^2 - 25*b^15*g^2 - b^11*c^4*e^2 - 9*
b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^4*b*c^10*d^2 + 27*a*b^9*c^5*e^2 + 3840*a^5*b*c^9*e^
2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c^3*f^2 - 26880*a^6*b*c^8*f^2 + 80640*a^7*b*c^7*g^2 + 30
*b^14*c*f*g + 96*a^2*b^5*c^8*d^2 - 512*a^3*b^3*c^9*d^2 - 288*a^2*b^7*c^6*e^2 + 1504*a^3*b^5*c^7*e^2 - 3840*a^4
*b^3*c^8*e^2 - 2077*a^2*b^9*c^4*f^2 + 10656*a^3*b^7*c^5*f^2 - 30240*a^4*b^5*c^6*f^2 + 44800*a^5*b^3*c^7*f^2 +
25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 6366*a^2*b^11*c^2*g^2 + 35767
*a^3*b^9*c^3*g^2 - 116928*a^4*b^7*c^4*g^2 + 219744*a^5*b^5*c^5*g^2 - 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(
-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 615*a*b^13*c*g^2 - 3072*a^5*c^10*d*e - 2*b^
10*c^5*d*e + 7168*a^6*c^9*d*g + 15360*a^6*c^9*e*f + 6*b^11*c^4*d*f - 10*b^12*c^3*d*g + 6*b^12*c^3*e*f - 35840*
a^7*c^8*f*g - 10*b^13*c^2*e*g + 36*a*b^8*c^6*d*e - 98*a*b^9*c^5*d*f + 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a
*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 168*a*b^10*c^4*d*g - 152*a*b^10*c^4*e*f + 258*a*b^
11*c^3*e*g - 43520*a^6*b*c^8*e*g - 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^
2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 192*a^2*b^6*c^7*d*e + 128*a^3*b^4*c^8*d*e + 1536*a^4*b^2*c^9*d*e - 165*a*b^4*
c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 576*a^2*b^7*c^6*d*f - 1344*a^3*b^5*c^7*d*f + 512*a^4*b^3*c^8*d*f - 1044*a^2*b
^8*c^5*d*g + 1548*a^2*b^8*c^5*e*f + 2688*a^3*b^6*c^6*d*g - 8064*a^3*b^6*c^6*e*f - 1152*a^4*b^4*c^7*d*g + 22400
*a^4*b^4*c^7*e*f - 6144*a^5*b^2*c^8*d*g - 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 270
6*a^2*b^9*c^4*e*g + 14784*a^3*b^7*c^5*e*g - 44352*a^4*b^5*c^6*e*g + 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(
4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 727
8*a^2*b^10*c^3*f*g - 39132*a^3*b^8*c^4*f*g + 119616*a^4*b^6*c^5*f*g - 201600*a^5*b^4*c^6*f*g + 161280*a^6*b^2*
c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g
*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2
) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^1
3 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^
(1/2) - (x*(25*b^10*g^2 + 8*a^2*c^8*d^2 - 72*a^3*c^7*e^2 + b^4*c^6*d^2 + 200*a^4*c^6*f^2 + b^6*c^4*e^2 - 392*a
^5*c^5*g^2 + 9*b^8*c^2*f^2 + 2*a*b^2*c^7*d^2 - 16*a*b^4*c^5*e^2 - 114*a*b^6*c^3*f^2 - 30*b^9*c*f*g + 74*a^2*b^
2*c^6*e^2 + 481*a^2*b^4*c^4*f^2 - 718*a^3*b^2*c^5*f^2 + 1676*a^2*b^6*c^2*g^2 - 3536*a^3*b^4*c^3*g^2 + 2794*a^4
