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

Optimal. Leaf size=9 \[ \frac{e^{x^2}}{2} \]

[Out]

E^x^2/2

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Rubi [A]  time = 0.0118742, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{e^{x^2}}{2} \]

Antiderivative was successfully verified.

[In]  Int[E^x^2*x,x]

[Out]

E^x^2/2

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Rubi in Sympy [A]  time = 1.06089, size = 5, normalized size = 0.56 \[ \frac{e^{x^{2}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(x**2)*x,x)

[Out]

exp(x**2)/2

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Mathematica [A]  time = 0.00116154, size = 9, normalized size = 1. \[ \frac{e^{x^2}}{2} \]

Antiderivative was successfully verified.

[In]  Integrate[E^x^2*x,x]

[Out]

E^x^2/2

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Maple [A]  time = 0., size = 7, normalized size = 0.8 \[{\frac{{{\rm e}^{{x}^{2}}}}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(x^2)*x,x)

[Out]

1/2*exp(x^2)

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Maxima [A]  time = 1.35177, size = 8, normalized size = 0.89 \[ \frac{1}{2} \, e^{\left (x^{2}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*e^(x^2),x, algorithm="maxima")

[Out]

1/2*e^(x^2)

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Fricas [A]  time = 0.212342, size = 8, normalized size = 0.89 \[ \frac{1}{2} \, e^{\left (x^{2}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*e^(x^2),x, algorithm="fricas")

[Out]

1/2*e^(x^2)

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Sympy [A]  time = 0.05864, size = 5, normalized size = 0.56 \[ \frac{e^{x^{2}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(x**2)*x,x)

[Out]

exp(x**2)/2

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GIAC/XCAS [A]  time = 0.223895, size = 8, normalized size = 0.89 \[ \frac{1}{2} \, e^{\left (x^{2}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*e^(x^2),x, algorithm="giac")

[Out]

1/2*e^(x^2)