3.1362 \(\int \frac{x^5}{1+x^6} \, dx\)

Optimal. Leaf size=10 \[ \frac{1}{6} \log \left (x^6+1\right ) \]

[Out]

Log[1 + x^6]/6

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Rubi [A]  time = 0.00591617, antiderivative size = 10, 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 \[ \frac{1}{6} \log \left (x^6+1\right ) \]

Antiderivative was successfully verified.

[In]  Int[x^5/(1 + x^6),x]

[Out]

Log[1 + x^6]/6

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Rubi in Sympy [A]  time = 1.65465, size = 7, normalized size = 0.7 \[ \frac{\log{\left (x^{6} + 1 \right )}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**5/(x**6+1),x)

[Out]

log(x**6 + 1)/6

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Mathematica [A]  time = 0.00398635, size = 10, normalized size = 1. \[ \frac{1}{6} \log \left (x^6+1\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[x^5/(1 + x^6),x]

[Out]

Log[1 + x^6]/6

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Maple [A]  time = 0.001, size = 9, normalized size = 0.9 \[{\frac{\ln \left ({x}^{6}+1 \right ) }{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^5/(x^6+1),x)

[Out]

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

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Maxima [A]  time = 1.44864, size = 11, normalized size = 1.1 \[ \frac{1}{6} \, \log \left (x^{6} + 1\right ) \]

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)

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Fricas [A]  time = 0.207723, size = 11, normalized size = 1.1 \[ \frac{1}{6} \, \log \left (x^{6} + 1\right ) \]

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)

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Sympy [A]  time = 0.176035, size = 7, normalized size = 0.7 \[ \frac{\log{\left (x^{6} + 1 \right )}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**5/(x**6+1),x)

[Out]

log(x**6 + 1)/6

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GIAC/XCAS [A]  time = 0.225783, size = 11, normalized size = 1.1 \[ \frac{1}{6} \,{\rm ln}\left (x^{6} + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*ln(x^6 + 1)