Optimal. Leaf size=15 \[ \frac{\log ^q\left (c x^n\right )}{n q} \]
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Rubi [A] time = 0.0217537, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {2302, 30} \[ \frac{\log ^q\left (c x^n\right )}{n q} \]
Antiderivative was successfully verified.
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Rule 2302
Rule 30
Rubi steps
\begin{align*} \int \frac{\log ^{-1+q}\left (c x^n\right )}{x} \, dx &=\frac{\operatorname{Subst}\left (\int x^{-1+q} \, dx,x,\log \left (c x^n\right )\right )}{n}\\ &=\frac{\log ^q\left (c x^n\right )}{n q}\\ \end{align*}
Mathematica [A] time = 0.0020717, size = 15, normalized size = 1. \[ \frac{\log ^q\left (c x^n\right )}{n q} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 16, normalized size = 1.1 \begin{align*}{\frac{ \left ( \ln \left ( c{x}^{n} \right ) \right ) ^{q}}{nq}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.94719, size = 74, normalized size = 4.93 \begin{align*} \frac{{\left (n \log \left (x\right ) + \log \left (c\right )\right )}{\left (n \log \left (x\right ) + \log \left (c\right )\right )}^{q - 1}}{n q} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log{\left (c x^{n} \right )}^{q - 1}}{x}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.30102, size = 22, normalized size = 1.47 \begin{align*} \frac{{\left (n \log \left (x\right ) + \log \left (c\right )\right )}^{q}}{n q} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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