Optimal. Leaf size=32 \[ -\frac{1}{2} e^{-2 x} x^2-\frac{1}{2} e^{-2 x} x-\frac{e^{-2 x}}{4} \]
[Out]
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Rubi [A] time = 0.0300944, antiderivative size = 32, 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 \[ -\frac{1}{2} e^{-2 x} x^2-\frac{1}{2} e^{-2 x} x-\frac{e^{-2 x}}{4} \]
Antiderivative was successfully verified.
[In] Int[x^2/E^(2*x),x]
[Out]
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Rubi in Sympy [A] time = 1.89209, size = 27, normalized size = 0.84 \[ - \frac{x^{2} e^{- 2 x}}{2} - \frac{x e^{- 2 x}}{2} - \frac{e^{- 2 x}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/exp(2*x),x)
[Out]
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Mathematica [A] time = 0.00410474, size = 19, normalized size = 0.59 \[ -\frac{1}{4} e^{-2 x} \left (2 x^2+2 x+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^2/E^(2*x),x]
[Out]
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Maple [A] time = 0.003, size = 19, normalized size = 0.6 \[ -{\frac{2\,{x}^{2}+2\,x+1}{4\,{{\rm e}^{2\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/exp(2*x),x)
[Out]
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Maxima [A] time = 1.41579, size = 22, normalized size = 0.69 \[ -\frac{1}{4} \,{\left (2 \, x^{2} + 2 \, x + 1\right )} e^{\left (-2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^(-2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208442, size = 22, normalized size = 0.69 \[ -\frac{1}{4} \,{\left (2 \, x^{2} + 2 \, x + 1\right )} e^{\left (-2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^(-2*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.078853, size = 17, normalized size = 0.53 \[ \frac{\left (- 2 x^{2} - 2 x - 1\right ) e^{- 2 x}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/exp(2*x),x)
[Out]
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GIAC/XCAS [A] time = 0.237221, size = 22, normalized size = 0.69 \[ -\frac{1}{4} \,{\left (2 \, x^{2} + 2 \, x + 1\right )} e^{\left (-2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^(-2*x),x, algorithm="giac")
[Out]