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 = 0.03, antiderivative size = 27, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, 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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fricas [A] time = 0.38, size = 16, normalized size = 0.59 \[ {\left (t^{3} - 3 \, t^{2} + 6 \, t - 6\right )} e^{t} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.07, size = 16, normalized size = 0.59 \[ {\left (t^{3} - 3 \, t^{2} + 6 \, t - 6\right )} e^{t} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.63 \[ \left (t^{3}-3 t^{2}+6 t -6\right ) {\mathrm e}^{t} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 16, normalized size = 0.59 \[ {\left (t^{3} - 3 \, t^{2} + 6 \, t - 6\right )} e^{t} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 16, normalized size = 0.59 \[ {\mathrm {e}}^t\,\left (t^3-3\,t^2+6\,t-6\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 0.56 \[ \left (t^{3} - 3 t^{2} + 6 t - 6\right ) e^{t} \]
Verification of antiderivative is not currently implemented for this CAS.
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