Optimal. Leaf size=15 \[ \log \left (e^{-x} x^3 (6+x)^2\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 14, normalized size of antiderivative = 0.93, number of steps
used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {1607, 907}
\begin {gather*} -x+3 \log (x)+2 \log (x+6) \end {gather*}
Antiderivative was successfully verified.
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Rule 907
Rule 1607
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {18-x-x^2}{x (6+x)} \, dx\\ &=\int \left (-1+\frac {3}{x}+\frac {2}{6+x}\right ) \, dx\\ &=-x+3 \log (x)+2 \log (6+x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 0.93 \begin {gather*} -x+3 \log (x)+2 \log (6+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.14, size = 15, normalized size = 1.00
method | result | size |
default | \(-x +2 \ln \left (x +6\right )+3 \ln \left (x \right )\) | \(15\) |
norman | \(-x +2 \ln \left (x +6\right )+3 \ln \left (x \right )\) | \(15\) |
risch | \(-x +2 \ln \left (x +6\right )+3 \ln \left (x \right )\) | \(15\) |
meijerg | \(2 \ln \left (1+\frac {x}{6}\right )+3 \ln \left (x \right )-3 \ln \left (2\right )-3 \ln \left (3\right )-x\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 14, normalized size = 0.93 \begin {gather*} -x + 2 \, \log \left (x + 6\right ) + 3 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.44, size = 14, normalized size = 0.93 \begin {gather*} -x + 2 \, \log \left (x + 6\right ) + 3 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 12, normalized size = 0.80 \begin {gather*} - x + 3 \log {\left (x \right )} + 2 \log {\left (x + 6 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 16, normalized size = 1.07 \begin {gather*} -x + 2 \, \log \left ({\left | x + 6 \right |}\right ) + 3 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.83, size = 14, normalized size = 0.93 \begin {gather*} 2\,\ln \left (x+6\right )-x+3\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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