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

Optimal. Leaf size=542 \[ \frac {2 b d-a e}{a^3 x}-\frac {d}{3 a^2 x^3}+\frac {x \left (a^2 \left (\frac {b^4 d}{a^2}-\frac {b^2 (b e+4 c d)}{a}-a (b g+2 c f)+b^2 f+3 b c e+2 c^2 d\right )+c x^2 \left (2 a^2 (c e-a g)-a b^2 e-a b (3 c d-a f)+b^3 d\right )\right )}{2 a^3 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {\sqrt {c} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right ) \left (\frac {4 a^2 b (a g+4 c e)+4 a^2 c (7 c d-3 a f)-3 a b^3 e-a b^2 (29 c d-a f)+5 b^4 d}{\sqrt {b^2-4 a c}}+2 a^2 (5 c e-a g)-3 a b^2 e-a b (19 c d-a f)+5 b^3 d\right )}{2 \sqrt {2} a^3 \left (b^2-4 a c\right ) \sqrt {b-\sqrt {b^2-4 a c}}}+\frac {\sqrt {c} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {\sqrt {b^2-4 a c}+b}}\right ) \left (-\frac {4 a^2 b (a g+4 c e)+4 a^2 c (7 c d-3 a f)-3 a b^3 e-a b^2 (29 c d-a f)+5 b^4 d}{\sqrt {b^2-4 a c}}+2 a^2 (5 c e-a g)-3 a b^2 e-a b (19 c d-a f)+5 b^3 d\right )}{2 \sqrt {2} a^3 \left (b^2-4 a c\right ) \sqrt {\sqrt {b^2-4 a c}+b}} \]

[Out]

-1/3*d/a^2/x^3+(-a*e+2*b*d)/a^3/x+1/2*x*(a^2*(b^4*d/a^2+2*c^2*d+3*b*c*e-b^2*(b*e+4*c*d)/a+b^2*f-a*(b*g+2*c*f))
+c*(b^3*d-a*b^2*e-a*b*(-a*f+3*c*d)+2*a^2*(-a*g+c*e))*x^2)/a^3/(-4*a*c+b^2)/(c*x^4+b*x^2+a)+1/4*arctan(x*2^(1/2
)*c^(1/2)/(b-(-4*a*c+b^2)^(1/2))^(1/2))*c^(1/2)*(5*b^3*d-3*a*b^2*e-a*b*(-a*f+19*c*d)+2*a^2*(-a*g+5*c*e)+(5*b^4
*d-3*a*b^3*e+4*a^2*c*(-3*a*f+7*c*d)-a*b^2*(-a*f+29*c*d)+4*a^2*b*(a*g+4*c*e))/(-4*a*c+b^2)^(1/2))/a^3/(-4*a*c+b
^2)*2^(1/2)/(b-(-4*a*c+b^2)^(1/2))^(1/2)+1/4*arctan(x*2^(1/2)*c^(1/2)/(b+(-4*a*c+b^2)^(1/2))^(1/2))*c^(1/2)*(5
*b^3*d-3*a*b^2*e-a*b*(-a*f+19*c*d)+2*a^2*(-a*g+5*c*e)+(-5*b^4*d+3*a*b^3*e-4*a^2*c*(-3*a*f+7*c*d)+a*b^2*(-a*f+2
9*c*d)-4*a^2*b*(a*g+4*c*e))/(-4*a*c+b^2)^(1/2))/a^3/(-4*a*c+b^2)*2^(1/2)/(b+(-4*a*c+b^2)^(1/2))^(1/2)

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Rubi [A]  time = 7.26, antiderivative size = 542, 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 = {1669, 1664, 1166, 205} \[ \frac {x \left (a^2 \left (\frac {b^4 d}{a^2}-\frac {b^2 (b e+4 c d)}{a}-a (b g+2 c f)+b^2 f+3 b c e+2 c^2 d\right )+c x^2 \left (2 a^2 (c e-a g)-a b^2 e-a b (3 c d-a f)+b^3 d\right )\right )}{2 a^3 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {\sqrt {c} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right ) \left (\frac {4 a^2 b (a g+4 c e)+4 a^2 c (7 c d-3 a f)-a b^2 (29 c d-a f)-3 a b^3 e+5 b^4 d}{\sqrt {b^2-4 a c}}+2 a^2 (5 c e-a g)-3 a b^2 e-a b (19 c d-a f)+5 b^3 d\right )}{2 \sqrt {2} a^3 \left (b^2-4 a c\right ) \sqrt {b-\sqrt {b^2-4 a c}}}+\frac {\sqrt {c} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {\sqrt {b^2-4 a c}+b}}\right ) \left (-\frac {4 a^2 b (a g+4 c e)+4 a^2 c (7 c d-3 a f)-a b^2 (29 c d-a f)-3 a b^3 e+5 b^4 d}{\sqrt {b^2-4 a c}}+2 a^2 (5 c e-a g)-3 a b^2 e-a b (19 c d-a f)+5 b^3 d\right )}{2 \sqrt {2} a^3 \left (b^2-4 a c\right ) \sqrt {\sqrt {b^2-4 a c}+b}}+\frac {2 b d-a e}{a^3 x}-\frac {d}{3 a^2 x^3} \]

Antiderivative was successfully verified.

[In]

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

[Out]

-d/(3*a^2*x^3) + (2*b*d - a*e)/(a^3*x) + (x*(a^2*((b^4*d)/a^2 + 2*c^2*d + 3*b*c*e - (b^2*(4*c*d + b*e))/a + b^
2*f - a*(2*c*f + b*g)) + c*(b^3*d - a*b^2*e - a*b*(3*c*d - a*f) + 2*a^2*(c*e - a*g))*x^2))/(2*a^3*(b^2 - 4*a*c
)*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(5*b^3*d - 3*a*b^2*e - a*b*(19*c*d - a*f) + 2*a^2*(5*c*e - a*g) + (5*b^4*d -
3*a*b^3*e + 4*a^2*c*(7*c*d - 3*a*f) - a*b^2*(29*c*d - a*f) + 4*a^2*b*(4*c*e + 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]*a^3*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) +
(Sqrt[c]*(5*b^3*d - 3*a*b^2*e - a*b*(19*c*d - a*f) + 2*a^2*(5*c*e - a*g) - (5*b^4*d - 3*a*b^3*e + 4*a^2*c*(7*
c*d - 3*a*f) - a*b^2*(29*c*d - a*f) + 4*a^2*b*(4*c*e + a*g))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqr
t[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^3*(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 1664

Int[(Pq_)*((d_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4)^(p_.), x_Symbol] :> Int[ExpandIntegrand[(d*x
)^m*Pq*(a + b*x^2 + c*x^4)^p, x], x] /; FreeQ[{a, b, c, d, m}, x] && PolyQ[Pq, x^2] && IGtQ[p, -2]

Rule 1669

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[x^m*(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])/x^m + (b^2*d*(2*p + 3) - 2*a*c*d*(4*p + 5) - a*b*e)
/x^m + c*(4*p + 7)*(b*d - 2*a*e)*x^(2 - m), 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] && ILtQ[m/2, 0]

Rubi steps

\begin {align*} \int \frac {d+e x^2+f x^4+g x^6}{x^4 \left (a+b x^2+c x^4\right )^2} \, dx &=\frac {x \left (a^2 \left (\frac {b^4 d}{a^2}+2 c^2 d+3 b c e-\frac {b^2 (4 c d+b e)}{a}+b^2 f-a (2 c f+b g)\right )+c \left (b^3 d-a b^2 e-a b (3 c d-a f)+2 a^2 (c e-a g)\right ) x^2\right )}{2 a^3 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\int \frac {-2 \left (b^2-4 a c\right ) d+\frac {2 \left (b^2-4 a c\right ) (b d-a e) x^2}{a}-\frac {\left (b^4 d-a b^3 e+6 a^2 c (c d-a f)-a b^2 (6 c d-a f)+a^2 b (5 c e+a g)\right ) x^4}{a^2}-c \left (\frac {b^3 d}{a^2}+2 c e-\frac {b (3 c d+b e)}{a}+b f-2 a g\right ) x^6}{x^4 \left (a+b x^2+c x^4\right )} \, dx}{2 a \left (b^2-4 a c\right )}\\ &=\frac {x \left (a^2 \left (\frac {b^4 d}{a^2}+2 c^2 d+3 b c e-\frac {b^2 (4 c d+b e)}{a}+b^2 f-a (2 c f+b g)\right )+c \left (b^3 d-a b^2 e-a b (3 c d-a f)+2 a^2 (c e-a g)\right ) x^2\right )}{2 a^3 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\int \left (\frac {2 \left (-b^2+4 a c\right ) d}{a x^4}+\frac {2 \left (-b^2+4 a c\right ) (-2 b d+a e)}{a^2 x^2}+\frac {-5 b^4 d+3 a b^3 e-2 a^2 c (7 c d-3 a f)+a b^2 (24 c d-a f)-a^2 b (13 c e+a g)-c \left (5 b^3 d-3 a b^2 e-a b (19 c d-a f)+2 a^2 (5 c e-a g)\right ) x^2}{a^2 \left (a+b x^2+c x^4\right )}\right ) \, dx}{2 a \left (b^2-4 a c\right )}\\ &=-\frac {d}{3 a^2 x^3}+\frac {2 b d-a e}{a^3 x}+\frac {x \left (a^2 \left (\frac {b^4 d}{a^2}+2 c^2 d+3 b c e-\frac {b^2 (4 c d+b e)}{a}+b^2 f-a (2 c f+b g)\right )+c \left (b^3 d-a b^2 e-a b (3 c d-a f)+2 a^2 (c e-a g)\right ) x^2\right )}{2 a^3 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\int \frac {-5 b^4 d+3 a b^3 e-2 a^2 c (7 c d-3 a f)+a b^2 (24 c d-a f)-a^2 b (13 c e+a g)-c \left (5 b^3 d-3 a b^2 e-a b (19 c d-a f)+2 a^2 (5 c e-a g)\right ) x^2}{a+b x^2+c x^4} \, dx}{2 a^3 \left (b^2-4 a c\right )}\\ &=-\frac {d}{3 a^2 x^3}+\frac {2 b d-a e}{a^3 x}+\frac {x \left (a^2 \left (\frac {b^4 d}{a^2}+2 c^2 d+3 b c e-\frac {b^2 (4 c d+b e)}{a}+b^2 f-a (2 c f+b g)\right )+c \left (b^3 d-a b^2 e-a b (3 c d-a f)+2 a^2 (c e-a g)\right ) x^2\right )}{2 a^3 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {\left (c \left (5 b^3 d-3 a b^2 e-a b (19 c d-a f)+2 a^2 (5 c e-a g)-\frac {5 b^4 d-3 a b^3 e+4 a^2 c (7 c d-3 a f)-a b^2 (29 c d-a f)+4 a^2 b (4 c e+a g)}{\sqrt {b^2-4 a c}}\right )\right ) \int \frac {1}{\frac {b}{2}+\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx}{4 a^3 \left (b^2-4 a c\right )}+\frac {\left (c \left (5 b^3 d-3 a b^2 e-a b (19 c d-a f)+2 a^2 (5 c e-a g)+\frac {5 b^4 d-3 a b^3 e+4 a^2 c (7 c d-3 a f)-a b^2 (29 c d-a f)+4 a^2 b (4 c e+a g)}{\sqrt {b^2-4 a c}}\right )\right ) \int \frac {1}{\frac {b}{2}-\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx}{4 a^3 \left (b^2-4 a c\right )}\\ &=-\frac {d}{3 a^2 x^3}+\frac {2 b d-a e}{a^3 x}+\frac {x \left (a^2 \left (\frac {b^4 d}{a^2}+2 c^2 d+3 b c e-\frac {b^2 (4 c d+b e)}{a}+b^2 f-a (2 c f+b g)\right )+c \left (b^3 d-a b^2 e-a b (3 c d-a f)+2 a^2 (c e-a g)\right ) x^2\right )}{2 a^3 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {\sqrt {c} \left (5 b^3 d-3 a b^2 e-a b (19 c d-a f)+2 a^2 (5 c e-a g)+\frac {5 b^4 d-3 a b^3 e+4 a^2 c (7 c d-3 a f)-a b^2 (29 c d-a f)+4 a^2 b (4 c e+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} a^3 \left (b^2-4 a c\right ) \sqrt {b-\sqrt {b^2-4 a c}}}+\frac {\sqrt {c} \left (5 b^3 d-3 a b^2 e-a b (19 c d-a f)+2 a^2 (5 c e-a g)-\frac {5 b^4 d-3 a b^3 e+4 a^2 c (7 c d-3 a f)-a b^2 (29 c d-a f)+4 a^2 b (4 c e+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} a^3 \left (b^2-4 a c\right ) \sqrt {b+\sqrt {b^2-4 a c}}}\\ \end {align*}

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Mathematica [A]  time = 2.15, size = 612, normalized size = 1.13 \[ \frac {\frac {6 x \left (a b \left (a^2 (-g)+a c \left (3 e+f x^2\right )-3 c^2 d x^2\right )+2 a^2 c \left (c \left (d+e x^2\right )-a \left (f+g x^2\right )\right )+b^3 \left (c d x^2-a e\right )+a b^2 \left (a f-c \left (4 d+e x^2\right )\right )+b^4 d\right )}{\left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {3 \sqrt {2} \sqrt {c} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right ) \left (-2 a^2 \left (-5 c e \sqrt {b^2-4 a c}+a g \sqrt {b^2-4 a c}+6 a c f-14 c^2 d\right )+a b \left (4 a^2 g-19 c d \sqrt {b^2-4 a c}+a f \sqrt {b^2-4 a c}+16 a c e\right )+a b^2 \left (-3 e \sqrt {b^2-4 a c}+a f-29 c d\right )+b^3 \left (5 d \sqrt {b^2-4 a c}-3 a e\right )+5 b^4 d\right )}{\left (b^2-4 a c\right )^{3/2} \sqrt {b-\sqrt {b^2-4 a c}}}-\frac {3 \sqrt {2} \sqrt {c} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {\sqrt {b^2-4 a c}+b}}\right ) \left (2 a^2 \left (-5 c e \sqrt {b^2-4 a c}+a g \sqrt {b^2-4 a c}-6 a c f+14 c^2 d\right )+a b \left (4 a^2 g+19 c d \sqrt {b^2-4 a c}-a f \sqrt {b^2-4 a c}+16 a c e\right )+a b^2 \left (3 e \sqrt {b^2-4 a c}+a f-29 c d\right )-b^3 \left (5 d \sqrt {b^2-4 a c}+3 a e\right )+5 b^4 d\right )}{\left (b^2-4 a c\right )^{3/2} \sqrt {\sqrt {b^2-4 a c}+b}}+\frac {24 b d-12 a e}{x}-\frac {4 a d}{x^3}}{12 a^3} \]

Antiderivative was successfully verified.

[In]

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

[Out]

