3.1295 \(\int \frac{x^4}{1+x^5} \, dx\)

Optimal. Leaf size=10 \[ \frac{1}{5} \log \left (x^5+1\right ) \]

[Out]

Log[1 + x^5]/5

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Rubi [A]  time = 0.00559394, 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 \[ \frac{1}{5} \log \left (x^5+1\right ) \]

Antiderivative was successfully verified.

[In]  Int[x^4/(1 + x^5),x]

[Out]

Log[1 + x^5]/5

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Rubi in Sympy [A]  time = 1.67403, size = 7, normalized size = 0.7 \[ \frac{\log{\left (x^{5} + 1 \right )}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**4/(x**5+1),x)

[Out]

log(x**5 + 1)/5

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Mathematica [A]  time = 0.00361357, size = 10, normalized size = 1. \[ \frac{1}{5} \log \left (x^5+1\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[x^4/(1 + x^5),x]

[Out]

Log[1 + x^5]/5

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Maple [A]  time = 0.001, size = 9, normalized size = 0.9 \[{\frac{\ln \left ({x}^{5}+1 \right ) }{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^4/(x^5+1),x)

[Out]

1/5*ln(x^5+1)

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Maxima [A]  time = 1.44382, size = 11, normalized size = 1.1 \[ \frac{1}{5} \, \log \left (x^{5} + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^4/(x^5 + 1),x, algorithm="maxima")

[Out]

1/5*log(x^5 + 1)

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Fricas [A]  time = 0.214503, size = 11, normalized size = 1.1 \[ \frac{1}{5} \, \log \left (x^{5} + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^4/(x^5 + 1),x, algorithm="fricas")

[Out]

1/5*log(x^5 + 1)

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Sympy [A]  time = 0.159688, size = 7, normalized size = 0.7 \[ \frac{\log{\left (x^{5} + 1 \right )}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**4/(x**5+1),x)

[Out]

log(x**5 + 1)/5

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GIAC/XCAS [A]  time = 0.228637, size = 12, normalized size = 1.2 \[ \frac{1}{5} \,{\rm ln}\left ({\left | x^{5} + 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^4/(x^5 + 1),x, algorithm="giac")

[Out]

1/5*ln(abs(x^5 + 1))