Optimal. Leaf size=27 \[ e^t t^3-3 e^t t^2+6 e^t t-6 e^t \]
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Rubi [A] time = 0.0307144, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286, 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*}
Mathematica [A] time = 0.0060535, size = 17, normalized size = 0.63 \[ e^t \left (t^3-3 t^2+6 t-6\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 17, normalized size = 0.6 \begin{align*} \left ({t}^{3}-3\,{t}^{2}+6\,t-6 \right ){{\rm e}^{t}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.93371, size = 22, normalized size = 0.81 \begin{align*}{\left (t^{3} - 3 \, t^{2} + 6 \, t - 6\right )} e^{t} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.83083, size = 39, normalized size = 1.44 \begin{align*}{\left (t^{3} - 3 \, t^{2} + 6 \, t - 6\right )} e^{t} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.079841, size = 15, normalized size = 0.56 \begin{align*} \left (t^{3} - 3 t^{2} + 6 t - 6\right ) e^{t} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05015, size = 22, normalized size = 0.81 \begin{align*}{\left (t^{3} - 3 \, t^{2} + 6 \, t - 6\right )} e^{t} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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