((-4*a*d)/x^3 + (24*b*d - 12*a*e)/x + (6*x*(b^4*d + b^3*(-(a*e) + c*d*x^2) + a*b^2*(a*f - c*(4*d + e*x^2)) + a
*b*(-(a^2*g) - 3*c^2*d*x^2 + a*c*(3*e + f*x^2)) + 2*a^2*c*(c*(d + e*x^2) - a*(f + g*x^2))))/((b^2 - 4*a*c)*(a
+ b*x^2 + c*x^4)) + (3*Sqrt[2]*Sqrt[c]*(5*b^4*d + b^3*(5*Sqrt[b^2 - 4*a*c]*d - 3*a*e) + a*b^2*(-29*c*d - 3*Sqr
t[b^2 - 4*a*c]*e + a*f) + a*b*(-19*c*Sqrt[b^2 - 4*a*c]*d + 16*a*c*e + a*Sqrt[b^2 - 4*a*c]*f + 4*a^2*g) - 2*a^2
*(-14*c^2*d - 5*c*Sqrt[b^2 - 4*a*c]*e + 6*a*c*f + a*Sqrt[b^2 - 4*a*c]*g))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b -
Sqrt[b^2 - 4*a*c]]])/((b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (3*Sqrt[2]*Sqrt[c]*(5*b^4*d - b^3*(5*
Sqrt[b^2 - 4*a*c]*d + 3*a*e) + a*b^2*(-29*c*d + 3*Sqrt[b^2 - 4*a*c]*e + a*f) + a*b*(19*c*Sqrt[b^2 - 4*a*c]*d +
16*a*c*e - a*Sqrt[b^2 - 4*a*c]*f + 4*a^2*g) + 2*a^2*(14*c^2*d - 5*c*Sqrt[b^2 - 4*a*c]*e - 6*a*c*f + a*Sqrt[b^
2 - 4*a*c]*g))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/((b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2
- 4*a*c]]))/(12*a^3)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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giac [B]  time = 9.06, size = 10422, normalized size = 19.23 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*(b^3*c*d*x^3 - 3*a*b*c^2*d*x^3 + a^2*b*c*f*x^3 - 2*a^3*c*g*x^3 - a*b^2*c*x^3*e + 2*a^2*c^2*x^3*e + b^4*d*x
- 4*a*b^2*c*d*x + 2*a^2*c^2*d*x + a^2*b^2*f*x - 2*a^3*c*f*x - a^3*b*g*x - a*b^3*x*e + 3*a^2*b*c*x*e)/((a^3*b^
2 - 4*a^4*c)*(c*x^4 + b*x^2 + a)) + 1/16*((10*b^5*c^2 - 78*a*b^3*c^3 + 152*a^2*b*c^4 - 5*sqrt(2)*sqrt(b^2 - 4*
a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 39*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*
c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 76*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
+ sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 38*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 5
*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + s
qrt(b^2 - 4*a*c)*c)*a*b*c^3 - 10*(b^2 - 4*a*c)*b^3*c^2 + 38*(b^2 - 4*a*c)*a*b*c^3)*(a^3*b^2 - 4*a^4*c)^2*d + (
2*a^2*b^3*c^2 - 8*a^3*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3 + 4*sqrt(2)*sq
rt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*
a*c)*c)*a^2*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 2*(b^2 - 4*a*c)*a^2*
b*c^2)*(a^3*b^2 - 4*a^4*c)^2*f - 2*(2*a^3*b^2*c^2 - 8*a^4*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2
- 4*a*c)*c)*a^3*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c + 2*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^
3*c^2 - 2*(b^2 - 4*a*c)*a^3*c^2)*(a^3*b^2 - 4*a^4*c)^2*g - (6*a*b^4*c^2 - 44*a^2*b^2*c^3 + 80*a^3*c^4 - 3*sqrt
(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2
- 4*a*c)*c)*a^2*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 40*sqrt(2)*sqrt
(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a
*c)*c)*a^2*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 10*sqrt(2)*sqrt(b^2
- 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 6*(b^2 - 4*a*c)*a*b^2*c^2 + 20*(b^2 - 4*a*c)*a^2*c^3)*(a^3
*b^2 - 4*a^4*c)^2*e + 2*(5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^8 - 64*sqrt(2)*sqrt(b*c + sqrt(b^2 -
4*a*c)*c)*a^4*b^6*c - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c - 10*a^3*b^8*c + 286*sqrt(2)*sqrt(b
*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 88*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 + 5*sqrt(2)*sqr
t(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^2 + 128*a^4*b^6*c^2 - 496*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b
^2*c^3 - 220*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 - 44*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*
a^4*b^4*c^3 - 572*a^5*b^4*c^3 + 224*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*c^4 + 112*sqrt(2)*sqrt(b*c + s
qrt(b^2 - 4*a*c)*c)*a^6*b*c^4 + 110*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^4 + 992*a^6*b^2*c^4 - 56
*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*c^5 - 448*a^7*c^5 + 10*(b^2 - 4*a*c)*a^3*b^6*c - 88*(b^2 - 4*a*c)
*a^4*b^4*c^2 + 220*(b^2 - 4*a*c)*a^5*b^2*c^3 - 112*(b^2 - 4*a*c)*a^6*c^4)*d*abs(a^3*b^2 - 4*a^4*c) + 2*(sqrt(2
)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6 - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c - 2*sqrt(2)*s
qrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c - 2*a^5*b^6*c + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^
2 + 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c
^2 + 28*a^6*b^4*c^2 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*c^3 - 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*
a*c)*c)*a^7*b*c^3 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 128*a^7*b^2*c^3 + 24*sqrt(2)*sqrt
(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*c^4 + 192*a^8*c^4 + 2*(b^2 - 4*a*c)*a^5*b^4*c - 20*(b^2 - 4*a*c)*a^6*b^2*c^2 +
48*(b^2 - 4*a*c)*a^7*c^3)*f*abs(a^3*b^2 - 4*a^4*c) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5 - 8*s
qrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c - 2*a^6
*b^5*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*
b^2*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 + 16*a^7*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2
- 4*a*c)*c)*a^7*b*c^3 - 32*a^8*b*c^3 + 2*(b^2 - 4*a*c)*a^6*b^3*c - 8*(b^2 - 4*a*c)*a^7*b*c^2)*g*abs(a^3*b^2 -
4*a^4*c) - 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7 - 37*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*
a^5*b^5*c - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c - 6*a^4*b^7*c + 152*sqrt(2)*sqrt(b*c + sqrt(b^
2 - 4*a*c)*c)*a^6*b^3*c^2 + 50*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 3*sqrt(2)*sqrt(b*c + sqrt
(b^2 - 4*a*c)*c)*a^4*b^5*c^2 + 74*a^5*b^5*c^2 - 208*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 - 104*sq
rt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 25*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 - 3
04*a^6*b^3*c^3 + 52*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 + 416*a^7*b*c^4 + 6*(b^2 - 4*a*c)*a^4*b^
5*c - 50*(b^2 - 4*a*c)*a^5*b^3*c^2 + 104*(b^2 - 4*a*c)*a^6*b*c^3)*abs(a^3*b^2 - 4*a^4*c)*e + (10*a^6*b^9*c^2 -
138*a^7*b^7*c^3 + 680*a^8*b^5*c^4 - 1376*a^9*b^3*c^5 + 896*a^10*b*c^6 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
+ sqrt(b^2 - 4*a*c)*c)*a^6*b^9 + 69*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c + 10*s
qrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^8*c - 340*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c +
sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 98*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 -
5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^7*c^2 + 688*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b
*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 288*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^4*
c^3 + 49*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^5*c^3 - 448*sqrt(2)*sqrt(b^2 - 4*a*c)
*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^
9*b^2*c^4 - 144*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^3*c^4 + 112*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b*c^5 - 10*(b^2 - 4*a*c)*a^6*b^7*c^2 + 98*(b^2 - 4*a*c)*a^7*b^5*c^
3 - 288*(b^2 - 4*a*c)*a^8*b^3*c^4 + 224*(b^2 - 4*a*c)*a^9*b*c^5)*d + (2*a^8*b^7*c^2 - 40*a^9*b^5*c^3 + 224*a^1
0*b^3*c^4 - 384*a^11*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^7 + 20*sqrt(2)*sq
rt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 -
4*a*c)*c)*a^8*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^3*c^2 - 32*sqrt(2)*
sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2
- 4*a*c)*c)*a^8*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b*c^3 + 96*sqrt(2
)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqr
t(b^2 - 4*a*c)*c)*a^9*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 2*(b
^2 - 4*a*c)*a^8*b^5*c^2 + 32*(b^2 - 4*a*c)*a^9*b^3*c^3 - 96*(b^2 - 4*a*c)*a^10*b*c^4)*f + 4*(2*a^9*b^6*c^2 - 1
6*a^10*b^4*c^3 + 32*a^11*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^6 + 8*sqrt(
2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(
b^2 - 4*a*c)*c)*a^9*b^5*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^2*c^2 - 8*sqrt
(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt
(b^2 - 4*a*c)*c)*a^9*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 - 2*(b
^2 - 4*a*c)*a^9*b^4*c^2 + 8*(b^2 - 4*a*c)*a^10*b^2*c^3)*g - (6*a^7*b^8*c^2 - 80*a^8*b^6*c^3 + 352*a^9*b^4*c^4
- 512*a^10*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^8 + 40*sqrt(2)*sqrt(b^2
- 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^6*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)
*c)*a^7*b^7*c - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 - 56*sqrt(2)*sqrt(b^
2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a
*c)*c)*a^7*b^6*c^2 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 + 128*sqrt(2)*
sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b
^2 - 4*a*c)*c)*a^8*b^4*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 6*(b^2
- 4*a*c)*a^7*b^6*c^2 + 56*(b^2 - 4*a*c)*a^8*b^4*c^3 - 128*(b^2 - 4*a*c)*a^9*b^2*c^4)*e)*arctan(2*sqrt(1/2)*x/
sqrt((a^3*b^3 - 4*a^4*b*c + sqrt((a^3*b^3 - 4*a^4*b*c)^2 - 4*(a^4*b^2 - 4*a^5*c)*(a^3*b^2*c - 4*a^4*c^2)))/(a^
3*b^2*c - 4*a^4*c^2)))/((a^7*b^6 - 12*a^8*b^4*c - 2*a^7*b^5*c + 48*a^9*b^2*c^2 + 16*a^8*b^3*c^2 + a^7*b^4*c^2
- 64*a^10*c^3 - 32*a^9*b*c^3 - 8*a^8*b^2*c^3 + 16*a^9*c^4)*abs(a^3*b^2 - 4*a^4*c)*abs(c)) - 1/16*((10*b^5*c^2
- 78*a*b^3*c^3 + 152*a^2*b*c^4 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 39*sqrt(2)*
sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*b^4*c - 76*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 38*sqrt(2)*sqrt(b^
2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c
)*c)*b^3*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 10*(b^2 - 4*a*c)*b^3*c^2
+ 38*(b^2 - 4*a*c)*a*b*c^3)*(a^3*b^2 - 4*a^4*c)^2*d + (2*a^2*b^3*c^2 - 8*a^3*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c
)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*
c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
- sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 2*(b^2 - 4*a*c)*a^2*b*c^2)*(a^3*b^2 - 4*a^4*c)^2*f - 2*(2*a^3*b^2*c^2 - 8*
a^4*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt
(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c - sqrt
(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 2*(b^2 - 4*a*c)*a^3*c^2)*(a^3*b^2 - 4*a^4*c)^2
*g - (6*a*b^4*c^2 - 44*a^2*b^2*c^3 + 80*a^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*
a*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*s
qrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^2
- 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*
c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 6*
(b^2 - 4*a*c)*a*b^2*c^2 + 20*(b^2 - 4*a*c)*a^2*c^3)*(a^3*b^2 - 4*a^4*c)^2*e - 2*(5*sqrt(2)*sqrt(b*c - sqrt(b^2
- 4*a*c)*c)*a^3*b^8 - 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*a^3*b^7*c + 10*a^3*b^8*c + 286*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 88*sqrt(2)*sqr
t(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 + 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^2 - 128*a^4*b^6
*c^2 - 496*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 220*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a
^5*b^3*c^3 - 44*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^3 + 572*a^5*b^4*c^3 + 224*sqrt(2)*sqrt(b*c -
sqrt(b^2 - 4*a*c)*c)*a^7*c^4 + 112*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 + 110*sqrt(2)*sqrt(b*c -
sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^4 - 992*a^6*b^2*c^4 - 56*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*c^5 + 448
*a^7*c^5 - 10*(b^2 - 4*a*c)*a^3*b^6*c + 88*(b^2 - 4*a*c)*a^4*b^4*c^2 - 220*(b^2 - 4*a*c)*a^5*b^2*c^3 + 112*(b^
2 - 4*a*c)*a^6*c^4)*d*abs(a^3*b^2 - 4*a^4*c) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6 - 14*sqrt(2)
*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c + 2*a^5*b^6*c
+ 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^2 + 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3
*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 - 28*a^6*b^4*c^2 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*a^8*c^3 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4
*a*c)*c)*a^6*b^2*c^3 + 128*a^7*b^2*c^3 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*c^4 - 192*a^8*c^4 - 2*
(b^2 - 4*a*c)*a^5*b^4*c + 20*(b^2 - 4*a*c)*a^6*b^2*c^2 - 48*(b^2 - 4*a*c)*a^7*c^3)*f*abs(a^3*b^2 - 4*a^4*c) -
2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c - 2*s
qrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c + 2*a^6*b^5*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^
8*b*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*
b^3*c^2 - 16*a^7*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 + 32*a^8*b*c^3 - 2*(b^2 - 4*a*c
)*a^6*b^3*c + 8*(b^2 - 4*a*c)*a^7*b*c^2)*g*abs(a^3*b^2 - 4*a^4*c) + 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*
c)*a^4*b^7 - 37*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*
a^4*b^6*c + 6*a^4*b^7*c + 152*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 + 50*sqrt(2)*sqrt(b*c - sqrt
(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 - 74*a^5*b^5*c^2 - 208*sq
rt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 - 104*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 25
*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 + 304*a^6*b^3*c^3 + 52*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*
c)*c)*a^6*b*c^4 - 416*a^7*b*c^4 - 6*(b^2 - 4*a*c)*a^4*b^5*c + 50*(b^2 - 4*a*c)*a^5*b^3*c^2 - 104*(b^2 - 4*a*c)
*a^6*b*c^3)*abs(a^3*b^2 - 4*a^4*c)*e + (10*a^6*b^9*c^2 - 138*a^7*b^7*c^3 + 680*a^8*b^5*c^4 - 1376*a^9*b^3*c^5
+ 896*a^10*b*c^6 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^9 + 69*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*
c)*a^6*b^8*c - 340*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 98*sqrt(2)*sqrt(b^2
- 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*
c)*c)*a^6*b^7*c^2 + 688*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 288*sqrt(2)*sq
rt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 + 49*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2
- 4*a*c)*c)*a^7*b^5*c^3 - 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 224*sqrt
(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 144*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - s
qrt(b^2 - 4*a*c)*c)*a^8*b^3*c^4 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b*c^5 - 10
*(b^2 - 4*a*c)*a^6*b^7*c^2 + 98*(b^2 - 4*a*c)*a^7*b^5*c^3 - 288*(b^2 - 4*a*c)*a^8*b^3*c^4 + 224*(b^2 - 4*a*c)*
a^9*b*c^5)*d + (2*a^8*b^7*c^2 - 40*a^9*b^5*c^3 + 224*a^10*b^3*c^4 - 384*a^11*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)
*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^
5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sq
rt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*
b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c
)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^
10*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 2*(b^2 - 4*a*c)*a^8*b^5*c^2 + 32*(b^2 - 4*a*c)*a^9*b^3*c^3
- 96*(b^2 - 4*a*c)*a^10*b*c^4)*f + 4*(2*a^9*b^6*c^2 - 16*a^10*b^4*c^3 + 32*a^11*b^2*c^4 - sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^6 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a
^10*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^5*c - 16*sqrt(2)*sqrt(b^2 - 4*a*
c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*
a^10*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*
a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 - 2*(b^2 - 4*a*c)*a^9*b^4*c^2 + 8*(b^2 - 4*a*c)*a^10*b^2*c^3
)*g - (6*a^7*b^8*c^2 - 80*a^8*b^6*c^3 + 352*a^9*b^4*c^4 - 512*a^10*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(
b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^8 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^6*c +
6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
- sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2
- 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqr
t(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*
b^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a
*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 6*(b^2 - 4*a*c)*a^7*b^6*c^2 + 56*(b^2 - 4*a*c)*a^8*b^4*c^3 -
128*(b^2 - 4*a*c)*a^9*b^2*c^4)*e)*arctan(2*sqrt(1/2)*x/sqrt((a^3*b^3 - 4*a^4*b*c - sqrt((a^3*b^3 - 4*a^4*b*c)
^2 - 4*(a^4*b^2 - 4*a^5*c)*(a^3*b^2*c - 4*a^4*c^2)))/(a^3*b^2*c - 4*a^4*c^2)))/((a^7*b^6 - 12*a^8*b^4*c - 2*a^
7*b^5*c + 48*a^9*b^2*c^2 + 16*a^8*b^3*c^2 + a^7*b^4*c^2 - 64*a^10*c^3 - 32*a^9*b*c^3 - 8*a^8*b^2*c^3 + 16*a^9*
c^4)*abs(a^3*b^2 - 4*a^4*c)*abs(c)) + 1/3*(6*b*d*x^2 - 3*a*x^2*e - a*d)/(a^3*x^3)

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maple [B]  time = 0.07, size = 2503, normalized size = 4.62 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/3/a^2*d/x^3+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*g+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)*b*g+2/a^3*b*d/x-1/2*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)*g+1/2*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)*g-5/4/(4*a*c-b^2)*2^(1/2)/((b
+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a^3*b^3*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+7/a*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)*d+1/4/a*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)*b*f-3/4/a^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)*b^2*e-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a*b*c*f*arctan
(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+3/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a^2*b^
2*c*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+19/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)
^(1/2)/a^2*b*c^2*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+7/(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^3*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-19/4/a^2*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
*d+5/4/a^3*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)*b^3*d+1/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*g+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b*g-29/4/a^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)*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)/a*b^2*c*f*arc
tan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+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*c^2*e*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)/a^2*b^3*c*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+4/
a*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*e-3/4/a^2*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+1/4/a*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^2*f+5/4/(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^3*b^4*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))
*c)^(1/2)*c*x)+5/4/a^3*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^4*d-29/4/(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^2*b^2*c^2*d*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)/a*b*c*f*x^3+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a^2*b^2*c*e*x^3+3/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a^2*b*c^2*d*x
^3-3/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a*b*c*e*x+2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a^2*b^2*c*d*x-1/2/(c*x^4+b*x^2+a)/(
4*a*c-b^2)/a^3*b^3*c*d*x^3+5/2/a*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)*e-5/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a*c^2*e*arctan(
2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-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)*c^2*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-3*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)*f+1/(c*x^4+b*x^2+
a)/(4*a*c-b^2)*c*f*x-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a*c^2*e*x^3-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a^3*b^4*d*x-1/2
/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a*b^2*f*x-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a*c^2*d*x+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)
/a^2*b^3*e*x-1/a^2*e/x

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \frac {3 \, {\left (a^{2} b c f - 2 \, a^{3} c g + {\left (5 \, b^{3} c - 19 \, a b c^{2}\right )} d - {\left (3 \, a b^{2} c - 10 \, a^{2} c^{2}\right )} e\right )} x^{6} - {\left (3 \, a^{3} b g - {\left (15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2}\right )} d + 3 \, {\left (3 \, a b^{3} - 11 \, a^{2} b c\right )} e - 3 \, {\left (a^{2} b^{2} - 2 \, a^{3} c\right )} f\right )} x^{4} + 2 \, {\left (5 \, {\left (a b^{3} - 4 \, a^{2} b c\right )} d - 3 \, {\left (a^{2} b^{2} - 4 \, a^{3} c\right )} e\right )} x^{2} - 2 \, {\left (a^{2} b^{2} - 4 \, a^{3} c\right )} d}{6 \, {\left ({\left (a^{3} b^{2} c - 4 \, a^{4} c^{2}\right )} x^{7} + {\left (a^{3} b^{3} - 4 \, a^{4} b c\right )} x^{5} + {\left (a^{4} b^{2} - 4 \, a^{5} c\right )} x^{3}\right )}} - \frac {-\int \frac {a^{3} b g + {\left (a^{2} b c f - 2 \, a^{3} c g + {\left (5 \, b^{3} c - 19 \, a b c^{2}\right )} d - {\left (3 \, a b^{2} c - 10 \, a^{2} c^{2}\right )} e\right )} x^{2} + {\left (5 \, b^{4} - 24 \, a b^{2} c + 14 \, a^{2} c^{2}\right )} d - {\left (3 \, a b^{3} - 13 \, a^{2} b c\right )} e + {\left (a^{2} b^{2} - 6 \, a^{3} c\right )} f}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left (a^{3} b^{2} - 4 \, a^{4} c\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/6*(3*(a^2*b*c*f - 2*a^3*c*g + (5*b^3*c - 19*a*b*c^2)*d - (3*a*b^2*c - 10*a^2*c^2)*e)*x^6 - (3*a^3*b*g - (15*
b^4 - 62*a*b^2*c + 14*a^2*c^2)*d + 3*(3*a*b^3 - 11*a^2*b*c)*e - 3*(a^2*b^2 - 2*a^3*c)*f)*x^4 + 2*(5*(a*b^3 - 4
*a^2*b*c)*d - 3*(a^2*b^2 - 4*a^3*c)*e)*x^2 - 2*(a^2*b^2 - 4*a^3*c)*d)/((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3
- 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3) - 1/2*integrate(-(a^3*b*g + (a^2*b*c*f - 2*a^3*c*g + (5*b^3*c - 19
*a*b*c^2)*d - (3*a*b^2*c - 10*a^2*c^2)*e)*x^2 + (5*b^4 - 24*a*b^2*c + 14*a^2*c^2)*d - (3*a*b^3 - 13*a^2*b*c)*e
+ (a^2*b^2 - 6*a^3*c)*f)/(c*x^4 + b*x^2 + a), x)/(a^3*b^2 - 4*a^4*c)

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mupad [B]  time = 8.47, size = 51386, normalized size = 94.81 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