*b^2*c^4*g^2 - 340*a*b^8*c*g^2 - 80*a^3*c^7*d*f + 2*b^5*c^5*d*e - 6*b^6*c^4*d*f + 336*a^4*c^6*e*g + 10*b^7*c^3
*d*g - 6*b^7*c^3*e*f + 10*b^8*c^2*e*g - 14*a*b^3*c^6*d*e - 8*a^2*b*c^7*d*e + 32*a*b^4*c^5*d*f - 58*a*b^5*c^4*d
*g + 86*a*b^5*c^4*e*f + 152*a^3*b*c^6*d*g + 472*a^3*b*c^6*e*f - 148*a*b^6*c^3*e*g + 394*a*b^7*c^2*f*g - 1768*a
^4*b*c^5*f*g + 4*a^2*b^2*c^6*d*f + 26*a^2*b^3*c^5*d*g - 374*a^2*b^3*c^5*e*f + 698*a^2*b^4*c^4*e*g - 1132*a^3*b
^2*c^5*e*g - 1804*a^2*b^5*c^3*f*g + 3266*a^3*b^3*c^4*f*g))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))*((c^6*d^2
*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^6*d^2 - 25*b^15*g^2 - b^11*c^4*e^2 - 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c -
b^2)^9)^(1/2) + 768*a^4*b*c^10*d^2 + 27*a*b^9*c^5*e^2 + 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1
/2) + 213*a*b^11*c^3*f^2 - 26880*a^6*b*c^8*f^2 + 80640*a^7*b*c^7*g^2 + 30*b^14*c*f*g + 96*a^2*b^5*c^8*d^2 - 51
2*a^3*b^3*c^9*d^2 - 288*a^2*b^7*c^6*e^2 + 1504*a^3*b^5*c^7*e^2 - 3840*a^4*b^3*c^8*e^2 - 2077*a^2*b^9*c^4*f^2 +
10656*a^3*b^7*c^5*f^2 - 30240*a^4*b^5*c^6*f^2 + 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/
2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 6366*a^2*b^11*c^2*g^2 + 35767*a^3*b^9*c^3*g^2 - 116928*a^4*b^7*c^4
*g^2 + 219744*a^5*b^5*c^5*g^2 - 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f
^2*(-(4*a*c - b^2)^9)^(1/2) + 615*a*b^13*c*g^2 - 3072*a^5*c^10*d*e - 2*b^10*c^5*d*e + 7168*a^6*c^9*d*g + 15360
*a^6*c^9*e*f + 6*b^11*c^4*d*f - 10*b^12*c^3*d*g + 6*b^12*c^3*e*f - 35840*a^7*c^8*f*g - 10*b^13*c^2*e*g + 36*a*
b^8*c^6*d*e - 98*a*b^9*c^5*d*f + 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4
*a*c - b^2)^9)^(1/2) + 168*a*b^10*c^4*d*g - 152*a*b^10*c^4*e*f + 258*a*b^11*c^3*e*g - 43520*a^6*b*c^8*e*g - 72
4*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 192*
a^2*b^6*c^7*d*e + 128*a^3*b^4*c^8*d*e + 1536*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 576*
a^2*b^7*c^6*d*f - 1344*a^3*b^5*c^7*d*f + 512*a^4*b^3*c^8*d*f - 1044*a^2*b^8*c^5*d*g + 1548*a^2*b^8*c^5*e*f + 2
688*a^3*b^6*c^6*d*g - 8064*a^3*b^6*c^6*e*f - 1152*a^4*b^4*c^7*d*g + 22400*a^4*b^4*c^7*e*f - 6144*a^5*b^2*c^8*d
*g - 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^2*b^9*c^4*e*g + 14784*a^3*b^7*c^5
*e*g - 44352*a^4*b^5*c^6*e*g + 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*
g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^2*b^10*c^3*f*g - 39132*a^3*b^8*c^
4*f*g + 119616*a^4*b^6*c^5*f*g - 201600*a^5*b^4*c^6*f*g + 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b
^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^
4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)
