Optimal. Leaf size=12 \[ \frac{1}{5} \log \left (a^5+x^5\right ) \]
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Rubi [A] time = 0.002512, 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, Rules used = {260} \[ \frac{1}{5} \log \left (a^5+x^5\right ) \]
Antiderivative was successfully verified.
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Rule 260
Rubi steps
\begin{align*} \int \frac{x^4}{a^5+x^5} \, dx &=\frac{1}{5} \log \left (a^5+x^5\right )\\ \end{align*}
Mathematica [A] time = 0.0023469, size = 12, normalized size = 1. \[ \frac{1}{5} \log \left (a^5+x^5\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 11, normalized size = 0.9 \begin{align*}{\frac{\ln \left ({a}^{5}+{x}^{5} \right ) }{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.929379, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{5} \, \log \left (a^{5} + x^{5}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.79827, size = 27, normalized size = 2.25 \begin{align*} \frac{1}{5} \, \log \left (a^{5} + x^{5}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.101514, size = 8, normalized size = 0.67 \begin{align*} \frac{\log{\left (a^{5} + x^{5} \right )}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0589, size = 15, normalized size = 1.25 \begin{align*} \frac{1}{5} \, \log \left ({\left | a^{5} + x^{5} \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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