3.20 \(\int \frac{1}{(a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3)^3} \, dx\)

Optimal. Leaf size=495 \[ \frac{3 b^5 \log (a+b x) \left (7 a^2 d^2 f^2-7 a b d f (c f+d e)+b^2 \left (2 c^2 f^2+3 c d e f+2 d^2 e^2\right )\right )}{(b c-a d)^5 (b e-a f)^5}-\frac{3 d^5 \log (c+d x) \left (2 a^2 d^2 f^2+a b d f (3 d e-7 c f)+b^2 \left (7 c^2 f^2-7 c d e f+2 d^2 e^2\right )\right )}{(b c-a d)^5 (d e-c f)^5}+\frac{3 f^5 \log (e+f x) \left (2 a^2 d^2 f^2-a b d f (7 d e-3 c f)+b^2 \left (2 c^2 f^2-7 c d e f+7 d^2 e^2\right )\right )}{(b e-a f)^5 (d e-c f)^5}+\frac{3 b^5 (-2 a d f+b c f+b d e)}{(a+b x) (b c-a d)^4 (b e-a f)^4}-\frac{b^5}{2 (a+b x)^2 (b c-a d)^3 (b e-a f)^3}+\frac{3 d^5 (a d f-2 b c f+b d e)}{(c+d x) (b c-a d)^4 (d e-c f)^4}+\frac{d^5}{2 (c+d x)^2 (b c-a d)^3 (d e-c f)^3}-\frac{3 f^5 (-a d f-b c f+2 b d e)}{(e+f x) (b e-a f)^4 (d e-c f)^4}-\frac{f^5}{2 (e+f x)^2 (b e-a f)^3 (d e-c f)^3} \]

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 1.46179, antiderivative size = 495, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 46, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.022, Rules used = {2058} \[ \frac{3 b^5 \log (a+b x) \left (7 a^2 d^2 f^2-7 a b d f (c f+d e)+b^2 \left (2 c^2 f^2+3 c d e f+2 d^2 e^2\right )\right )}{(b c-a d)^5 (b e-a f)^5}-\frac{3 d^5 \log (c+d x) \left (2 a^2 d^2 f^2+a b d f (3 d e-7 c f)+b^2 \left (7 c^2 f^2-7 c d e f+2 d^2 e^2\right )\right )}{(b c-a d)^5 (d e-c f)^5}+\frac{3 f^5 \log (e+f x) \left (2 a^2 d^2 f^2-a b d f (7 d e-3 c f)+b^2 \left (2 c^2 f^2-7 c d e f+7 d^2 e^2\right )\right )}{(b e-a f)^5 (d e-c f)^5}+\frac{3 b^5 (-2 a d f+b c f+b d e)}{(a+b x) (b c-a d)^4 (b e-a f)^4}-\frac{b^5}{2 (a+b x)^2 (b c-a d)^3 (b e-a f)^3}+\frac{3 d^5 (a d f-2 b c f+b d e)}{(c+d x) (b c-a d)^4 (d e-c f)^4}+\frac{d^5}{2 (c+d x)^2 (b c-a d)^3 (d e-c f)^3}-\frac{3 f^5 (-a d f-b c f+2 b d e)}{(e+f x) (b e-a f)^4 (d e-c f)^4}-\frac{f^5}{2 (e+f x)^2 (b e-a f)^3 (d e-c f)^3} \]

Antiderivative was successfully verified.

[In]

Int[(a*c*e + (b*c*e + a*d*e + a*c*f)*x + (b*d*e + b*c*f + a*d*f)*x^2 + b*d*f*x^3)^(-3),x]

[Out]

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

Rule 2058

Int[(P_)^(p_), x_Symbol] :> With[{u = Factor[P]}, Int[ExpandIntegrand[u^p, x], x] /;  !SumQ[NonfreeFactors[u,
x]]] /; PolyQ[P, x] && ILtQ[p, 0]

Rubi steps

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

Mathematica [A]  time = 1.2813, size = 490, normalized size = 0.99 \[ \frac{1}{2} \left (\frac{6 b^5 \log (a+b x) \left (7 a^2 d^2 f^2-7 a b d f (c f+d e)+b^2 \left (2 c^2 f^2+3 c d e f+2 d^2 e^2\right )\right )}{(b c-a d)^5 (b e-a f)^5}+\frac{6 d^5 \log (c+d x) \left (2 a^2 d^2 f^2+a b d f (3 d e-7 c f)+b^2 \left (7 c^2 f^2-7 c d e f+2 d^2 e^2\right )\right )}{(b c-a d)^5 (c f-d e)^5}+\frac{6 f^5 \log (e+f x) \left (2 a^2 d^2 f^2+a b d f (3 c f-7 d e)+b^2 \left (2 c^2 f^2-7 c d e f+7 d^2 e^2\right )\right )}{(b e-a f)^5 (d e-c f)^5}+\frac{6 b^5 (-2 a d f+b c f+b d e)}{(a+b x) (b c-a d)^4 (b e-a f)^4}-\frac{b^5}{(a+b x)^2 (b c-a d)^3 (b e-a f)^3}+\frac{6 d^5 (a d f-2 b c f+b d e)}{(c+d x) (b c-a d)^4 (d e-c f)^4}-\frac{d^5}{(c+d x)^2 (b c-a d)^3 (c f-d e)^3}+\frac{6 f^5 (a d f+b c f-2 b d e)}{(e+f x) (b e-a f)^4 (d e-c f)^4}-\frac{f^5}{(e+f x)^2 (b e-a f)^3 (d e-c f)^3}\right ) \]

Antiderivative was successfully verified.