^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^
2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^(1/2) + (((2048*a^4*c^10*d - 10240*a^
5*c^9*f + 384*a^2*b^4*c^8*d - 1536*a^3*b^2*c^9*d - 192*a^2*b^5*c^7*e + 768*a^3*b^3*c^8*e + 736*a^2*b^6*c^6*f -
4224*a^3*b^4*c^7*f + 10752*a^4*b^2*c^8*f - 1264*a^2*b^7*c^5*g + 7488*a^3*b^5*c^6*g - 19712*a^4*b^3*c^7*g - 32
*a*b^6*c^7*d + 16*a*b^7*c^6*e - 1024*a^4*b*c^9*e - 48*a*b^8*c^5*f + 80*a*b^9*c^4*g + 19456*a^5*b*c^8*g)/(8*(64
*a^3*c^8 - b^6*c^5 + 12*a*b^4*c^6 - 48*a^2*b^2*c^7)) + (x*((c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^6*d^2 - 2
5*b^15*g^2 - b^11*c^4*e^2 - 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^4*b*c^10*d^2 + 27*a*b
^9*c^5*e^2 + 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c^3*f^2 - 26880*a^6*b*c^8*
f^2 + 80640*a^7*b*c^7*g^2 + 30*b^14*c*f*g + 96*a^2*b^5*c^8*d^2 - 512*a^3*b^3*c^9*d^2 - 288*a^2*b^7*c^6*e^2 + 1
504*a^3*b^5*c^7*e^2 - 3840*a^4*b^3*c^8*e^2 - 2077*a^2*b^9*c^4*f^2 + 10656*a^3*b^7*c^5*f^2 - 30240*a^4*b^5*c^6*
f^2 + 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) -
6366*a^2*b^11*c^2*g^2 + 35767*a^3*b^9*c^3*g^2 - 116928*a^4*b^7*c^4*g^2 + 219744*a^5*b^5*c^5*g^2 - 215040*a^6*
b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 615*a*b^13*c*
g^2 - 3072*a^5*c^10*d*e - 2*b^10*c^5*d*e + 7168*a^6*c^9*d*g + 15360*a^6*c^9*e*f + 6*b^11*c^4*d*f - 10*b^12*c^3
*d*g + 6*b^12*c^3*e*f - 35840*a^7*c^8*f*g - 10*b^13*c^2*e*g + 36*a*b^8*c^6*d*e - 98*a*b^9*c^5*d*f + 1536*a^5*b
*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 168*a*b^10*c^4*d*g -
152*a*b^10*c^4*e*f + 258*a*b^11*c^3*e*g - 43520*a^6*b*c^8*e*g - 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c -
b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 192*a^2*b^6*c^7*d*e + 128*a^3*b^4*c^8*d*e + 153
6*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 576*a^2*b^7*c^6*d*f - 1344*a^3*b^5*c^7*d*f + 51
2*a^4*b^3*c^8*d*f - 1044*a^2*b^8*c^5*d*g + 1548*a^2*b^8*c^5*e*f + 2688*a^3*b^6*c^6*d*g - 8064*a^3*b^6*c^6*e*f
- 1152*a^4*b^4*c^7*d*g + 22400*a^4*b^4*c^7*e*f - 6144*a^5*b^2*c^8*d*g - 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*
(-(4*a*c - b^2)^9)^(1/2) - 2706*a^2*b^9*c^4*e*g + 14784*a^3*b^7*c^5*e*g - 44352*a^4*b^5*c^6*e*g + 69120*a^5*b^
3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*
(-(4*a*c - b^2)^9)^(1/2) + 7278*a^2*b^10*c^3*f*g - 39132*a^3*b^8*c^4*f*g + 119616*a^4*b^6*c^5*f*g - 201600*a^5
*b^4*c^6*f*g + 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c -
b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c
^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^
