Optimal. Leaf size=36 \[ -e^{-t} t^3-3 e^{-t} t^2-6 e^{-t} t-6 e^{-t} \]
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Rubi [A] time = 0.03, antiderivative size = 36, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {2176, 2194} \[ -e^{-t} t^3-3 e^{-t} t^2-6 e^{-t} t-6 e^{-t} \]
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {align*} \int e^{-t} t^3 \, dt &=-e^{-t} t^3+3 \int e^{-t} t^2 \, dt\\ &=-3 e^{-t} t^2-e^{-t} t^3+6 \int e^{-t} t \, dt\\ &=-6 e^{-t} t-3 e^{-t} t^2-e^{-t} t^3+6 \int e^{-t} \, dt\\ &=-6 e^{-t}-6 e^{-t} t-3 e^{-t} t^2-e^{-t} t^3\\ \end {align*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 0.58 \[ e^{-t} \left (-t^3-3 t^2-6 t-6\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 19, normalized size = 0.53 \[ -{\left (t^{3} + 3 \, t^{2} + 6 \, t + 6\right )} e^{\left (-t\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 19, normalized size = 0.53 \[ -{\left (t^{3} + 3 \, t^{2} + 6 \, t + 6\right )} e^{\left (-t\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 20, normalized size = 0.56 \[ -\left (t^{3}+3 t^{2}+6 t +6\right ) {\mathrm e}^{-t} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 19, normalized size = 0.53 \[ -{\left (t^{3} + 3 \, t^{2} + 6 \, t + 6\right )} e^{\left (-t\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 19, normalized size = 0.53 \[ -{\mathrm {e}}^{-t}\,\left (t^3+3\,t^2+6\,t+6\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 17, normalized size = 0.47 \[ \left (- t^{3} - 3 t^{2} - 6 t - 6\right ) e^{- t} \]
Verification of antiderivative is not currently implemented for this CAS.
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