Optimal. Leaf size=22 \[ x^2 \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}} \]
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Rubi [A]
time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {1971, 8}
\begin {gather*} x^2 \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 1971
Rubi steps
\begin {align*} \int x \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}} \, dx &=\left (x \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}}\right ) \int 1 \, dx\\ &=x^2 \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 22, normalized size = 1.00 \begin {gather*} x^2 \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.04, size = 0, normalized size = 0.00 \[\int x \left (a \left (b \,x^{m}\right )^{n}\right )^{-\frac {1}{m n}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.40, size = 37, normalized size = 1.68 \begin {gather*} \frac {x^{2}}{a^{\frac {1}{m n}} b^{\left (\frac {1}{m}\right )} {\left ({\left (x^{m}\right )}^{n}\right )}^{\frac {1}{m n}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 18, normalized size = 0.82 \begin {gather*} x e^{\left (-\frac {n \log \left (b\right ) + \log \left (a\right )}{m n}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.66, size = 15, normalized size = 0.68 \begin {gather*} x^{2} \left (a \left (b x^{m}\right )^{n}\right )^{- \frac {1}{m n}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.77, size = 18, normalized size = 0.82 \begin {gather*} x e^{\left (-\frac {n \log \left (b\right ) + \log \left (a\right )}{m n}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.98, size = 23, normalized size = 1.05 \begin {gather*} \frac {x^2}{{\left (a\,{\left (b\,x^m\right )}^n\right )}^{\frac {1}{m\,n}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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