atan((((-(25*b^15*d^2 + 9*a^2*b^13*e^2 + 25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + a^4*b^11*f^2 + a^6*b^9*g^2 + a^
6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7*d^2 - 213*a^3*b^11*c*e^2 + 26880*a^8*b*c^6*e^2 - 27*a^5*b^9*c
*f^2 - 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^10*b*c^4*g^2 - 30*a*b^14*d*e + 6366*a
^2*b^11*c^2*d^2 - 35767*a^3*b^9*c^3*d^2 + 116928*a^4*b^7*c^4*d^2 - 219744*a^5*b^5*c^5*d^2 + 215040*a^6*b^3*c^6
*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) + 2077*a^4*b^9*c^2*e^2
- 10656*a^5*b^7*c^3*e^2 + 30240*a^6*b^5*c^4*e^2 - 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2
) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) + 288*a^6*b^7*c^2*f^2 - 1504*a^7*b^5*c^3*f^2 + 3840*a^8*b^3*c^4*f^
2 - 96*a^8*b^5*c^2*g^2 + 512*a^9*b^3*c^3*g^2 - 615*a*b^13*c*d^2 + 10*a^2*b^13*d*f + 35840*a^8*c^7*d*e + 10*a^3
*b^12*d*g - 6*a^3*b^12*e*f - 6*a^4*b^11*e*g - 7168*a^9*c^6*d*g - 15360*a^9*c^6*e*f + 2*a^5*b^10*f*g + 3072*a^1
0*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 724*a^2*b^12*c*d*e - 258*a^3*b^11*c*d*f + 43520*a^8*b*c^6*
d*f - 168*a^4*b^10*c*d*g + 152*a^4*b^10*c*e*f + 98*a^5*b^9*c*e*g - 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c -
b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) - 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2
)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^3*b^10*c^2*d*e + 39132*a^4*b^8*c^3*d*e - 119616
*a^5*b^6*c^4*d*e + 201600*a^6*b^4*c^5*d*e - 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) +
2706*a^4*b^9*c^2*d*f - 14784*a^5*b^7*c^3*d*f + 44352*a^6*b^5*c^4*d*f - 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g
*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) +
1044*a^5*b^8*c^2*d*g - 1548*a^5*b^8*c^2*e*f - 2688*a^6*b^6*c^3*d*g + 8064*a^6*b^6*c^3*e*f + 1152*a^7*b^4*c^4*
d*g - 22400*a^7*b^4*c^4*e*f + 6144*a^8*b^2*c^5*d*g + 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^
(1/2) - 576*a^6*b^7*c^2*e*g + 1344*a^7*b^5*c^3*e*g - 512*a^8*b^3*c^4*e*g + 192*a^7*b^6*c^2*f*g - 128*a^8*b^4*c
^3*f*g - 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^
(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d
*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^
8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(393216*a^20*c
^8*f - 917504*a^19*c^9*d + x*(-(25*b^15*d^2 + 9*a^2*b^13*e^2 + 25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + a^4*b^11*
f^2 + a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7*d^2 - 213*a^3*b^11*c*e^2 + 26880*a^8*b*
c^6*e^2 - 27*a^5*b^9*c*f^2 - 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^10*b*c^4*g^2 -
30*a*b^14*d*e + 6366*a^2*b^11*c^2*d^2 - 35767*a^3*b^9*c^3*d^2 + 116928*a^4*b^7*c^4*d^2 - 219744*a^5*b^5*c^5*d^
2 + 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2)
+ 2077*a^4*b^9*c^2*e^2 - 10656*a^5*b^7*c^3*e^2 + 30240*a^6*b^5*c^4*e^2 - 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(
-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) + 288*a^6*b^7*c^2*f^2 - 1504*a^7*b^5*c^3*f^2
+ 3840*a^8*b^3*c^4*f^2 - 96*a^8*b^5*c^2*g^2 + 512*a^9*b^3*c^3*g^2 - 615*a*b^13*c*d^2 + 10*a^2*b^13*d*f + 3584
0*a^8*c^7*d*e + 10*a^3*b^12*d*g - 6*a^3*b^12*e*f - 6*a^4*b^11*e*g - 7168*a^9*c^6*d*g - 15360*a^9*c^6*e*f + 2*a
^5*b^10*f*g + 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 724*a^2*b^12*c*d*e - 258*a^3*b^11*c*
d*f + 43520*a^8*b*c^6*d*f - 168*a^4*b^10*c*d*g + 152*a^4*b^10*c*e*f + 98*a^5*b^9*c*e*g - 1536*a^9*b*c^5*e*g +
2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) - 36*a^6*b^8*c*f*g + 246*a^2*b^2*
c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^3*b^10*c^2*d*e + 39132*a^
4*b^8*c^3*d*e - 119616*a^5*b^6*c^4*d*e + 201600*a^6*b^4*c^5*d*e - 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4
*a*c - b^2)^9)^(1/2) + 2706*a^4*b^9*c^2*d*f - 14784*a^5*b^7*c^3*d*f + 44352*a^6*b^5*c^4*d*f - 69120*a^7*b^3*c^
5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4
*a*c - b^2)^9)^(1/2) + 1044*a^5*b^8*c^2*d*g - 1548*a^5*b^8*c^2*e*f - 2688*a^6*b^6*c^3*d*g + 8064*a^6*b^6*c^3*e
*f + 1152*a^7*b^4*c^4*d*g - 22400*a^7*b^4*c^4*e*f + 6144*a^8*b^2*c^5*d*g + 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e
*g*(-(4*a*c - b^2)^9)^(1/2) - 576*a^6*b^7*c^2*e*g + 1344*a^7*b^5*c^3*e*g - 512*a^8*b^3*c^4*e*g + 192*a^7*b^6*c
^2*f*g - 128*a^8*b^4*c^3*f*g - 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d
*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(
1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 +
4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5))
)^(1/2)*(1048576*a^21*b*c^8 + 256*a^15*b^13*c^2 - 6144*a^16*b^11*c^3 + 61440*a^17*b^9*c^4 - 327680*a^18*b^7*c^
5 + 983040*a^19*b^5*c^6 - 1572864*a^20*b^3*c^7) + 320*a^12*b^14*c^2*d - 7936*a^13*b^12*c^3*d + 82816*a^14*b^10
*c^4*d - 468480*a^15*b^8*c^5*d + 1536000*a^16*b^6*c^6*d - 2867200*a^17*b^4*c^7*d + 2719744*a^18*b^2*c^8*d - 19
2*a^13*b^13*c^2*e + 4672*a^14*b^11*c^3*e - 47360*a^15*b^9*c^4*e + 256000*a^16*b^7*c^5*e - 778240*a^17*b^5*c^6*
e + 1261568*a^18*b^3*c^7*e + 64*a^14*b^12*c^2*f - 1664*a^15*b^10*c^3*f + 17920*a^16*b^8*c^4*f - 102400*a^17*b^
6*c^5*f + 327680*a^18*b^4*c^6*f - 557056*a^19*b^2*c^7*f + 64*a^15*b^11*c^2*g - 1280*a^16*b^9*c^3*g + 10240*a^1
7*b^7*c^4*g - 40960*a^18*b^5*c^5*g + 81920*a^19*b^3*c^6*g - 851968*a^19*b*c^8*e - 65536*a^20*b*c^7*g) + x*(204
800*a^17*c^9*e^2 - 401408*a^16*c^10*d^2 - 73728*a^18*c^8*f^2 + 8192*a^19*c^7*g^2 + 400*a^9*b^14*c^3*d^2 - 9440
*a^10*b^12*c^4*d^2 + 92816*a^11*b^10*c^5*d^2 - 488096*a^12*b^8*c^6*d^2 + 1458688*a^13*b^6*c^7*d^2 - 2401280*a^
14*b^4*c^8*d^2 + 1871872*a^15*b^2*c^9*d^2 + 144*a^11*b^12*c^3*e^2 - 3264*a^12*b^10*c^4*e^2 + 30112*a^13*b^8*c^
5*e^2 - 143360*a^14*b^6*c^6*e^2 + 365568*a^15*b^4*c^7*e^2 - 458752*a^16*b^2*c^8*e^2 + 16*a^13*b^10*c^3*f^2 - 4
16*a^14*b^8*c^4*f^2 + 4608*a^15*b^6*c^5*f^2 - 25600*a^16*b^4*c^6*f^2 + 69632*a^17*b^2*c^7*f^2 + 160*a^15*b^8*c
^3*g^2 - 2048*a^16*b^6*c^4*g^2 + 9216*a^17*b^4*c^5*g^2 - 16384*a^18*b^2*c^6*g^2 + 344064*a^17*c^9*d*f - 81920*
a^18*c^8*e*g - 1236992*a^16*b*c^9*d*e + 40960*a^17*b*c^8*d*g + 237568*a^17*b*c^8*e*f + 40960*a^18*b*c^7*f*g -
480*a^10*b^13*c^3*d*e + 11104*a^11*b^11*c^4*d*e - 105824*a^12*b^9*c^5*d*e + 530432*a^13*b^7*c^6*d*e - 1469440*
a^14*b^5*c^7*d*e + 2121728*a^15*b^3*c^8*d*e + 160*a^11*b^12*c^3*d*f - 3968*a^12*b^10*c^4*d*f + 39488*a^13*b^8*
c^5*d*f - 200704*a^14*b^6*c^6*d*f + 542720*a^15*b^4*c^7*d*f - 720896*a^16*b^2*c^8*d*f + 160*a^12*b^11*c^3*d*g
- 96*a^12*b^11*c^3*e*f - 2528*a^13*b^9*c^4*d*g + 2336*a^13*b^9*c^4*e*f + 14336*a^14*b^7*c^5*d*g - 22528*a^14*b
^7*c^5*e*f - 31744*a^15*b^5*c^6*d*g + 107520*a^15*b^5*c^6*e*f + 8192*a^16*b^3*c^7*d*g - 253952*a^16*b^3*c^7*e*
f - 96*a^13*b^10*c^3*e*g + 1472*a^14*b^8*c^4*e*g - 7168*a^15*b^6*c^5*e*g + 6144*a^16*b^4*c^6*e*g + 40960*a^17*
b^2*c^7*e*g + 32*a^14*b^9*c^3*f*g - 1024*a^15*b^7*c^4*f*g + 9216*a^16*b^5*c^5*f*g - 32768*a^17*b^3*c^6*f*g))*(
-(25*b^15*d^2 + 9*a^2*b^13*e^2 + 25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + a^4*b^11*f^2 + a^6*b^9*g^2 + a^6*g^2*(-
(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7*d^2 - 213*a^3*b^11*c*e^2 + 26880*a^8*b*c^6*e^2 - 27*a^5*b^9*c*f^2 - 3
840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^10*b*c^4*g^2 - 30*a*b^14*d*e + 6366*a^2*b^11*
c^2*d^2 - 35767*a^3*b^9*c^3*d^2 + 116928*a^4*b^7*c^4*d^2 - 219744*a^5*b^5*c^5*d^2 + 215040*a^6*b^3*c^6*d^2 + 9
*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) + 2077*a^4*b^9*c^2*e^2 - 10656
*a^5*b^7*c^3*e^2 + 30240*a^6*b^5*c^4*e^2 - 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a
^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) + 288*a^6*b^7*c^2*f^2 - 1504*a^7*b^5*c^3*f^2 + 3840*a^8*b^3*c^4*f^2 - 96*a
^8*b^5*c^2*g^2 + 512*a^9*b^3*c^3*g^2 - 615*a*b^13*c*d^2 + 10*a^2*b^13*d*f + 35840*a^8*c^7*d*e + 10*a^3*b^12*d*
g - 6*a^3*b^12*e*f - 6*a^4*b^11*e*g - 7168*a^9*c^6*d*g - 15360*a^9*c^6*e*f + 2*a^5*b^10*f*g + 3072*a^10*c^5*f*
g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 724*a^2*b^12*c*d*e - 258*a^3*b^11*c*d*f + 43520*a^8*b*c^6*d*f - 16
8*a^4*b^10*c*d*g + 152*a^4*b^10*c*e*f + 98*a^5*b^9*c*e*g - 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)
^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) - 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/
2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^3*b^10*c^2*d*e + 39132*a^4*b^8*c^3*d*e - 119616*a^5*b^6
*c^4*d*e + 201600*a^6*b^4*c^5*d*e - 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^
4*b^9*c^2*d*f - 14784*a^5*b^7*c^3*d*f + 44352*a^6*b^5*c^4*d*f - 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*
c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) + 1044*a^
5*b^8*c^2*d*g - 1548*a^5*b^8*c^2*e*f - 2688*a^6*b^6*c^3*d*g + 8064*a^6*b^6*c^3*e*f + 1152*a^7*b^4*c^4*d*g - 22
400*a^7*b^4*c^4*e*f + 6144*a^8*b^2*c^5*d*g + 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) -
576*a^6*b^7*c^2*e*g + 1344*a^7*b^5*c^3*e*g - 512*a^8*b^3*c^4*e*g + 192*a^7*b^6*c^2*f*g - 128*a^8*b^4*c^3*f*g -
1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) +
44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*
a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c
+ 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*1i + ((-(25*b^15*d^2 +
9*a^2*b^13*e^2 + 25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + a^4*b^11*f^2 + a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9
)^(1/2) - 80640*a^7*b*c^7*d^2 - 213*a^3*b^11*c*e^2 + 26880*a^8*b*c^6*e^2 - 27*a^5*b^9*c*f^2 - 3840*a^9*b*c^5*f
^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^10*b*c^4*g^2 - 30*a*b^14*d*e + 6366*a^2*b^11*c^2*d^2 - 35767
*a^3*b^9*c^3*d^2 + 116928*a^4*b^7*c^4*d^2 - 219744*a^5*b^5*c^5*d^2 + 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-
(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) + 2077*a^4*b^9*c^2*e^2 - 10656*a^5*b^7*c^3*e^
2 + 30240*a^6*b^5*c^4*e^2 - 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4
*a*c - b^2)^9)^(1/2) + 288*a^6*b^7*c^2*f^2 - 1504*a^7*b^5*c^3*f^2 + 3840*a^8*b^3*c^4*f^2 - 96*a^8*b^5*c^2*g^2
+ 512*a^9*b^3*c^3*g^2 - 615*a*b^13*c*d^2 + 10*a^2*b^13*d*f + 35840*a^8*c^7*d*e + 10*a^3*b^12*d*g - 6*a^3*b^12*
e*f - 6*a^4*b^11*e*g - 7168*a^9*c^6*d*g - 15360*a^9*c^6*e*f + 2*a^5*b^10*f*g + 3072*a^10*c^5*f*g - 30*a*b^5*d*
e*(-(4*a*c - b^2)^9)^(1/2) + 724*a^2*b^12*c*d*e - 258*a^3*b^11*c*d*f + 43520*a^8*b*c^6*d*f - 168*a^4*b^10*c*d*
g + 152*a^4*b^10*c*e*f + 98*a^5*b^9*c*e*g - 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5
*c*e*g*(-(4*a*c - b^2)^9)^(1/2) - 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*
c*d^2*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^3*b^10*c^2*d*e + 39132*a^4*b^8*c^3*d*e - 119616*a^5*b^6*c^4*d*e + 2016
00*a^6*b^4*c^5*d*e - 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^4*b^9*c^2*d*f -
14784*a^5*b^7*c^3*d*f + 44352*a^6*b^5*c^4*d*f - 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/
2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) + 1044*a^5*b^8*c^2*d*g -
1548*a^5*b^8*c^2*e*f - 2688*a^6*b^6*c^3*d*g + 8064*a^6*b^6*c^3*e*f + 1152*a^7*b^4*c^4*d*g - 22400*a^7*b^4*c^4
*e*f + 6144*a^8*b^2*c^5*d*g + 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 576*a^6*b^7*c^2
*e*g + 1344*a^7*b^5*c^3*e*g - 512*a^8*b^3*c^4*e*g + 192*a^7*b^6*c^2*f*g - 128*a^8*b^4*c^3*f*g - 1536*a^9*b^2*c
^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*
(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(
1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*
c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(917504*a^19*c^9*d - 393216*a^20*c^8*
f + x*(-(25*b^15*d^2 + 9*a^2*b^13*e^2 + 25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + a^4*b^11*f^2 + a^6*b^9*g^2 + a^6
*g^2*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7*d^2 - 213*a^3*b^11*c*e^2 + 26880*a^8*b*c^6*e^2 - 27*a^5*b^9*c*
f^2 - 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^10*b*c^4*g^2 - 30*a*b^14*d*e + 6366*a^
2*b^11*c^2*d^2 - 35767*a^3*b^9*c^3*d^2 + 116928*a^4*b^7*c^4*d^2 - 219744*a^5*b^5*c^5*d^2 + 215040*a^6*b^3*c^6*
d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) + 2077*a^4*b^9*c^2*e^2
- 10656*a^5*b^7*c^3*e^2 + 30240*a^6*b^5*c^4*e^2 - 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2)
+ 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) + 288*a^6*b^7*c^2*f^2 - 1504*a^7*b^5*c^3*f^2 + 3840*a^8*b^3*c^4*f^2
- 96*a^8*b^5*c^2*g^2 + 512*a^9*b^3*c^3*g^2 - 615*a*b^13*c*d^2 + 10*a^2*b^13*d*f + 35840*a^8*c^7*d*e + 10*a^3*
b^12*d*g - 6*a^3*b^12*e*f - 6*a^4*b^11*e*g - 7168*a^9*c^6*d*g - 15360*a^9*c^6*e*f + 2*a^5*b^10*f*g + 3072*a^10
*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 724*a^2*b^12*c*d*e - 258*a^3*b^11*c*d*f + 43520*a^8*b*c^6*d
*f - 168*a^4*b^10*c*d*g + 152*a^4*b^10*c*e*f + 98*a^5*b^9*c*e*g - 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c -
b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) - 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)
^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^3*b^10*c^2*d*e + 39132*a^4*b^8*c^3*d*e - 119616*
a^5*b^6*c^4*d*e + 201600*a^6*b^4*c^5*d*e - 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) +
2706*a^4*b^9*c^2*d*f - 14784*a^5*b^7*c^3*d*f + 44352*a^6*b^5*c^4*d*f - 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*
(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) +
1044*a^5*b^8*c^2*d*g - 1548*a^5*b^8*c^2*e*f - 2688*a^6*b^6*c^3*d*g + 8064*a^6*b^6*c^3*e*f + 1152*a^7*b^4*c^4*d
*g - 22400*a^7*b^4*c^4*e*f + 6144*a^8*b^2*c^5*d*g + 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(
1/2) - 576*a^6*b^7*c^2*e*g + 1344*a^7*b^5*c^3*e*g - 512*a^8*b^3*c^4*e*g + 192*a^7*b^6*c^2*f*g - 128*a^8*b^4*c^
3*f*g - 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(
1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*
e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8
*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(1048576*a^21*b
*c^8 + 256*a^15*b^13*c^2 - 6144*a^16*b^11*c^3 + 61440*a^17*b^9*c^4 - 327680*a^18*b^7*c^5 + 983040*a^19*b^5*c^6
