Optimal. Leaf size=18 \[ 6+e^2-e^x (3-x)-x \]
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Rubi [A]
time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.06, number of steps
used = 3, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {2207, 2225}
\begin {gather*} -e^x (2-x)-e^x-x \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x+\int e^x (-2+x) \, dx\\ &=-e^x (2-x)-x-\int e^x \, dx\\ &=-e^x-e^x (2-x)-x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 11, normalized size = 0.61 \begin {gather*} e^x (-3+x)-x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 13, normalized size = 0.72
method | result | size |
risch | \(\left (x -3\right ) {\mathrm e}^{x}-x\) | \(11\) |
default | \(-x +{\mathrm e}^{x} x -3 \,{\mathrm e}^{x}\) | \(13\) |
norman | \(-x +{\mathrm e}^{x} x -3 \,{\mathrm e}^{x}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 14, normalized size = 0.78 \begin {gather*} {\left (x - 1\right )} e^{x} - x - 2 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 10, normalized size = 0.56 \begin {gather*} {\left (x - 3\right )} e^{x} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 7, normalized size = 0.39 \begin {gather*} - x + \left (x - 3\right ) e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 10, normalized size = 0.56 \begin {gather*} {\left (x - 3\right )} e^{x} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.46, size = 12, normalized size = 0.67 \begin {gather*} x\,{\mathrm {e}}^x-3\,{\mathrm {e}}^x-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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