Optimal. Leaf size=22 \[ x \log (x) \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}} \]
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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 = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {6679, 29} \[ x \log (x) \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}} \]
Antiderivative was successfully verified.
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Rule 29
Rule 6679
Rubi steps
\begin {align*} \int \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 \frac {1}{x} \, dx\\ &=x \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}} \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \[ x \log (x) \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 19, normalized size = 0.86 \[ e^{\left (-\frac {n \log \relax (b) + \log \relax (a)}{m n}\right )} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 19, normalized size = 0.86 \[ e^{\left (-\frac {n \log \relax (b) + \log \relax (a)}{m n}\right )} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.05, size = 0, normalized size = 0.00 \[ \int \left (a \left (b \,x^{m}\right )^{n}\right )^{-\frac {1}{m n}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (\left (b x^{m}\right )^{n} a\right )^{\frac {1}{m n}}}\,{d x} \]
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 \[ \int \frac {1}{{\left (a\,{\left (b\,x^m\right )}^n\right )}^{\frac {1}{m\,n}}} \,d x \]
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 \[ \int \left (a \left (b x^{m}\right )^{n}\right )^{- \frac {1}{m n}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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