3.1345 \(\int \frac{x^5}{1-x^6} \, dx\)

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

[Out]

-Log[1 - x^6]/6

_______________________________________________________________________________________

Rubi [A]  time = 0.00669084, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{6} \log \left (1-x^6\right ) \]

Antiderivative was successfully verified.

[In]  Int[x^5/(1 - x^6),x]

[Out]

-Log[1 - x^6]/6

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.19015, size = 24, normalized size = 2. \[ - \frac{\log{\left (\left (x - 1\right ) \left (x + 1\right ) \left (x^{2} - x + 1\right ) \left (x^{2} + x + 1\right ) \right )}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-log((x - 1)*(x + 1)*(x**2 - x + 1)*(x**2 + x + 1))/6

_______________________________________________________________________________________

Mathematica [A]  time = 0.00502213, size = 12, normalized size = 1. \[ -\frac{1}{6} \log \left (1-x^6\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[x^5/(1 - x^6),x]

[Out]

-Log[1 - x^6]/6

_______________________________________________________________________________________

Maple [A]  time = 0.004, size = 18, normalized size = 1.5 \[ -{\frac{\ln \left ({x}^{3}-1 \right ) }{6}}-{\frac{\ln \left ({x}^{3}+1 \right ) }{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^5/(-x^6+1),x)

[Out]

-1/6*ln(x^3-1)-1/6*ln(x^3+1)

_______________________________________________________________________________________

Maxima [A]  time = 1.41554, size = 11, normalized size = 0.92 \[ -\frac{1}{6} \, \log \left (x^{6} - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6*log(x^6 - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.219095, size = 11, normalized size = 0.92 \[ -\frac{1}{6} \, \log \left (x^{6} - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6*log(x^6 - 1)

_______________________________________________________________________________________

Sympy [A]  time = 0.186533, size = 8, normalized size = 0.67 \[ - \frac{\log{\left (x^{6} - 1 \right )}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**5/(-x**6+1),x)

[Out]

-log(x**6 - 1)/6

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.228417, size = 12, normalized size = 1. \[ -\frac{1}{6} \,{\rm ln}\left ({\left | x^{6} - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6*ln(abs(x^6 - 1))