[In]

Integrate[(a*c*e + (b*c*e + a*d*e + a*c*f)*x + (b*d*e + b*c*f + a*d*f)*x^2 + b*d*f*x^3)^(-3),x]

[Out]

(-(b^5/((b*c - a*d)^3*(b*e - a*f)^3*(a + b*x)^2)) + (6*b^5*(b*d*e + b*c*f - 2*a*d*f))/((b*c - a*d)^4*(b*e - a*
f)^4*(a + b*x)) - d^5/((b*c - a*d)^3*(-(d*e) + c*f)^3*(c + d*x)^2) + (6*d^5*(b*d*e - 2*b*c*f + a*d*f))/((b*c -
a*d)^4*(d*e - c*f)^4*(c + d*x)) - f^5/((b*e - a*f)^3*(d*e - c*f)^3*(e + f*x)^2) + (6*f^5*(-2*b*d*e + b*c*f +
a*d*f))/((b*e - a*f)^4*(d*e - c*f)^4*(e + f*x)) + (6*b^5*(7*a^2*d^2*f^2 - 7*a*b*d*f*(d*e + c*f) + b^2*(2*d^2*e
^2 + 3*c*d*e*f + 2*c^2*f^2))*Log[a + b*x])/((b*c - a*d)^5*(b*e - a*f)^5) + (6*d^5*(2*a^2*d^2*f^2 + a*b*d*f*(3*
d*e - 7*c*f) + b^2*(2*d^2*e^2 - 7*c*d*e*f + 7*c^2*f^2))*Log[c + d*x])/((b*c - a*d)^5*(-(d*e) + c*f)^5) + (6*f^
5*(2*a^2*d^2*f^2 + a*b*d*f*(-7*d*e + 3*c*f) + b^2*(7*d^2*e^2 - 7*c*d*e*f + 2*c^2*f^2))*Log[e + f*x])/((b*e - a
*f)^5*(d*e - c*f)^5))/2

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Maple [B]  time = 0.032, size = 1076, normalized size = 2.2 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^3,x)

[Out]

6*f^7/(c*f-d*e)^5/(a*f-b*e)^5*ln(f*x+e)*a^2*d^2+6*f^7/(c*f-d*e)^5/(a*f-b*e)^5*ln(f*x+e)*c^2*b^2-6*d^7/(c*f-d*e
)^5/(a*d-b*c)^5*ln(d*x+c)*a^2*f^2-6*d^7/(c*f-d*e)^5/(a*d-b*c)^5*ln(d*x+c)*e^2*b^2+3*f^6/(c*f-d*e)^4/(a*f-b*e)^
4/(f*x+e)*a*d+3*f^6/(c*f-d*e)^4/(a*f-b*e)^4/(f*x+e)*b*c+3*b^6/(a*f-b*e)^4/(a*d-b*c)^4/(b*x+a)*d*e+6*b^7/(a*f-b
*e)^5/(a*d-b*c)^5*ln(b*x+a)*c^2*f^2+6*b^7/(a*f-b*e)^5/(a*d-b*c)^5*ln(b*x+a)*e^2*d^2+3*d^6/(c*f-d*e)^4/(a*d-b*c
)^4/(d*x+c)*a*f+3*d^6/(c*f-d*e)^4/(a*d-b*c)^4/(d*x+c)*b*e+3*b^6/(a*f-b*e)^4/(a*d-b*c)^4/(b*x+a)*c*f+1/2*d^5/(c
*f-d*e)^3/(a*d-b*c)^3/(d*x+c)^2-1/2*f^5/(c*f-d*e)^3/(a*f-b*e)^3/(f*x+e)^2-1/2*b^5/(a*f-b*e)^3/(a*d-b*c)^3/(b*x
+a)^2-6*b^5/(a*f-b*e)^4/(a*d-b*c)^4/(b*x+a)*a*d*f+21*b^5/(a*f-b*e)^5/(a*d-b*c)^5*ln(b*x+a)*a^2*d^2*f^2-6*d^5/(
c*f-d*e)^4/(a*d-b*c)^4/(d*x+c)*b*c*f-21*d^5/(c*f-d*e)^5/(a*d-b*c)^5*ln(d*x+c)*c^2*f^2*b^2-6*f^5/(c*f-d*e)^4/(a
*f-b*e)^4/(f*x+e)*b*d*e+21*f^5/(c*f-d*e)^5/(a*f-b*e)^5*ln(f*x+e)*e^2*d^2*b^2+9*f^7/(c*f-d*e)^5/(a*f-b*e)^5*ln(
f*x+e)*a*b*c*d-21*f^6/(c*f-d*e)^5/(a*f-b*e)^5*ln(f*x+e)*a*b*d^2*e+21*d^6/(c*f-d*e)^5/(a*d-b*c)^5*ln(d*x+c)*c*e
*f*b^2-21*b^6/(a*f-b*e)^5/(a*d-b*c)^5*ln(b*x+a)*a*d^2*e*f+9*b^7/(a*f-b*e)^5/(a*d-b*c)^5*ln(b*x+a)*c*d*e*f+21*d
^6/(c*f-d*e)^5/(a*d-b*c)^5*ln(d*x+c)*a*b*c*f^2-9*d^7/(c*f-d*e)^5/(a*d-b*c)^5*ln(d*x+c)*a*b*e*f-21*b^6/(a*f-b*e
)^5/(a*d-b*c)^5*ln(b*x+a)*a*c*d*f^2-21*f^6/(c*f-d*e)^5/(a*f-b*e)^5*ln(f*x+e)*c*d*e*b^2

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Maxima [B]  time = 4.52537, size = 14857, normalized size = 30.01 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^3,x, algorithm="maxima")

[Out]