- 1572864*a^20*b^3*c^7) - 320*a^12*b^14*c^2*d + 7936*a^13*b^12*c^3*d - 82816*a^14*b^10*c^4*d + 468480*a^15*b^
8*c^5*d - 1536000*a^16*b^6*c^6*d + 2867200*a^17*b^4*c^7*d - 2719744*a^18*b^2*c^8*d + 192*a^13*b^13*c^2*e - 467
2*a^14*b^11*c^3*e + 47360*a^15*b^9*c^4*e - 256000*a^16*b^7*c^5*e + 778240*a^17*b^5*c^6*e - 1261568*a^18*b^3*c^
7*e - 64*a^14*b^12*c^2*f + 1664*a^15*b^10*c^3*f - 17920*a^16*b^8*c^4*f + 102400*a^17*b^6*c^5*f - 327680*a^18*b
^4*c^6*f + 557056*a^19*b^2*c^7*f - 64*a^15*b^11*c^2*g + 1280*a^16*b^9*c^3*g - 10240*a^17*b^7*c^4*g + 40960*a^1
8*b^5*c^5*g - 81920*a^19*b^3*c^6*g + 851968*a^19*b*c^8*e + 65536*a^20*b*c^7*g) + x*(204800*a^17*c^9*e^2 - 4014
08*a^16*c^10*d^2 - 73728*a^18*c^8*f^2 + 8192*a^19*c^7*g^2 + 400*a^9*b^14*c^3*d^2 - 9440*a^10*b^12*c^4*d^2 + 92
816*a^11*b^10*c^5*d^2 - 488096*a^12*b^8*c^6*d^2 + 1458688*a^13*b^6*c^7*d^2 - 2401280*a^14*b^4*c^8*d^2 + 187187
2*a^15*b^2*c^9*d^2 + 144*a^11*b^12*c^3*e^2 - 3264*a^12*b^10*c^4*e^2 + 30112*a^13*b^8*c^5*e^2 - 143360*a^14*b^6
*c^6*e^2 + 365568*a^15*b^4*c^7*e^2 - 458752*a^16*b^2*c^8*e^2 + 16*a^13*b^10*c^3*f^2 - 416*a^14*b^8*c^4*f^2 + 4
608*a^15*b^6*c^5*f^2 - 25600*a^16*b^4*c^6*f^2 + 69632*a^17*b^2*c^7*f^2 + 160*a^15*b^8*c^3*g^2 - 2048*a^16*b^6*
c^4*g^2 + 9216*a^17*b^4*c^5*g^2 - 16384*a^18*b^2*c^6*g^2 + 344064*a^17*c^9*d*f - 81920*a^18*c^8*e*g - 1236992*
a^16*b*c^9*d*e + 40960*a^17*b*c^8*d*g + 237568*a^17*b*c^8*e*f + 40960*a^18*b*c^7*f*g - 480*a^10*b^13*c^3*d*e +
11104*a^11*b^11*c^4*d*e - 105824*a^12*b^9*c^5*d*e + 530432*a^13*b^7*c^6*d*e - 1469440*a^14*b^5*c^7*d*e + 2121
728*a^15*b^3*c^8*d*e + 160*a^11*b^12*c^3*d*f - 3968*a^12*b^10*c^4*d*f + 39488*a^13*b^8*c^5*d*f - 200704*a^14*b
^6*c^6*d*f + 542720*a^15*b^4*c^7*d*f - 720896*a^16*b^2*c^8*d*f + 160*a^12*b^11*c^3*d*g - 96*a^12*b^11*c^3*e*f
- 2528*a^13*b^9*c^4*d*g + 2336*a^13*b^9*c^4*e*f + 14336*a^14*b^7*c^5*d*g - 22528*a^14*b^7*c^5*e*f - 31744*a^15
*b^5*c^6*d*g + 107520*a^15*b^5*c^6*e*f + 8192*a^16*b^3*c^7*d*g - 253952*a^16*b^3*c^7*e*f - 96*a^13*b^10*c^3*e*
g + 1472*a^14*b^8*c^4*e*g - 7168*a^15*b^6*c^5*e*g + 6144*a^16*b^4*c^6*e*g + 40960*a^17*b^2*c^7*e*g + 32*a^14*b
^9*c^3*f*g - 1024*a^15*b^7*c^4*f*g + 9216*a^16*b^5*c^5*f*g - 32768*a^17*b^3*c^6*f*g))*(-(25*b^15*d^2 + 9*a^2*b
^13*e^2 + 25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + a^4*b^11*f^2 + a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2)
- 80640*a^7*b*c^7*d^2 - 213*a^3*b^11*c*e^2 + 26880*a^8*b*c^6*e^2 - 27*a^5*b^9*c*f^2 - 3840*a^9*b*c^5*f^2 - 9*a
^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^10*b*c^4*g^2 - 30*a*b^14*d*e + 6366*a^2*b^11*c^2*d^2 - 35767*a^3*b^9
*c^3*d^2 + 116928*a^4*b^7*c^4*d^2 - 219744*a^5*b^5*c^5*d^2 + 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c -
b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) + 2077*a^4*b^9*c^2*e^2 - 10656*a^5*b^7*c^3*e^2 + 3024
0*a^6*b^5*c^4*e^2 - 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b
^2)^9)^(1/2) + 288*a^6*b^7*c^2*f^2 - 1504*a^7*b^5*c^3*f^2 + 3840*a^8*b^3*c^4*f^2 - 96*a^8*b^5*c^2*g^2 + 512*a^
9*b^3*c^3*g^2 - 615*a*b^13*c*d^2 + 10*a^2*b^13*d*f + 35840*a^8*c^7*d*e + 10*a^3*b^12*d*g - 6*a^3*b^12*e*f - 6*
a^4*b^11*e*g - 7168*a^9*c^6*d*g - 15360*a^9*c^6*e*f + 2*a^5*b^10*f*g + 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a
*c - b^2)^9)^(1/2) + 724*a^2*b^12*c*d*e - 258*a^3*b^11*c*d*f + 43520*a^8*b*c^6*d*f - 168*a^4*b^10*c*d*g + 152*
a^4*b^10*c*e*f + 98*a^5*b^9*c*e*g - 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(
-(4*a*c - b^2)^9)^(1/2) - 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-
(4*a*c - b^2)^9)^(1/2) - 7278*a^3*b^10*c^2*d*e + 39132*a^4*b^8*c^3*d*e - 119616*a^5*b^6*c^4*d*e + 201600*a^6*b
^4*c^5*d*e - 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^4*b^9*c^2*d*f - 14784*a
^5*b^7*c^3*d*f + 44352*a^6*b^5*c^4*d*f - 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a
^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) + 1044*a^5*b^8*c^2*d*g - 1548*a^
5*b^8*c^2*e*f - 2688*a^6*b^6*c^3*d*g + 8064*a^6*b^6*c^3*e*f + 1152*a^7*b^4*c^4*d*g - 22400*a^7*b^4*c^4*e*f + 6
144*a^8*b^2*c^5*d*g + 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 576*a^6*b^7*c^2*e*g + 1
344*a^7*b^5*c^3*e*g - 512*a^8*b^3*c^4*e*g + 192*a^7*b^6*c^2*f*g - 128*a^8*b^4*c^3*f*g - 1536*a^9*b^2*c^4*f*g -
51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c
- b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 7
8*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 12
80*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*1i)/(((-(25*b^15*d^2 + 9*a^2*b^13*e^2 + 25*b^
6*d^2*(-(4*a*c - b^2)^9)^(1/2) + a^4*b^11*f^2 + a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c
^7*d^2 - 213*a^3*b^11*c*e^2 + 26880*a^8*b*c^6*e^2 - 27*a^5*b^9*c*f^2 - 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a
*c - b^2)^9)^(1/2) - 768*a^10*b*c^4*g^2 - 30*a*b^14*d*e + 6366*a^2*b^11*c^2*d^2 - 35767*a^3*b^9*c^3*d^2 + 1169
28*a^4*b^7*c^4*d^2 - 219744*a^5*b^5*c^5*d^2 + 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2)
- 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) + 2077*a^4*b^9*c^2*e^2 - 10656*a^5*b^7*c^3*e^2 + 30240*a^6*b^5*c^4*e
^2 - 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) +
288*a^6*b^7*c^2*f^2 - 1504*a^7*b^5*c^3*f^2 + 3840*a^8*b^3*c^4*f^2 - 96*a^8*b^5*c^2*g^2 + 512*a^9*b^3*c^3*g^2 -
615*a*b^13*c*d^2 + 10*a^2*b^13*d*f + 35840*a^8*c^7*d*e + 10*a^3*b^12*d*g - 6*a^3*b^12*e*f - 6*a^4*b^11*e*g -
7168*a^9*c^6*d*g - 15360*a^9*c^6*e*f + 2*a^5*b^10*f*g + 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1
/2) + 724*a^2*b^12*c*d*e - 258*a^3*b^11*c*d*f + 43520*a^8*b*c^6*d*f - 168*a^4*b^10*c*d*g + 152*a^4*b^10*c*e*f
+ 98*a^5*b^9*c*e*g - 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^
9)^(1/2) - 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9
)^(1/2) - 7278*a^3*b^10*c^2*d*e + 39132*a^4*b^8*c^3*d*e - 119616*a^5*b^6*c^4*d*e + 201600*a^6*b^4*c^5*d*e - 16
1280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^4*b^9*c^2*d*f - 14784*a^5*b^7*c^3*d*f
+ 44352*a^6*b^5*c^4*d*f - 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4
*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) + 1044*a^5*b^8*c^2*d*g - 1548*a^5*b^8*c^2*e*f -
2688*a^6*b^6*c^3*d*g + 8064*a^6*b^6*c^3*e*f + 1152*a^7*b^4*c^4*d*g - 22400*a^7*b^4*c^4*e*f + 6144*a^8*b^2*c^5
*d*g + 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 576*a^6*b^7*c^2*e*g + 1344*a^7*b^5*c^3
*e*g - 512*a^8*b^3*c^4*e*g + 192*a^7*b^6*c^2*f*g - 128*a^8*b^4*c^3*f*g - 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e
^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2
) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f
*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3
+ 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(393216*a^20*c^8*f - 917504*a^19*c^9*d + x*(-(25*b^15*d^2 +
9*a^2*b^13*e^2 + 25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + a^4*b^11*f^2 + a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)
^(1/2) - 80640*a^7*b*c^7*d^2 - 213*a^3*b^11*c*e^2 + 26880*a^8*b*c^6*e^2 - 27*a^5*b^9*c*f^2 - 3840*a^9*b*c^5*f^
2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^10*b*c^4*g^2 - 30*a*b^14*d*e + 6366*a^2*b^11*c^2*d^2 - 35767*
a^3*b^9*c^3*d^2 + 116928*a^4*b^7*c^4*d^2 - 219744*a^5*b^5*c^5*d^2 + 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(
4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) + 2077*a^4*b^9*c^2*e^2 - 10656*a^5*b^7*c^3*e^2
+ 30240*a^6*b^5*c^4*e^2 - 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*
a*c - b^2)^9)^(1/2) + 288*a^6*b^7*c^2*f^2 - 1504*a^7*b^5*c^3*f^2 + 3840*a^8*b^3*c^4*f^2 - 96*a^8*b^5*c^2*g^2 +
512*a^9*b^3*c^3*g^2 - 615*a*b^13*c*d^2 + 10*a^2*b^13*d*f + 35840*a^8*c^7*d*e + 10*a^3*b^12*d*g - 6*a^3*b^12*e
*f - 6*a^4*b^11*e*g - 7168*a^9*c^6*d*g - 15360*a^9*c^6*e*f + 2*a^5*b^10*f*g + 3072*a^10*c^5*f*g - 30*a*b^5*d*e
*(-(4*a*c - b^2)^9)^(1/2) + 724*a^2*b^12*c*d*e - 258*a^3*b^11*c*d*f + 43520*a^8*b*c^6*d*f - 168*a^4*b^10*c*d*g
+ 152*a^4*b^10*c*e*f + 98*a^5*b^9*c*e*g - 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*
c*e*g*(-(4*a*c - b^2)^9)^(1/2) - 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c
*d^2*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^3*b^10*c^2*d*e + 39132*a^4*b^8*c^3*d*e - 119616*a^5*b^6*c^4*d*e + 20160
0*a^6*b^4*c^5*d*e - 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^4*b^9*c^2*d*f -
14784*a^5*b^7*c^3*d*f + 44352*a^6*b^5*c^4*d*f - 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2
) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) + 1044*a^5*b^8*c^2*d*g -
1548*a^5*b^8*c^2*e*f - 2688*a^6*b^6*c^3*d*g + 8064*a^6*b^6*c^3*e*f + 1152*a^7*b^4*c^4*d*g - 22400*a^7*b^4*c^4*
e*f + 6144*a^8*b^2*c^5*d*g + 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 576*a^6*b^7*c^2*
e*g + 1344*a^7*b^5*c^3*e*g - 512*a^8*b^3*c^4*e*g + 192*a^7*b^6*c^2*f*g - 128*a^8*b^4*c^3*f*g - 1536*a^9*b^2*c^
4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(
-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1
/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c
^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(1048576*a^21*b*c^8 + 256*a^15*b^13*c^
2 - 6144*a^16*b^11*c^3 + 61440*a^17*b^9*c^4 - 327680*a^18*b^7*c^5 + 983040*a^19*b^5*c^6 - 1572864*a^20*b^3*c^7
) + 320*a^12*b^14*c^2*d - 7936*a^13*b^12*c^3*d + 82816*a^14*b^10*c^4*d - 468480*a^15*b^8*c^5*d + 1536000*a^16*
b^6*c^6*d - 2867200*a^17*b^4*c^7*d + 2719744*a^18*b^2*c^8*d - 192*a^13*b^13*c^2*e + 4672*a^14*b^11*c^3*e - 473
60*a^15*b^9*c^4*e + 256000*a^16*b^7*c^5*e - 778240*a^17*b^5*c^6*e + 1261568*a^18*b^3*c^7*e + 64*a^14*b^12*c^2*
f - 1664*a^15*b^10*c^3*f + 17920*a^16*b^8*c^4*f - 102400*a^17*b^6*c^5*f + 327680*a^18*b^4*c^6*f - 557056*a^19*
b^2*c^7*f + 64*a^15*b^11*c^2*g - 1280*a^16*b^9*c^3*g + 10240*a^17*b^7*c^4*g - 40960*a^18*b^5*c^5*g + 81920*a^1
9*b^3*c^6*g - 851968*a^19*b*c^8*e - 65536*a^20*b*c^7*g) + x*(204800*a^17*c^9*e^2 - 401408*a^16*c^10*d^2 - 7372
8*a^18*c^8*f^2 + 8192*a^19*c^7*g^2 + 400*a^9*b^14*c^3*d^2 - 9440*a^10*b^12*c^4*d^2 + 92816*a^11*b^10*c^5*d^2 -
488096*a^12*b^8*c^6*d^2 + 1458688*a^13*b^6*c^7*d^2 - 2401280*a^14*b^4*c^8*d^2 + 1871872*a^15*b^2*c^9*d^2 + 14
4*a^11*b^12*c^3*e^2 - 3264*a^12*b^10*c^4*e^2 + 30112*a^13*b^8*c^5*e^2 - 143360*a^14*b^6*c^6*e^2 + 365568*a^15*
b^4*c^7*e^2 - 458752*a^16*b^2*c^8*e^2 + 16*a^13*b^10*c^3*f^2 - 416*a^14*b^8*c^4*f^2 + 4608*a^15*b^6*c^5*f^2 -
25600*a^16*b^4*c^6*f^2 + 69632*a^17*b^2*c^7*f^2 + 160*a^15*b^8*c^3*g^2 - 2048*a^16*b^6*c^4*g^2 + 9216*a^17*b^4
*c^5*g^2 - 16384*a^18*b^2*c^6*g^2 + 344064*a^17*c^9*d*f - 81920*a^18*c^8*e*g - 1236992*a^16*b*c^9*d*e + 40960*
a^17*b*c^8*d*g + 237568*a^17*b*c^8*e*f + 40960*a^18*b*c^7*f*g - 480*a^10*b^13*c^3*d*e + 11104*a^11*b^11*c^4*d*
e - 105824*a^12*b^9*c^5*d*e + 530432*a^13*b^7*c^6*d*e - 1469440*a^14*b^5*c^7*d*e + 2121728*a^15*b^3*c^8*d*e +
160*a^11*b^12*c^3*d*f - 3968*a^12*b^10*c^4*d*f + 39488*a^13*b^8*c^5*d*f - 200704*a^14*b^6*c^6*d*f + 542720*a^1
5*b^4*c^7*d*f - 720896*a^16*b^2*c^8*d*f + 160*a^12*b^11*c^3*d*g - 96*a^12*b^11*c^3*e*f - 2528*a^13*b^9*c^4*d*g
+ 2336*a^13*b^9*c^4*e*f + 14336*a^14*b^7*c^5*d*g - 22528*a^14*b^7*c^5*e*f - 31744*a^15*b^5*c^6*d*g + 107520*a
^15*b^5*c^6*e*f + 8192*a^16*b^3*c^7*d*g - 253952*a^16*b^3*c^7*e*f - 96*a^13*b^10*c^3*e*g + 1472*a^14*b^8*c^4*e
*g - 7168*a^15*b^6*c^5*e*g + 6144*a^16*b^4*c^6*e*g + 40960*a^17*b^2*c^7*e*g + 32*a^14*b^9*c^3*f*g - 1024*a^15*
b^7*c^4*f*g + 9216*a^16*b^5*c^5*f*g - 32768*a^17*b^3*c^6*f*g))*(-(25*b^15*d^2 + 9*a^2*b^13*e^2 + 25*b^6*d^2*(-
(4*a*c - b^2)^9)^(1/2) + a^4*b^11*f^2 + a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7*d^2 -
213*a^3*b^11*c*e^2 + 26880*a^8*b*c^6*e^2 - 27*a^5*b^9*c*f^2 - 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2
)^9)^(1/2) - 768*a^10*b*c^4*g^2 - 30*a*b^14*d*e + 6366*a^2*b^11*c^2*d^2 - 35767*a^3*b^9*c^3*d^2 + 116928*a^4*b
^7*c^4*d^2 - 219744*a^5*b^5*c^5*d^2 + 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3
*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) + 2077*a^4*b^9*c^2*e^2 - 10656*a^5*b^7*c^3*e^2 + 30240*a^6*b^5*c^4*e^2 - 448
00*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) + 288*a^6*
b^7*c^2*f^2 - 1504*a^7*b^5*c^3*f^2 + 3840*a^8*b^3*c^4*f^2 - 96*a^8*b^5*c^2*g^2 + 512*a^9*b^3*c^3*g^2 - 615*a*b
^13*c*d^2 + 10*a^2*b^13*d*f + 35840*a^8*c^7*d*e + 10*a^3*b^12*d*g - 6*a^3*b^12*e*f - 6*a^4*b^11*e*g - 7168*a^9
*c^6*d*g - 15360*a^9*c^6*e*f + 2*a^5*b^10*f*g + 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 72
4*a^2*b^12*c*d*e - 258*a^3*b^11*c*d*f + 43520*a^8*b*c^6*d*f - 168*a^4*b^10*c*d*g + 152*a^4*b^10*c*e*f + 98*a^5
*b^9*c*e*g - 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2)
- 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2)
- 7278*a^3*b^10*c^2*d*e + 39132*a^4*b^8*c^3*d*e - 119616*a^5*b^6*c^4*d*e + 201600*a^6*b^4*c^5*d*e - 161280*a^7
*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^4*b^9*c^2*d*f - 14784*a^5*b^7*c^3*d*f + 44352*
a^6*b^5*c^4*d*f - 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b
^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) + 1044*a^5*b^8*c^2*d*g - 1548*a^5*b^8*c^2*e*f - 2688*a^
6*b^6*c^3*d*g + 8064*a^6*b^6*c^3*e*f + 1152*a^7*b^4*c^4*d*g - 22400*a^7*b^4*c^4*e*f + 6144*a^8*b^2*c^5*d*g + 3
0720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 576*a^6*b^7*c^2*e*g + 1344*a^7*b^5*c^3*e*g - 5
12*a^8*b^3*c^4*e*g + 192*a^7*b^6*c^2*f*g - 128*a^8*b^4*c^3*f*g - 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*
a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*
a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*
c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*
a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2) - ((-(25*b^15*d^2 + 9*a^2*b^13*e^2 + 25*b^6*d^2*(-(4*a*c - b^2)^9)^(
1/2) + a^4*b^11*f^2 + a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7*d^2 - 213*a^3*b^11*c*e^
2 + 26880*a^8*b*c^6*e^2 - 27*a^5*b^9*c*f^2 - 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a
^10*b*c^4*g^2 - 30*a*b^14*d*e + 6366*a^2*b^11*c^2*d^2 - 35767*a^3*b^9*c^3*d^2 + 116928*a^4*b^7*c^4*d^2 - 21974
