Optimal. Leaf size=20 \[ \frac {1}{4} \left (-7+e^4+(1-x)^2\right ) (4+\log (9)) \]
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Rubi [A]
time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12}
\begin {gather*} x^2-2 x+\frac {1}{4} (1-x)^2 \log (9) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int (-4+4 x+(-1+x) \log (9)) \, dx\\ &=-2 x+x^2+\frac {1}{4} (1-x)^2 \log (9)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 19, normalized size = 0.95 \begin {gather*} \frac {1}{2} \left (-x+\frac {x^2}{2}\right ) (4+\log (9)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 15, normalized size = 0.75
method | result | size |
gosper | \(\frac {\left (2+\ln \left (3\right )\right ) \left (x -2\right ) x}{2}\) | \(11\) |
default | \(\left (2+\ln \left (3\right )\right ) \left (\frac {1}{2} x^{2}-x \right )\) | \(15\) |
norman | \(\left (-2-\ln \left (3\right )\right ) x +\left (1+\frac {\ln \left (3\right )}{2}\right ) x^{2}\) | \(20\) |
risch | \(\frac {x^{2} \ln \left (3\right )}{2}-x \ln \left (3\right )+x^{2}-2 x\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 18, normalized size = 0.90 \begin {gather*} x^{2} + \frac {1}{2} \, {\left (x^{2} - 2 \, x\right )} \log \left (3\right ) - 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 18, normalized size = 0.90 \begin {gather*} x^{2} + \frac {1}{2} \, {\left (x^{2} - 2 \, x\right )} \log \left (3\right ) - 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 17, normalized size = 0.85 \begin {gather*} x^{2} \left (\frac {\log {\left (3 \right )}}{2} + 1\right ) + x \left (-2 - \log {\left (3 \right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 18, normalized size = 0.90 \begin {gather*} x^{2} + \frac {1}{2} \, {\left (x^{2} - 2 \, x\right )} \log \left (3\right ) - 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 10, normalized size = 0.50 \begin {gather*} \frac {x\,\left (\ln \left (3\right )+2\right )\,\left (x-2\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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