3*(2*b^7*d^2*e^2 + (3*b^7*c*d - 7*a*b^6*d^2)*e*f + (2*b^7*c^2 - 7*a*b^6*c*d + 7*a^2*b^5*d^2)*f^2)*log(b*x + a)
/((b^10*c^5 - 5*a*b^9*c^4*d + 10*a^2*b^8*c^3*d^2 - 10*a^3*b^7*c^2*d^3 + 5*a^4*b^6*c*d^4 - a^5*b^5*d^5)*e^5 - 5
*(a*b^9*c^5 - 5*a^2*b^8*c^4*d + 10*a^3*b^7*c^3*d^2 - 10*a^4*b^6*c^2*d^3 + 5*a^5*b^5*c*d^4 - a^6*b^4*d^5)*e^4*f
+ 10*(a^2*b^8*c^5 - 5*a^3*b^7*c^4*d + 10*a^4*b^6*c^3*d^2 - 10*a^5*b^5*c^2*d^3 + 5*a^6*b^4*c*d^4 - a^7*b^3*d^5
)*e^3*f^2 - 10*(a^3*b^7*c^5 - 5*a^4*b^6*c^4*d + 10*a^5*b^5*c^3*d^2 - 10*a^6*b^4*c^2*d^3 + 5*a^7*b^3*c*d^4 - a^
8*b^2*d^5)*e^2*f^3 + 5*(a^4*b^6*c^5 - 5*a^5*b^5*c^4*d + 10*a^6*b^4*c^3*d^2 - 10*a^7*b^3*c^2*d^3 + 5*a^8*b^2*c*
d^4 - a^9*b*d^5)*e*f^4 - (a^5*b^5*c^5 - 5*a^6*b^4*c^4*d + 10*a^7*b^3*c^3*d^2 - 10*a^8*b^2*c^2*d^3 + 5*a^9*b*c*
d^4 - a^10*d^5)*f^5) - 3*(2*b^2*d^7*e^2 - (7*b^2*c*d^6 - 3*a*b*d^7)*e*f + (7*b^2*c^2*d^5 - 7*a*b*c*d^6 + 2*a^2
*d^7)*f^2)*log(d*x + c)/((b^5*c^5*d^5 - 5*a*b^4*c^4*d^6 + 10*a^2*b^3*c^3*d^7 - 10*a^3*b^2*c^2*d^8 + 5*a^4*b*c*
d^9 - a^5*d^10)*e^5 - 5*(b^5*c^6*d^4 - 5*a*b^4*c^5*d^5 + 10*a^2*b^3*c^4*d^6 - 10*a^3*b^2*c^3*d^7 + 5*a^4*b*c^2
*d^8 - a^5*c*d^9)*e^4*f + 10*(b^5*c^7*d^3 - 5*a*b^4*c^6*d^4 + 10*a^2*b^3*c^5*d^5 - 10*a^3*b^2*c^4*d^6 + 5*a^4*
b*c^3*d^7 - a^5*c^2*d^8)*e^3*f^2 - 10*(b^5*c^8*d^2 - 5*a*b^4*c^7*d^3 + 10*a^2*b^3*c^6*d^4 - 10*a^3*b^2*c^5*d^5
+ 5*a^4*b*c^4*d^6 - a^5*c^3*d^7)*e^2*f^3 + 5*(b^5*c^9*d - 5*a*b^4*c^8*d^2 + 10*a^2*b^3*c^7*d^3 - 10*a^3*b^2*c
^6*d^4 + 5*a^4*b*c^5*d^5 - a^5*c^4*d^6)*e*f^4 - (b^5*c^10 - 5*a*b^4*c^9*d + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^
7*d^3 + 5*a^4*b*c^6*d^4 - a^5*c^5*d^5)*f^5) + 3*(7*b^2*d^2*e^2*f^5 - 7*(b^2*c*d + a*b*d^2)*e*f^6 + (2*b^2*c^2
+ 3*a*b*c*d + 2*a^2*d^2)*f^7)*log(f*x + e)/(b^5*d^5*e^10 + a^5*c^5*f^10 - 5*(b^5*c*d^4 + a*b^4*d^5)*e^9*f + 5*
(2*b^5*c^2*d^3 + 5*a*b^4*c*d^4 + 2*a^2*b^3*d^5)*e^8*f^2 - 10*(b^5*c^3*d^2 + 5*a*b^4*c^2*d^3 + 5*a^2*b^3*c*d^4
+ a^3*b^2*d^5)*e^7*f^3 + 5*(b^5*c^4*d + 10*a*b^4*c^3*d^2 + 20*a^2*b^3*c^2*d^3 + 10*a^3*b^2*c*d^4 + a^4*b*d^5)*
e^6*f^4 - (b^5*c^5 + 25*a*b^4*c^4*d + 100*a^2*b^3*c^3*d^2 + 100*a^3*b^2*c^2*d^3 + 25*a^4*b*c*d^4 + a^5*d^5)*e^
5*f^5 + 5*(a*b^4*c^5 + 10*a^2*b^3*c^4*d + 20*a^3*b^2*c^3*d^2 + 10*a^4*b*c^2*d^3 + a^5*c*d^4)*e^4*f^6 - 10*(a^2
*b^3*c^5 + 5*a^3*b^2*c^4*d + 5*a^4*b*c^3*d^2 + a^5*c^2*d^3)*e^3*f^7 + 5*(2*a^3*b^2*c^5 + 5*a^4*b*c^4*d + 2*a^5
*c^3*d^2)*e^2*f^8 - 5*(a^4*b*c^5 + a^5*c^4*d)*e*f^9) - 1/2*((b^7*c^3*d^4 - 7*a*b^6*c^2*d^5 - 7*a^2*b^5*c*d^6 +
a^3*b^4*d^7)*e^7 - (4*b^7*c^4*d^3 - 21*a*b^6*c^3*d^4 - 26*a^2*b^5*c^2*d^5 - 21*a^3*b^4*c*d^6 + 4*a^4*b^3*d^7)
*e^6*f + 2*(3*b^7*c^5*d^2 - 7*a*b^6*c^4*d^3 - 26*a^2*b^5*c^3*d^4 - 26*a^3*b^4*c^2*d^5 - 7*a^4*b^3*c*d^6 + 3*a^
5*b^2*d^7)*e^5*f^2 - 2*(2*b^7*c^6*d + 7*a*b^6*c^5*d^2 - 39*a^2*b^5*c^4*d^3 - 39*a^4*b^3*c^2*d^5 + 7*a^5*b^2*c*
