Optimal. Leaf size=21 \[ \log (x) x^{-n p q} \left (a \left (b x^n\right )^p\right )^q \]
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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 = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {6679, 29} \[ \log (x) x^{-n p q} \left (a \left (b x^n\right )^p\right )^q \]
Antiderivative was successfully verified.
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Rule 29
Rule 6679
Rubi steps
\begin {align*} \int x^{-1-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 \frac {1}{x} \, dx\\ &=x^{-n p q} \left (a \left (b x^n\right )^p\right )^q \log (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.00 \[ \log (x) x^{-n p q} \left (a \left (b x^n\right )^p\right )^q \]
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 14, normalized size = 0.67 \[ e^{\left (p q \log \relax (b) + q \log \relax (a)\right )} \log \relax (x) \]
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 \[ \int \left (\left (b x^{n}\right )^{p} a\right )^{q} x^{-n p q - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.17, size = 0, normalized size = 0.00 \[ \int x^{-n p q -1} \left (a \left (b \,x^{n}\right )^{p}\right )^{q}\, dx \]
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 \[ \int \left (\left (b x^{n}\right )^{p} a\right )^{q} x^{-n p q - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {{\left (a\,{\left (b\,x^n\right )}^p\right )}^q}{x^{n\,p\,q+1}} \,d x \]
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 \[ \int x^{- n p q - 1} \left (a \left (b x^{n}\right )^{p}\right )^{q}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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