Optimal. Leaf size=15 \[ \log \left (\left (4+5 e^3\right )^2 x (4+x)\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.53, number of steps
used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {642}
\begin {gather*} \log \left (x^2+4 x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 642
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (4 x+x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.13 \begin {gather*} 2 \left (\frac {\log (x)}{2}+\frac {1}{2} \log (4+x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.73, size = 7, normalized size = 0.47
method | result | size |
default | \(\ln \left (\left (4+x \right ) x \right )\) | \(7\) |
norman | \(\ln \left (x \right )+\ln \left (4+x \right )\) | \(8\) |
derivativedivides | \(\ln \left (x^{2}+4 x \right )\) | \(9\) |
risch | \(\ln \left (x^{2}+4 x \right )\) | \(9\) |
meijerg | \(\ln \left (1+\frac {x}{4}\right )+\ln \left (x \right )-2 \ln \left (2\right )\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 8, normalized size = 0.53 \begin {gather*} \log \left (x^{2} + 4 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 8, normalized size = 0.53 \begin {gather*} \log \left (x^{2} + 4 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 7, normalized size = 0.47 \begin {gather*} \log {\left (x^{2} + 4 x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 13, normalized size = 0.87 \begin {gather*} \log \left (2 \, {\left | \frac {1}{2} \, x^{2} + 2 \, x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 6, normalized size = 0.40 \begin {gather*} \ln \left (x\,\left (x+4\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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