3.54 \(\int e^{x^2} x^5 \, dx\)

Optimal. Leaf size=28 \[ -e^{x^2} x^2+e^{x^2}+\frac{1}{2} e^{x^2} x^4 \]

[Out]

E^x^2 - E^x^2*x^2 + (E^x^2*x^4)/2

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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]

E^x^2 - E^x^2*x^2 + (E^x^2*x^4)/2

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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]

x**4*exp(x**2)/2 - x**2*exp(x**2) + exp(x**2)

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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]

(E^x^2*(2 - 2*x^2 + x^4))/2

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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]

1/2*(x^4-2*x^2+2)*exp(x^2)

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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]

1/2*(x^4 - 2*x^2 + 2)*e^(x^2)

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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]

1/2*(x^4 - 2*x^2 + 2)*e^(x^2)

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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]

(x**4 - 2*x**2 + 2)*exp(x**2)/2

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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]

1/2*(x^4 - 2*x^2 + 2)*e^(x^2)