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 = 0.0062455, 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, Rules used = {2209} \[ \frac{e^{x^2}}{2} \]

Antiderivative was successfully verified.

[In]

Int[E^x^2*x,x]

[Out]

E^x^2/2

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

\begin{align*} \int e^{x^2} x \, dx &=\frac{e^{x^2}}{2}\\ \end{align*}

Mathematica [A]  time = 0.000582, 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 \begin{align*}{\frac{{{\rm e}^{{x}^{2}}}}{2}} \end{align*}

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 = 0.925133, size = 8, normalized size = 0.89 \begin{align*} \frac{1}{2} \, e^{\left (x^{2}\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x^2)*x,x, algorithm="maxima")

[Out]

1/2*e^(x^2)

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Fricas [A]  time = 1.91346, size = 18, normalized size = 2. \begin{align*} \frac{1}{2} \, e^{\left (x^{2}\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x^2)*x,x, algorithm="fricas")

[Out]

1/2*e^(x^2)

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Sympy [A]  time = 0.075075, size = 5, normalized size = 0.56 \begin{align*} \frac{e^{x^{2}}}{2} \end{align*}

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 [A]  time = 1.07024, size = 8, normalized size = 0.89 \begin{align*} \frac{1}{2} \, e^{\left (x^{2}\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x^2)*x,x, algorithm="giac")

[Out]

1/2*e^(x^2)