Optimal. Leaf size=20 \[ -1+(3-x)^2+\frac {x}{2}+\log \left ((4+x)^2\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.75, number of steps
used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {712}
\begin {gather*} x^2-\frac {11 x}{2}+2 \log (x+4) \end {gather*}
Antiderivative was successfully verified.
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Rule 712
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {11}{2}+2 x+\frac {2}{4+x}\right ) \, dx\\ &=-\frac {11 x}{2}+x^2+2 \log (4+x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 18, normalized size = 0.90 \begin {gather*} -38-\frac {11 x}{2}+x^2+2 \log (2 (4+x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.56, size = 14, normalized size = 0.70
method | result | size |
default | \(x^{2}-\frac {11 x}{2}+2 \ln \left (4+x \right )\) | \(14\) |
risch | \(x^{2}-\frac {11 x}{2}+2 \ln \left (4+x \right )\) | \(14\) |
norman | \(x^{2}-\frac {11 x}{2}+2 \ln \left (2 x +8\right )\) | \(16\) |
meijerg | \(2 \ln \left (1+\frac {x}{4}\right )-\frac {4 x \left (-\frac {3 x}{4}+6\right )}{3}+\frac {5 x}{2}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 13, normalized size = 0.65 \begin {gather*} x^{2} - \frac {11}{2} \, x + 2 \, \log \left (x + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 13, normalized size = 0.65 \begin {gather*} x^{2} - \frac {11}{2} \, x + 2 \, \log \left (x + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 14, normalized size = 0.70 \begin {gather*} x^{2} - \frac {11 x}{2} + 2 \log {\left (x + 4 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 14, normalized size = 0.70 \begin {gather*} x^{2} - \frac {11}{2} \, x + 2 \, \log \left ({\left | x + 4 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.06, size = 13, normalized size = 0.65 \begin {gather*} 2\,\ln \left (x+4\right )-\frac {11\,x}{2}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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