2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^
4*c^11 - 6144*a^5*b^2*c^12)))^(1/2)*(16*b^7*c^7 - 192*a*b^5*c^8 - 1024*a^3*b*c^10 + 768*a^2*b^3*c^9))/(2*(16*a
^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))*((c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^6*d^2 - 25*b^15*g^2 - b^11*c^4*e^
2 - 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^4*b*c^10*d^2 + 27*a*b^9*c^5*e^2 + 3840*a^5*b*
c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c^3*f^2 - 26880*a^6*b*c^8*f^2 + 80640*a^7*b*c^7*g^
2 + 30*b^14*c*f*g + 96*a^2*b^5*c^8*d^2 - 512*a^3*b^3*c^9*d^2 - 288*a^2*b^7*c^6*e^2 + 1504*a^3*b^5*c^7*e^2 - 38
40*a^4*b^3*c^8*e^2 - 2077*a^2*b^9*c^4*f^2 + 10656*a^3*b^7*c^5*f^2 - 30240*a^4*b^5*c^6*f^2 + 44800*a^5*b^3*c^7*
f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 6366*a^2*b^11*c^2*g^2 +
35767*a^3*b^9*c^3*g^2 - 116928*a^4*b^7*c^4*g^2 + 219744*a^5*b^5*c^5*g^2 - 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3
*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 615*a*b^13*c*g^2 - 3072*a^5*c^10*d*e
- 2*b^10*c^5*d*e + 7168*a^6*c^9*d*g + 15360*a^6*c^9*e*f + 6*b^11*c^4*d*f - 10*b^12*c^3*d*g + 6*b^12*c^3*e*f -
35840*a^7*c^8*f*g - 10*b^13*c^2*e*g + 36*a*b^8*c^6*d*e - 98*a*b^9*c^5*d*f + 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*
(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 168*a*b^10*c^4*d*g - 152*a*b^10*c^4*e*f + 25
8*a*b^11*c^3*e*g - 43520*a^6*b*c^8*e*g - 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*
b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 192*a^2*b^6*c^7*d*e + 128*a^3*b^4*c^8*d*e + 1536*a^4*b^2*c^9*d*e - 165*
a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 576*a^2*b^7*c^6*d*f - 1344*a^3*b^5*c^7*d*f + 512*a^4*b^3*c^8*d*f - 1044
*a^2*b^8*c^5*d*g + 1548*a^2*b^8*c^5*e*f + 2688*a^3*b^6*c^6*d*g - 8064*a^3*b^6*c^6*e*f - 1152*a^4*b^4*c^7*d*g +
22400*a^4*b^4*c^7*e*f - 6144*a^5*b^2*c^8*d*g - 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2)
- 2706*a^2*b^9*c^4*e*g + 14784*a^3*b^7*c^5*e*g - 44352*a^4*b^5*c^6*e*g + 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e
*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2)
+ 7278*a^2*b^10*c^3*f*g - 39132*a^3*b^8*c^4*f*g + 119616*a^4*b^6*c^5*f*g - 201600*a^5*b^4*c^6*f*g + 161280*a^
6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c
^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9
)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a
^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^
12)))^(1/2) + (x*(25*b^10*g^2 + 8*a^2*c^8*d^2 - 72*a^3*c^7*e^2 + b^4*c^6*d^2 + 200*a^4*c^6*f^2 + b^6*c^4*e^2 -
