Optimal. Leaf size=15 \[ x \log \left (\frac {5 e^{-x}}{2 x}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2628}
\begin {gather*} x \log \left (\frac {5 e^{-x}}{2 x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2628
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x-\frac {x^2}{2}+\int \log \left (\frac {5 e^{-x}}{2 x}\right ) \, dx\\ &=-x-\frac {x^2}{2}+x \log \left (\frac {5 e^{-x}}{2 x}\right )-\int (-1-x) \, dx\\ &=x \log \left (\frac {5 e^{-x}}{2 x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} x \log \left (\frac {5 e^{-x}}{2 x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.66, size = 13, normalized size = 0.87
method | result | size |
default | \(x \ln \left (\frac {5 \,{\mathrm e}^{-x}}{2 x}\right )\) | \(13\) |
norman | \(x \ln \left (\frac {5 \,{\mathrm e}^{-x}}{2 x}\right )\) | \(13\) |
risch | \(-x \ln \left ({\mathrm e}^{x}\right )+\frac {i \pi x \,\mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{-x}}{x}\right )^{2}}{2}-\frac {i \pi x \,\mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{-x}}{x}\right ) \mathrm {csgn}\left (\frac {i}{x}\right )}{2}+\frac {i \pi x \mathrm {csgn}\left (\frac {i {\mathrm e}^{-x}}{x}\right )^{2} \mathrm {csgn}\left (\frac {i}{x}\right )}{2}-\frac {i \pi x \mathrm {csgn}\left (\frac {i {\mathrm e}^{-x}}{x}\right )^{3}}{2}+x \ln \left (5\right )-x \ln \left (2\right )-x \ln \left (x \right )\) | \(122\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 12, normalized size = 0.80 \begin {gather*} x \log \left (\frac {5 \, e^{\left (-x\right )}}{2 \, x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 12, normalized size = 0.80 \begin {gather*} x \log \left (\frac {5 \, e^{\left (-x\right )}}{2 \, x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 10, normalized size = 0.67 \begin {gather*} x \log {\left (\frac {5 e^{- x}}{2 x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 20, normalized size = 1.33 \begin {gather*} -x^{2} + x \log \left (5\right ) - x \log \left (2\right ) - x \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.10, size = 13, normalized size = 0.87 \begin {gather*} -x\,\left (x-\ln \left (\frac {5}{2\,x}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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