Optimal. Leaf size=23 \[ 3+x \left (4-x+\frac {\left (\frac {x}{2}+\log (3)\right )^2}{x}\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.57, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {9} \begin {gather*} -\frac {1}{12} (-3 x+8+\log (9))^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 9
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{12} (8-3 x+\log (9))^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 0.65 \begin {gather*} 4 x-\frac {3 x^2}{4}+x \log (3) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 13, normalized size = 0.57 \begin {gather*} -\frac {3}{4} \, x^{2} + x \log \relax (3) + 4 \, x \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 = 0.57 \begin {gather*} -\frac {3}{4} \, x^{2} + x \log \relax (3) + 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 13, normalized size = 0.57
method | result | size |
gosper | \(\frac {x \left (-3 x +4 \ln \relax (3)+16\right )}{4}\) | \(13\) |
norman | \(\left (\ln \relax (3)+4\right ) x -\frac {3 x^{2}}{4}\) | \(13\) |
default | \(x \ln \relax (3)-\frac {3 x^{2}}{4}+4 x\) | \(14\) |
risch | \(x \ln \relax (3)-\frac {3 x^{2}}{4}+4 x\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 13, normalized size = 0.57 \begin {gather*} -\frac {3}{4} \, x^{2} + x \log \relax (3) + 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.11, size = 12, normalized size = 0.52 \begin {gather*} x\,\left (\ln \relax (3)+4\right )-\frac {3\,x^2}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 12, normalized size = 0.52 \begin {gather*} - \frac {3 x^{2}}{4} + x \left (\log {\relax (3 )} + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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