Optimal. Leaf size=21 \[ x^{1-n p q} \left (a \left (b x^n\right )^p\right )^q \]
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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {1971, 8}
\begin {gather*} x^{1-n p q} \left (a \left (b x^n\right )^p\right )^q \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 1971
Rubi steps
\begin {align*} \int x^{-n p q} \left (a \left (b x^n\right )^p\right )^q \, dx &=\left (x^{-n p q} \left (a \left (b x^n\right )^p\right )^q\right ) \int 1 \, dx\\ &=x^{1-n p q} \left (a \left (b x^n\right )^p\right )^q\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 21, normalized size = 1.00 \begin {gather*} x^{1-n p q} \left (a \left (b x^n\right )^p\right )^q \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.16, size = 0, normalized size = 0.00 \[\int \left (a \left (b \,x^{n}\right )^{p}\right )^{q} x^{-n p q}\, dx\]
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 = 0.36, size = 13, normalized size = 0.62 \begin {gather*} x e^{\left (p q \log \left (b\right ) + q \log \left (a\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.48, size = 17, normalized size = 0.81 \begin {gather*} x x^{- n p q} \left (a \left (b x^{n}\right )^{p}\right )^{q} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.60, size = 27, normalized size = 1.29 \begin {gather*} \frac {x e^{\left (n p q \log \left (x\right ) + p q \log \left (b\right ) + q \log \left (a\right )\right )}}{x^{n p q}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.00, size = 21, normalized size = 1.00 \begin {gather*} x^{1-n\,p\,q}\,{\left (a\,{\left (b\,x^n\right )}^p\right )}^q \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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