Optimal. Leaf size=16 \[ -e^{-t}-e^{-t} t \]
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Rubi [A]
time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {2207, 2225}
\begin {gather*} -e^{-t} t-e^{-t} \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rubi steps
\begin {align*} \int e^{-t} t \, dt &=-e^{-t} t+\int e^{-t} \, dt\\ &=-e^{-t}-e^{-t} t\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 11, normalized size = 0.69 \begin {gather*} e^{-t} (-1-t) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 15, normalized size = 0.94
method | result | size |
gosper | \(-\left (1+t \right ) {\mathrm e}^{-t}\) | \(10\) |
norman | \(\left (-1-t \right ) {\mathrm e}^{-t}\) | \(11\) |
risch | \(\left (-1-t \right ) {\mathrm e}^{-t}\) | \(11\) |
meijerg | \(1-\frac {\left (2 t +2\right ) {\mathrm e}^{-t}}{2}\) | \(14\) |
default | \(-{\mathrm e}^{-t}-t \,{\mathrm e}^{-t}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.93, size = 9, normalized size = 0.56 \begin {gather*} -{\left (t + 1\right )} e^{\left (-t\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.67, size = 9, normalized size = 0.56 \begin {gather*} -{\left (t + 1\right )} e^{\left (-t\right )} \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 = 0.44 \begin {gather*} \left (- t - 1\right ) e^{- t} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 9, normalized size = 0.56 \begin {gather*} -{\left (t + 1\right )} e^{\left (-t\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 9, normalized size = 0.56 \begin {gather*} -{\mathrm {e}}^{-t}\,\left (t+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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