Optimal. Leaf size=13 \[ x^{-2 p} \left (x^2\right )^p \log (x) \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {15, 29} \[ x^{-2 p} \left (x^2\right )^p \log (x) \]
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rubi steps
\begin {align*} \int x^{-1-2 p} \left (x^2\right )^p \, dx &=\left (x^{-2 p} \left (x^2\right )^p\right ) \int \frac {1}{x} \, dx\\ &=x^{-2 p} \left (x^2\right )^p \log (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 1.00 \[ x^{-2 p} \left (x^2\right )^p \log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 2, normalized size = 0.15 \[ \log \relax (x) \]
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 \[ \int {\left (x^{2}\right )}^{p} x^{-2 \, p - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 21, normalized size = 1.62 \[ x \,{\mathrm e}^{p \ln \left (x^{2}\right )} {\mathrm e}^{\left (-2 p -1\right ) \ln \relax (x )} \ln \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.28, size = 2, normalized size = 0.15 \[ \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {{\left (x^2\right )}^p}{x^{2\,p+1}} \,d x \]
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 \[ \int x^{- 2 p - 1} \left (x^{2}\right )^{p}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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