d^6 + 2*a^6*b*d^7)*e^4*f^3 + (b^7*c^7 + 21*a*b^6*c^6*d - 52*a^2*b^5*c^5*d^2 - 52*a^5*b^2*c^2*d^5 + 21*a^6*b*c*
d^6 + a^7*d^7)*e^3*f^4 - (7*a*b^6*c^7 - 26*a^2*b^5*c^6*d + 52*a^3*b^4*c^5*d^2 - 78*a^4*b^3*c^4*d^3 + 52*a^5*b^
2*c^3*d^4 - 26*a^6*b*c^2*d^5 + 7*a^7*c*d^6)*e^2*f^5 - 7*(a^2*b^5*c^7 - 3*a^3*b^4*c^6*d + 2*a^4*b^3*c^5*d^2 + 2
*a^5*b^2*c^4*d^3 - 3*a^6*b*c^3*d^4 + a^7*c^2*d^5)*e*f^6 + (a^3*b^4*c^7 - 4*a^4*b^3*c^6*d + 6*a^5*b^2*c^5*d^2 -
4*a^6*b*c^4*d^3 + a^7*c^3*d^4)*f^7 - 6*(2*b^7*d^7*e^5*f^2 - 5*(b^7*c*d^6 + a*b^6*d^7)*e^4*f^3 + 2*(b^7*c^2*d^
5 + 8*a*b^6*c*d^6 + a^2*b^5*d^7)*e^3*f^4 + 2*(b^7*c^3*d^4 - 6*a*b^6*c^2*d^5 - 6*a^2*b^5*c*d^6 + a^3*b^4*d^7)*e
^2*f^5 - (5*b^7*c^4*d^3 - 16*a*b^6*c^3*d^4 + 12*a^2*b^5*c^2*d^5 - 16*a^3*b^4*c*d^6 + 5*a^4*b^3*d^7)*e*f^6 + (2
*b^7*c^5*d^2 - 5*a*b^6*c^4*d^3 + 2*a^2*b^5*c^3*d^4 + 2*a^3*b^4*c^2*d^5 - 5*a^4*b^3*c*d^6 + 2*a^5*b^2*d^7)*f^7)
*x^5 - 3*(8*b^7*d^7*e^6*f - 14*(b^7*c*d^6 + a*b^6*d^7)*e^5*f^2 - (7*b^7*c^2*d^5 - 34*a*b^6*c*d^6 + 7*a^2*b^5*d
^7)*e^4*f^3 + 2*(7*b^7*c^3*d^4 + 3*a*b^6*c^2*d^5 + 3*a^2*b^5*c*d^6 + 7*a^3*b^4*d^7)*e^3*f^4 - (7*b^7*c^4*d^3 -
6*a*b^6*c^3*d^4 + 78*a^2*b^5*c^2*d^5 - 6*a^3*b^4*c*d^6 + 7*a^4*b^3*d^7)*e^2*f^5 - 2*(7*b^7*c^5*d^2 - 17*a*b^6
*c^4*d^3 - 3*a^2*b^5*c^3*d^4 - 3*a^3*b^4*c^2*d^5 - 17*a^4*b^3*c*d^6 + 7*a^5*b^2*d^7)*e*f^6 + (8*b^7*c^6*d - 14
*a*b^6*c^5*d^2 - 7*a^2*b^5*c^4*d^3 + 14*a^3*b^4*c^3*d^4 - 7*a^4*b^3*c^2*d^5 - 14*a^5*b^2*c*d^6 + 8*a^6*b*d^7)*
f^7)*x^4 - 2*(6*b^7*d^7*e^7 + 3*(b^7*c*d^6 + a*b^6*d^7)*e^6*f - (37*b^7*c^2*d^5 + 28*a*b^6*c*d^6 + 37*a^2*b^5*
d^7)*e^5*f^2 + (19*b^7*c^3*d^4 + 86*a*b^6*c^2*d^5 + 86*a^2*b^5*c*d^6 + 19*a^3*b^4*d^7)*e^4*f^3 + (19*b^7*c^4*d
^3 - 68*a*b^6*c^3*d^4 - 52*a^2*b^5*c^2*d^5 - 68*a^3*b^4*c*d^6 + 19*a^4*b^3*d^7)*e^3*f^4 - (37*b^7*c^5*d^2 - 86
*a*b^6*c^4*d^3 + 52*a^2*b^5*c^3*d^4 + 52*a^3*b^4*c^2*d^5 - 86*a^4*b^3*c*d^6 + 37*a^5*b^2*d^7)*e^2*f^5 + (3*b^7
*c^6*d - 28*a*b^6*c^5*d^2 + 86*a^2*b^5*c^4*d^3 - 68*a^3*b^4*c^3*d^4 + 86*a^4*b^3*c^2*d^5 - 28*a^5*b^2*c*d^6 +
3*a^6*b*d^7)*e*f^6 + (6*b^7*c^7 + 3*a*b^6*c^6*d - 37*a^2*b^5*c^5*d^2 + 19*a^3*b^4*c^4*d^3 + 19*a^4*b^3*c^3*d^4
- 37*a^5*b^2*c^2*d^5 + 3*a^6*b*c*d^6 + 6*a^7*d^7)*f^7)*x^3 - (18*(b^7*c*d^6 + a*b^6*d^7)*e^7 - (37*b^7*c^2*d^
5 + 34*a*b^6*c*d^6 + 37*a^2*b^5*d^7)*e^6*f - 3*(b^7*c^3*d^4 - 3*a*b^6*c^2*d^5 - 3*a^2*b^5*c*d^6 + a^3*b^4*d^7)
*e^5*f^2 + (32*b^7*c^4*d^3 + a*b^6*c^3*d^4 + 234*a^2*b^5*c^2*d^5 + a^3*b^4*c*d^6 + 32*a^4*b^3*d^7)*e^4*f^3 - (
3*b^7*c^5*d^2 - a*b^6*c^4*d^3 + 208*a^2*b^5*c^3*d^4 + 208*a^3*b^4*c^2*d^5 - a^4*b^3*c*d^6 + 3*a^5*b^2*d^7)*e^3
*f^4 - (37*b^7*c^6*d - 9*a*b^6*c^5*d^2 - 234*a^2*b^5*c^4*d^3 + 208*a^3*b^4*c^3*d^4 - 234*a^4*b^3*c^2*d^5 - 9*a
^5*b^2*c*d^6 + 37*a^6*b*d^7)*e^2*f^5 + (18*b^7*c^7 - 34*a*b^6*c^6*d + 9*a^2*b^5*c^5*d^2 + a^3*b^4*c^4*d^3 + a^
