Optimal. Leaf size=18 \[ (-5+x)^2-x-\frac {x^2}{\log (3)} \]
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Rubi [A]
time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.17, number of steps
used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {12}
\begin {gather*} \frac {1}{4} (11-2 x)^2-\frac {x^2}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int (-2 x+(-11+2 x) \log (3)) \, dx}{\log (3)}\\ &=\frac {1}{4} (11-2 x)^2-\frac {x^2}{\log (3)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 19, normalized size = 1.06 \begin {gather*} -11 x+\frac {x^2 (-2+\log (9))}{2 \log (3)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 23, normalized size = 1.28
method | result | size |
norman | \(\frac {\left (\ln \left (3\right )-1\right ) x^{2}}{\ln \left (3\right )}-11 x\) | \(17\) |
risch | \(x^{2}-11 x -\frac {x^{2}}{\ln \left (3\right )}\) | \(17\) |
gosper | \(\frac {x \left (x \ln \left (3\right )-11 \ln \left (3\right )-x \right )}{\ln \left (3\right )}\) | \(19\) |
default | \(\frac {x^{2} \ln \left (3\right )-11 x \ln \left (3\right )-x^{2}}{\ln \left (3\right )}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 21, normalized size = 1.17 \begin {gather*} -\frac {x^{2} - {\left (x^{2} - 11 \, x\right )} \log \left (3\right )}{\log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 21, normalized size = 1.17 \begin {gather*} -\frac {x^{2} - {\left (x^{2} - 11 \, x\right )} \log \left (3\right )}{\log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 14, normalized size = 0.78 \begin {gather*} \frac {x^{2} \left (-1 + \log {\left (3 \right )}\right )}{\log {\left (3 \right )}} - 11 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 21, normalized size = 1.17 \begin {gather*} -\frac {x^{2} - {\left (x^{2} - 11 \, x\right )} \log \left (3\right )}{\log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 16, normalized size = 0.89 \begin {gather*} \frac {x^2\,\left (\ln \left (3\right )-1\right )}{\ln \left (3\right )}-11\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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