392*a^5*c^5*g^2 + 9*b^8*c^2*f^2 + 2*a*b^2*c^7*d^2 - 16*a*b^4*c^5*e^2 - 114*a*b^6*c^3*f^2 - 30*b^9*c*f*g + 74*
a^2*b^2*c^6*e^2 + 481*a^2*b^4*c^4*f^2 - 718*a^3*b^2*c^5*f^2 + 1676*a^2*b^6*c^2*g^2 - 3536*a^3*b^4*c^3*g^2 + 27
94*a^4*b^2*c^4*g^2 - 340*a*b^8*c*g^2 - 80*a^3*c^7*d*f + 2*b^5*c^5*d*e - 6*b^6*c^4*d*f + 336*a^4*c^6*e*g + 10*b
^7*c^3*d*g - 6*b^7*c^3*e*f + 10*b^8*c^2*e*g - 14*a*b^3*c^6*d*e - 8*a^2*b*c^7*d*e + 32*a*b^4*c^5*d*f - 58*a*b^5
*c^4*d*g + 86*a*b^5*c^4*e*f + 152*a^3*b*c^6*d*g + 472*a^3*b*c^6*e*f - 148*a*b^6*c^3*e*g + 394*a*b^7*c^2*f*g -
1768*a^4*b*c^5*f*g + 4*a^2*b^2*c^6*d*f + 26*a^2*b^3*c^5*d*g - 374*a^2*b^3*c^5*e*f + 698*a^2*b^4*c^4*e*g - 1132
*a^3*b^2*c^5*e*g - 1804*a^2*b^5*c^3*f*g + 3266*a^3*b^3*c^4*f*g))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))*((c
^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^6*d^2 - 25*b^15*g^2 - b^11*c^4*e^2 - 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*
a*c - b^2)^9)^(1/2) + 768*a^4*b*c^10*d^2 + 27*a*b^9*c^5*e^2 + 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)
^9)^(1/2) + 213*a*b^11*c^3*f^2 - 26880*a^6*b*c^8*f^2 + 80640*a^7*b*c^7*g^2 + 30*b^14*c*f*g + 96*a^2*b^5*c^8*d^
2 - 512*a^3*b^3*c^9*d^2 - 288*a^2*b^7*c^6*e^2 + 1504*a^3*b^5*c^7*e^2 - 3840*a^4*b^3*c^8*e^2 - 2077*a^2*b^9*c^4
*f^2 + 10656*a^3*b^7*c^5*f^2 - 30240*a^4*b^5*c^6*f^2 + 44800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^
9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 6366*a^2*b^11*c^2*g^2 + 35767*a^3*b^9*c^3*g^2 - 116928*a^4*b
^7*c^4*g^2 + 219744*a^5*b^5*c^5*g^2 - 215040*a^6*b^3*c^6*g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4
*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 615*a*b^13*c*g^2 - 3072*a^5*c^10*d*e - 2*b^10*c^5*d*e + 7168*a^6*c^9*d*g +
15360*a^6*c^9*e*f + 6*b^11*c^4*d*f - 10*b^12*c^3*d*g + 6*b^12*c^3*e*f - 35840*a^7*c^8*f*g - 10*b^13*c^2*e*g +
36*a*b^8*c^6*d*e - 98*a*b^9*c^5*d*f + 1536*a^5*b*c^9*d*f - 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*
e*(-(4*a*c - b^2)^9)^(1/2) + 168*a*b^10*c^4*d*g - 152*a*b^10*c^4*e*f + 258*a*b^11*c^3*e*g - 43520*a^6*b*c^8*e*
g - 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2)
- 192*a^2*b^6*c^7*d*e + 128*a^3*b^4*c^8*d*e + 1536*a^4*b^2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2)
+ 576*a^2*b^7*c^6*d*f - 1344*a^3*b^5*c^7*d*f + 512*a^4*b^3*c^8*d*f - 1044*a^2*b^8*c^5*d*g + 1548*a^2*b^8*c^5*e
*f + 2688*a^3*b^6*c^6*d*g - 8064*a^3*b^6*c^6*e*f - 1152*a^4*b^4*c^7*d*g + 22400*a^4*b^4*c^7*e*f - 6144*a^5*b^2
*c^8*d*g - 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^2*b^9*c^4*e*g + 14784*a^3*b
