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 = 0.04, 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 = {6679, 8} \[ x^{1-n p q} \left (a \left (b x^n\right )^p\right )^q \]
Antiderivative was successfully verified.
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Rule 8
Rule 6679
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 = 0.01, size = 21, normalized size = 1.00 \[ x^{1-n p q} \left (a \left (b x^n\right )^p\right )^q \]
Antiderivative was successfully verified.
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fricas [A] time = 0.74, size = 13, normalized size = 0.62 \[ x e^{\left (p q \log \relax (b) + q \log \relax (a)\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.43, size = 27, normalized size = 1.29 \[ \frac {x e^{\left (n p q \log \relax (x) + p q \log \relax (b) + q \log \relax (a)\right )}}{x^{n p q}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.21, size = 0, normalized size = 0.00 \[ \int x^{-n p q} \left (a \left (b \,x^{n}\right )^{p}\right )^{q}\, dx \]
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 \[ \int \frac {\left (\left (b x^{n}\right )^{p} a\right )^{q}}{x^{n p q}}\,{d x} \]
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 \[ x^{1-n\,p\,q}\,{\left (a\,{\left (b\,x^n\right )}^p\right )}^q \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.63, size = 22, normalized size = 1.05 \[ a^{q} x x^{- n p q} \left (b^{p}\right )^{q} \left (\left (x^{n}\right )^{p}\right )^{q} \]
Verification of antiderivative is not currently implemented for this CAS.
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