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

Optimal. Leaf size=13 \[ -\frac {1}{2} e^{2-x^2} \]

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2209} \[ -\frac {1}{2} e^{2-x^2} \]

Antiderivative was successfully verified.

[In]

Int[E^(2 - x^2)*x,x]

[Out]

-E^(2 - 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^{2-x^2} x \, dx &=-\frac {1}{2} e^{2-x^2}\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 13, normalized size = 1.00 \[ -\frac {1}{2} e^{2-x^2} \]

Antiderivative was successfully verified.

[In]

Integrate[E^(2 - x^2)*x,x]

[Out]

-1/2*E^(2 - x^2)

________________________________________________________________________________________

fricas [A]  time = 0.40, size = 10, normalized size = 0.77 \[ -\frac {1}{2} \, e^{\left (-x^{2} + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/2*e^(-x^2 + 2)

________________________________________________________________________________________

giac [A]  time = 0.21, size = 10, normalized size = 0.77 \[ -\frac {1}{2} \, e^{\left (-x^{2} + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/2*e^(-x^2 + 2)

________________________________________________________________________________________

maple [A]  time = 0.02, size = 11, normalized size = 0.85 \[ -\frac {{\mathrm e}^{-x^{2}+2}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-x^2+2)*x,x)

[Out]

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

________________________________________________________________________________________

maxima [A]  time = 0.80, size = 10, normalized size = 0.77 \[ -\frac {1}{2} \, e^{\left (-x^{2} + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/2*e^(-x^2 + 2)

________________________________________________________________________________________

mupad [B]  time = 0.06, size = 10, normalized size = 0.77 \[ -\frac {{\mathrm {e}}^2\,{\mathrm {e}}^{-x^2}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x*exp(2 - x^2),x)

[Out]

-(exp(2)*exp(-x^2))/2

________________________________________________________________________________________

sympy [A]  time = 0.09, size = 8, normalized size = 0.62 \[ - \frac {e^{2 - x^{2}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(-x**2+2)*x,x)

[Out]

-exp(2 - x**2)/2

________________________________________________________________________________________