Optimal. Leaf size=22 \[ \frac{1}{2} e^{x^2} x^2-\frac{e^{x^2}}{2} \]
[Out]
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Rubi [A] time = 0.0321641, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{1}{2} e^{x^2} x^2-\frac{e^{x^2}}{2} \]
Antiderivative was successfully verified.
[In] Int[E^x^2*x^3,x]
[Out]
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Rubi in Sympy [A] time = 3.78177, size = 15, normalized size = 0.68 \[ \frac{x^{2} e^{x^{2}}}{2} - \frac{e^{x^{2}}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(x**2)*x**3,x)
[Out]
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Mathematica [A] time = 0.00335246, size = 14, normalized size = 0.64 \[ \frac{1}{2} e^{x^2} \left (x^2-1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[E^x^2*x^3,x]
[Out]
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Maple [A] time = 0.004, size = 12, normalized size = 0.6 \[{\frac{ \left ({x}^{2}-1 \right ){{\rm e}^{{x}^{2}}}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(x^2)*x^3,x)
[Out]
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Maxima [A] time = 0.785365, size = 15, normalized size = 0.68 \[ \frac{1}{2} \,{\left (x^{2} - 1\right )} e^{\left (x^{2}\right )} \]
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 = 0.234235, size = 15, normalized size = 0.68 \[ \frac{1}{2} \,{\left (x^{2} - 1\right )} e^{\left (x^{2}\right )} \]
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 = 0.059248, size = 10, normalized size = 0.45 \[ \frac{\left (x^{2} - 1\right ) e^{x^{2}}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(x**2)*x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.223341, size = 15, normalized size = 0.68 \[ \frac{1}{2} \,{\left (x^{2} - 1\right )} e^{\left (x^{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*e^(x^2),x, algorithm="giac")
[Out]