Optimal. Leaf size=17 \[ \log \left (50 x^2 (-3-x+\log (5-x))\right ) \]
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Rubi [A]
time = 0.28, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 53, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {6873, 6874,
6816} \begin {gather*} 2 \log (x)+\log (x-\log (5-x)+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {30+10 x-3 x^2+(-10+2 x) \log (5-x)}{(5-x) x (3+x-\log (5-x))} \, dx\\ &=\int \left (\frac {2}{x}+\frac {-6+x}{(-5+x) (3+x-\log (5-x))}\right ) \, dx\\ &=2 \log (x)+\int \frac {-6+x}{(-5+x) (3+x-\log (5-x))} \, dx\\ &=2 \log (x)+\log (3+x-\log (5-x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 17, normalized size = 1.00 \begin {gather*} 2 \log (x)+\log (3+x-\log (5-x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.34, size = 20, normalized size = 1.18
method | result | size |
norman | \(2 \ln \left (x \right )+\ln \left (x -\ln \left (5-x \right )+3\right )\) | \(18\) |
risch | \(2 \ln \left (x \right )+\ln \left (\ln \left (5-x \right )-x -3\right )\) | \(18\) |
derivativedivides | \(2 \ln \left (-x \right )+\ln \left (\ln \left (5-x \right )-x -3\right )\) | \(20\) |
default | \(2 \ln \left (-x \right )+\ln \left (\ln \left (5-x \right )-x -3\right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 17, normalized size = 1.00 \begin {gather*} 2 \, \log \left (x\right ) + \log \left (-x + \log \left (-x + 5\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 17, normalized size = 1.00 \begin {gather*} 2 \, \log \left (x\right ) + \log \left (-x + \log \left (-x + 5\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 14, normalized size = 0.82 \begin {gather*} 2 \log {\left (x \right )} + \log {\left (- x + \log {\left (5 - x \right )} - 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 19, normalized size = 1.12 \begin {gather*} 2 \, \log \left (-x\right ) + \log \left (x - \log \left (-x + 5\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.96, size = 17, normalized size = 1.00 \begin {gather*} \ln \left (x-\ln \left (5-x\right )+3\right )+2\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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