Optimal. Leaf size=12 \[ \log (x (3-x+x \log (4))) \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.33, number of steps used = 3, number of rules used = 2, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {6, 628} \begin {gather*} \log \left (3 x-x^2 (1-\log (4))\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 628
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3+x (-2+2 \log (4))}{3 x-x^2+x^2 \log (4)} \, dx\\ &=\int \frac {3+x (-2+2 \log (4))}{3 x+x^2 (-1+\log (4))} \, dx\\ &=\log \left (3 x-x^2 (1-\log (4))\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 1.08 \begin {gather*} \log (x)+\log (3-x+x \log (4)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 17, normalized size = 1.42 \begin {gather*} \log \left (2 \, x^{2} \log \relax (2) - x^{2} + 3 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 18, normalized size = 1.50 \begin {gather*} \log \left ({\left | 2 \, x^{2} \log \relax (2) - x^{2} + 3 \, x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.40, size = 14, normalized size = 1.17
method | result | size |
default | \(\ln \left (\left (3+2 x \ln \relax (2)-x \right ) x \right )\) | \(14\) |
norman | \(\ln \relax (x )+\ln \left (3+2 x \ln \relax (2)-x \right )\) | \(15\) |
risch | \(\ln \left (\left (2 \ln \relax (2)-1\right ) x^{2}+3 x \right )\) | \(16\) |
derivativedivides | \(\ln \left (2 x^{2} \ln \relax (2)-x^{2}+3 x \right )\) | \(18\) |
meijerg | \(\frac {3 \left (\frac {2 \ln \relax (2)}{3}-\frac {1}{3}\right ) \left (\ln \relax (x )-\ln \relax (3)+\ln \left (2 \ln \relax (2)-1\right )-\ln \left (1+\frac {\left (2 \ln \relax (2)-1\right ) x}{3}\right )\right )}{2 \ln \relax (2)-1}+\frac {3 \left (\frac {4 \ln \relax (2)}{3}-\frac {2}{3}\right ) \ln \left (1+\frac {\left (2 \ln \relax (2)-1\right ) x}{3}\right )}{2 \ln \relax (2)-1}\) | \(74\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 17, normalized size = 1.42 \begin {gather*} \log \left (2 \, x^{2} \log \relax (2) - x^{2} + 3 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.29, size = 28, normalized size = 2.33 \begin {gather*} \ln \relax (x)+\ln \left (2\,x\,\ln \relax (2)-x+3\right )\,\left (\frac {\ln \left (16\right )-2}{\ln \relax (4)-1}-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 14, normalized size = 1.17 \begin {gather*} \log {\left (x^{2} \left (-1 + 2 \log {\relax (2 )}\right ) + 3 x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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