Optimal. Leaf size=26 \[ \frac {4 x \left (-\frac {1}{\log (9)}+\frac {\log (x)}{x}\right )}{-5+\frac {4}{\log (3)}} \]
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Rubi [A]
time = 0.01, antiderivative size = 32, normalized size of antiderivative = 1.23, number of steps
used = 4, number of rules used = 3, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.107, Rules used = {6, 12, 45}
\begin {gather*} \frac {4 \log (3) \log (x)}{4-\log (243)}-\frac {x \log (81)}{\log (9) (4-\log (243))} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 x \log (3)-4 \log (3) \log (9)}{x (-4+5 \log (3)) \log (9)} \, dx\\ &=-\frac {\int \frac {4 x \log (3)-4 \log (3) \log (9)}{x} \, dx}{\log (9) (4-\log (243))}\\ &=-\frac {\int \left (-\frac {4 \log (3) \log (9)}{x}+\log (81)\right ) \, dx}{\log (9) (4-\log (243))}\\ &=-\frac {x \log (81)}{\log (9) (4-\log (243))}+\frac {4 \log (3) \log (x)}{4-\log (243)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 22, normalized size = 0.85 \begin {gather*} \frac {4 \log (3) (x-\log (9) \log (x))}{\log (9) (-4+\log (243))} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.20, size = 19, normalized size = 0.73
method | result | size |
default | \(\frac {2 x -4 \ln \left (3\right ) \ln \left (x \right )}{5 \ln \left (3\right )-4}\) | \(19\) |
norman | \(\frac {2 x}{5 \ln \left (3\right )-4}-\frac {4 \ln \left (3\right ) \ln \left (x \right )}{5 \ln \left (3\right )-4}\) | \(27\) |
risch | \(\frac {2 x}{5 \ln \left (3\right )-4}-\frac {4 \ln \left (3\right ) \ln \left (x \right )}{5 \ln \left (3\right )-4}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 36, normalized size = 1.38 \begin {gather*} -\frac {2 \, {\left (\frac {2 \, \log \left (3\right )^{2} \log \left (x\right )}{5 \, \log \left (3\right ) - 4} - \frac {x \log \left (3\right )}{5 \, \log \left (3\right ) - 4}\right )}}{\log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 20, normalized size = 0.77 \begin {gather*} -\frac {2 \, {\left (2 \, \log \left (3\right ) \log \left (x\right ) - x\right )}}{5 \, \log \left (3\right ) - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 17, normalized size = 0.65 \begin {gather*} \frac {2 x - 4 \log {\left (3 \right )} \log {\left (x \right )}}{-4 + 5 \log {\left (3 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 37, normalized size = 1.42 \begin {gather*} -\frac {2 \, {\left (\frac {2 \, \log \left (3\right )^{2} \log \left ({\left | x \right |}\right )}{5 \, \log \left (3\right ) - 4} - \frac {x \log \left (3\right )}{5 \, \log \left (3\right ) - 4}\right )}}{\log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 16, normalized size = 0.62 \begin {gather*} \frac {2\,\left (x-2\,\ln \left (3\right )\,\ln \left (x\right )\right )}{\ln \left (243\right )-4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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