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}
\begin {gather*} x^{-2 p} \left (x^2\right )^p \log (x) \end {gather*}
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 = 0.00, size = 13, normalized size = 1.00 \begin {gather*} x^{-2 p} \left (x^2\right )^p \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 21, normalized size = 1.62
method | result | size |
norman | \(x \ln \left (x \right ) {\mathrm e}^{p \ln \left (x^{2}\right )} {\mathrm e}^{\left (-1-2 p \right ) \ln \left (x \right )}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 2, normalized size = 0.15 \begin {gather*} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 2, normalized size = 0.15 \begin {gather*} \log \left (x\right ) \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^{- 2 p - 1} \left (x^{2}\right )^{p}\, 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 = -0.08 \begin {gather*} \int \frac {{\left (x^2\right )}^p}{x^{2\,p+1}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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