Optimal. Leaf size=37 \[ -\frac{\log ^3(c x)}{x}-\frac{3 \log ^2(c x)}{x}-\frac{6 \log (c x)}{x}-\frac{6}{x} \]
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Rubi [A] time = 0.0339765, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {2305, 2304} \[ -\frac{\log ^3(c x)}{x}-\frac{3 \log ^2(c x)}{x}-\frac{6 \log (c x)}{x}-\frac{6}{x} \]
Antiderivative was successfully verified.
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Rule 2305
Rule 2304
Rubi steps
\begin{align*} \int \frac{\log ^3(c x)}{x^2} \, dx &=-\frac{\log ^3(c x)}{x}+3 \int \frac{\log ^2(c x)}{x^2} \, dx\\ &=-\frac{3 \log ^2(c x)}{x}-\frac{\log ^3(c x)}{x}+6 \int \frac{\log (c x)}{x^2} \, dx\\ &=-\frac{6}{x}-\frac{6 \log (c x)}{x}-\frac{3 \log ^2(c x)}{x}-\frac{\log ^3(c x)}{x}\\ \end{align*}
Mathematica [A] time = 0.0014595, size = 37, normalized size = 1. \[ -\frac{\log ^3(c x)}{x}-\frac{3 \log ^2(c x)}{x}-\frac{6 \log (c x)}{x}-\frac{6}{x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.036, size = 38, normalized size = 1. \begin{align*} -6\,{x}^{-1}-6\,{\frac{\ln \left ( cx \right ) }{x}}-3\,{\frac{ \left ( \ln \left ( cx \right ) \right ) ^{2}}{x}}-{\frac{ \left ( \ln \left ( cx \right ) \right ) ^{3}}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0759, size = 36, normalized size = 0.97 \begin{align*} -\frac{\log \left (c x\right )^{3} + 3 \, \log \left (c x\right )^{2} + 6 \, \log \left (c x\right ) + 6}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.836164, size = 66, normalized size = 1.78 \begin{align*} -\frac{\log \left (c x\right )^{3} + 3 \, \log \left (c x\right )^{2} + 6 \, \log \left (c x\right ) + 6}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.138687, size = 31, normalized size = 0.84 \begin{align*} - \frac{\log{\left (c x \right )}^{3}}{x} - \frac{3 \log{\left (c x \right )}^{2}}{x} - \frac{6 \log{\left (c x \right )}}{x} - \frac{6}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.47079, size = 50, normalized size = 1.35 \begin{align*} -\frac{\log \left (c x\right )^{3}}{x} - \frac{3 \, \log \left (c x\right )^{2}}{x} - \frac{6 \, \log \left (c x\right )}{x} - \frac{6}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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