Optimal. Leaf size=19 \[ x \log ^2(c x)-2 x \log (c x)+2 x \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, 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 2295
Rule 2296
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*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \[ x \log ^2(c x)-2 x \log (c x)+2 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 19, normalized size = 1.00 \[ x \log \left (c x\right )^{2} - 2 \, x \log \left (c x\right ) + 2 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 19, normalized size = 1.00 \[ x \log \left (c x\right )^{2} - 2 \, x \log \left (c x\right ) + 2 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 20, normalized size = 1.05 \[ x \ln \left (c x \right )^{2}-2 x \ln \left (c x \right )+2 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 16, normalized size = 0.84 \[ {\left (\log \left (c x\right )^{2} - 2 \, \log \left (c x\right ) + 2\right )} x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.59, size = 16, normalized size = 0.84 \[ x\,\left ({\ln \left (c\,x\right )}^2-2\,\ln \left (c\,x\right )+2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 19, normalized size = 1.00 \[ x \log {\left (c x \right )}^{2} - 2 x \log {\left (c x \right )} + 2 x \]
Verification of antiderivative is not currently implemented for this CAS.
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