4*b^3*c^3*d^4 + 9*a^5*b^2*c^2*d^5 - 34*a^6*b*c*d^6 + 18*a^7*d^7)*e*f^6 + (18*a*b^6*c^7 - 37*a^2*b^5*c^6*d - 3*
a^3*b^4*c^5*d^2 + 32*a^4*b^3*c^4*d^3 - 3*a^5*b^2*c^3*d^4 - 37*a^6*b*c^2*d^5 + 18*a^7*c*d^6)*f^7)*x^2 - 2*(2*(b
^7*c^2*d^5 + 7*a*b^6*c*d^6 + a^2*b^5*d^7)*e^7 - 3*(2*b^7*c^3*d^4 + 11*a*b^6*c^2*d^5 + 11*a^2*b^5*c*d^6 + 2*a^3
*b^4*d^7)*e^6*f + (4*b^7*c^4*d^3 + 17*a*b^6*c^3*d^4 + 78*a^2*b^5*c^2*d^5 + 17*a^3*b^4*c*d^6 + 4*a^4*b^3*d^7)*e
^5*f^2 + 2*(2*b^7*c^5*d^2 - 4*a*b^6*c^4*d^3 - 13*a^2*b^5*c^3*d^4 - 13*a^3*b^4*c^2*d^5 - 4*a^4*b^3*c*d^6 + 2*a^
5*b^2*d^7)*e^4*f^3 - (6*b^7*c^6*d - 17*a*b^6*c^5*d^2 + 26*a^2*b^5*c^4*d^3 + 26*a^4*b^3*c^2*d^5 - 17*a^5*b^2*c*
d^6 + 6*a^6*b*d^7)*e^3*f^4 + (2*b^7*c^7 - 33*a*b^6*c^6*d + 78*a^2*b^5*c^5*d^2 - 26*a^3*b^4*c^4*d^3 - 26*a^4*b^
3*c^3*d^4 + 78*a^5*b^2*c^2*d^5 - 33*a^6*b*c*d^6 + 2*a^7*d^7)*e^2*f^5 + (14*a*b^6*c^7 - 33*a^2*b^5*c^6*d + 17*a
^3*b^4*c^5*d^2 - 8*a^4*b^3*c^4*d^3 + 17*a^5*b^2*c^3*d^4 - 33*a^6*b*c^2*d^5 + 14*a^7*c*d^6)*e*f^6 + 2*(a^2*b^5*
c^7 - 3*a^3*b^4*c^6*d + 2*a^4*b^3*c^5*d^2 + 2*a^5*b^2*c^4*d^3 - 3*a^6*b*c^3*d^4 + a^7*c^2*d^5)*f^7)*x)/((a^2*b
^8*c^6*d^4 - 4*a^3*b^7*c^5*d^5 + 6*a^4*b^6*c^4*d^6 - 4*a^5*b^5*c^3*d^7 + a^6*b^4*c^2*d^8)*e^10 - 4*(a^2*b^8*c^
7*d^3 - 3*a^3*b^7*c^6*d^4 + 2*a^4*b^6*c^5*d^5 + 2*a^5*b^5*c^4*d^6 - 3*a^6*b^4*c^3*d^7 + a^7*b^3*c^2*d^8)*e^9*f
+ 2*(3*a^2*b^8*c^8*d^2 - 4*a^3*b^7*c^7*d^3 - 11*a^4*b^6*c^6*d^4 + 24*a^5*b^5*c^5*d^5 - 11*a^6*b^4*c^4*d^6 - 4
*a^7*b^3*c^3*d^7 + 3*a^8*b^2*c^2*d^8)*e^8*f^2 - 4*(a^2*b^8*c^9*d + 2*a^3*b^7*c^8*d^2 - 12*a^4*b^6*c^7*d^3 + 9*
a^5*b^5*c^6*d^4 + 9*a^6*b^4*c^5*d^5 - 12*a^7*b^3*c^4*d^6 + 2*a^8*b^2*c^3*d^7 + a^9*b*c^2*d^8)*e^7*f^3 + (a^2*b
^8*c^10 + 12*a^3*b^7*c^9*d - 22*a^4*b^6*c^8*d^2 - 36*a^5*b^5*c^7*d^3 + 90*a^6*b^4*c^6*d^4 - 36*a^7*b^3*c^5*d^5
- 22*a^8*b^2*c^4*d^6 + 12*a^9*b*c^3*d^7 + a^10*c^2*d^8)*e^6*f^4 - 4*(a^3*b^7*c^10 + 2*a^4*b^6*c^9*d - 12*a^5*
b^5*c^8*d^2 + 9*a^6*b^4*c^7*d^3 + 9*a^7*b^3*c^6*d^4 - 12*a^8*b^2*c^5*d^5 + 2*a^9*b*c^4*d^6 + a^10*c^3*d^7)*e^5
*f^5 + 2*(3*a^4*b^6*c^10 - 4*a^5*b^5*c^9*d - 11*a^6*b^4*c^8*d^2 + 24*a^7*b^3*c^7*d^3 - 11*a^8*b^2*c^6*d^4 - 4*
a^9*b*c^5*d^5 + 3*a^10*c^4*d^6)*e^4*f^6 - 4*(a^5*b^5*c^10 - 3*a^6*b^4*c^9*d + 2*a^7*b^3*c^8*d^2 + 2*a^8*b^2*c^
7*d^3 - 3*a^9*b*c^6*d^4 + a^10*c^5*d^5)*e^3*f^7 + (a^6*b^4*c^10 - 4*a^7*b^3*c^9*d + 6*a^8*b^2*c^8*d^2 - 4*a^9*
b*c^7*d^3 + a^10*c^6*d^4)*e^2*f^8 + ((b^10*c^4*d^6 - 4*a*b^9*c^3*d^7 + 6*a^2*b^8*c^2*d^8 - 4*a^3*b^7*c*d^9 + a
^4*b^6*d^10)*e^8*f^2 - 4*(b^10*c^5*d^5 - 3*a*b^9*c^4*d^6 + 2*a^2*b^8*c^3*d^7 + 2*a^3*b^7*c^2*d^8 - 3*a^4*b^6*c
*d^9 + a^5*b^5*d^10)*e^7*f^3 + 2*(3*b^10*c^6*d^4 - 4*a*b^9*c^5*d^5 - 11*a^2*b^8*c^4*d^6 + 24*a^3*b^7*c^3*d^7 -
11*a^4*b^6*c^2*d^8 - 4*a^5*b^5*c*d^9 + 3*a^6*b^4*d^10)*e^6*f^4 - 4*(b^10*c^7*d^3 + 2*a*b^9*c^6*d^4 - 12*a^2*b
