Optimal. Leaf size=19 \[ 2+x+\frac {\left (-1+(6-x)^2\right ) \log (3)}{\log (4)} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.84, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {12} \begin {gather*} x+\frac {(6-x)^2 \log (3)}{\log (4)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int ((-12+2 x) \log (3)+\log (4)) \, dx}{\log (4)}\\ &=x+\frac {(6-x)^2 \log (3)}{\log (4)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.11 \begin {gather*} x-\frac {12 x \log (3)}{\log (4)}+\frac {x^2 \log (3)}{\log (4)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 22, normalized size = 1.16 \begin {gather*} \frac {{\left (x^{2} - 12 \, x\right )} \log \relax (3) + 2 \, x \log \relax (2)}{2 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 22, normalized size = 1.16 \begin {gather*} \frac {{\left (x^{2} - 12 \, x\right )} \log \relax (3) + 2 \, x \log \relax (2)}{2 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 21, normalized size = 1.11
method | result | size |
gosper | \(\frac {x \left (x \ln \relax (3)+2 \ln \relax (2)-12 \ln \relax (3)\right )}{2 \ln \relax (2)}\) | \(21\) |
default | \(\frac {2 x \ln \relax (2)+\ln \relax (3) \left (x^{2}-12 x \right )}{2 \ln \relax (2)}\) | \(23\) |
risch | \(\frac {\ln \relax (3) x^{2}}{2 \ln \relax (2)}+x -\frac {6 x \ln \relax (3)}{\ln \relax (2)}\) | \(23\) |
norman | \(\frac {\left (\ln \relax (2)-6 \ln \relax (3)\right ) x}{\ln \relax (2)}+\frac {\ln \relax (3) x^{2}}{2 \ln \relax (2)}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 22, normalized size = 1.16 \begin {gather*} \frac {{\left (x^{2} - 12 \, x\right )} \log \relax (3) + 2 \, x \log \relax (2)}{2 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.56, size = 24, normalized size = 1.26 \begin {gather*} \frac {{\left (\ln \relax (2)+\frac {\ln \relax (3)\,\left (2\,x-12\right )}{2}\right )}^2}{2\,\ln \relax (2)\,\ln \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 24, normalized size = 1.26 \begin {gather*} \frac {x^{2} \log {\relax (3 )}}{2 \log {\relax (2 )}} + \frac {x \left (- 6 \log {\relax (3 )} + \log {\relax (2 )}\right )}{\log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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