Optimal. Leaf size=14 \[ \log \left (\frac {16}{(-18+x+\log (-2-x))^2}\right ) \]
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Rubi [A]
time = 0.08, antiderivative size = 16, normalized size of antiderivative = 1.14, number of steps
used = 2, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {6873, 6816}
\begin {gather*} -2 \log (-x-\log (-x-2)+18) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {6+2 x}{(2+x) (18-x-\log (-2-x))} \, dx\\ &=-2 \log (18-x-\log (-2-x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 12, normalized size = 0.86 \begin {gather*} -2 \log (-18+x+\log (-2-x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.42, size = 17, normalized size = 1.21
method | result | size |
norman | \(-2 \ln \left (\ln \left (-x -2\right )+x -18\right )\) | \(13\) |
risch | \(-2 \ln \left (\ln \left (-x -2\right )+x -18\right )\) | \(13\) |
derivativedivides | \(-2 \ln \left (-\ln \left (-x -2\right )-x +18\right )\) | \(17\) |
default | \(-2 \ln \left (-\ln \left (-x -2\right )-x +18\right )\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 12, normalized size = 0.86 \begin {gather*} -2 \, \log \left (x + \log \left (-x - 2\right ) - 18\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 12, normalized size = 0.86 \begin {gather*} -2 \, \log \left (x + \log \left (-x - 2\right ) - 18\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 14, normalized size = 1.00 \begin {gather*} - 2 \log {\left (x + \log {\left (- x - 2 \right )} - 18 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 16, normalized size = 1.14 \begin {gather*} -2 \, \log \left (-x - \log \left (-x - 2\right ) + 18\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.24, size = 12, normalized size = 0.86 \begin {gather*} -2\,\ln \left (x+\ln \left (-x-2\right )-18\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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