Optimal. Leaf size=15 \[ x \log (x) \left (a x^n\right )^{-1/n} \]
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Rubi [A] time = 0.0015194, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {15, 29} \[ x \log (x) \left (a x^n\right )^{-1/n} \]
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rubi steps
\begin{align*} \int \left (a x^n\right )^{-1/n} \, dx &=\left (x \left (a x^n\right )^{-1/n}\right ) \int \frac{1}{x} \, dx\\ &=x \left (a x^n\right )^{-1/n} \log (x)\\ \end{align*}
Mathematica [A] time = 0.0007678, size = 15, normalized size = 1. \[ x \log (x) \left (a x^n\right )^{-1/n} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.017, size = 29, normalized size = 1.9 \begin{align*}{\frac{x\ln \left ( a{{\rm e}^{n\ln \left ( x \right ) }} \right ) }{n} \left ({{\rm e}^{{\frac{\ln \left ( a{{\rm e}^{n\ln \left ( x \right ) }} \right ) }{n}}}} \right ) ^{-1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\left (a x^{n}\right )^{\left (\frac{1}{n}\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.7949, size = 22, normalized size = 1.47 \begin{align*} \frac{\log \left (x\right )}{a^{\left (\frac{1}{n}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (a x^{n}\right )^{- \frac{1}{n}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12788, size = 14, normalized size = 0.93 \begin{align*} \frac{\log \left (x\right )}{a^{\left (\frac{1}{n}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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