Optimal. Leaf size=13 \[ x^{-2 p} \left (x^2\right )^p \log (x) \]
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Rubi [A] time = 0.0024992, antiderivative size = 13, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0051337, size = 13, normalized size = 1. \[ x^{-2 p} \left (x^2\right )^p \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.018, size = 21, normalized size = 1.6 \begin{align*} x\ln \left ( x \right ){{\rm e}^{p\ln \left ({x}^{2} \right ) }}{{\rm e}^{ \left ( -1-2\,p \right ) \ln \left ( x \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.996348, size = 3, normalized size = 0.23 \begin{align*} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.04296, size = 11, normalized size = 0.85 \begin{align*} \log \left (x\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 x^{- 2 p - 1} \left (x^{2}\right )^{p}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (x^{2}\right )}^{p} x^{-2 \, p - 1}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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