Optimal. Leaf size=26 \[ -\frac{1}{2} e^{-x^2} x^2-\frac{e^{-x^2}}{2} \]
[Out]
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Rubi [A] time = 0.0340855, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ -\frac{1}{2} e^{-x^2} x^2-\frac{e^{-x^2}}{2} \]
Antiderivative was successfully verified.
[In] Int[x^3/E^x^2,x]
[Out]
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Rubi in Sympy [A] time = 1.91424, size = 19, normalized size = 0.73 \[ - \frac{x^{2} e^{- x^{2}}}{2} - \frac{e^{- x^{2}}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/exp(x**2),x)
[Out]
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Mathematica [A] time = 0.00428297, size = 18, normalized size = 0.69 \[ \frac{1}{2} e^{-x^2} \left (-x^2-1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^3/E^x^2,x]
[Out]
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Maple [A] time = 0.004, size = 14, normalized size = 0.5 \[ -{\frac{{x}^{2}+1}{2\,{{\rm e}^{{x}^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/exp(x^2),x)
[Out]
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Maxima [A] time = 1.40734, size = 18, normalized size = 0.69 \[ -\frac{1}{2} \,{\left (x^{2} + 1\right )} e^{\left (-x^{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*e^(-x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212363, size = 18, normalized size = 0.69 \[ -\frac{1}{2} \,{\left (x^{2} + 1\right )} e^{\left (-x^{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*e^(-x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.079511, size = 12, normalized size = 0.46 \[ \frac{\left (- x^{2} - 1\right ) e^{- x^{2}}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/exp(x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.236536, size = 18, normalized size = 0.69 \[ -\frac{1}{2} \,{\left (x^{2} + 1\right )} e^{\left (-x^{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*e^(-x^2),x, algorithm="giac")
[Out]