Optimal. Leaf size=28 \[ -e^{x^2} x^2+e^{x^2}+\frac{1}{2} e^{x^2} x^4 \]
[Out]
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Rubi [A] time = 0.0503848, antiderivative size = 28, 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 \[ -e^{x^2} x^2+e^{x^2}+\frac{1}{2} e^{x^2} x^4 \]
Antiderivative was successfully verified.
[In] Int[E^x^2*x^5,x]
[Out]
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Rubi in Sympy [A] time = 2.87378, size = 22, normalized size = 0.79 \[ \frac{x^{4} e^{x^{2}}}{2} - x^{2} e^{x^{2}} + e^{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(x**2)*x**5,x)
[Out]
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Mathematica [A] time = 0.00367308, size = 19, normalized size = 0.68 \[ \frac{1}{2} e^{x^2} \left (x^4-2 x^2+2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[E^x^2*x^5,x]
[Out]
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Maple [A] time = 0.004, size = 17, normalized size = 0.6 \[{\frac{ \left ({x}^{4}-2\,{x}^{2}+2 \right ){{\rm e}^{{x}^{2}}}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(x^2)*x^5,x)
[Out]
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Maxima [A] time = 1.45211, size = 22, normalized size = 0.79 \[ \frac{1}{2} \,{\left (x^{4} - 2 \, x^{2} + 2\right )} e^{\left (x^{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5*e^(x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213719, size = 22, normalized size = 0.79 \[ \frac{1}{2} \,{\left (x^{4} - 2 \, x^{2} + 2\right )} e^{\left (x^{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5*e^(x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.081417, size = 15, normalized size = 0.54 \[ \frac{\left (x^{4} - 2 x^{2} + 2\right ) e^{x^{2}}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(x**2)*x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.204191, size = 22, normalized size = 0.79 \[ \frac{1}{2} \,{\left (x^{4} - 2 \, x^{2} + 2\right )} e^{\left (x^{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5*e^(x^2),x, algorithm="giac")
[Out]