Optimal. Leaf size=22 \[ x^{1+m} \left (a x^n\right )^{-\frac {1+m}{n}} \log (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {15, 29}
\begin {gather*} x^{m+1} \log (x) \left (a x^n\right )^{-\frac {m+1}{n}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rubi steps
\begin {align*} \int x^m \left (a x^n\right )^{-\frac {1+m}{n}} \, dx &=\left (x^{1+m} \left (a x^n\right )^{-\frac {1+m}{n}}\right ) \int \frac {1}{x} \, dx\\ &=x^{1+m} \left (a x^n\right )^{-\frac {1+m}{n}} \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 22, normalized size = 1.00 \begin {gather*} x^{1+m} \left (a x^n\right )^{-\frac {1+m}{n}} \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.03, size = 0, normalized size = 0.00 \[\int x^{m} \left (a \,x^{n}\right )^{-\frac {1+m}{n}}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 14, normalized size = 0.64 \begin {gather*} \frac {\log \left (x\right )}{a^{\frac {m + 1}{n}}} \end {gather*}
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 \begin {gather*} \int x^{m} \left (a x^{n}\right )^{- \frac {m + 1}{n}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {x^m}{{\left (a\,x^n\right )}^{\frac {m+1}{n}}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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