Optimal. Leaf size=24 \[ \frac {1}{2} x^{2-n p q} \left (a \left (b x^n\right )^p\right )^q \]
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Rubi [A] time = 0.04, antiderivative size = 24, 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, 30} \[ \frac {1}{2} x^{2-n p q} \left (a \left (b x^n\right )^p\right )^q \]
Antiderivative was successfully verified.
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Rule 30
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 x \, dx\\ &=\frac {1}{2} x^{2-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 = 24, normalized size = 1.00 \[ \frac {1}{2} x^{2-n p q} \left (a \left (b x^n\right )^p\right )^q \]
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 16, normalized size = 0.67 \[ \frac {1}{2} \, x^{2} e^{\left (p q \log \relax (b) + q \log \relax (a)\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 16, normalized size = 0.67 \[ \frac {1}{2} \, x e^{\left (p q \log \relax (b) + q \log \relax (a) + \log \relax (x)\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 23, normalized size = 0.96 \[ \frac {x^{-n p q +2} \left (a \left (b \,x^{n}\right )^{p}\right )^{q}}{2} \]
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 [B] time = 1.00, size = 22, normalized size = 0.92 \[ \frac {x^{2-n\,p\,q}\,{\left (a\,{\left (b\,x^n\right )}^p\right )}^q}{2} \]
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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