^8*c^5*d^5 + 9*a^3*b^7*c^4*d^6 + 9*a^4*b^6*c^3*d^7 - 12*a^5*b^5*c^2*d^8 + 2*a^6*b^4*c*d^9 + a^7*b^3*d^10)*e^5*
f^5 + (b^10*c^8*d^2 + 12*a*b^9*c^7*d^3 - 22*a^2*b^8*c^6*d^4 - 36*a^3*b^7*c^5*d^5 + 90*a^4*b^6*c^4*d^6 - 36*a^5
*b^5*c^3*d^7 - 22*a^6*b^4*c^2*d^8 + 12*a^7*b^3*c*d^9 + a^8*b^2*d^10)*e^4*f^6 - 4*(a*b^9*c^8*d^2 + 2*a^2*b^8*c^
7*d^3 - 12*a^3*b^7*c^6*d^4 + 9*a^4*b^6*c^5*d^5 + 9*a^5*b^5*c^4*d^6 - 12*a^6*b^4*c^3*d^7 + 2*a^7*b^3*c^2*d^8 +
a^8*b^2*c*d^9)*e^3*f^7 + 2*(3*a^2*b^8*c^8*d^2 - 4*a^3*b^7*c^7*d^3 - 11*a^4*b^6*c^6*d^4 + 24*a^5*b^5*c^5*d^5 -
11*a^6*b^4*c^4*d^6 - 4*a^7*b^3*c^3*d^7 + 3*a^8*b^2*c^2*d^8)*e^2*f^8 - 4*(a^3*b^7*c^8*d^2 - 3*a^4*b^6*c^7*d^3 +
2*a^5*b^5*c^6*d^4 + 2*a^6*b^4*c^5*d^5 - 3*a^7*b^3*c^4*d^6 + a^8*b^2*c^3*d^7)*e*f^9 + (a^4*b^6*c^8*d^2 - 4*a^5
*b^5*c^7*d^3 + 6*a^6*b^4*c^6*d^4 - 4*a^7*b^3*c^5*d^5 + a^8*b^2*c^4*d^6)*f^10)*x^6 + 2*((b^10*c^4*d^6 - 4*a*b^9
*c^3*d^7 + 6*a^2*b^8*c^2*d^8 - 4*a^3*b^7*c*d^9 + a^4*b^6*d^10)*e^9*f - 3*(b^10*c^5*d^5 - 3*a*b^9*c^4*d^6 + 2*a
^2*b^8*c^3*d^7 + 2*a^3*b^7*c^2*d^8 - 3*a^4*b^6*c*d^9 + a^5*b^5*d^10)*e^8*f^2 + 2*(b^10*c^6*d^4 - 9*a^2*b^8*c^4
*d^6 + 16*a^3*b^7*c^3*d^7 - 9*a^4*b^6*c^2*d^8 + a^6*b^4*d^10)*e^7*f^3 + 2*(b^10*c^7*d^3 - 5*a*b^9*c^6*d^4 + 9*
a^2*b^8*c^5*d^5 - 5*a^3*b^7*c^4*d^6 - 5*a^4*b^6*c^3*d^7 + 9*a^5*b^5*c^2*d^8 - 5*a^6*b^4*c*d^9 + a^7*b^3*d^10)*
e^6*f^4 - 3*(b^10*c^8*d^2 - 6*a^2*b^8*c^6*d^4 + 8*a^3*b^7*c^5*d^5 - 6*a^4*b^6*c^4*d^6 + 8*a^5*b^5*c^3*d^7 - 6*
a^6*b^4*c^2*d^8 + a^8*b^2*d^10)*e^5*f^5 + (b^10*c^9*d + 9*a*b^9*c^8*d^2 - 18*a^2*b^8*c^7*d^3 - 10*a^3*b^7*c^6*
d^4 + 18*a^4*b^6*c^5*d^5 + 18*a^5*b^5*c^4*d^6 - 10*a^6*b^4*c^3*d^7 - 18*a^7*b^3*c^2*d^8 + 9*a^8*b^2*c*d^9 + a^
9*b*d^10)*e^4*f^6 - 2*(2*a*b^9*c^9*d + 3*a^2*b^8*c^8*d^2 - 16*a^3*b^7*c^7*d^3 + 5*a^4*b^6*c^6*d^4 + 12*a^5*b^5
*c^5*d^5 + 5*a^6*b^4*c^4*d^6 - 16*a^7*b^3*c^3*d^7 + 3*a^8*b^2*c^2*d^8 + 2*a^9*b*c*d^9)*e^3*f^7 + 6*(a^2*b^8*c^
9*d - a^3*b^7*c^8*d^2 - 3*a^4*b^6*c^7*d^3 + 3*a^5*b^5*c^6*d^4 + 3*a^6*b^4*c^5*d^5 - 3*a^7*b^3*c^4*d^6 - a^8*b^
2*c^3*d^7 + a^9*b*c^2*d^8)*e^2*f^8 - (4*a^3*b^7*c^9*d - 9*a^4*b^6*c^8*d^2 + 10*a^6*b^4*c^6*d^4 - 9*a^8*b^2*c^4
*d^6 + 4*a^9*b*c^3*d^7)*e*f^9 + (a^4*b^6*c^9*d - 3*a^5*b^5*c^8*d^2 + 2*a^6*b^4*c^7*d^3 + 2*a^7*b^3*c^6*d^4 - 3
*a^8*b^2*c^5*d^5 + a^9*b*c^4*d^6)*f^10)*x^5 + ((b^10*c^4*d^6 - 4*a*b^9*c^3*d^7 + 6*a^2*b^8*c^2*d^8 - 4*a^3*b^7
*c*d^9 + a^4*b^6*d^10)*e^10 - 3*(3*b^10*c^6*d^4 - 8*a*b^9*c^5*d^5 + 5*a^2*b^8*c^4*d^6 + 5*a^4*b^6*c^2*d^8 - 8*
a^5*b^5*c*d^9 + 3*a^6*b^4*d^10)*e^8*f^2 + 4*(4*b^10*c^7*d^3 - 5*a*b^9*c^6*d^4 - 9*a^2*b^8*c^5*d^5 + 10*a^3*b^7
*c^4*d^6 + 10*a^4*b^6*c^3*d^7 - 9*a^5*b^5*c^2*d^8 - 5*a^6*b^4*c*d^9 + 4*a^7*b^3*d^10)*e^7*f^3 - (9*b^10*c^8*d^
2 + 20*a*b^9*c^7*d^3 - 90*a^2*b^8*c^6*d^4 + 36*a^3*b^7*c^5*d^5 + 50*a^4*b^6*c^4*d^6 + 36*a^5*b^5*c^3*d^7 - 90*
