Optimal. Leaf size=22 \[ x-2 e^{-4-x} x \left (-5+\log \left (x^{-2/x}\right )\right ) \]
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Rubi [A]
time = 0.43, antiderivative size = 25, normalized size of antiderivative = 1.14, number of steps
used = 3, number of rules used = 2, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {6874, 2326}
\begin {gather*} \frac {2 e^{-x-4} \left (5 x^2+2 x \log (x)\right )}{x}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-\frac {2 e^{-4-x} \left (-2-5 x+5 x^2+2 x \log (x)\right )}{x}\right ) \, dx\\ &=x-2 \int \frac {e^{-4-x} \left (-2-5 x+5 x^2+2 x \log (x)\right )}{x} \, dx\\ &=x+\frac {2 e^{-4-x} \left (5 x^2+2 x \log (x)\right )}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 23, normalized size = 1.05 \begin {gather*} x+10 e^{-4-x} x+4 e^{-4-x} \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.28, size = 18, normalized size = 0.82
method | result | size |
default | \(x +\left (10 x +4 \ln \left (x \right )\right ) {\mathrm e}^{-x -4}\) | \(18\) |
norman | \(\left (x \,{\mathrm e}^{4+x}+10 x +4 \ln \left (x \right )\right ) {\mathrm e}^{-x -4}\) | \(22\) |
risch | \(4 \,{\mathrm e}^{-x -4} \ln \left (x \right )+x \left ({\mathrm e}^{4+x}+10\right ) {\mathrm e}^{-x -4}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 31, normalized size = 1.41 \begin {gather*} 10 \, {\left (x + 1\right )} e^{\left (-x - 4\right )} + 4 \, e^{\left (-x - 4\right )} \log \left (x\right ) + x - 10 \, e^{\left (-x - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 21, normalized size = 0.95 \begin {gather*} {\left (x e^{\left (x + 4\right )} + 10 \, x + 4 \, \log \left (x\right )\right )} e^{\left (-x - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 15, normalized size = 0.68 \begin {gather*} x + \left (10 x + 4 \log {\left (x \right )}\right ) e^{- x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 23, normalized size = 1.05 \begin {gather*} {\left (x e^{4} + 10 \, x e^{\left (-x\right )} + 4 \, e^{\left (-x\right )} \log \left (x\right )\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.01, size = 21, normalized size = 0.95 \begin {gather*} x+10\,x\,{\mathrm {e}}^{-x-4}+4\,{\mathrm {e}}^{-x-4}\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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