3.223 \(\int \frac{2-x^2}{\left (1-6 x+x^3\right )^5} \, dx\)

Optimal. Leaf size=14 \[ \frac{1}{12 \left (x^3-6 x+1\right )^4} \]

[Out]

1/(12*(1 - 6*x + x^3)^4)

_______________________________________________________________________________________

Rubi [A]  time = 0.00863122, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{1}{12 \left (x^3-6 x+1\right )^4} \]

Antiderivative was successfully verified.

[In]  Int[(2 - x^2)/(1 - 6*x + x^3)^5,x]

[Out]

1/(12*(1 - 6*x + x^3)^4)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.93853, size = 12, normalized size = 0.86 \[ \frac{1}{12 \left (x^{3} - 6 x + 1\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((-x**2+2)/(x**3-6*x+1)**5,x)

[Out]

1/(12*(x**3 - 6*x + 1)**4)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00842163, size = 14, normalized size = 1. \[ \frac{1}{12 \left (x^3-6 x+1\right )^4} \]

Antiderivative was successfully verified.

[In]  Integrate[(2 - x^2)/(1 - 6*x + x^3)^5,x]

[Out]

1/(12*(1 - 6*x + x^3)^4)

_______________________________________________________________________________________

Maple [A]  time = 0.002, size = 13, normalized size = 0.9 \[{\frac{1}{12\, \left ({x}^{3}-6\,x+1 \right ) ^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((-x^2+2)/(x^3-6*x+1)^5,x)

[Out]

1/12/(x^3-6*x+1)^4

_______________________________________________________________________________________

Maxima [A]  time = 0.810874, size = 16, normalized size = 1.14 \[ \frac{1}{12 \,{\left (x^{3} - 6 \, x + 1\right )}^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(x^2 - 2)/(x^3 - 6*x + 1)^5,x, algorithm="maxima")

[Out]

1/12/(x^3 - 6*x + 1)^4

_______________________________________________________________________________________

Fricas [A]  time = 0.244749, size = 77, normalized size = 5.5 \[ \frac{1}{12 \,{\left (x^{12} - 24 \, x^{10} + 4 \, x^{9} + 216 \, x^{8} - 72 \, x^{7} - 858 \, x^{6} + 432 \, x^{5} + 1224 \, x^{4} - 860 \, x^{3} + 216 \, x^{2} - 24 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(x^2 - 2)/(x^3 - 6*x + 1)^5,x, algorithm="fricas")

[Out]

1/12/(x^12 - 24*x^10 + 4*x^9 + 216*x^8 - 72*x^7 - 858*x^6 + 432*x^5 + 1224*x^4 -
860*x^3 + 216*x^2 - 24*x + 1)

_______________________________________________________________________________________

Sympy [A]  time = 0.666687, size = 56, normalized size = 4. \[ \frac{1}{12 x^{12} - 288 x^{10} + 48 x^{9} + 2592 x^{8} - 864 x^{7} - 10296 x^{6} + 5184 x^{5} + 14688 x^{4} - 10320 x^{3} + 2592 x^{2} - 288 x + 12} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((-x**2+2)/(x**3-6*x+1)**5,x)

[Out]

1/(12*x**12 - 288*x**10 + 48*x**9 + 2592*x**8 - 864*x**7 - 10296*x**6 + 5184*x**
5 + 14688*x**4 - 10320*x**3 + 2592*x**2 - 288*x + 12)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.259587, size = 16, normalized size = 1.14 \[ \frac{1}{12 \,{\left (x^{3} - 6 \, x + 1\right )}^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(x^2 - 2)/(x^3 - 6*x + 1)^5,x, algorithm="giac")

[Out]

1/12/(x^3 - 6*x + 1)^4