a^6*b^4*c^2*d^8 + 20*a^7*b^3*c*d^9 + 9*a^8*b^2*d^10)*e^6*f^4 + 12*(2*a*b^9*c^8*d^2 - 3*a^2*b^8*c^7*d^3 - 3*a^3
*b^7*c^6*d^4 + 4*a^4*b^6*c^5*d^5 + 4*a^5*b^5*c^4*d^6 - 3*a^6*b^4*c^3*d^7 - 3*a^7*b^3*c^2*d^8 + 2*a^8*b^2*c*d^9
)*e^5*f^5 + (b^10*c^10 - 15*a^2*b^8*c^8*d^2 + 40*a^3*b^7*c^7*d^3 - 50*a^4*b^6*c^6*d^4 + 48*a^5*b^5*c^5*d^5 - 5
0*a^6*b^4*c^4*d^6 + 40*a^7*b^3*c^3*d^7 - 15*a^8*b^2*c^2*d^8 + a^10*d^10)*e^4*f^6 - 4*(a*b^9*c^10 - 10*a^4*b^6*
c^7*d^3 + 9*a^5*b^5*c^6*d^4 + 9*a^6*b^4*c^5*d^5 - 10*a^7*b^3*c^4*d^6 + a^10*c*d^9)*e^3*f^7 + 3*(2*a^2*b^8*c^10
- 5*a^4*b^6*c^8*d^2 - 12*a^5*b^5*c^7*d^3 + 30*a^6*b^4*c^6*d^4 - 12*a^7*b^3*c^5*d^5 - 5*a^8*b^2*c^4*d^6 + 2*a^
10*c^2*d^8)*e^2*f^8 - 4*(a^3*b^7*c^10 - 6*a^5*b^5*c^8*d^2 + 5*a^6*b^4*c^7*d^3 + 5*a^7*b^3*c^6*d^4 - 6*a^8*b^2*
c^5*d^5 + a^10*c^3*d^7)*e*f^9 + (a^4*b^6*c^10 - 9*a^6*b^4*c^8*d^2 + 16*a^7*b^3*c^7*d^3 - 9*a^8*b^2*c^6*d^4 + a
^10*c^4*d^6)*f^10)*x^4 + 2*((b^10*c^5*d^5 - 3*a*b^9*c^4*d^6 + 2*a^2*b^8*c^3*d^7 + 2*a^3*b^7*c^2*d^8 - 3*a^4*b^
6*c*d^9 + a^5*b^5*d^10)*e^10 - (3*b^10*c^6*d^4 - 8*a*b^9*c^5*d^5 + 5*a^2*b^8*c^4*d^6 + 5*a^4*b^6*c^2*d^8 - 8*a
^5*b^5*c*d^9 + 3*a^6*b^4*d^10)*e^9*f + (2*b^10*c^7*d^3 - 5*a*b^9*c^6*d^4 + 3*a^2*b^8*c^5*d^5 + 3*a^5*b^5*c^2*d
^8 - 5*a^6*b^4*c*d^9 + 2*a^7*b^3*d^10)*e^8*f^2 + 2*(b^10*c^8*d^2 - 16*a^3*b^7*c^5*d^5 + 30*a^4*b^6*c^4*d^6 - 1
6*a^5*b^5*c^3*d^7 + a^8*b^2*d^10)*e^7*f^3 - (3*b^10*c^9*d + 5*a*b^9*c^8*d^2 - 60*a^3*b^7*c^6*d^4 + 52*a^4*b^6*
c^5*d^5 + 52*a^5*b^5*c^4*d^6 - 60*a^6*b^4*c^3*d^7 + 5*a^8*b^2*c*d^9 + 3*a^9*b*d^10)*e^6*f^4 + (b^10*c^10 + 8*a
*b^9*c^9*d + 3*a^2*b^8*c^8*d^2 - 32*a^3*b^7*c^7*d^3 - 52*a^4*b^6*c^6*d^4 + 144*a^5*b^5*c^5*d^5 - 52*a^6*b^4*c^
4*d^6 - 32*a^7*b^3*c^3*d^7 + 3*a^8*b^2*c^2*d^8 + 8*a^9*b*c*d^9 + a^10*d^10)*e^5*f^5 - (3*a*b^9*c^10 + 5*a^2*b^
8*c^9*d - 60*a^4*b^6*c^7*d^3 + 52*a^5*b^5*c^6*d^4 + 52*a^6*b^4*c^5*d^5 - 60*a^7*b^3*c^4*d^6 + 5*a^9*b*c^2*d^8
+ 3*a^10*c*d^9)*e^4*f^6 + 2*(a^2*b^8*c^10 - 16*a^5*b^5*c^7*d^3 + 30*a^6*b^4*c^6*d^4 - 16*a^7*b^3*c^5*d^5 + a^1
0*c^2*d^8)*e^3*f^7 + (2*a^3*b^7*c^10 - 5*a^4*b^6*c^9*d + 3*a^5*b^5*c^8*d^2 + 3*a^8*b^2*c^5*d^5 - 5*a^9*b*c^4*d
^6 + 2*a^10*c^3*d^7)*e^2*f^8 - (3*a^4*b^6*c^10 - 8*a^5*b^5*c^9*d + 5*a^6*b^4*c^8*d^2 + 5*a^8*b^2*c^6*d^4 - 8*a
^9*b*c^5*d^5 + 3*a^10*c^4*d^6)*e*f^9 + (a^5*b^5*c^10 - 3*a^6*b^4*c^9*d + 2*a^7*b^3*c^8*d^2 + 2*a^8*b^2*c^7*d^3
- 3*a^9*b*c^6*d^4 + a^10*c^5*d^5)*f^10)*x^3 + ((b^10*c^6*d^4 - 9*a^2*b^8*c^4*d^6 + 16*a^3*b^7*c^3*d^7 - 9*a^4
*b^6*c^2*d^8 + a^6*b^4*d^10)*e^10 - 4*(b^10*c^7*d^3 - 6*a^2*b^8*c^5*d^5 + 5*a^3*b^7*c^4*d^6 + 5*a^4*b^6*c^3*d^
7 - 6*a^5*b^5*c^2*d^8 + a^7*b^3*d^10)*e^9*f + 3*(2*b^10*c^8*d^2 - 5*a^2*b^8*c^6*d^4 - 12*a^3*b^7*c^5*d^5 + 30*
a^4*b^6*c^4*d^6 - 12*a^5*b^5*c^3*d^7 - 5*a^6*b^4*c^2*d^8 + 2*a^8*b^2*d^10)*e^8*f^2 - 4*(b^10*c^9*d - 10*a^3*b^
