Optimal. Leaf size=15 \[ \log \left ((4+5 \log (3)-\log (2 x))^2\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.87, number of steps
used = 4, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {6, 12, 31}
\begin {gather*} 2 \log (-\log (2 x)+4+\log (243)) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 31
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2}{x (-4-5 \log (3))+x \log (2 x)} \, dx\\ &=2 \int \frac {1}{x (-4-5 \log (3))+x \log (2 x)} \, dx\\ &=-\left (2 \text {Subst}\left (\int \frac {1}{4-x+5 \log (3)} \, dx,x,\log (2 x)\right )\right )\\ &=2 \log (4+\log (243)-\log (2 x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 11, normalized size = 0.73 \begin {gather*} 2 \log \left (-4+\log \left (\frac {2 x}{243}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.47, size = 16, normalized size = 1.07
method | result | size |
risch | \(2 \ln \left (-4+\ln \left (2 x \right )-5 \ln \left (3\right )\right )\) | \(14\) |
derivativedivides | \(2 \ln \left (4-\ln \left (2 x \right )+5 \ln \left (3\right )\right )\) | \(16\) |
default | \(2 \ln \left (4-\ln \left (2 x \right )+5 \ln \left (3\right )\right )\) | \(16\) |
norman | \(2 \ln \left (4-\ln \left (2 x \right )+5 \ln \left (3\right )\right )\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.49, size = 13, normalized size = 0.87 \begin {gather*} 2 \, \log \left (-5 \, \log \left (3\right ) + \log \left (2\right ) + \log \left (x\right ) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 13, normalized size = 0.87 \begin {gather*} 2 \, \log \left (-5 \, \log \left (3\right ) + \log \left (2 \, x\right ) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 14, normalized size = 0.93 \begin {gather*} 2 \log {\left (\log {\left (2 x \right )} - 5 \log {\left (3 \right )} - 4 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 15, normalized size = 1.00 \begin {gather*} 2 \, \log \left (5 \, \log \left (3\right ) - \log \left (2 \, x\right ) + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.29, size = 9, normalized size = 0.60 \begin {gather*} 2\,\ln \left (\ln \left (\frac {2\,x}{243}\right )-4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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