Optimal. Leaf size=23 \[ \log \left (\frac {4 \left (x+e^2 x\right ) \log (x)}{x \log (-2+3 x)}\right ) \]
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Rubi [A]
time = 0.21, antiderivative size = 13, normalized size of antiderivative = 0.57, number of steps
used = 8, number of rules used = 5, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.119, Rules used = {1607, 6820,
2339, 29, 2437} \begin {gather*} \log (\log (x))-\log (\log (3 x-2)) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 1607
Rule 2339
Rule 2437
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-3 x \log (x)+(-2+3 x) \log (-2+3 x)}{x (-2+3 x) \log (x) \log (-2+3 x)} \, dx\\ &=\int \left (\frac {1}{x \log (x)}-\frac {3}{(-2+3 x) \log (-2+3 x)}\right ) \, dx\\ &=-\left (3 \int \frac {1}{(-2+3 x) \log (-2+3 x)} \, dx\right )+\int \frac {1}{x \log (x)} \, dx\\ &=\text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )-\text {Subst}\left (\int \frac {1}{x \log (x)} \, dx,x,-2+3 x\right )\\ &=\log (\log (x))-\text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (-2+3 x)\right )\\ &=\log (\log (x))-\log (\log (-2+3 x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 13, normalized size = 0.57 \begin {gather*} \log (\log (x))-\log (\log (-2+3 x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 14, normalized size = 0.61
method | result | size |
default | \(\ln \left (\ln \left (x \right )\right )-\ln \left (\ln \left (3 x -2\right )\right )\) | \(14\) |
norman | \(\ln \left (\ln \left (x \right )\right )-\ln \left (\ln \left (3 x -2\right )\right )\) | \(14\) |
risch | \(\ln \left (\ln \left (x \right )\right )-\ln \left (\ln \left (3 x -2\right )\right )\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 13, normalized size = 0.57 \begin {gather*} -\log \left (\log \left (3 \, x - 2\right )\right ) + \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 = 0.33, size = 13, normalized size = 0.57 \begin {gather*} -\log \left (\log \left (3 \, x - 2\right )\right ) + \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 = 0.07, size = 12, normalized size = 0.52 \begin {gather*} \log {\left (\log {\left (x \right )} \right )} - \log {\left (\log {\left (3 x - 2 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 13, normalized size = 0.57 \begin {gather*} -\log \left (\log \left (3 \, x - 2\right )\right ) + \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 = 0.65, size = 13, normalized size = 0.57 \begin {gather*} \ln \left (\ln \left (x\right )\right )-\ln \left (\ln \left (3\,x-2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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