Optimal. Leaf size=36 \[ -e^{-t} t^3-3 e^{-t} t^2-6 e^{-t} t-6 e^{-t} \]
[Out]
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Rubi [A] time = 0.0537962, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ -e^{-t} t^3-3 e^{-t} t^2-6 e^{-t} t-6 e^{-t} \]
Antiderivative was successfully verified.
[In] Int[t^3/E^t,t]
[Out]
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Rubi in Sympy [A] time = 2.57745, size = 27, normalized size = 0.75 \[ - t^{3} e^{- t} - 3 t^{2} e^{- t} - 6 t e^{- t} - 6 e^{- t} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(t**3/exp(t),t)
[Out]
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Mathematica [A] time = 0.00420394, size = 21, normalized size = 0.58 \[ e^{-t} \left (-t^3-3 t^2-6 t-6\right ) \]
Antiderivative was successfully verified.
[In] Integrate[t^3/E^t,t]
[Out]
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Maple [A] time = 0.004, size = 20, normalized size = 0.6 \[ -{\frac{{t}^{3}+3\,{t}^{2}+6\,t+6}{{{\rm e}^{t}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(t^3/exp(t),t)
[Out]
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Maxima [A] time = 1.3571, size = 26, normalized size = 0.72 \[ -{\left (t^{3} + 3 \, t^{2} + 6 \, t + 6\right )} e^{\left (-t\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(t^3*e^(-t),t, algorithm="maxima")
[Out]
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Fricas [A] time = 0.198283, size = 26, normalized size = 0.72 \[ -{\left (t^{3} + 3 \, t^{2} + 6 \, t + 6\right )} e^{\left (-t\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(t^3*e^(-t),t, algorithm="fricas")
[Out]
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Sympy [A] time = 0.125162, 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.
[In] integrate(t**3/exp(t),t)
[Out]
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GIAC/XCAS [A] time = 0.227735, size = 26, normalized size = 0.72 \[ -{\left (t^{3} + 3 \, t^{2} + 6 \, t + 6\right )} e^{\left (-t\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(t^3*e^(-t),t, algorithm="giac")
[Out]