Optimal. Leaf size=26 \[ -e^{-t} t^2-2 e^{-t} t-2 e^{-t} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0349204, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ -e^{-t} t^2-2 e^{-t} t-2 e^{-t} \]
Antiderivative was successfully verified.
[In] Int[t^2/E^t,t]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.75476, size = 19, normalized size = 0.73 \[ - t^{2} e^{- t} - 2 t e^{- t} - 2 e^{- t} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(t**2/exp(t),t)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0034347, size = 16, normalized size = 0.62 \[ e^{-t} \left (-t^2-2 t-2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[t^2/E^t,t]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.004, size = 15, normalized size = 0.6 \[ -{\frac{{t}^{2}+2\,t+2}{{{\rm e}^{t}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(t^2/exp(t),t)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34743, size = 19, normalized size = 0.73 \[ -{\left (t^{2} + 2 \, t + 2\right )} e^{\left (-t\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(t^2*e^(-t),t, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.212409, size = 19, normalized size = 0.73 \[ -{\left (t^{2} + 2 \, t + 2\right )} e^{\left (-t\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(t^2*e^(-t),t, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.088941, size = 12, normalized size = 0.46 \[ \left (- t^{2} - 2 t - 2\right ) e^{- t} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(t**2/exp(t),t)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.215646, size = 19, normalized size = 0.73 \[ -{\left (t^{2} + 2 \, t + 2\right )} e^{\left (-t\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(t^2*e^(-t),t, algorithm="giac")
[Out]