7*c^6*d^4 + 9*a^4*b^6*c^5*d^5 + 9*a^5*b^5*c^4*d^6 - 10*a^6*b^4*c^3*d^7 + a^9*b*d^10)*e^7*f^3 + (b^10*c^10 - 15
*a^2*b^8*c^8*d^2 + 40*a^3*b^7*c^7*d^3 - 50*a^4*b^6*c^6*d^4 + 48*a^5*b^5*c^5*d^5 - 50*a^6*b^4*c^4*d^6 + 40*a^7*
b^3*c^3*d^7 - 15*a^8*b^2*c^2*d^8 + a^10*d^10)*e^6*f^4 + 12*(2*a^2*b^8*c^9*d - 3*a^3*b^7*c^8*d^2 - 3*a^4*b^6*c^
7*d^3 + 4*a^5*b^5*c^6*d^4 + 4*a^6*b^4*c^5*d^5 - 3*a^7*b^3*c^4*d^6 - 3*a^8*b^2*c^3*d^7 + 2*a^9*b*c^2*d^8)*e^5*f
^5 - (9*a^2*b^8*c^10 + 20*a^3*b^7*c^9*d - 90*a^4*b^6*c^8*d^2 + 36*a^5*b^5*c^7*d^3 + 50*a^6*b^4*c^6*d^4 + 36*a^
7*b^3*c^5*d^5 - 90*a^8*b^2*c^4*d^6 + 20*a^9*b*c^3*d^7 + 9*a^10*c^2*d^8)*e^4*f^6 + 4*(4*a^3*b^7*c^10 - 5*a^4*b^
6*c^9*d - 9*a^5*b^5*c^8*d^2 + 10*a^6*b^4*c^7*d^3 + 10*a^7*b^3*c^6*d^4 - 9*a^8*b^2*c^5*d^5 - 5*a^9*b*c^4*d^6 +
4*a^10*c^3*d^7)*e^3*f^7 - 3*(3*a^4*b^6*c^10 - 8*a^5*b^5*c^9*d + 5*a^6*b^4*c^8*d^2 + 5*a^8*b^2*c^6*d^4 - 8*a^9*
b*c^5*d^5 + 3*a^10*c^4*d^6)*e^2*f^8 + (a^6*b^4*c^10 - 4*a^7*b^3*c^9*d + 6*a^8*b^2*c^8*d^2 - 4*a^9*b*c^7*d^3 +
a^10*c^6*d^4)*f^10)*x^2 + 2*((a*b^9*c^6*d^4 - 3*a^2*b^8*c^5*d^5 + 2*a^3*b^7*c^4*d^6 + 2*a^4*b^6*c^3*d^7 - 3*a^
5*b^5*c^2*d^8 + a^6*b^4*c*d^9)*e^10 - (4*a*b^9*c^7*d^3 - 9*a^2*b^8*c^6*d^4 + 10*a^4*b^6*c^4*d^6 - 9*a^6*b^4*c^
2*d^8 + 4*a^7*b^3*c*d^9)*e^9*f + 6*(a*b^9*c^8*d^2 - a^2*b^8*c^7*d^3 - 3*a^3*b^7*c^6*d^4 + 3*a^4*b^6*c^5*d^5 +
3*a^5*b^5*c^4*d^6 - 3*a^6*b^4*c^3*d^7 - a^7*b^3*c^2*d^8 + a^8*b^2*c*d^9)*e^8*f^2 - 2*(2*a*b^9*c^9*d + 3*a^2*b^
8*c^8*d^2 - 16*a^3*b^7*c^7*d^3 + 5*a^4*b^6*c^6*d^4 + 12*a^5*b^5*c^5*d^5 + 5*a^6*b^4*c^4*d^6 - 16*a^7*b^3*c^3*d
^7 + 3*a^8*b^2*c^2*d^8 + 2*a^9*b*c*d^9)*e^7*f^3 + (a*b^9*c^10 + 9*a^2*b^8*c^9*d - 18*a^3*b^7*c^8*d^2 - 10*a^4*
b^6*c^7*d^3 + 18*a^5*b^5*c^6*d^4 + 18*a^6*b^4*c^5*d^5 - 10*a^7*b^3*c^4*d^6 - 18*a^8*b^2*c^3*d^7 + 9*a^9*b*c^2*
d^8 + a^10*c*d^9)*e^6*f^4 - 3*(a^2*b^8*c^10 - 6*a^4*b^6*c^8*d^2 + 8*a^5*b^5*c^7*d^3 - 6*a^6*b^4*c^6*d^4 + 8*a^
7*b^3*c^5*d^5 - 6*a^8*b^2*c^4*d^6 + a^10*c^2*d^8)*e^5*f^5 + 2*(a^3*b^7*c^10 - 5*a^4*b^6*c^9*d + 9*a^5*b^5*c^8*
d^2 - 5*a^6*b^4*c^7*d^3 - 5*a^7*b^3*c^6*d^4 + 9*a^8*b^2*c^5*d^5 - 5*a^9*b*c^4*d^6 + a^10*c^3*d^7)*e^4*f^6 + 2*
(a^4*b^6*c^10 - 9*a^6*b^4*c^8*d^2 + 16*a^7*b^3*c^7*d^3 - 9*a^8*b^2*c^6*d^4 + a^10*c^4*d^6)*e^3*f^7 - 3*(a^5*b^
5*c^10 - 3*a^6*b^4*c^9*d + 2*a^7*b^3*c^8*d^2 + 2*a^8*b^2*c^7*d^3 - 3*a^9*b*c^6*d^4 + a^10*c^5*d^5)*e^2*f^8 + (
a^6*b^4*c^10 - 4*a^7*b^3*c^9*d + 6*a^8*b^2*c^8*d^2 - 4*a^9*b*c^7*d^3 + a^10*c^6*d^4)*e*f^9)*x)

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Fricas [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^3,x, algorithm="fricas")

[Out]

Timed out

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x**2+b*d*f*x**3)**3,x)

[Out]

Timed out

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Giac [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^3,x, algorithm="giac")

[Out]

Timed out