4*a^5*b^5*c^5*d^2 + 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c
- b^2)^9)^(1/2) + 2077*a^4*b^9*c^2*e^2 - 10656*a^5*b^7*c^3*e^2 + 30240*a^6*b^5*c^4*e^2 - 44800*a^7*b^3*c^5*e^2
+ a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) + 288*a^6*b^7*c^2*f^2 - 1504
*a^7*b^5*c^3*f^2 + 3840*a^8*b^3*c^4*f^2 - 96*a^8*b^5*c^2*g^2 + 512*a^9*b^3*c^3*g^2 - 615*a*b^13*c*d^2 + 10*a^2
*b^13*d*f + 35840*a^8*c^7*d*e + 10*a^3*b^12*d*g - 6*a^3*b^12*e*f - 6*a^4*b^11*e*g - 7168*a^9*c^6*d*g - 15360*a
^9*c^6*e*f + 2*a^5*b^10*f*g + 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 724*a^2*b^12*c*d*e -
258*a^3*b^11*c*d*f + 43520*a^8*b*c^6*d*f - 168*a^4*b^10*c*d*g + 152*a^4*b^10*c*e*f + 98*a^5*b^9*c*e*g - 1536*
a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) - 36*a^6*b^8*c*f*
g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^3*b^10*c^
2*d*e + 39132*a^4*b^8*c^3*d*e - 119616*a^5*b^6*c^4*d*e + 201600*a^6*b^4*c^5*d*e - 161280*a^7*b^2*c^6*d*e + 10*
a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^4*b^9*c^2*d*f - 14784*a^5*b^7*c^3*d*f + 44352*a^6*b^5*c^4*d*f -
69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*
a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) + 1044*a^5*b^8*c^2*d*g - 1548*a^5*b^8*c^2*e*f - 2688*a^6*b^6*c^3*d*g + 80
64*a^6*b^6*c^3*e*f + 1152*a^7*b^4*c^4*d*g - 22400*a^7*b^4*c^4*e*f + 6144*a^8*b^2*c^5*d*g + 30720*a^8*b^2*c^5*e
*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 576*a^6*b^7*c^2*e*g + 1344*a^7*b^5*c^3*e*g - 512*a^8*b^3*c^4*e*g
+ 192*a^7*b^6*c^2*f*g - 128*a^8*b^4*c^3*f*g - 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2
) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4
*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))
/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 614
4*a^12*b^2*c^5)))^(1/2)*(917504*a^19*c^9*d - 393216*a^20*c^8*f + x*(-(25*b^15*d^2 + 9*a^2*b^13*e^2 + 25*b^6*d^
2*(-(4*a*c - b^2)^9)^(1/2) + a^4*b^11*f^2 + a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7*d
^2 - 213*a^3*b^11*c*e^2 + 26880*a^8*b*c^6*e^2 - 27*a^5*b^9*c*f^2 - 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c -
b^2)^9)^(1/2) - 768*a^10*b*c^4*g^2 - 30*a*b^14*d*e + 6366*a^2*b^11*c^2*d^2 - 35767*a^3*b^9*c^3*d^2 + 116928*a
^4*b^7*c^4*d^2 - 219744*a^5*b^5*c^5*d^2 + 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49
*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) + 2077*a^4*b^9*c^2*e^2 - 10656*a^5*b^7*c^3*e^2 + 30240*a^6*b^5*c^4*e^2 -
44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) + 288*
a^6*b^7*c^2*f^2 - 1504*a^7*b^5*c^3*f^2 + 3840*a^8*b^3*c^4*f^2 - 96*a^8*b^5*c^2*g^2 + 512*a^9*b^3*c^3*g^2 - 615
*a*b^13*c*d^2 + 10*a^2*b^13*d*f + 35840*a^8*c^7*d*e + 10*a^3*b^12*d*g - 6*a^3*b^12*e*f - 6*a^4*b^11*e*g - 7168
*a^9*c^6*d*g - 15360*a^9*c^6*e*f + 2*a^5*b^10*f*g + 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2)
+ 724*a^2*b^12*c*d*e - 258*a^3*b^11*c*d*f + 43520*a^8*b*c^6*d*f - 168*a^4*b^10*c*d*g + 152*a^4*b^10*c*e*f + 98
*a^5*b^9*c*e*g - 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(
1/2) - 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1
/2) - 7278*a^3*b^10*c^2*d*e + 39132*a^4*b^8*c^3*d*e - 119616*a^5*b^6*c^4*d*e + 201600*a^6*b^4*c^5*d*e - 161280
*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^4*b^9*c^2*d*f - 14784*a^5*b^7*c^3*d*f + 44
352*a^6*b^5*c^4*d*f - 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c
- b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) + 1044*a^5*b^8*c^2*d*g - 1548*a^5*b^8*c^2*e*f - 268
8*a^6*b^6*c^3*d*g + 8064*a^6*b^6*c^3*e*f + 1152*a^7*b^4*c^4*d*g - 22400*a^7*b^4*c^4*e*f + 6144*a^8*b^2*c^5*d*g
+ 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 576*a^6*b^7*c^2*e*g + 1344*a^7*b^5*c^3*e*g
- 512*a^8*b^3*c^4*e*g + 192*a^7*b^6*c^2*f*g - 128*a^8*b^4*c^3*f*g - 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(
-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) +
184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(
4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3
840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(1048576*a^21*b*c^8 + 256*a^15*b^13*c^2 - 6144*a^16*b^11*c^3 + 6
1440*a^17*b^9*c^4 - 327680*a^18*b^7*c^5 + 983040*a^19*b^5*c^6 - 1572864*a^20*b^3*c^7) - 320*a^12*b^14*c^2*d +
7936*a^13*b^12*c^3*d - 82816*a^14*b^10*c^4*d + 468480*a^15*b^8*c^5*d - 1536000*a^16*b^6*c^6*d + 2867200*a^17*b
^4*c^7*d - 2719744*a^18*b^2*c^8*d + 192*a^13*b^13*c^2*e - 4672*a^14*b^11*c^3*e + 47360*a^15*b^9*c^4*e - 256000
*a^16*b^7*c^5*e + 778240*a^17*b^5*c^6*e - 1261568*a^18*b^3*c^7*e - 64*a^14*b^12*c^2*f + 1664*a^15*b^10*c^3*f -
17920*a^16*b^8*c^4*f + 102400*a^17*b^6*c^5*f - 327680*a^18*b^4*c^6*f + 557056*a^19*b^2*c^7*f - 64*a^15*b^11*c
^2*g + 1280*a^16*b^9*c^3*g - 10240*a^17*b^7*c^4*g + 40960*a^18*b^5*c^5*g - 81920*a^19*b^3*c^6*g + 851968*a^19*
b*c^8*e + 65536*a^20*b*c^7*g) + x*(204800*a^17*c^9*e^2 - 401408*a^16*c^10*d^2 - 73728*a^18*c^8*f^2 + 8192*a^19
*c^7*g^2 + 400*a^9*b^14*c^3*d^2 - 9440*a^10*b^12*c^4*d^2 + 92816*a^11*b^10*c^5*d^2 - 488096*a^12*b^8*c^6*d^2 +
1458688*a^13*b^6*c^7*d^2 - 2401280*a^14*b^4*c^8*d^2 + 1871872*a^15*b^2*c^9*d^2 + 144*a^11*b^12*c^3*e^2 - 3264
*a^12*b^10*c^4*e^2 + 30112*a^13*b^8*c^5*e^2 - 143360*a^14*b^6*c^6*e^2 + 365568*a^15*b^4*c^7*e^2 - 458752*a^16*
b^2*c^8*e^2 + 16*a^13*b^10*c^3*f^2 - 416*a^14*b^8*c^4*f^2 + 4608*a^15*b^6*c^5*f^2 - 25600*a^16*b^4*c^6*f^2 + 6
9632*a^17*b^2*c^7*f^2 + 160*a^15*b^8*c^3*g^2 - 2048*a^16*b^6*c^4*g^2 + 9216*a^17*b^4*c^5*g^2 - 16384*a^18*b^2*
c^6*g^2 + 344064*a^17*c^9*d*f - 81920*a^18*c^8*e*g - 1236992*a^16*b*c^9*d*e + 40960*a^17*b*c^8*d*g + 237568*a^
17*b*c^8*e*f + 40960*a^18*b*c^7*f*g - 480*a^10*b^13*c^3*d*e + 11104*a^11*b^11*c^4*d*e - 105824*a^12*b^9*c^5*d*
e + 530432*a^13*b^7*c^6*d*e - 1469440*a^14*b^5*c^7*d*e + 2121728*a^15*b^3*c^8*d*e + 160*a^11*b^12*c^3*d*f - 39
68*a^12*b^10*c^4*d*f + 39488*a^13*b^8*c^5*d*f - 200704*a^14*b^6*c^6*d*f + 542720*a^15*b^4*c^7*d*f - 720896*a^1
6*b^2*c^8*d*f + 160*a^12*b^11*c^3*d*g - 96*a^12*b^11*c^3*e*f - 2528*a^13*b^9*c^4*d*g + 2336*a^13*b^9*c^4*e*f +
14336*a^14*b^7*c^5*d*g - 22528*a^14*b^7*c^5*e*f - 31744*a^15*b^5*c^6*d*g + 107520*a^15*b^5*c^6*e*f + 8192*a^1
6*b^3*c^7*d*g - 253952*a^16*b^3*c^7*e*f - 96*a^13*b^10*c^3*e*g + 1472*a^14*b^8*c^4*e*g - 7168*a^15*b^6*c^5*e*g
+ 6144*a^16*b^4*c^6*e*g + 40960*a^17*b^2*c^7*e*g + 32*a^14*b^9*c^3*f*g - 1024*a^15*b^7*c^4*f*g + 9216*a^16*b^
5*c^5*f*g - 32768*a^17*b^3*c^6*f*g))*(-(25*b^15*d^2 + 9*a^2*b^13*e^2 + 25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + a
^4*b^11*f^2 + a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7*d^2 - 213*a^3*b^11*c*e^2 + 2688
0*a^8*b*c^6*e^2 - 27*a^5*b^9*c*f^2 - 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^10*b*c^
4*g^2 - 30*a*b^14*d*e + 6366*a^2*b^11*c^2*d^2 - 35767*a^3*b^9*c^3*d^2 + 116928*a^4*b^7*c^4*d^2 - 219744*a^5*b^
5*c^5*d^2 + 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9
)^(1/2) + 2077*a^4*b^9*c^2*e^2 - 10656*a^5*b^7*c^3*e^2 + 30240*a^6*b^5*c^4*e^2 - 44800*a^7*b^3*c^5*e^2 + a^4*b
^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) + 288*a^6*b^7*c^2*f^2 - 1504*a^7*b^5
*c^3*f^2 + 3840*a^8*b^3*c^4*f^2 - 96*a^8*b^5*c^2*g^2 + 512*a^9*b^3*c^3*g^2 - 615*a*b^13*c*d^2 + 10*a^2*b^13*d*
f + 35840*a^8*c^7*d*e + 10*a^3*b^12*d*g - 6*a^3*b^12*e*f - 6*a^4*b^11*e*g - 7168*a^9*c^6*d*g - 15360*a^9*c^6*e
*f + 2*a^5*b^10*f*g + 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) + 724*a^2*b^12*c*d*e - 258*a^3
*b^11*c*d*f + 43520*a^8*b*c^6*d*f - 168*a^4*b^10*c*d*g + 152*a^4*b^10*c*e*f + 98*a^5*b^9*c*e*g - 1536*a^9*b*c^
5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) - 36*a^6*b^8*c*f*g + 246*
a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) - 7278*a^3*b^10*c^2*d*e +
39132*a^4*b^8*c^3*d*e - 119616*a^5*b^6*c^4*d*e + 201600*a^6*b^4*c^5*d*e - 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*
d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^4*b^9*c^2*d*f - 14784*a^5*b^7*c^3*d*f + 44352*a^6*b^5*c^4*d*f - 69120*a^
7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*
d*f*(-(4*a*c - b^2)^9)^(1/2) + 1044*a^5*b^8*c^2*d*g - 1548*a^5*b^8*c^2*e*f - 2688*a^6*b^6*c^3*d*g + 8064*a^6*b
^6*c^3*e*f + 1152*a^7*b^4*c^4*d*g - 22400*a^7*b^4*c^4*e*f + 6144*a^8*b^2*c^5*d*g + 30720*a^8*b^2*c^5*e*f - 6*a
^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 576*a^6*b^7*c^2*e*g + 1344*a^7*b^5*c^3*e*g - 512*a^8*b^3*c^4*e*g + 192*a
^7*b^6*c^2*f*g - 128*a^8*b^4*c^3*f*g - 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a
^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b
^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^
7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b
^2*c^5)))^(1/2) - 128000*a^15*c^9*e^3 + 1024*a^18*c^6*g^3 + 476672*a^13*b*c^10*d^3 - 4608*a^16*b*c^7*f^3 - 250
880*a^14*c^10*d^2*e + 50176*a^15*c^9*d^2*g - 46080*a^16*c^8*e*f^2 + 76800*a^16*c^8*e^2*g - 15360*a^17*c^7*e*g^
2 + 9216*a^17*c^7*f^2*g + 1800*a^9*b^9*c^6*d^3 - 29080*a^10*b^7*c^7*d^3 + 176032*a^11*b^5*c^8*d^3 - 473216*a^1
2*b^3*c^9*d^3 - 504*a^11*b^8*c^5*e^3 + 8112*a^12*b^6*c^6*e^3 - 48704*a^13*b^4*c^7*e^3 + 129280*a^14*b^2*c^8*e^
3 + 40*a^13*b^7*c^4*f^3 - 608*a^14*b^5*c^5*f^3 + 2944*a^15*b^3*c^6*f^3 + 48*a^15*b^6*c^3*g^3 - 320*a^16*b^4*c^
4*g^3 + 256*a^17*b^2*c^5*g^3 + 215040*a^15*c^9*d*e*f - 43008*a^16*c^8*d*f*g + 442880*a^14*b*c^9*d*e^2 - 433664
*a^14*b*c^9*d^2*f + 109056*a^15*b*c^8*d*f^2 + 84480*a^15*b*c^8*e^2*f + 43520*a^16*b*c^7*d*g^2 - 7680*a^17*b*c^
6*f*g^2 - 1400*a^9*b^10*c^5*d^2*e + 21680*a^10*b^8*c^6*d^2*e + 1680*a^10*b^9*c^5*d*e^2 - 121648*a^11*b^6*c^7*d
^2*e - 27176*a^11*b^7*c^6*d*e^2 + 275264*a^12*b^4*c^8*d^2*e + 164448*a^12*b^5*c^7*d*e^2 - 121088*a^13*b^2*c^9*
d^2*e - 441216*a^13*b^3*c^8*d*e^2 + 1000*a^9*b^11*c^4*d^2*f - 17800*a^10*b^9*c^5*d^2*f + 124280*a^11*b^7*c^6*d
^2*f + 400*a^11*b^9*c^4*d*f^2 - 422944*a^12*b^5*c^7*d^2*f - 6600*a^12*b^7*c^5*d*f^2 + 694912*a^13*b^3*c^8*d^2*
f + 40416*a^13*b^5*c^6*d*f^2 - 108928*a^14*b^3*c^7*d*f^2 - 600*a^9*b^12*c^3*d^2*g + 10960*a^10*b^10*c^4*d^2*g
- 78904*a^11*b^8*c^5*d^2*g + 360*a^11*b^9*c^4*e^2*f + 278096*a^12*b^6*c^6*d^2*g - 5736*a^12*b^7*c^5*e^2*f - 24
0*a^12*b^8*c^4*e*f^2 + 120*a^12*b^9*c^3*d*g^2 - 472000*a^13*b^4*c^7*d^2*g + 33888*a^13*b^5*c^6*e^2*f + 3792*a^
13*b^6*c^5*e*f^2 - 2216*a^13*b^7*c^4*d*g^2 + 284416*a^14*b^2*c^8*d^2*g - 87936*a^14*b^3*c^7*e^2*f - 21696*a^14
*b^4*c^6*e*f^2 + 14688*a^14*b^5*c^5*d*g^2 + 52992*a^15*b^2*c^7*e*f^2 - 41856*a^15*b^3*c^6*d*g^2 - 216*a^11*b^1
0*c^3*e^2*g + 3744*a^12*b^8*c^4*e^2*g - 25200*a^13*b^6*c^5*e^2*g - 72*a^13*b^8*c^3*e*g^2 + 81984*a^14*b^4*c^6*
e^2*g + 1296*a^14*b^6*c^4*e*g^2 - 128256*a^15*b^2*c^7*e^2*g - 7872*a^15*b^4*c^5*e*g^2 + 19200*a^16*b^2*c^6*e*g
^2 - 24*a^13*b^8*c^3*f^2*g + 336*a^14*b^6*c^4*f^2*g + 24*a^14*b^7*c^3*f*g^2 - 960*a^15*b^4*c^5*f^2*g - 672*a^1
5*b^5*c^4*f*g^2 - 2304*a^16*b^2*c^6*f^2*g + 4224*a^16*b^3*c^5*f*g^2 - 306176*a^15*b*c^8*d*e*g + 21504*a^16*b*c
^7*e*f*g - 1200*a^10*b^10*c^4*d*e*f + 20240*a^11*b^8*c^5*d*e*f - 130656*a^12*b^6*c^6*d*e*f + 394368*a^13*b^4*c
^7*d*e*f - 528896*a^14*b^2*c^8*d*e*f + 720*a^10*b^11*c^3*d*e*g - 12816*a^11*b^9*c^4*d*e*g + 89264*a^12*b^7*c^5
*d*e*g - 302400*a^13*b^5*c^6*d*e*g + 493824*a^14*b^3*c^7*d*e*g - 240*a^11*b^10*c^3*d*f*g + 3872*a^12*b^8*c^4*d
*f*g - 22368*a^13*b^6*c^5*d*f*g + 51840*a^14*b^4*c^6*d*f*g - 25088*a^15*b^2*c^7*d*f*g + 144*a^12*b^9*c^3*e*f*g
- 2256*a^13*b^7*c^4*e*f*g + 12480*a^14*b^5*c^5*e*f*g - 28416*a^15*b^3*c^6*e*f*g))*(-(25*b^15*d^2 + 9*a^2*b^13
*e^2 + 25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) + a^4*b^11*f^2 + a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) - 8
0640*a^7*b*c^7*d^2 - 213*a^3*b^11*c*e^2 + 26880*a^8*b*c^6*e^2 - 27*a^5*b^9*c*f^2 - 3840*a^9*b*c^5*f^2 - 9*a^5*
c*f^2*(-(4*a*c - b^2)^9)^(1/2) - 768*a^10*b*c^4*g^2 - 30*a*b^14*d*e + 6366*a^2*b^11*c^2*d^2 - 35767*a^3*b^9*c^
3*d^2 + 116928*a^4*b^7*c^4*d^2 - 219744*a^5*b^5*c^5*d^2 + 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^
2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) + 2077*a^4*b^9*c^2*e^2 - 10656*a^5*b^7*c^3*e^2 + 30240*a
^6*b^5*c^4*e^2 - 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)
^9)^(1/2) + 288*a^6*b^7*c^2*f^2 - 1504*a^7*b^5*c^3*f^2 + 3840*a^8*b^3*c^4*f^2 - 96*a^8*b^5*c^2*g^2 + 512*a^9*b
^3*c^3*g^2 - 615*a*b^13*c*d^2 + 10*a^2*b^13*d*f + 35840*a^8*c^7*d*e + 10*a^3*b^12*d*g - 6*a^3*b^12*e*f - 6*a^4
*b^11*e*g - 7168*a^9*c^6*d*g - 15360*a^9*c^6*e*f + 2*a^5*b^10*f*g + 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c
- b^2)^9)^(1/2) + 724*a^2*b^12*c*d*e - 258*a^3*b^11*c*d*f + 43520*a^8*b*c^6*d*f - 168*a^4*b^10*c*d*g + 152*a^4
*b^10*c*e*f + 98*a^5*b^9*c*e*g - 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4
*a*c - b^2)^9)^(1/2) - 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*
a*c - b^2)^9)^(1/2) - 7278*a^3*b^10*c^2*d*e + 39132*a^4*b^8*c^3*d*e - 119616*a^5*b^6*c^4*d*e + 201600*a^6*b^4*
c^5*d*e - 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) + 2706*a^4*b^9*c^2*d*f - 14784*a^5*
b^7*c^3*d*f + 44352*a^6*b^5*c^4*d*f - 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*
b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) + 1044*a^5*b^8*c^2*d*g - 1548*a^5*b
^8*c^2*e*f - 2688*a^6*b^6*c^3*d*g + 8064*a^6*b^6*c^3*e*f + 1152*a^7*b^4*c^4*d*g - 22400*a^7*b^4*c^4*e*f + 6144
*a^8*b^2*c^5*d*g + 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) - 576*a^6*b^7*c^2*e*g + 1344
*a^7*b^5*c^3*e*g - 512*a^8*b^3*c^4*e*g + 192*a^7*b^6*c^2*f*g - 128*a^8*b^4*c^3*f*g - 1536*a^9*b^2*c^4*f*g - 51
*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c -
b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a
^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*
a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*2i - (d/(3*a) + (x^2*(3*a*e - 5*b*d))/(3*a^2) +
(x^4*(15*b^4*d + 14*a^2*c^2*d + 3*a^2*b^2*f - 9*a*b^3*e - 3*a^3*b*g - 6*a^3*c*f - 62*a*b^2*c*d + 33*a^2*b*c*e)
)/(6*a^3*(4*a*c - b^2)) + (c*x^6*(5*b^3*d - 2*a^3*g - 3*a*b^2*e + a^2*b*f + 10*a^2*c*e - 19*a*b*c*d))/(2*a^3*(
4*a*c - b^2)))/(a*x^3 + b*x^5 + c*x^7) + atan(((((25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a^2*b^13*e^2 - 25*b^
