Optimal. Leaf size=26 \[ -e^{-x} x^2-2 e^{-x} x-2 e^{-x} \]
[Out]
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Rubi [A] time = 0.0321554, 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 \[ -e^{-x} x^2-2 e^{-x} x-2 e^{-x} \]
Antiderivative was successfully verified.
[In] Int[x^2/E^x,x]
[Out]
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Rubi in Sympy [A] time = 1.95296, size = 19, normalized size = 0.73 \[ - x^{2} e^{- x} - 2 x e^{- x} - 2 e^{- x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/exp(x),x)
[Out]
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Mathematica [A] time = 0.00363885, size = 16, normalized size = 0.62 \[ e^{-x} \left (-x^2-2 x-2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^2/E^x,x]
[Out]
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Maple [A] time = 0.003, size = 15, normalized size = 0.6 \[ -{\frac{{x}^{2}+2\,x+2}{{{\rm e}^{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/exp(x),x)
[Out]
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Maxima [A] time = 1.35939, size = 19, normalized size = 0.73 \[ -{\left (x^{2} + 2 \, x + 2\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^(-x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.242986, size = 19, normalized size = 0.73 \[ -{\left (x^{2} + 2 \, x + 2\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^(-x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.069028, size = 12, normalized size = 0.46 \[ \left (- x^{2} - 2 x - 2\right ) e^{- x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/exp(x),x)
[Out]
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GIAC/XCAS [A] time = 0.218072, size = 19, normalized size = 0.73 \[ -{\left (x^{2} + 2 \, x + 2\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^(-x),x, algorithm="giac")
[Out]