Optimal. Leaf size=11 \[ -e^x+e^x x \]
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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {2207, 2225}
\begin {gather*} e^x x-e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rubi steps
\begin {align*} \int e^x x \, dx &=e^x x-\int e^x \, dx\\ &=-e^x+e^x x\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 7, normalized size = 0.64 \begin {gather*} e^x (-1+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 10, normalized size = 0.91
method | result | size |
gosper | \(\left (-1+x \right ) {\mathrm e}^{x}\) | \(7\) |
risch | \(\left (-1+x \right ) {\mathrm e}^{x}\) | \(7\) |
default | \(-{\mathrm e}^{x}+{\mathrm e}^{x} x\) | \(10\) |
norman | \(-{\mathrm e}^{x}+{\mathrm e}^{x} x\) | \(10\) |
meijerg | \(1-\frac {\left (-2 x +2\right ) {\mathrm e}^{x}}{2}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 2.48, size = 6, normalized size = 0.55 \begin {gather*} {\left (x - 1\right )} e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.90, size = 6, normalized size = 0.55 \begin {gather*} {\left (x - 1\right )} e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 5, normalized size = 0.45 \begin {gather*} \left (x - 1\right ) e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 6, normalized size = 0.55 \begin {gather*} {\left (x - 1\right )} e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 6, normalized size = 0.55 \begin {gather*} {\mathrm {e}}^x\,\left (x-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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