Optimal. Leaf size=12 \[ \log \left (9+2 (-4+x)^2 \log (3)\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.25, number of steps
used = 2, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {12, 1601}
\begin {gather*} \log \left (2 \left (x^2-8 x+16\right ) \log (3)+9\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1601
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log (3) \int \frac {-16+4 x}{9+\left (32-16 x+2 x^2\right ) \log (3)} \, dx\\ &=\log \left (9+2 \left (16-8 x+x^2\right ) \log (3)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 12, normalized size = 1.00 \begin {gather*} \log \left (9+2 (-4+x)^2 \log (3)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.04, size = 20, normalized size = 1.67
method | result | size |
derivativedivides | \(\ln \left (\left (2 x^{2}-16 x +32\right ) \ln \left (3\right )+9\right )\) | \(17\) |
default | \(\ln \left (2 x^{2} \ln \left (3\right )-16 x \ln \left (3\right )+32 \ln \left (3\right )+9\right )\) | \(20\) |
norman | \(\ln \left (2 x^{2} \ln \left (3\right )-16 x \ln \left (3\right )+32 \ln \left (3\right )+9\right )\) | \(20\) |
risch | \(\ln \left (2 x^{2} \ln \left (3\right )-16 x \ln \left (3\right )+32 \ln \left (3\right )+9\right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 19, normalized size = 1.58 \begin {gather*} \log \left (2 \, x^{2} \log \left (3\right ) - 16 \, x \log \left (3\right ) + 32 \, \log \left (3\right ) + 9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 15, normalized size = 1.25 \begin {gather*} \log \left (2 \, {\left (x^{2} - 8 \, x + 16\right )} \log \left (3\right ) + 9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 22, normalized size = 1.83 \begin {gather*} \log {\left (2 x^{2} \log {\left (3 \right )} - 16 x \log {\left (3 \right )} + 9 + 32 \log {\left (3 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 18, normalized size = 1.50 \begin {gather*} \log \left (2 \, {\left (x^{2} - 8 \, x\right )} \log \left (3\right ) + 32 \, \log \left (3\right ) + 9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.11, size = 19, normalized size = 1.58 \begin {gather*} \ln \left (2\,\ln \left (3\right )\,x^2-16\,\ln \left (3\right )\,x+32\,\ln \left (3\right )+9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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