Optimal. Leaf size=44 \[ -2 e^{-x/2} x^3-12 e^{-x/2} x^2-48 e^{-x/2} x-96 e^{-x/2} \]
[Out]
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Rubi [A] time = 0.0544157, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ -2 e^{-x/2} x^3-12 e^{-x/2} x^2-48 e^{-x/2} x-96 e^{-x/2} \]
Antiderivative was successfully verified.
[In] Int[x^3/E^(x/2),x]
[Out]
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Rubi in Sympy [A] time = 3.04113, size = 36, normalized size = 0.82 \[ - 2 x^{3} e^{- \frac{x}{2}} - 12 x^{2} e^{- \frac{x}{2}} - 48 x e^{- \frac{x}{2}} - 96 e^{- \frac{x}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/exp(1/2*x),x)
[Out]
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Mathematica [A] time = 0.00522756, size = 23, normalized size = 0.52 \[ e^{-x/2} \left (-2 x^3-12 x^2-48 x-96\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^3/E^(x/2),x]
[Out]
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Maple [A] time = 0.003, size = 22, normalized size = 0.5 \[ -2\,{\frac{{x}^{3}+6\,{x}^{2}+24\,x+48}{{{\rm e}^{x/2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/exp(1/2*x),x)
[Out]
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Maxima [A] time = 1.37629, size = 26, normalized size = 0.59 \[ -2 \,{\left (x^{3} + 6 \, x^{2} + 24 \, x + 48\right )} e^{\left (-\frac{1}{2} \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*e^(-1/2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214349, size = 26, normalized size = 0.59 \[ -2 \,{\left (x^{3} + 6 \, x^{2} + 24 \, x + 48\right )} e^{\left (-\frac{1}{2} \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*e^(-1/2*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.075999, size = 20, normalized size = 0.45 \[ \left (- 2 x^{3} - 12 x^{2} - 48 x - 96\right ) e^{- \frac{x}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/exp(1/2*x),x)
[Out]
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GIAC/XCAS [A] time = 0.21273, size = 26, normalized size = 0.59 \[ -2 \,{\left (x^{3} + 6 \, x^{2} + 24 \, x + 48\right )} e^{\left (-\frac{1}{2} \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*e^(-1/2*x),x, algorithm="giac")
[Out]