Optimal. Leaf size=27 \[ e^t t^3-3 e^t t^2+6 e^t t-6 e^t \]
[Out]
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Rubi [A] time = 0.047074, 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 \[ e^t t^3-3 e^t t^2+6 e^t t-6 e^t \]
Antiderivative was successfully verified.
[In] Int[E^t*t^3,t]
[Out]
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Rubi in Sympy [A] time = 2.64576, size = 26, normalized size = 0.96 \[ t^{3} e^{t} - 3 t^{2} e^{t} + 6 t e^{t} - 6 e^{t} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(t)*t**3,t)
[Out]
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Mathematica [A] time = 0.00284049, size = 17, normalized size = 0.63 \[ e^t \left (t^3-3 t^2+6 t-6\right ) \]
Antiderivative was successfully verified.
[In] Integrate[E^t*t^3,t]
[Out]
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Maple [A] time = 0.004, size = 17, normalized size = 0.6 \[ \left ({t}^{3}-3\,{t}^{2}+6\,t-6 \right ){{\rm e}^{t}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(t)*t^3,t)
[Out]
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Maxima [A] time = 1.40972, size = 22, normalized size = 0.81 \[{\left (t^{3} - 3 \, t^{2} + 6 \, t - 6\right )} e^{t} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(t^3*e^t,t, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205059, size = 22, normalized size = 0.81 \[{\left (t^{3} - 3 \, t^{2} + 6 \, t - 6\right )} e^{t} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(t^3*e^t,t, algorithm="fricas")
[Out]
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Sympy [A] time = 0.06951, 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.
[In] integrate(exp(t)*t**3,t)
[Out]
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GIAC/XCAS [A] time = 0.198196, size = 22, normalized size = 0.81 \[{\left (t^{3} - 3 \, t^{2} + 6 \, t - 6\right )} e^{t} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(t^3*e^t,t, algorithm="giac")
[Out]