Optimal. Leaf size=15 \[ x \log (x) \left (a x^n\right )^{-1/n} \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ x \log (x) \left (a x^n\right )^{-1/n} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 10, normalized size = 0.67 \[ \frac {\log \relax (x)}{a^{\left (\frac {1}{n}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 10, normalized size = 0.67 \[ \frac {\log \relax (x)}{a^{\left (\frac {1}{n}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 29, normalized size = 1.93 \[ \frac {x \,{\mathrm e}^{-\frac {\ln \left (a \,{\mathrm e}^{n \ln \relax (x )}\right )}{n}} \ln \left (a \,{\mathrm e}^{n \ln \relax (x )}\right )}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (a x^{n}\right )^{\left (\frac {1}{n}\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {1}{{\left (a\,x^n\right )}^{1/n}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (a x^{n}\right )^{- \frac {1}{n}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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