15*d^2 - a^4*b^11*f^2 - a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 80640*a^7*b*c^7*d^2 + 213*a^3*b^11*c*
e^2 - 26880*a^8*b*c^6*e^2 + 27*a^5*b^9*c*f^2 + 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) + 768
*a^10*b*c^4*g^2 + 30*a*b^14*d*e - 6366*a^2*b^11*c^2*d^2 + 35767*a^3*b^9*c^3*d^2 - 116928*a^4*b^7*c^4*d^2 + 219
744*a^5*b^5*c^5*d^2 - 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*
c - b^2)^9)^(1/2) - 2077*a^4*b^9*c^2*e^2 + 10656*a^5*b^7*c^3*e^2 - 30240*a^6*b^5*c^4*e^2 + 44800*a^7*b^3*c^5*e
^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) - 288*a^6*b^7*c^2*f^2 + 15
04*a^7*b^5*c^3*f^2 - 3840*a^8*b^3*c^4*f^2 + 96*a^8*b^5*c^2*g^2 - 512*a^9*b^3*c^3*g^2 + 615*a*b^13*c*d^2 - 10*a
^2*b^13*d*f - 35840*a^8*c^7*d*e - 10*a^3*b^12*d*g + 6*a^3*b^12*e*f + 6*a^4*b^11*e*g + 7168*a^9*c^6*d*g + 15360
*a^9*c^6*e*f - 2*a^5*b^10*f*g - 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 724*a^2*b^12*c*d*e
+ 258*a^3*b^11*c*d*f - 43520*a^8*b*c^6*d*f + 168*a^4*b^10*c*d*g - 152*a^4*b^10*c*e*f - 98*a^5*b^9*c*e*g + 153
6*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) + 36*a^6*b^8*c*
f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^3*b^10*
c^2*d*e - 39132*a^4*b^8*c^3*d*e + 119616*a^5*b^6*c^4*d*e - 201600*a^6*b^4*c^5*d*e + 161280*a^7*b^2*c^6*d*e + 1
0*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^4*b^9*c^2*d*f + 14784*a^5*b^7*c^3*d*f - 44352*a^6*b^5*c^4*d*f
+ 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 4
2*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) - 1044*a^5*b^8*c^2*d*g + 1548*a^5*b^8*c^2*e*f + 2688*a^6*b^6*c^3*d*g -
8064*a^6*b^6*c^3*e*f - 1152*a^7*b^4*c^4*d*g + 22400*a^7*b^4*c^4*e*f - 6144*a^8*b^2*c^5*d*g - 30720*a^8*b^2*c^5
*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 576*a^6*b^7*c^2*e*g - 1344*a^7*b^5*c^3*e*g + 512*a^8*b^3*c^4*e
*g - 192*a^7*b^6*c^2*f*g + 128*a^8*b^4*c^3*f*g + 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1
/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-
(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2
))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6
144*a^12*b^2*c^5)))^(1/2)*(393216*a^20*c^8*f - 917504*a^19*c^9*d + x*((25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9
*a^2*b^13*e^2 - 25*b^15*d^2 - a^4*b^11*f^2 - a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 80640*a^7*b*c^7*
d^2 + 213*a^3*b^11*c*e^2 - 26880*a^8*b*c^6*e^2 + 27*a^5*b^9*c*f^2 + 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c
- b^2)^9)^(1/2) + 768*a^10*b*c^4*g^2 + 30*a*b^14*d*e - 6366*a^2*b^11*c^2*d^2 + 35767*a^3*b^9*c^3*d^2 - 116928*
a^4*b^7*c^4*d^2 + 219744*a^5*b^5*c^5*d^2 - 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 4
9*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^4*b^9*c^2*e^2 + 10656*a^5*b^7*c^3*e^2 - 30240*a^6*b^5*c^4*e^2
+ 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) - 288
*a^6*b^7*c^2*f^2 + 1504*a^7*b^5*c^3*f^2 - 3840*a^8*b^3*c^4*f^2 + 96*a^8*b^5*c^2*g^2 - 512*a^9*b^3*c^3*g^2 + 61
5*a*b^13*c*d^2 - 10*a^2*b^13*d*f - 35840*a^8*c^7*d*e - 10*a^3*b^12*d*g + 6*a^3*b^12*e*f + 6*a^4*b^11*e*g + 716
8*a^9*c^6*d*g + 15360*a^9*c^6*e*f - 2*a^5*b^10*f*g - 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2)
- 724*a^2*b^12*c*d*e + 258*a^3*b^11*c*d*f - 43520*a^8*b*c^6*d*f + 168*a^4*b^10*c*d*g - 152*a^4*b^10*c*e*f - 9
8*a^5*b^9*c*e*g + 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^
(1/2) + 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(
1/2) + 7278*a^3*b^10*c^2*d*e - 39132*a^4*b^8*c^3*d*e + 119616*a^5*b^6*c^4*d*e - 201600*a^6*b^4*c^5*d*e + 16128
0*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^4*b^9*c^2*d*f + 14784*a^5*b^7*c^3*d*f - 4
4352*a^6*b^5*c^4*d*f + 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*
c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) - 1044*a^5*b^8*c^2*d*g + 1548*a^5*b^8*c^2*e*f + 26
88*a^6*b^6*c^3*d*g - 8064*a^6*b^6*c^3*e*f - 1152*a^7*b^4*c^4*d*g + 22400*a^7*b^4*c^4*e*f - 6144*a^8*b^2*c^5*d*
g - 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 576*a^6*b^7*c^2*e*g - 1344*a^7*b^5*c^3*e*
g + 512*a^8*b^3*c^4*e*g - 192*a^7*b^6*c^2*f*g + 128*a^8*b^4*c^3*f*g + 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*
(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) +
184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-
(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 +
3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(1048576*a^21*b*c^8 + 256*a^15*b^13*c^2 - 6144*a^16*b^11*c^3 +
61440*a^17*b^9*c^4 - 327680*a^18*b^7*c^5 + 983040*a^19*b^5*c^6 - 1572864*a^20*b^3*c^7) + 320*a^12*b^14*c^2*d -
7936*a^13*b^12*c^3*d + 82816*a^14*b^10*c^4*d - 468480*a^15*b^8*c^5*d + 1536000*a^16*b^6*c^6*d - 2867200*a^17*
b^4*c^7*d + 2719744*a^18*b^2*c^8*d - 192*a^13*b^13*c^2*e + 4672*a^14*b^11*c^3*e - 47360*a^15*b^9*c^4*e + 25600
0*a^16*b^7*c^5*e - 778240*a^17*b^5*c^6*e + 1261568*a^18*b^3*c^7*e + 64*a^14*b^12*c^2*f - 1664*a^15*b^10*c^3*f
+ 17920*a^16*b^8*c^4*f - 102400*a^17*b^6*c^5*f + 327680*a^18*b^4*c^6*f - 557056*a^19*b^2*c^7*f + 64*a^15*b^11*
c^2*g - 1280*a^16*b^9*c^3*g + 10240*a^17*b^7*c^4*g - 40960*a^18*b^5*c^5*g + 81920*a^19*b^3*c^6*g - 851968*a^19
*b*c^8*e - 65536*a^20*b*c^7*g) + x*(204800*a^17*c^9*e^2 - 401408*a^16*c^10*d^2 - 73728*a^18*c^8*f^2 + 8192*a^1
9*c^7*g^2 + 400*a^9*b^14*c^3*d^2 - 9440*a^10*b^12*c^4*d^2 + 92816*a^11*b^10*c^5*d^2 - 488096*a^12*b^8*c^6*d^2
+ 1458688*a^13*b^6*c^7*d^2 - 2401280*a^14*b^4*c^8*d^2 + 1871872*a^15*b^2*c^9*d^2 + 144*a^11*b^12*c^3*e^2 - 326
4*a^12*b^10*c^4*e^2 + 30112*a^13*b^8*c^5*e^2 - 143360*a^14*b^6*c^6*e^2 + 365568*a^15*b^4*c^7*e^2 - 458752*a^16
*b^2*c^8*e^2 + 16*a^13*b^10*c^3*f^2 - 416*a^14*b^8*c^4*f^2 + 4608*a^15*b^6*c^5*f^2 - 25600*a^16*b^4*c^6*f^2 +
69632*a^17*b^2*c^7*f^2 + 160*a^15*b^8*c^3*g^2 - 2048*a^16*b^6*c^4*g^2 + 9216*a^17*b^4*c^5*g^2 - 16384*a^18*b^2
*c^6*g^2 + 344064*a^17*c^9*d*f - 81920*a^18*c^8*e*g - 1236992*a^16*b*c^9*d*e + 40960*a^17*b*c^8*d*g + 237568*a
^17*b*c^8*e*f + 40960*a^18*b*c^7*f*g - 480*a^10*b^13*c^3*d*e + 11104*a^11*b^11*c^4*d*e - 105824*a^12*b^9*c^5*d
*e + 530432*a^13*b^7*c^6*d*e - 1469440*a^14*b^5*c^7*d*e + 2121728*a^15*b^3*c^8*d*e + 160*a^11*b^12*c^3*d*f - 3
968*a^12*b^10*c^4*d*f + 39488*a^13*b^8*c^5*d*f - 200704*a^14*b^6*c^6*d*f + 542720*a^15*b^4*c^7*d*f - 720896*a^
16*b^2*c^8*d*f + 160*a^12*b^11*c^3*d*g - 96*a^12*b^11*c^3*e*f - 2528*a^13*b^9*c^4*d*g + 2336*a^13*b^9*c^4*e*f
+ 14336*a^14*b^7*c^5*d*g - 22528*a^14*b^7*c^5*e*f - 31744*a^15*b^5*c^6*d*g + 107520*a^15*b^5*c^6*e*f + 8192*a^
16*b^3*c^7*d*g - 253952*a^16*b^3*c^7*e*f - 96*a^13*b^10*c^3*e*g + 1472*a^14*b^8*c^4*e*g - 7168*a^15*b^6*c^5*e*
g + 6144*a^16*b^4*c^6*e*g + 40960*a^17*b^2*c^7*e*g + 32*a^14*b^9*c^3*f*g - 1024*a^15*b^7*c^4*f*g + 9216*a^16*b
^5*c^5*f*g - 32768*a^17*b^3*c^6*f*g))*((25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a^2*b^13*e^2 - 25*b^15*d^2 - a
^4*b^11*f^2 - a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 80640*a^7*b*c^7*d^2 + 213*a^3*b^11*c*e^2 - 2688
0*a^8*b*c^6*e^2 + 27*a^5*b^9*c*f^2 + 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^10*b*c^
4*g^2 + 30*a*b^14*d*e - 6366*a^2*b^11*c^2*d^2 + 35767*a^3*b^9*c^3*d^2 - 116928*a^4*b^7*c^4*d^2 + 219744*a^5*b^
5*c^5*d^2 - 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9
)^(1/2) - 2077*a^4*b^9*c^2*e^2 + 10656*a^5*b^7*c^3*e^2 - 30240*a^6*b^5*c^4*e^2 + 44800*a^7*b^3*c^5*e^2 + a^4*b
^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) - 288*a^6*b^7*c^2*f^2 + 1504*a^7*b^5
*c^3*f^2 - 3840*a^8*b^3*c^4*f^2 + 96*a^8*b^5*c^2*g^2 - 512*a^9*b^3*c^3*g^2 + 615*a*b^13*c*d^2 - 10*a^2*b^13*d*
f - 35840*a^8*c^7*d*e - 10*a^3*b^12*d*g + 6*a^3*b^12*e*f + 6*a^4*b^11*e*g + 7168*a^9*c^6*d*g + 15360*a^9*c^6*e
*f - 2*a^5*b^10*f*g - 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 724*a^2*b^12*c*d*e + 258*a^3
*b^11*c*d*f - 43520*a^8*b*c^6*d*f + 168*a^4*b^10*c*d*g - 152*a^4*b^10*c*e*f - 98*a^5*b^9*c*e*g + 1536*a^9*b*c^
5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) + 36*a^6*b^8*c*f*g + 246*
a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^3*b^10*c^2*d*e -
39132*a^4*b^8*c^3*d*e + 119616*a^5*b^6*c^4*d*e - 201600*a^6*b^4*c^5*d*e + 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*
d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^4*b^9*c^2*d*f + 14784*a^5*b^7*c^3*d*f - 44352*a^6*b^5*c^4*d*f + 69120*a^
7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*
d*f*(-(4*a*c - b^2)^9)^(1/2) - 1044*a^5*b^8*c^2*d*g + 1548*a^5*b^8*c^2*e*f + 2688*a^6*b^6*c^3*d*g - 8064*a^6*b
^6*c^3*e*f - 1152*a^7*b^4*c^4*d*g + 22400*a^7*b^4*c^4*e*f - 6144*a^8*b^2*c^5*d*g - 30720*a^8*b^2*c^5*e*f - 6*a
^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 576*a^6*b^7*c^2*e*g - 1344*a^7*b^5*c^3*e*g + 512*a^8*b^3*c^4*e*g - 192*a
^7*b^6*c^2*f*g + 128*a^8*b^4*c^3*f*g + 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a
^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b
^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^
7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b
^2*c^5)))^(1/2)*1i + (((25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a^2*b^13*e^2 - 25*b^15*d^2 - a^4*b^11*f^2 - a^
6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 80640*a^7*b*c^7*d^2 + 213*a^3*b^11*c*e^2 - 26880*a^8*b*c^6*e^2
+ 27*a^5*b^9*c*f^2 + 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^10*b*c^4*g^2 + 30*a*b^1
4*d*e - 6366*a^2*b^11*c^2*d^2 + 35767*a^3*b^9*c^3*d^2 - 116928*a^4*b^7*c^4*d^2 + 219744*a^5*b^5*c^5*d^2 - 2150
40*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a
^4*b^9*c^2*e^2 + 10656*a^5*b^7*c^3*e^2 - 30240*a^6*b^5*c^4*e^2 + 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c
- b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) - 288*a^6*b^7*c^2*f^2 + 1504*a^7*b^5*c^3*f^2 - 3840*
a^8*b^3*c^4*f^2 + 96*a^8*b^5*c^2*g^2 - 512*a^9*b^3*c^3*g^2 + 615*a*b^13*c*d^2 - 10*a^2*b^13*d*f - 35840*a^8*c^
7*d*e - 10*a^3*b^12*d*g + 6*a^3*b^12*e*f + 6*a^4*b^11*e*g + 7168*a^9*c^6*d*g + 15360*a^9*c^6*e*f - 2*a^5*b^10*
f*g - 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 724*a^2*b^12*c*d*e + 258*a^3*b^11*c*d*f - 43
520*a^8*b*c^6*d*f + 168*a^4*b^10*c*d*g - 152*a^4*b^10*c*e*f - 98*a^5*b^9*c*e*g + 1536*a^9*b*c^5*e*g + 2*a^5*b*
f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) + 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*
(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^3*b^10*c^2*d*e - 39132*a^4*b^8*c^
3*d*e + 119616*a^5*b^6*c^4*d*e - 201600*a^6*b^4*c^5*d*e + 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b
^2)^9)^(1/2) - 2706*a^4*b^9*c^2*d*f + 14784*a^5*b^7*c^3*d*f - 44352*a^6*b^5*c^4*d*f + 69120*a^7*b^3*c^5*d*f +
10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b
^2)^9)^(1/2) - 1044*a^5*b^8*c^2*d*g + 1548*a^5*b^8*c^2*e*f + 2688*a^6*b^6*c^3*d*g - 8064*a^6*b^6*c^3*e*f - 115
2*a^7*b^4*c^4*d*g + 22400*a^7*b^4*c^4*e*f - 6144*a^8*b^2*c^5*d*g - 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*
a*c - b^2)^9)^(1/2) + 576*a^6*b^7*c^2*e*g - 1344*a^7*b^5*c^3*e*g + 512*a^8*b^3*c^4*e*g - 192*a^7*b^6*c^2*f*g +
128*a^8*b^4*c^3*f*g + 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*
a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 1
86*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^
13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*
(917504*a^19*c^9*d - 393216*a^20*c^8*f + x*((25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a^2*b^13*e^2 - 25*b^15*d^
2 - a^4*b^11*f^2 - a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 80640*a^7*b*c^7*d^2 + 213*a^3*b^11*c*e^2 -
26880*a^8*b*c^6*e^2 + 27*a^5*b^9*c*f^2 + 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^10
*b*c^4*g^2 + 30*a*b^14*d*e - 6366*a^2*b^11*c^2*d^2 + 35767*a^3*b^9*c^3*d^2 - 116928*a^4*b^7*c^4*d^2 + 219744*a
^5*b^5*c^5*d^2 - 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b
^2)^9)^(1/2) - 2077*a^4*b^9*c^2*e^2 + 10656*a^5*b^7*c^3*e^2 - 30240*a^6*b^5*c^4*e^2 + 44800*a^7*b^3*c^5*e^2 +
a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) - 288*a^6*b^7*c^2*f^2 + 1504*a^
7*b^5*c^3*f^2 - 3840*a^8*b^3*c^4*f^2 + 96*a^8*b^5*c^2*g^2 - 512*a^9*b^3*c^3*g^2 + 615*a*b^13*c*d^2 - 10*a^2*b^
13*d*f - 35840*a^8*c^7*d*e - 10*a^3*b^12*d*g + 6*a^3*b^12*e*f + 6*a^4*b^11*e*g + 7168*a^9*c^6*d*g + 15360*a^9*
c^6*e*f - 2*a^5*b^10*f*g - 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 724*a^2*b^12*c*d*e + 25
8*a^3*b^11*c*d*f - 43520*a^8*b*c^6*d*f + 168*a^4*b^10*c*d*g - 152*a^4*b^10*c*e*f - 98*a^5*b^9*c*e*g + 1536*a^9
*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) + 36*a^6*b^8*c*f*g +
246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^3*b^10*c^2*d
*e - 39132*a^4*b^8*c^3*d*e + 119616*a^5*b^6*c^4*d*e - 201600*a^6*b^4*c^5*d*e + 161280*a^7*b^2*c^6*d*e + 10*a^2
*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^4*b^9*c^2*d*f + 14784*a^5*b^7*c^3*d*f - 44352*a^6*b^5*c^4*d*f + 691
20*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4
*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) - 1044*a^5*b^8*c^2*d*g + 1548*a^5*b^8*c^2*e*f + 2688*a^6*b^6*c^3*d*g - 8064*
a^6*b^6*c^3*e*f - 1152*a^7*b^4*c^4*d*g + 22400*a^7*b^4*c^4*e*f - 6144*a^8*b^2*c^5*d*g - 30720*a^8*b^2*c^5*e*f
- 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 576*a^6*b^7*c^2*e*g - 1344*a^7*b^5*c^3*e*g + 512*a^8*b^3*c^4*e*g -
192*a^7*b^6*c^2*f*g + 128*a^8*b^4*c^3*f*g + 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) +
12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*
c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(3
2*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a
^12*b^2*c^5)))^(1/2)*(1048576*a^21*b*c^8 + 256*a^15*b^13*c^2 - 6144*a^16*b^11*c^3 + 61440*a^17*b^9*c^4 - 32768
0*a^18*b^7*c^5 + 983040*a^19*b^5*c^6 - 1572864*a^20*b^3*c^7) - 320*a^12*b^14*c^2*d + 7936*a^13*b^12*c^3*d - 82
816*a^14*b^10*c^4*d + 468480*a^15*b^8*c^5*d - 1536000*a^16*b^6*c^6*d + 2867200*a^17*b^4*c^7*d - 2719744*a^18*b
^2*c^8*d + 192*a^13*b^13*c^2*e - 4672*a^14*b^11*c^3*e + 47360*a^15*b^9*c^4*e - 256000*a^16*b^7*c^5*e + 778240*
