3.423 \(\int \frac{x}{\left (1-x^2\right )^5} \, dx\)

Optimal. Leaf size=13 \[ \frac{1}{8 \left (1-x^2\right )^4} \]

[Out]

1/(8*(1 - x^2)^4)

_______________________________________________________________________________________

Rubi [A]  time = 0.0078271, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{1}{8 \left (1-x^2\right )^4} \]

Antiderivative was successfully verified.

[In]  Int[x/(1 - x^2)^5,x]

[Out]

1/(8*(1 - x^2)^4)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 1.92051, size = 8, normalized size = 0.62 \[ \frac{1}{8 \left (- x^{2} + 1\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/(8*(-x**2 + 1)**4)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0037918, size = 11, normalized size = 0.85 \[ \frac{1}{8 \left (x^2-1\right )^4} \]

Antiderivative was successfully verified.

[In]  Integrate[x/(1 - x^2)^5,x]

[Out]

1/(8*(-1 + x^2)^4)

_______________________________________________________________________________________

Maple [A]  time = 0.001, size = 10, normalized size = 0.8 \[{\frac{1}{8\, \left ({x}^{2}-1 \right ) ^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x/(-x^2+1)^5,x)

[Out]

1/8/(x^2-1)^4

_______________________________________________________________________________________

Maxima [A]  time = 0.782708, size = 12, normalized size = 0.92 \[ \frac{1}{8 \,{\left (x^{2} - 1\right )}^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/8/(x^2 - 1)^4

_______________________________________________________________________________________

Fricas [A]  time = 0.263157, size = 32, normalized size = 2.46 \[ \frac{1}{8 \,{\left (x^{8} - 4 \, x^{6} + 6 \, x^{4} - 4 \, x^{2} + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/8/(x^8 - 4*x^6 + 6*x^4 - 4*x^2 + 1)

_______________________________________________________________________________________

Sympy [A]  time = 0.320626, size = 22, normalized size = 1.69 \[ \frac{1}{8 x^{8} - 32 x^{6} + 48 x^{4} - 32 x^{2} + 8} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(-x**2+1)**5,x)

[Out]

1/(8*x**8 - 32*x**6 + 48*x**4 - 32*x**2 + 8)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.25912, size = 12, normalized size = 0.92 \[ \frac{1}{8 \,{\left (x^{2} - 1\right )}^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/8/(x^2 - 1)^4