Optimal. Leaf size=19 \[ x \log ^2(c x)-2 x \log (c x)+2 x \]
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Rubi [A] time = 0.0045393, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {2296, 2295} \[ x \log ^2(c x)-2 x \log (c x)+2 x \]
Antiderivative was successfully verified.
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Rule 2296
Rule 2295
Rubi steps
\begin{align*} \int \log ^2(c x) \, dx &=x \log ^2(c x)-2 \int \log (c x) \, dx\\ &=2 x-2 x \log (c x)+x \log ^2(c x)\\ \end{align*}
Mathematica [A] time = 0.000852, size = 19, normalized size = 1. \[ x \log ^2(c x)-2 x \log (c x)+2 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.036, size = 20, normalized size = 1.1 \begin{align*} 2\,x-2\,x\ln \left ( cx \right ) +x \left ( \ln \left ( cx \right ) \right ) ^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.995963, size = 22, normalized size = 1.16 \begin{align*}{\left (\log \left (c x\right )^{2} - 2 \, \log \left (c x\right ) + 2\right )} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.815711, size = 47, normalized size = 2.47 \begin{align*} x \log \left (c x\right )^{2} - 2 \, x \log \left (c x\right ) + 2 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.095907, size = 19, normalized size = 1. \begin{align*} x \log{\left (c x \right )}^{2} - 2 x \log{\left (c x \right )} + 2 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09678, size = 26, normalized size = 1.37 \begin{align*} x \log \left (c x\right )^{2} - 2 \, x \log \left (c x\right ) + 2 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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