a^17*b^5*c^6*e - 1261568*a^18*b^3*c^7*e - 64*a^14*b^12*c^2*f + 1664*a^15*b^10*c^3*f - 17920*a^16*b^8*c^4*f + 1
02400*a^17*b^6*c^5*f - 327680*a^18*b^4*c^6*f + 557056*a^19*b^2*c^7*f - 64*a^15*b^11*c^2*g + 1280*a^16*b^9*c^3*
g - 10240*a^17*b^7*c^4*g + 40960*a^18*b^5*c^5*g - 81920*a^19*b^3*c^6*g + 851968*a^19*b*c^8*e + 65536*a^20*b*c^
7*g) + x*(204800*a^17*c^9*e^2 - 401408*a^16*c^10*d^2 - 73728*a^18*c^8*f^2 + 8192*a^19*c^7*g^2 + 400*a^9*b^14*c
^3*d^2 - 9440*a^10*b^12*c^4*d^2 + 92816*a^11*b^10*c^5*d^2 - 488096*a^12*b^8*c^6*d^2 + 1458688*a^13*b^6*c^7*d^2
- 2401280*a^14*b^4*c^8*d^2 + 1871872*a^15*b^2*c^9*d^2 + 144*a^11*b^12*c^3*e^2 - 3264*a^12*b^10*c^4*e^2 + 3011
2*a^13*b^8*c^5*e^2 - 143360*a^14*b^6*c^6*e^2 + 365568*a^15*b^4*c^7*e^2 - 458752*a^16*b^2*c^8*e^2 + 16*a^13*b^1
0*c^3*f^2 - 416*a^14*b^8*c^4*f^2 + 4608*a^15*b^6*c^5*f^2 - 25600*a^16*b^4*c^6*f^2 + 69632*a^17*b^2*c^7*f^2 + 1
60*a^15*b^8*c^3*g^2 - 2048*a^16*b^6*c^4*g^2 + 9216*a^17*b^4*c^5*g^2 - 16384*a^18*b^2*c^6*g^2 + 344064*a^17*c^9
*d*f - 81920*a^18*c^8*e*g - 1236992*a^16*b*c^9*d*e + 40960*a^17*b*c^8*d*g + 237568*a^17*b*c^8*e*f + 40960*a^18
*b*c^7*f*g - 480*a^10*b^13*c^3*d*e + 11104*a^11*b^11*c^4*d*e - 105824*a^12*b^9*c^5*d*e + 530432*a^13*b^7*c^6*d
*e - 1469440*a^14*b^5*c^7*d*e + 2121728*a^15*b^3*c^8*d*e + 160*a^11*b^12*c^3*d*f - 3968*a^12*b^10*c^4*d*f + 39
488*a^13*b^8*c^5*d*f - 200704*a^14*b^6*c^6*d*f + 542720*a^15*b^4*c^7*d*f - 720896*a^16*b^2*c^8*d*f + 160*a^12*
b^11*c^3*d*g - 96*a^12*b^11*c^3*e*f - 2528*a^13*b^9*c^4*d*g + 2336*a^13*b^9*c^4*e*f + 14336*a^14*b^7*c^5*d*g -
22528*a^14*b^7*c^5*e*f - 31744*a^15*b^5*c^6*d*g + 107520*a^15*b^5*c^6*e*f + 8192*a^16*b^3*c^7*d*g - 253952*a^
16*b^3*c^7*e*f - 96*a^13*b^10*c^3*e*g + 1472*a^14*b^8*c^4*e*g - 7168*a^15*b^6*c^5*e*g + 6144*a^16*b^4*c^6*e*g
+ 40960*a^17*b^2*c^7*e*g + 32*a^14*b^9*c^3*f*g - 1024*a^15*b^7*c^4*f*g + 9216*a^16*b^5*c^5*f*g - 32768*a^17*b^
3*c^6*f*g))*((25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a^2*b^13*e^2 - 25*b^15*d^2 - a^4*b^11*f^2 - a^6*b^9*g^2
+ a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 80640*a^7*b*c^7*d^2 + 213*a^3*b^11*c*e^2 - 26880*a^8*b*c^6*e^2 + 27*a^5*b
^9*c*f^2 + 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^10*b*c^4*g^2 + 30*a*b^14*d*e - 63
66*a^2*b^11*c^2*d^2 + 35767*a^3*b^9*c^3*d^2 - 116928*a^4*b^7*c^4*d^2 + 219744*a^5*b^5*c^5*d^2 - 215040*a^6*b^3
*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^4*b^9*c^2
*e^2 + 10656*a^5*b^7*c^3*e^2 - 30240*a^6*b^5*c^4*e^2 + 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^
(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) - 288*a^6*b^7*c^2*f^2 + 1504*a^7*b^5*c^3*f^2 - 3840*a^8*b^3*c^
4*f^2 + 96*a^8*b^5*c^2*g^2 - 512*a^9*b^3*c^3*g^2 + 615*a*b^13*c*d^2 - 10*a^2*b^13*d*f - 35840*a^8*c^7*d*e - 10
*a^3*b^12*d*g + 6*a^3*b^12*e*f + 6*a^4*b^11*e*g + 7168*a^9*c^6*d*g + 15360*a^9*c^6*e*f - 2*a^5*b^10*f*g - 3072
*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 724*a^2*b^12*c*d*e + 258*a^3*b^11*c*d*f - 43520*a^8*b*
c^6*d*f + 168*a^4*b^10*c*d*g - 152*a^4*b^10*c*e*f - 98*a^5*b^9*c*e*g + 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a
*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) + 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c -
b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^3*b^10*c^2*d*e - 39132*a^4*b^8*c^3*d*e + 11
9616*a^5*b^6*c^4*d*e - 201600*a^6*b^4*c^5*d*e + 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/
2) - 2706*a^4*b^9*c^2*d*f + 14784*a^5*b^7*c^3*d*f - 44352*a^6*b^5*c^4*d*f + 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3
*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/
2) - 1044*a^5*b^8*c^2*d*g + 1548*a^5*b^8*c^2*e*f + 2688*a^6*b^6*c^3*d*g - 8064*a^6*b^6*c^3*e*f - 1152*a^7*b^4*
c^4*d*g + 22400*a^7*b^4*c^4*e*f - 6144*a^8*b^2*c^5*d*g - 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)
^9)^(1/2) + 576*a^6*b^7*c^2*e*g - 1344*a^7*b^5*c^3*e*g + 512*a^8*b^3*c^4*e*g - 192*a^7*b^6*c^2*f*g + 128*a^8*b
^4*c^3*f*g + 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)
^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c
^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 2
4*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*1i)/((((25
*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a^2*b^13*e^2 - 25*b^15*d^2 - a^4*b^11*f^2 - a^6*b^9*g^2 + a^6*g^2*(-(4*a
*c - b^2)^9)^(1/2) + 80640*a^7*b*c^7*d^2 + 213*a^3*b^11*c*e^2 - 26880*a^8*b*c^6*e^2 + 27*a^5*b^9*c*f^2 + 3840*
a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^10*b*c^4*g^2 + 30*a*b^14*d*e - 6366*a^2*b^11*c^2*
d^2 + 35767*a^3*b^9*c^3*d^2 - 116928*a^4*b^7*c^4*d^2 + 219744*a^5*b^5*c^5*d^2 - 215040*a^6*b^3*c^6*d^2 + 9*a^2
*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^4*b^9*c^2*e^2 + 10656*a^5
*b^7*c^3*e^2 - 30240*a^6*b^5*c^4*e^2 + 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c
^2*e^2*(-(4*a*c - b^2)^9)^(1/2) - 288*a^6*b^7*c^2*f^2 + 1504*a^7*b^5*c^3*f^2 - 3840*a^8*b^3*c^4*f^2 + 96*a^8*b
^5*c^2*g^2 - 512*a^9*b^3*c^3*g^2 + 615*a*b^13*c*d^2 - 10*a^2*b^13*d*f - 35840*a^8*c^7*d*e - 10*a^3*b^12*d*g +
6*a^3*b^12*e*f + 6*a^4*b^11*e*g + 7168*a^9*c^6*d*g + 15360*a^9*c^6*e*f - 2*a^5*b^10*f*g - 3072*a^10*c^5*f*g -
30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 724*a^2*b^12*c*d*e + 258*a^3*b^11*c*d*f - 43520*a^8*b*c^6*d*f + 168*a^
4*b^10*c*d*g - 152*a^4*b^10*c*e*f - 98*a^5*b^9*c*e*g + 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/
2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) + 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) -
165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^3*b^10*c^2*d*e - 39132*a^4*b^8*c^3*d*e + 119616*a^5*b^6*c^4
*d*e - 201600*a^6*b^4*c^5*d*e + 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^4*b^
9*c^2*d*f + 14784*a^5*b^7*c^3*d*f - 44352*a^6*b^5*c^4*d*f + 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c -
b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) - 1044*a^5*b^
8*c^2*d*g + 1548*a^5*b^8*c^2*e*f + 2688*a^6*b^6*c^3*d*g - 8064*a^6*b^6*c^3*e*f - 1152*a^7*b^4*c^4*d*g + 22400*
a^7*b^4*c^4*e*f - 6144*a^8*b^2*c^5*d*g - 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 576*
a^6*b^7*c^2*e*g - 1344*a^7*b^5*c^3*e*g + 512*a^8*b^3*c^4*e*g - 192*a^7*b^6*c^2*f*g + 128*a^8*b^4*c^3*f*g + 153
6*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a
^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c
- b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 2
40*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(393216*a^20*c^8*f - 91750
4*a^19*c^9*d + x*((25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a^2*b^13*e^2 - 25*b^15*d^2 - a^4*b^11*f^2 - a^6*b^9
*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 80640*a^7*b*c^7*d^2 + 213*a^3*b^11*c*e^2 - 26880*a^8*b*c^6*e^2 + 27*
a^5*b^9*c*f^2 + 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^10*b*c^4*g^2 + 30*a*b^14*d*e
- 6366*a^2*b^11*c^2*d^2 + 35767*a^3*b^9*c^3*d^2 - 116928*a^4*b^7*c^4*d^2 + 219744*a^5*b^5*c^5*d^2 - 215040*a^
6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^4*b^
9*c^2*e^2 + 10656*a^5*b^7*c^3*e^2 - 30240*a^6*b^5*c^4*e^2 + 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2
)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) - 288*a^6*b^7*c^2*f^2 + 1504*a^7*b^5*c^3*f^2 - 3840*a^8*b
^3*c^4*f^2 + 96*a^8*b^5*c^2*g^2 - 512*a^9*b^3*c^3*g^2 + 615*a*b^13*c*d^2 - 10*a^2*b^13*d*f - 35840*a^8*c^7*d*e
- 10*a^3*b^12*d*g + 6*a^3*b^12*e*f + 6*a^4*b^11*e*g + 7168*a^9*c^6*d*g + 15360*a^9*c^6*e*f - 2*a^5*b^10*f*g -
3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 724*a^2*b^12*c*d*e + 258*a^3*b^11*c*d*f - 43520*a
^8*b*c^6*d*f + 168*a^4*b^10*c*d*g - 152*a^4*b^10*c*e*f - 98*a^5*b^9*c*e*g + 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(
-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) + 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*
a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^3*b^10*c^2*d*e - 39132*a^4*b^8*c^3*d*e
+ 119616*a^5*b^6*c^4*d*e - 201600*a^6*b^4*c^5*d*e + 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9
)^(1/2) - 2706*a^4*b^9*c^2*d*f + 14784*a^5*b^7*c^3*d*f - 44352*a^6*b^5*c^4*d*f + 69120*a^7*b^3*c^5*d*f + 10*a^
3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9
)^(1/2) - 1044*a^5*b^8*c^2*d*g + 1548*a^5*b^8*c^2*e*f + 2688*a^6*b^6*c^3*d*g - 8064*a^6*b^6*c^3*e*f - 1152*a^7
*b^4*c^4*d*g + 22400*a^7*b^4*c^4*e*f - 6144*a^8*b^2*c^5*d*g - 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c -
b^2)^9)^(1/2) + 576*a^6*b^7*c^2*e*g - 1344*a^7*b^5*c^3*e*g + 512*a^8*b^3*c^4*e*g - 192*a^7*b^6*c^2*f*g + 128*
a^8*b^4*c^3*f*g + 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c -
b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^
3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^
6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(1048
576*a^21*b*c^8 + 256*a^15*b^13*c^2 - 6144*a^16*b^11*c^3 + 61440*a^17*b^9*c^4 - 327680*a^18*b^7*c^5 + 983040*a^
19*b^5*c^6 - 1572864*a^20*b^3*c^7) + 320*a^12*b^14*c^2*d - 7936*a^13*b^12*c^3*d + 82816*a^14*b^10*c^4*d - 4684
80*a^15*b^8*c^5*d + 1536000*a^16*b^6*c^6*d - 2867200*a^17*b^4*c^7*d + 2719744*a^18*b^2*c^8*d - 192*a^13*b^13*c
^2*e + 4672*a^14*b^11*c^3*e - 47360*a^15*b^9*c^4*e + 256000*a^16*b^7*c^5*e - 778240*a^17*b^5*c^6*e + 1261568*a
^18*b^3*c^7*e + 64*a^14*b^12*c^2*f - 1664*a^15*b^10*c^3*f + 17920*a^16*b^8*c^4*f - 102400*a^17*b^6*c^5*f + 327
680*a^18*b^4*c^6*f - 557056*a^19*b^2*c^7*f + 64*a^15*b^11*c^2*g - 1280*a^16*b^9*c^3*g + 10240*a^17*b^7*c^4*g -
40960*a^18*b^5*c^5*g + 81920*a^19*b^3*c^6*g - 851968*a^19*b*c^8*e - 65536*a^20*b*c^7*g) + x*(204800*a^17*c^9*
e^2 - 401408*a^16*c^10*d^2 - 73728*a^18*c^8*f^2 + 8192*a^19*c^7*g^2 + 400*a^9*b^14*c^3*d^2 - 9440*a^10*b^12*c^
4*d^2 + 92816*a^11*b^10*c^5*d^2 - 488096*a^12*b^8*c^6*d^2 + 1458688*a^13*b^6*c^7*d^2 - 2401280*a^14*b^4*c^8*d^
2 + 1871872*a^15*b^2*c^9*d^2 + 144*a^11*b^12*c^3*e^2 - 3264*a^12*b^10*c^4*e^2 + 30112*a^13*b^8*c^5*e^2 - 14336
0*a^14*b^6*c^6*e^2 + 365568*a^15*b^4*c^7*e^2 - 458752*a^16*b^2*c^8*e^2 + 16*a^13*b^10*c^3*f^2 - 416*a^14*b^8*c
^4*f^2 + 4608*a^15*b^6*c^5*f^2 - 25600*a^16*b^4*c^6*f^2 + 69632*a^17*b^2*c^7*f^2 + 160*a^15*b^8*c^3*g^2 - 2048
*a^16*b^6*c^4*g^2 + 9216*a^17*b^4*c^5*g^2 - 16384*a^18*b^2*c^6*g^2 + 344064*a^17*c^9*d*f - 81920*a^18*c^8*e*g
- 1236992*a^16*b*c^9*d*e + 40960*a^17*b*c^8*d*g + 237568*a^17*b*c^8*e*f + 40960*a^18*b*c^7*f*g - 480*a^10*b^13
*c^3*d*e + 11104*a^11*b^11*c^4*d*e - 105824*a^12*b^9*c^5*d*e + 530432*a^13*b^7*c^6*d*e - 1469440*a^14*b^5*c^7*
d*e + 2121728*a^15*b^3*c^8*d*e + 160*a^11*b^12*c^3*d*f - 3968*a^12*b^10*c^4*d*f + 39488*a^13*b^8*c^5*d*f - 200
704*a^14*b^6*c^6*d*f + 542720*a^15*b^4*c^7*d*f - 720896*a^16*b^2*c^8*d*f + 160*a^12*b^11*c^3*d*g - 96*a^12*b^1
1*c^3*e*f - 2528*a^13*b^9*c^4*d*g + 2336*a^13*b^9*c^4*e*f + 14336*a^14*b^7*c^5*d*g - 22528*a^14*b^7*c^5*e*f -
31744*a^15*b^5*c^6*d*g + 107520*a^15*b^5*c^6*e*f + 8192*a^16*b^3*c^7*d*g - 253952*a^16*b^3*c^7*e*f - 96*a^13*b
^10*c^3*e*g + 1472*a^14*b^8*c^4*e*g - 7168*a^15*b^6*c^5*e*g + 6144*a^16*b^4*c^6*e*g + 40960*a^17*b^2*c^7*e*g +
32*a^14*b^9*c^3*f*g - 1024*a^15*b^7*c^4*f*g + 9216*a^16*b^5*c^5*f*g - 32768*a^17*b^3*c^6*f*g))*((25*b^6*d^2*(
-(4*a*c - b^2)^9)^(1/2) - 9*a^2*b^13*e^2 - 25*b^15*d^2 - a^4*b^11*f^2 - a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^
9)^(1/2) + 80640*a^7*b*c^7*d^2 + 213*a^3*b^11*c*e^2 - 26880*a^8*b*c^6*e^2 + 27*a^5*b^9*c*f^2 + 3840*a^9*b*c^5*
f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^10*b*c^4*g^2 + 30*a*b^14*d*e - 6366*a^2*b^11*c^2*d^2 + 3576
7*a^3*b^9*c^3*d^2 - 116928*a^4*b^7*c^4*d^2 + 219744*a^5*b^5*c^5*d^2 - 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(
-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^4*b^9*c^2*e^2 + 10656*a^5*b^7*c^3*e
^2 - 30240*a^6*b^5*c^4*e^2 + 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(
4*a*c - b^2)^9)^(1/2) - 288*a^6*b^7*c^2*f^2 + 1504*a^7*b^5*c^3*f^2 - 3840*a^8*b^3*c^4*f^2 + 96*a^8*b^5*c^2*g^2
- 512*a^9*b^3*c^3*g^2 + 615*a*b^13*c*d^2 - 10*a^2*b^13*d*f - 35840*a^8*c^7*d*e - 10*a^3*b^12*d*g + 6*a^3*b^12
*e*f + 6*a^4*b^11*e*g + 7168*a^9*c^6*d*g + 15360*a^9*c^6*e*f - 2*a^5*b^10*f*g - 3072*a^10*c^5*f*g - 30*a*b^5*d
*e*(-(4*a*c - b^2)^9)^(1/2) - 724*a^2*b^12*c*d*e + 258*a^3*b^11*c*d*f - 43520*a^8*b*c^6*d*f + 168*a^4*b^10*c*d
*g - 152*a^4*b^10*c*e*f - 98*a^5*b^9*c*e*g + 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^
5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) + 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4
*c*d^2*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^3*b^10*c^2*d*e - 39132*a^4*b^8*c^3*d*e + 119616*a^5*b^6*c^4*d*e - 201
600*a^6*b^4*c^5*d*e + 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^4*b^9*c^2*d*f
+ 14784*a^5*b^7*c^3*d*f - 44352*a^6*b^5*c^4*d*f + 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1
/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) - 1044*a^5*b^8*c^2*d*g
+ 1548*a^5*b^8*c^2*e*f + 2688*a^6*b^6*c^3*d*g - 8064*a^6*b^6*c^3*e*f - 1152*a^7*b^4*c^4*d*g + 22400*a^7*b^4*c^
4*e*f - 6144*a^8*b^2*c^5*d*g - 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 576*a^6*b^7*c^
2*e*g - 1344*a^7*b^5*c^3*e*g + 512*a^8*b^3*c^4*e*g - 192*a^7*b^6*c^2*f*g + 128*a^8*b^4*c^3*f*g + 1536*a^9*b^2*
c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f
*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^
(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8
*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2) - (((25*b^6*d^2*(-(4*a*c - b^2)^9)^(
1/2) - 9*a^2*b^13*e^2 - 25*b^15*d^2 - a^4*b^11*f^2 - a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 80640*a^
7*b*c^7*d^2 + 213*a^3*b^11*c*e^2 - 26880*a^8*b*c^6*e^2 + 27*a^5*b^9*c*f^2 + 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(
-(4*a*c - b^2)^9)^(1/2) + 768*a^10*b*c^4*g^2 + 30*a*b^14*d*e - 6366*a^2*b^11*c^2*d^2 + 35767*a^3*b^9*c^3*d^2 -
116928*a^4*b^7*c^4*d^2 + 219744*a^5*b^5*c^5*d^2 - 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(
1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^4*b^9*c^2*e^2 + 10656*a^5*b^7*c^3*e^2 - 30240*a^6*b^5*
