Optimal. Leaf size=20 \[ \log \left (\frac {1}{5} e^3 (2-3 x) x^2 \log ^2(x)\right ) \]
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Rubi [A]
time = 0.14, antiderivative size = 16, normalized size of antiderivative = 0.80, number of steps
used = 7, number of rules used = 5, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.172, Rules used = {1607, 6874, 78,
2339, 29} \begin {gather*} \log (2-3 x)+2 \log (x)+2 \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 78
Rule 1607
Rule 2339
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4+6 x+(-4+9 x) \log (x)}{x (-2+3 x) \log (x)} \, dx\\ &=\int \left (\frac {-4+9 x}{x (-2+3 x)}+\frac {2}{x \log (x)}\right ) \, dx\\ &=2 \int \frac {1}{x \log (x)} \, dx+\int \frac {-4+9 x}{x (-2+3 x)} \, dx\\ &=2 \text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )+\int \left (\frac {2}{x}+\frac {3}{-2+3 x}\right ) \, dx\\ &=\log (2-3 x)+2 \log (x)+2 \log (\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 16, normalized size = 0.80 \begin {gather*} \log (2-3 x)+2 \log (x)+2 \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 17, normalized size = 0.85
method | result | size |
default | \(2 \ln \left (x \right )+\ln \left (3 x -2\right )+2 \ln \left (\ln \left (x \right )\right )\) | \(17\) |
norman | \(2 \ln \left (x \right )+\ln \left (3 x -2\right )+2 \ln \left (\ln \left (x \right )\right )\) | \(17\) |
risch | \(2 \ln \left (x \right )+\ln \left (3 x -2\right )+2 \ln \left (\ln \left (x \right )\right )\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 16, normalized size = 0.80 \begin {gather*} \log \left (3 \, x - 2\right ) + 2 \, \log \left (x\right ) + 2 \, \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 16, normalized size = 0.80 \begin {gather*} \log \left (3 \, x - 2\right ) + 2 \, \log \left (x\right ) + 2 \, \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 17, normalized size = 0.85 \begin {gather*} 2 \log {\left (x \right )} + \log {\left (x - \frac {2}{3} \right )} + 2 \log {\left (\log {\left (x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 16, normalized size = 0.80 \begin {gather*} \log \left (3 \, x - 2\right ) + 2 \, \log \left (x\right ) + 2 \, \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.05, size = 14, normalized size = 0.70 \begin {gather*} \ln \left (x-\frac {2}{3}\right )+2\,\ln \left (\ln \left (x\right )\right )+2\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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