Optimal. Leaf size=14 \[ x+(1-x) (x-\log (x)) \]
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Rubi [A]
time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.21, number of steps
used = 5, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {14, 2332}
\begin {gather*} -x^2+2 x+x \log (x)-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2332
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-1+3 x-2 x^2}{x}+\log (x)\right ) \, dx\\ &=\int \frac {-1+3 x-2 x^2}{x} \, dx+\int \log (x) \, dx\\ &=-x+x \log (x)+\int \left (3-\frac {1}{x}-2 x\right ) \, dx\\ &=2 x-x^2-\log (x)+x \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.21 \begin {gather*} 2 x-x^2-\log (x)+x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 18, normalized size = 1.29
method | result | size |
default | \(x \ln \left (x \right )+2 x -x^{2}-\ln \left (x \right )\) | \(18\) |
norman | \(x \ln \left (x \right )+2 x -x^{2}-\ln \left (x \right )\) | \(18\) |
risch | \(x \ln \left (x \right )+2 x -x^{2}-\ln \left (x \right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 17, normalized size = 1.21 \begin {gather*} -x^{2} + x \log \left (x\right ) + 2 \, x - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.31, size = 15, normalized size = 1.07 \begin {gather*} -x^{2} + {\left (x - 1\right )} \log \left (x\right ) + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 14, normalized size = 1.00 \begin {gather*} - x^{2} + x \log {\left (x \right )} + 2 x - \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 17, normalized size = 1.21 \begin {gather*} -x^{2} + x \log \left (x\right ) + 2 \, x - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.45, size = 17, normalized size = 1.21 \begin {gather*} 2\,x-\ln \left (x\right )+x\,\ln \left (x\right )-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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