3.140 \(\int \frac{x^4}{a^5+x^5} \, dx\)

Optimal. Leaf size=12 \[ \frac{1}{5} \log \left (a^5+x^5\right ) \]

[Out]

Log[a^5 + x^5]/5

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Rubi [A]  time = 0.00592801, 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 \[ \frac{1}{5} \log \left (a^5+x^5\right ) \]

Antiderivative was successfully verified.

[In]  Int[x^4/(a^5 + x^5),x]

[Out]

Log[a^5 + x^5]/5

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Rubi in Sympy [A]  time = 0.901328, size = 8, normalized size = 0.67 \[ \frac{\log{\left (a^{5} + x^{5} \right )}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**4/(a**5+x**5),x)

[Out]

log(a**5 + x**5)/5

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Mathematica [A]  time = 0.00356109, size = 12, normalized size = 1. \[ \frac{1}{5} \log \left (a^5+x^5\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[x^4/(a^5 + x^5),x]

[Out]

Log[a^5 + x^5]/5

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Maple [A]  time = 0.001, size = 11, normalized size = 0.9 \[{\frac{\ln \left ({a}^{5}+{x}^{5} \right ) }{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^4/(a^5+x^5),x)

[Out]

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

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Maxima [A]  time = 1.34269, size = 14, normalized size = 1.17 \[ \frac{1}{5} \, \log \left (a^{5} + x^{5}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/5*log(a^5 + x^5)

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Fricas [A]  time = 0.206842, size = 14, normalized size = 1.17 \[ \frac{1}{5} \, \log \left (a^{5} + x^{5}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/5*log(a^5 + x^5)

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Sympy [A]  time = 0.117478, size = 8, normalized size = 0.67 \[ \frac{\log{\left (a^{5} + x^{5} \right )}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**4/(a**5+x**5),x)

[Out]

log(a**5 + x**5)/5

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GIAC/XCAS [A]  time = 0.203886, size = 15, normalized size = 1.25 \[ \frac{1}{5} \,{\rm ln}\left ({\left | a^{5} + x^{5} \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/5*ln(abs(a^5 + x^5))