Optimal. Leaf size=21 \[ e+\log \left (\frac {e^5}{x \left (3-\frac {\log (x)}{x}\right )}\right ) \]
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Rubi [A]
time = 0.04, antiderivative size = 11, normalized size of antiderivative = 0.52, number of steps
used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2641, 6816}
\begin {gather*} -\log (3 x-\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 2641
Rule 6816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1+3 x}{x (-3 x+\log (x))} \, dx\\ &=-\log (3 x-\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 11, normalized size = 0.52 \begin {gather*} -\log (3 x-\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.41, size = 12, normalized size = 0.57
method | result | size |
risch | \(-\ln \left (\ln \left (x \right )-3 x \right )\) | \(10\) |
default | \(-\ln \left (-\ln \left (x \right )+3 x \right )\) | \(12\) |
norman | \(-\ln \left (-\ln \left (x \right )+3 x \right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 9, normalized size = 0.43 \begin {gather*} -\log \left (-3 \, x + \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 = 9, normalized size = 0.43 \begin {gather*} -\log \left (-3 \, x + \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 8, normalized size = 0.38 \begin {gather*} - \log {\left (- 3 x + \log {\left (x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 9, normalized size = 0.43 \begin {gather*} -\log \left (-3 \, x + \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.23, size = 11, normalized size = 0.52 \begin {gather*} -\ln \left (3\,x-\ln \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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