^7*c^5*e*g - 44352*a^4*b^5*c^6*e*g + 69120*a^5*b^3*c^7*e*g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*
c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^2*b^10*c^3*f*g - 39132*a^3*
b^8*c^4*f*g + 119616*a^4*b^6*c^5*f*g - 201600*a^5*b^4*c^6*f*g + 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a
*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*
a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c
- b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 +
240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 - 6144*a^5*b^2*c^12)))^(1/2) - (2744*a^7*c^3*g^3 - 225
*a^4*b^6*g^3 - 216*a^4*c^6*e^3 + 3*a*b^3*c^6*d^3 + 4*a^2*b*c^7*d^3 + 1300*a^5*b*c^4*f^3 - 24*a^3*c^7*d^2*e + 2
060*a^5*b^4*c*g^3 - 125*a^2*b^8*e*g^2 + 56*a^4*c^6*d^2*g - 600*a^5*c^5*e*f^2 + 175*a^3*b^7*f*g^2 + 1512*a^5*c^
5*e^2*g - 3528*a^6*c^4*e*g^2 + 1400*a^6*c^4*f^2*g - 5*a^2*b^4*c^4*e^3 + 66*a^3*b^2*c^5*e^3 + 63*a^3*b^5*c^2*f^
3 - 573*a^4*b^3*c^3*f^3 - 5334*a^6*b^2*c^2*g^3 + 75*a*b^9*d*g^2 + 240*a^4*c^6*d*e*f - 560*a^5*c^5*d*f*g + 6*a*
b^4*c^5*d^2*e + 3*a*b^5*c^4*d*e^2 + 204*a^3*b*c^6*d*e^2 - 18*a*b^5*c^4*d^2*f + 27*a*b^7*c^2*d*f^2 + 12*a^3*b*c
^6*d^2*f - 420*a^4*b*c^5*d*f^2 + 30*a*b^6*c^3*d^2*g - 845*a^2*b^7*c*d*g^2 + 924*a^4*b*c^5*e^2*f + 2044*a^5*b*c
^4*d*g^2 + 1350*a^3*b^6*c*e*g^2 - 210*a^3*b^6*c*f^2*g - 1485*a^4*b^5*c*f*g^2 + 364*a^6*b*c^3*f*g^2 - 42*a^2*b^
2*c^6*d^2*e - 51*a^2*b^3*c^5*d*e^2 + 81*a^2*b^3*c^5*d^2*f - 279*a^2*b^5*c^3*d*f^2 + 801*a^3*b^3*c^4*d*f^2 - 14
9*a^2*b^4*c^4*d^2*g + 30*a^2*b^5*c^3*e^2*f - 45*a^2*b^6*c^2*e*f^2 + 78*a^3*b^2*c^5*d^2*g - 339*a^3*b^3*c^4*e^2
*f + 402*a^3*b^4*c^3*e*f^2 + 3198*a^3*b^5*c^2*d*g^2 - 762*a^4*b^2*c^4*e*f^2 - 4571*a^4*b^3*c^3*d*g^2 - 50*a^2*
b^6*c^2*e^2*g + 600*a^3*b^4*c^3*e^2*g - 2002*a^4*b^2*c^4*e^2*g - 4835*a^4*b^4*c^2*e*g^2 + 6598*a^5*b^2*c^3*e*g
^2 + 1927*a^4*b^4*c^2*f^2*g - 4722*a^5*b^2*c^3*f^2*g + 3061*a^5*b^3*c^2*f*g^2 - 90*a*b^8*c*d*f*g - 18*a*b^6*c^
3*d*e*f + 30*a*b^7*c^2*d*e*g - 1352*a^4*b*c^5*d*e*g + 150*a^2*b^7*c*e*f*g - 2312*a^5*b*c^4*e*f*g + 246*a^2*b^4
*c^4*d*e*f - 804*a^3*b^2*c^5*d*e*f - 424*a^2*b^5*c^3*d*e*g + 1578*a^3*b^3*c^4*d*e*g + 972*a^2*b^6*c^2*d*f*g -
3244*a^3*b^4*c^3*d*f*g + 3276*a^4*b^2*c^4*d*f*g - 1480*a^3*b^5*c^2*e*f*g + 4122*a^4*b^3*c^3*e*f*g)/(4*(64*a^3*
c^8 - b^6*c^5 + 12*a*b^4*c^6 - 48*a^2*b^2*c^7))))*((c^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - b^9*c^6*d^2 - 25*b^15*g
^2 - b^11*c^4*e^2 - 9*b^13*c^2*f^2 + 25*b^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^4*b*c^10*d^2 + 27*a*b^9*c^5*e
^2 + 3840*a^5*b*c^9*e^2 - 9*a*c^5*e^2*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c^3*f^2 - 26880*a^6*b*c^8*f^2 + 80
