Optimal. Leaf size=15 \[ \log \left (\frac {-4+2 x}{16 (4+x)^4}\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.87, number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {632, 31} \begin {gather*} \log (2-x)-4 \log (x+4) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 632
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (4 \int \frac {1}{4+x} \, dx\right )+\int \frac {1}{-2+x} \, dx\\ &=\log (2-x)-4 \log (4+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.40 \begin {gather*} -3 \left (-\frac {1}{3} \log (2-x)+\frac {4}{3} \log (4+x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 11, normalized size = 0.73 \begin {gather*} -4 \, \log \left (x + 4\right ) + \log \left (x - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 0.87 \begin {gather*} -4 \, \log \left ({\left | x + 4 \right |}\right ) + \log \left ({\left | x - 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.39, size = 12, normalized size = 0.80
method | result | size |
default | \(-4 \ln \left (4+x \right )+\ln \left (x -2\right )\) | \(12\) |
norman | \(-4 \ln \left (4+x \right )+\ln \left (x -2\right )\) | \(12\) |
risch | \(-4 \ln \left (4+x \right )+\ln \left (x -2\right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 11, normalized size = 0.73 \begin {gather*} -4 \, \log \left (x + 4\right ) + \log \left (x - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.04, size = 11, normalized size = 0.73 \begin {gather*} \ln \left (x-2\right )-4\,\ln \left (x+4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 10, normalized size = 0.67 \begin {gather*} \log {\left (x - 2 \right )} - 4 \log {\left (x + 4 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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