Optimal. Leaf size=15 \[ \frac{\log ^2\left (c x^n\right )}{2 n} \]
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Rubi [A] time = 0.0074127, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {2301} \[ \frac{\log ^2\left (c x^n\right )}{2 n} \]
Antiderivative was successfully verified.
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Rule 2301
Rubi steps
\begin{align*} \int \frac{\log \left (c x^n\right )}{x} \, dx &=\frac{\log ^2\left (c x^n\right )}{2 n}\\ \end{align*}
Mathematica [A] time = 0.0008967, size = 15, normalized size = 1. \[ \frac{\log ^2\left (c x^n\right )}{2 n} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 14, normalized size = 0.9 \begin{align*}{\frac{ \left ( \ln \left ( c{x}^{n} \right ) \right ) ^{2}}{2\,n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00267, size = 18, normalized size = 1.2 \begin{align*} \frac{\log \left (c x^{n}\right )^{2}}{2 \, n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.83902, size = 43, normalized size = 2.87 \begin{align*} \frac{1}{2} \, n \log \left (x\right )^{2} + \log \left (c\right ) \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.68928, size = 51, normalized size = 3.4 \begin{align*} \begin{cases} \frac{\log{\left (c x^{n} \right )}^{2}}{2 n} & \text{for}\: \left |{c x^{n}}\right | < 1 \\\frac{\log{\left (\frac{x^{- n}}{c} \right )}^{2}}{2 n} & \text{for}\: \frac{1}{\left |{c x^{n}}\right |} < 1 \\\frac{{G_{3, 3}^{3, 0}\left (\begin{matrix} & 1, 1, 1 \\0, 0, 0 & \end{matrix} \middle |{c x^{n}} \right )}}{n} + \frac{{G_{3, 3}^{0, 3}\left (\begin{matrix} 1, 1, 1 & \\ & 0, 0, 0 \end{matrix} \middle |{c x^{n}} \right )}}{n} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.30343, size = 18, normalized size = 1.2 \begin{align*} \frac{1}{2} \, n \log \left (x\right )^{2} + \log \left (c\right ) \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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