640*a^7*b*c^7*g^2 + 30*b^14*c*f*g + 96*a^2*b^5*c^8*d^2 - 512*a^3*b^3*c^9*d^2 - 288*a^2*b^7*c^6*e^2 + 1504*a^3*
b^5*c^7*e^2 - 3840*a^4*b^3*c^8*e^2 - 2077*a^2*b^9*c^4*f^2 + 10656*a^3*b^7*c^5*f^2 - 30240*a^4*b^5*c^6*f^2 + 44
800*a^5*b^3*c^7*f^2 + 25*a^2*c^4*f^2*(-(4*a*c - b^2)^9)^(1/2) + b^2*c^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 6366*a^
2*b^11*c^2*g^2 + 35767*a^3*b^9*c^3*g^2 - 116928*a^4*b^7*c^4*g^2 + 219744*a^5*b^5*c^5*g^2 - 215040*a^6*b^3*c^6*
g^2 - 49*a^3*c^3*g^2*(-(4*a*c - b^2)^9)^(1/2) + 9*b^4*c^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 615*a*b^13*c*g^2 - 30
72*a^5*c^10*d*e - 2*b^10*c^5*d*e + 7168*a^6*c^9*d*g + 15360*a^6*c^9*e*f + 6*b^11*c^4*d*f - 10*b^12*c^3*d*g + 6
*b^12*c^3*e*f - 35840*a^7*c^8*f*g - 10*b^13*c^2*e*g + 36*a*b^8*c^6*d*e - 98*a*b^9*c^5*d*f + 1536*a^5*b*c^9*d*f
- 10*a*c^5*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2*b*c^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 168*a*b^10*c^4*d*g - 152*a*b
^10*c^4*e*f + 258*a*b^11*c^3*e*g - 43520*a^6*b*c^8*e*g - 724*a*b^12*c^2*f*g - 30*b^5*c*f*g*(-(4*a*c - b^2)^9)^
(1/2) + 246*a^2*b^2*c^2*g^2*(-(4*a*c - b^2)^9)^(1/2) - 192*a^2*b^6*c^7*d*e + 128*a^3*b^4*c^8*d*e + 1536*a^4*b^
2*c^9*d*e - 165*a*b^4*c*g^2*(-(4*a*c - b^2)^9)^(1/2) + 576*a^2*b^7*c^6*d*f - 1344*a^3*b^5*c^7*d*f + 512*a^4*b^
3*c^8*d*f - 1044*a^2*b^8*c^5*d*g + 1548*a^2*b^8*c^5*e*f + 2688*a^3*b^6*c^6*d*g - 8064*a^3*b^6*c^6*e*f - 1152*a
^4*b^4*c^7*d*g + 22400*a^4*b^4*c^7*e*f - 6144*a^5*b^2*c^8*d*g - 30720*a^5*b^2*c^8*e*f - 6*b^2*c^4*d*f*(-(4*a*c
- b^2)^9)^(1/2) - 2706*a^2*b^9*c^4*e*g + 14784*a^3*b^7*c^5*e*g - 44352*a^4*b^5*c^6*e*g + 69120*a^5*b^3*c^7*e*
g + 42*a^2*c^4*e*g*(-(4*a*c - b^2)^9)^(1/2) + 10*b^3*c^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*b^3*c^3*e*f*(-(4*a*c
- b^2)^9)^(1/2) + 7278*a^2*b^10*c^3*f*g - 39132*a^3*b^8*c^4*f*g + 119616*a^4*b^6*c^5*f*g - 201600*a^5*b^4*c^6
*f*g + 161280*a^6*b^2*c^7*f*g + 10*b^4*c^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 51*a*b^2*c^3*f^2*(-(4*a*c - b^2)^9)^
(1/2) + 12*a*b*c^4*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a*b*c^4*e*f*(-(4*a*c - b^2)^9)^(1/2) - 78*a*b^2*c^3*e*g*(
-(4*a*c - b^2)^9)^(1/2) + 184*a*b^3*c^2*f*g*(-(4*a*c - b^2)^9)^(1/2) - 186*a^2*b*c^3*f*g*(-(4*a*c - b^2)^9)^(1
/2))/(32*(4096*a^6*c^13 + b^12*c^7 - 24*a*b^10*c^8 + 240*a^2*b^8*c^9 - 1280*a^3*b^6*c^10 + 3840*a^4*b^4*c^11 -
6144*a^5*b^2*c^12)))^(1/2)*2i + (g*x^3)/(3*c^2)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**4*(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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