c^4*e^2 + 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/
2) - 288*a^6*b^7*c^2*f^2 + 1504*a^7*b^5*c^3*f^2 - 3840*a^8*b^3*c^4*f^2 + 96*a^8*b^5*c^2*g^2 - 512*a^9*b^3*c^3*
g^2 + 615*a*b^13*c*d^2 - 10*a^2*b^13*d*f - 35840*a^8*c^7*d*e - 10*a^3*b^12*d*g + 6*a^3*b^12*e*f + 6*a^4*b^11*e
*g + 7168*a^9*c^6*d*g + 15360*a^9*c^6*e*f - 2*a^5*b^10*f*g - 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^
9)^(1/2) - 724*a^2*b^12*c*d*e + 258*a^3*b^11*c*d*f - 43520*a^8*b*c^6*d*f + 168*a^4*b^10*c*d*g - 152*a^4*b^10*c
*e*f - 98*a^5*b^9*c*e*g + 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c -
b^2)^9)^(1/2) + 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b
^2)^9)^(1/2) + 7278*a^3*b^10*c^2*d*e - 39132*a^4*b^8*c^3*d*e + 119616*a^5*b^6*c^4*d*e - 201600*a^6*b^4*c^5*d*e
+ 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^4*b^9*c^2*d*f + 14784*a^5*b^7*c^3
*d*f - 44352*a^6*b^5*c^4*d*f + 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f
*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) - 1044*a^5*b^8*c^2*d*g + 1548*a^5*b^8*c^2*
e*f + 2688*a^6*b^6*c^3*d*g - 8064*a^6*b^6*c^3*e*f - 1152*a^7*b^4*c^4*d*g + 22400*a^7*b^4*c^4*e*f - 6144*a^8*b^
2*c^5*d*g - 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 576*a^6*b^7*c^2*e*g - 1344*a^7*b^
5*c^3*e*g + 512*a^8*b^3*c^4*e*g - 192*a^7*b^6*c^2*f*g + 128*a^8*b^4*c^3*f*g + 1536*a^9*b^2*c^4*f*g - 51*a^3*b^
2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)
^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*
c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^
6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(917504*a^19*c^9*d - 393216*a^20*c^8*f + x*((25*b^6*d^2
*(-(4*a*c - b^2)^9)^(1/2) - 9*a^2*b^13*e^2 - 25*b^15*d^2 - a^4*b^11*f^2 - a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2
)^9)^(1/2) + 80640*a^7*b*c^7*d^2 + 213*a^3*b^11*c*e^2 - 26880*a^8*b*c^6*e^2 + 27*a^5*b^9*c*f^2 + 3840*a^9*b*c^
5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^10*b*c^4*g^2 + 30*a*b^14*d*e - 6366*a^2*b^11*c^2*d^2 + 35
767*a^3*b^9*c^3*d^2 - 116928*a^4*b^7*c^4*d^2 + 219744*a^5*b^5*c^5*d^2 - 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2
*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^4*b^9*c^2*e^2 + 10656*a^5*b^7*c^3
*e^2 - 30240*a^6*b^5*c^4*e^2 + 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(
-(4*a*c - b^2)^9)^(1/2) - 288*a^6*b^7*c^2*f^2 + 1504*a^7*b^5*c^3*f^2 - 3840*a^8*b^3*c^4*f^2 + 96*a^8*b^5*c^2*g
^2 - 512*a^9*b^3*c^3*g^2 + 615*a*b^13*c*d^2 - 10*a^2*b^13*d*f - 35840*a^8*c^7*d*e - 10*a^3*b^12*d*g + 6*a^3*b^
12*e*f + 6*a^4*b^11*e*g + 7168*a^9*c^6*d*g + 15360*a^9*c^6*e*f - 2*a^5*b^10*f*g - 3072*a^10*c^5*f*g - 30*a*b^5
*d*e*(-(4*a*c - b^2)^9)^(1/2) - 724*a^2*b^12*c*d*e + 258*a^3*b^11*c*d*f - 43520*a^8*b*c^6*d*f + 168*a^4*b^10*c
*d*g - 152*a^4*b^10*c*e*f - 98*a^5*b^9*c*e*g + 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*
a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) + 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b
^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^3*b^10*c^2*d*e - 39132*a^4*b^8*c^3*d*e + 119616*a^5*b^6*c^4*d*e - 2
01600*a^6*b^4*c^5*d*e + 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^4*b^9*c^2*d*
f + 14784*a^5*b^7*c^3*d*f - 44352*a^6*b^5*c^4*d*f + 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^
(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) - 1044*a^5*b^8*c^2*d*
g + 1548*a^5*b^8*c^2*e*f + 2688*a^6*b^6*c^3*d*g - 8064*a^6*b^6*c^3*e*f - 1152*a^7*b^4*c^4*d*g + 22400*a^7*b^4*
c^4*e*f - 6144*a^8*b^2*c^5*d*g - 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 576*a^6*b^7*
c^2*e*g - 1344*a^7*b^5*c^3*e*g + 512*a^8*b^3*c^4*e*g - 192*a^7*b^6*c^2*f*g + 128*a^8*b^4*c^3*f*g + 1536*a^9*b^
2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e
*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9
)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b
^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(1048576*a^21*b*c^8 + 256*a^15*b^1
3*c^2 - 6144*a^16*b^11*c^3 + 61440*a^17*b^9*c^4 - 327680*a^18*b^7*c^5 + 983040*a^19*b^5*c^6 - 1572864*a^20*b^3
*c^7) - 320*a^12*b^14*c^2*d + 7936*a^13*b^12*c^3*d - 82816*a^14*b^10*c^4*d + 468480*a^15*b^8*c^5*d - 1536000*a
^16*b^6*c^6*d + 2867200*a^17*b^4*c^7*d - 2719744*a^18*b^2*c^8*d + 192*a^13*b^13*c^2*e - 4672*a^14*b^11*c^3*e +
47360*a^15*b^9*c^4*e - 256000*a^16*b^7*c^5*e + 778240*a^17*b^5*c^6*e - 1261568*a^18*b^3*c^7*e - 64*a^14*b^12*
c^2*f + 1664*a^15*b^10*c^3*f - 17920*a^16*b^8*c^4*f + 102400*a^17*b^6*c^5*f - 327680*a^18*b^4*c^6*f + 557056*a
^19*b^2*c^7*f - 64*a^15*b^11*c^2*g + 1280*a^16*b^9*c^3*g - 10240*a^17*b^7*c^4*g + 40960*a^18*b^5*c^5*g - 81920
*a^19*b^3*c^6*g + 851968*a^19*b*c^8*e + 65536*a^20*b*c^7*g) + x*(204800*a^17*c^9*e^2 - 401408*a^16*c^10*d^2 -
73728*a^18*c^8*f^2 + 8192*a^19*c^7*g^2 + 400*a^9*b^14*c^3*d^2 - 9440*a^10*b^12*c^4*d^2 + 92816*a^11*b^10*c^5*d
^2 - 488096*a^12*b^8*c^6*d^2 + 1458688*a^13*b^6*c^7*d^2 - 2401280*a^14*b^4*c^8*d^2 + 1871872*a^15*b^2*c^9*d^2
+ 144*a^11*b^12*c^3*e^2 - 3264*a^12*b^10*c^4*e^2 + 30112*a^13*b^8*c^5*e^2 - 143360*a^14*b^6*c^6*e^2 + 365568*a
^15*b^4*c^7*e^2 - 458752*a^16*b^2*c^8*e^2 + 16*a^13*b^10*c^3*f^2 - 416*a^14*b^8*c^4*f^2 + 4608*a^15*b^6*c^5*f^
2 - 25600*a^16*b^4*c^6*f^2 + 69632*a^17*b^2*c^7*f^2 + 160*a^15*b^8*c^3*g^2 - 2048*a^16*b^6*c^4*g^2 + 9216*a^17
*b^4*c^5*g^2 - 16384*a^18*b^2*c^6*g^2 + 344064*a^17*c^9*d*f - 81920*a^18*c^8*e*g - 1236992*a^16*b*c^9*d*e + 40
960*a^17*b*c^8*d*g + 237568*a^17*b*c^8*e*f + 40960*a^18*b*c^7*f*g - 480*a^10*b^13*c^3*d*e + 11104*a^11*b^11*c^
4*d*e - 105824*a^12*b^9*c^5*d*e + 530432*a^13*b^7*c^6*d*e - 1469440*a^14*b^5*c^7*d*e + 2121728*a^15*b^3*c^8*d*
e + 160*a^11*b^12*c^3*d*f - 3968*a^12*b^10*c^4*d*f + 39488*a^13*b^8*c^5*d*f - 200704*a^14*b^6*c^6*d*f + 542720
*a^15*b^4*c^7*d*f - 720896*a^16*b^2*c^8*d*f + 160*a^12*b^11*c^3*d*g - 96*a^12*b^11*c^3*e*f - 2528*a^13*b^9*c^4
*d*g + 2336*a^13*b^9*c^4*e*f + 14336*a^14*b^7*c^5*d*g - 22528*a^14*b^7*c^5*e*f - 31744*a^15*b^5*c^6*d*g + 1075
20*a^15*b^5*c^6*e*f + 8192*a^16*b^3*c^7*d*g - 253952*a^16*b^3*c^7*e*f - 96*a^13*b^10*c^3*e*g + 1472*a^14*b^8*c
^4*e*g - 7168*a^15*b^6*c^5*e*g + 6144*a^16*b^4*c^6*e*g + 40960*a^17*b^2*c^7*e*g + 32*a^14*b^9*c^3*f*g - 1024*a
^15*b^7*c^4*f*g + 9216*a^16*b^5*c^5*f*g - 32768*a^17*b^3*c^6*f*g))*((25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a
^2*b^13*e^2 - 25*b^15*d^2 - a^4*b^11*f^2 - a^6*b^9*g^2 + a^6*g^2*(-(4*a*c - b^2)^9)^(1/2) + 80640*a^7*b*c^7*d^
2 + 213*a^3*b^11*c*e^2 - 26880*a^8*b*c^6*e^2 + 27*a^5*b^9*c*f^2 + 3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c -
b^2)^9)^(1/2) + 768*a^10*b*c^4*g^2 + 30*a*b^14*d*e - 6366*a^2*b^11*c^2*d^2 + 35767*a^3*b^9*c^3*d^2 - 116928*a^
4*b^7*c^4*d^2 + 219744*a^5*b^5*c^5*d^2 - 215040*a^6*b^3*c^6*d^2 + 9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*
a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^4*b^9*c^2*e^2 + 10656*a^5*b^7*c^3*e^2 - 30240*a^6*b^5*c^4*e^2 +
44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) - 288*a
^6*b^7*c^2*f^2 + 1504*a^7*b^5*c^3*f^2 - 3840*a^8*b^3*c^4*f^2 + 96*a^8*b^5*c^2*g^2 - 512*a^9*b^3*c^3*g^2 + 615*
a*b^13*c*d^2 - 10*a^2*b^13*d*f - 35840*a^8*c^7*d*e - 10*a^3*b^12*d*g + 6*a^3*b^12*e*f + 6*a^4*b^11*e*g + 7168*
a^9*c^6*d*g + 15360*a^9*c^6*e*f - 2*a^5*b^10*f*g - 3072*a^10*c^5*f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) -
724*a^2*b^12*c*d*e + 258*a^3*b^11*c*d*f - 43520*a^8*b*c^6*d*f + 168*a^4*b^10*c*d*g - 152*a^4*b^10*c*e*f - 98*
a^5*b^9*c*e*g + 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1
/2) + 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/
2) + 7278*a^3*b^10*c^2*d*e - 39132*a^4*b^8*c^3*d*e + 119616*a^5*b^6*c^4*d*e - 201600*a^6*b^4*c^5*d*e + 161280*
a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*a^4*b^9*c^2*d*f + 14784*a^5*b^7*c^3*d*f - 443
52*a^6*b^5*c^4*d*f + 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c
- b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) - 1044*a^5*b^8*c^2*d*g + 1548*a^5*b^8*c^2*e*f + 2688
*a^6*b^6*c^3*d*g - 8064*a^6*b^6*c^3*e*f - 1152*a^7*b^4*c^4*d*g + 22400*a^7*b^4*c^4*e*f - 6144*a^8*b^2*c^5*d*g
- 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2) + 576*a^6*b^7*c^2*e*g - 1344*a^7*b^5*c^3*e*g
+ 512*a^8*b^3*c^4*e*g - 192*a^7*b^6*c^2*f*g + 128*a^8*b^4*c^3*f*g + 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-
(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2) + 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 1
84*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4
*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 38
40*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2) - 128000*a^15*c^9*e^3 + 1024*a^18*c^6*g^3 + 476672*a^13*b*c^10*d^
3 - 4608*a^16*b*c^7*f^3 - 250880*a^14*c^10*d^2*e + 50176*a^15*c^9*d^2*g - 46080*a^16*c^8*e*f^2 + 76800*a^16*c^
8*e^2*g - 15360*a^17*c^7*e*g^2 + 9216*a^17*c^7*f^2*g + 1800*a^9*b^9*c^6*d^3 - 29080*a^10*b^7*c^7*d^3 + 176032*
a^11*b^5*c^8*d^3 - 473216*a^12*b^3*c^9*d^3 - 504*a^11*b^8*c^5*e^3 + 8112*a^12*b^6*c^6*e^3 - 48704*a^13*b^4*c^7
*e^3 + 129280*a^14*b^2*c^8*e^3 + 40*a^13*b^7*c^4*f^3 - 608*a^14*b^5*c^5*f^3 + 2944*a^15*b^3*c^6*f^3 + 48*a^15*
b^6*c^3*g^3 - 320*a^16*b^4*c^4*g^3 + 256*a^17*b^2*c^5*g^3 + 215040*a^15*c^9*d*e*f - 43008*a^16*c^8*d*f*g + 442
880*a^14*b*c^9*d*e^2 - 433664*a^14*b*c^9*d^2*f + 109056*a^15*b*c^8*d*f^2 + 84480*a^15*b*c^8*e^2*f + 43520*a^16
*b*c^7*d*g^2 - 7680*a^17*b*c^6*f*g^2 - 1400*a^9*b^10*c^5*d^2*e + 21680*a^10*b^8*c^6*d^2*e + 1680*a^10*b^9*c^5*
d*e^2 - 121648*a^11*b^6*c^7*d^2*e - 27176*a^11*b^7*c^6*d*e^2 + 275264*a^12*b^4*c^8*d^2*e + 164448*a^12*b^5*c^7
*d*e^2 - 121088*a^13*b^2*c^9*d^2*e - 441216*a^13*b^3*c^8*d*e^2 + 1000*a^9*b^11*c^4*d^2*f - 17800*a^10*b^9*c^5*
d^2*f + 124280*a^11*b^7*c^6*d^2*f + 400*a^11*b^9*c^4*d*f^2 - 422944*a^12*b^5*c^7*d^2*f - 6600*a^12*b^7*c^5*d*f
^2 + 694912*a^13*b^3*c^8*d^2*f + 40416*a^13*b^5*c^6*d*f^2 - 108928*a^14*b^3*c^7*d*f^2 - 600*a^9*b^12*c^3*d^2*g
+ 10960*a^10*b^10*c^4*d^2*g - 78904*a^11*b^8*c^5*d^2*g + 360*a^11*b^9*c^4*e^2*f + 278096*a^12*b^6*c^6*d^2*g -
5736*a^12*b^7*c^5*e^2*f - 240*a^12*b^8*c^4*e*f^2 + 120*a^12*b^9*c^3*d*g^2 - 472000*a^13*b^4*c^7*d^2*g + 33888
*a^13*b^5*c^6*e^2*f + 3792*a^13*b^6*c^5*e*f^2 - 2216*a^13*b^7*c^4*d*g^2 + 284416*a^14*b^2*c^8*d^2*g - 87936*a^
14*b^3*c^7*e^2*f - 21696*a^14*b^4*c^6*e*f^2 + 14688*a^14*b^5*c^5*d*g^2 + 52992*a^15*b^2*c^7*e*f^2 - 41856*a^15
*b^3*c^6*d*g^2 - 216*a^11*b^10*c^3*e^2*g + 3744*a^12*b^8*c^4*e^2*g - 25200*a^13*b^6*c^5*e^2*g - 72*a^13*b^8*c^
3*e*g^2 + 81984*a^14*b^4*c^6*e^2*g + 1296*a^14*b^6*c^4*e*g^2 - 128256*a^15*b^2*c^7*e^2*g - 7872*a^15*b^4*c^5*e
*g^2 + 19200*a^16*b^2*c^6*e*g^2 - 24*a^13*b^8*c^3*f^2*g + 336*a^14*b^6*c^4*f^2*g + 24*a^14*b^7*c^3*f*g^2 - 960
*a^15*b^4*c^5*f^2*g - 672*a^15*b^5*c^4*f*g^2 - 2304*a^16*b^2*c^6*f^2*g + 4224*a^16*b^3*c^5*f*g^2 - 306176*a^15
*b*c^8*d*e*g + 21504*a^16*b*c^7*e*f*g - 1200*a^10*b^10*c^4*d*e*f + 20240*a^11*b^8*c^5*d*e*f - 130656*a^12*b^6*
c^6*d*e*f + 394368*a^13*b^4*c^7*d*e*f - 528896*a^14*b^2*c^8*d*e*f + 720*a^10*b^11*c^3*d*e*g - 12816*a^11*b^9*c
^4*d*e*g + 89264*a^12*b^7*c^5*d*e*g - 302400*a^13*b^5*c^6*d*e*g + 493824*a^14*b^3*c^7*d*e*g - 240*a^11*b^10*c^
3*d*f*g + 3872*a^12*b^8*c^4*d*f*g - 22368*a^13*b^6*c^5*d*f*g + 51840*a^14*b^4*c^6*d*f*g - 25088*a^15*b^2*c^7*d
*f*g + 144*a^12*b^9*c^3*e*f*g - 2256*a^13*b^7*c^4*e*f*g + 12480*a^14*b^5*c^5*e*f*g - 28416*a^15*b^3*c^6*e*f*g)
)*((25*b^6*d^2*(-(4*a*c - b^2)^9)^(1/2) - 9*a^2*b^13*e^2 - 25*b^15*d^2 - a^4*b^11*f^2 - a^6*b^9*g^2 + a^6*g^2*
(-(4*a*c - b^2)^9)^(1/2) + 80640*a^7*b*c^7*d^2 + 213*a^3*b^11*c*e^2 - 26880*a^8*b*c^6*e^2 + 27*a^5*b^9*c*f^2 +
3840*a^9*b*c^5*f^2 - 9*a^5*c*f^2*(-(4*a*c - b^2)^9)^(1/2) + 768*a^10*b*c^4*g^2 + 30*a*b^14*d*e - 6366*a^2*b^1
1*c^2*d^2 + 35767*a^3*b^9*c^3*d^2 - 116928*a^4*b^7*c^4*d^2 + 219744*a^5*b^5*c^5*d^2 - 215040*a^6*b^3*c^6*d^2 +
9*a^2*b^4*e^2*(-(4*a*c - b^2)^9)^(1/2) - 49*a^3*c^3*d^2*(-(4*a*c - b^2)^9)^(1/2) - 2077*a^4*b^9*c^2*e^2 + 106
56*a^5*b^7*c^3*e^2 - 30240*a^6*b^5*c^4*e^2 + 44800*a^7*b^3*c^5*e^2 + a^4*b^2*f^2*(-(4*a*c - b^2)^9)^(1/2) + 25
*a^4*c^2*e^2*(-(4*a*c - b^2)^9)^(1/2) - 288*a^6*b^7*c^2*f^2 + 1504*a^7*b^5*c^3*f^2 - 3840*a^8*b^3*c^4*f^2 + 96
*a^8*b^5*c^2*g^2 - 512*a^9*b^3*c^3*g^2 + 615*a*b^13*c*d^2 - 10*a^2*b^13*d*f - 35840*a^8*c^7*d*e - 10*a^3*b^12*
d*g + 6*a^3*b^12*e*f + 6*a^4*b^11*e*g + 7168*a^9*c^6*d*g + 15360*a^9*c^6*e*f - 2*a^5*b^10*f*g - 3072*a^10*c^5*
f*g - 30*a*b^5*d*e*(-(4*a*c - b^2)^9)^(1/2) - 724*a^2*b^12*c*d*e + 258*a^3*b^11*c*d*f - 43520*a^8*b*c^6*d*f +
168*a^4*b^10*c*d*g - 152*a^4*b^10*c*e*f - 98*a^5*b^9*c*e*g + 1536*a^9*b*c^5*e*g + 2*a^5*b*f*g*(-(4*a*c - b^2)^
9)^(1/2) - 10*a^5*c*e*g*(-(4*a*c - b^2)^9)^(1/2) + 36*a^6*b^8*c*f*g + 246*a^2*b^2*c^2*d^2*(-(4*a*c - b^2)^9)^(
1/2) - 165*a*b^4*c*d^2*(-(4*a*c - b^2)^9)^(1/2) + 7278*a^3*b^10*c^2*d*e - 39132*a^4*b^8*c^3*d*e + 119616*a^5*b
^6*c^4*d*e - 201600*a^6*b^4*c^5*d*e + 161280*a^7*b^2*c^6*d*e + 10*a^2*b^4*d*f*(-(4*a*c - b^2)^9)^(1/2) - 2706*
a^4*b^9*c^2*d*f + 14784*a^5*b^7*c^3*d*f - 44352*a^6*b^5*c^4*d*f + 69120*a^7*b^3*c^5*d*f + 10*a^3*b^3*d*g*(-(4*
a*c - b^2)^9)^(1/2) - 6*a^3*b^3*e*f*(-(4*a*c - b^2)^9)^(1/2) + 42*a^4*c^2*d*f*(-(4*a*c - b^2)^9)^(1/2) - 1044*
a^5*b^8*c^2*d*g + 1548*a^5*b^8*c^2*e*f + 2688*a^6*b^6*c^3*d*g - 8064*a^6*b^6*c^3*e*f - 1152*a^7*b^4*c^4*d*g +
22400*a^7*b^4*c^4*e*f - 6144*a^8*b^2*c^5*d*g - 30720*a^8*b^2*c^5*e*f - 6*a^4*b^2*e*g*(-(4*a*c - b^2)^9)^(1/2)
+ 576*a^6*b^7*c^2*e*g - 1344*a^7*b^5*c^3*e*g + 512*a^8*b^3*c^4*e*g - 192*a^7*b^6*c^2*f*g + 128*a^8*b^4*c^3*f*g
+ 1536*a^9*b^2*c^4*f*g - 51*a^3*b^2*c*e^2*(-(4*a*c - b^2)^9)^(1/2) + 12*a^4*b*c*d*g*(-(4*a*c - b^2)^9)^(1/2)
+ 44*a^4*b*c*e*f*(-(4*a*c - b^2)^9)^(1/2) + 184*a^2*b^3*c*d*e*(-(4*a*c - b^2)^9)^(1/2) - 186*a^3*b*c^2*d*e*(-(
4*a*c - b^2)^9)^(1/2) - 78*a^3*b^2*c*d*f*(-(4*a*c - b^2)^9)^(1/2))/(32*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10
*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*2i

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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