integrating this infinite gaussian integral How does one integrate 
$\int_{-\infty}^{+\infty}x e^{-\lambda ( x-a )^2 }dx $
where $\lambda$ is a positive constant.
My integral tables are not returning anything useable. The best it return is non-definite gaussian integrals. Useless!
Help please

If the integral is the one you wrote, then of course no table gives you any hint: that integral does not converge. Indeed:
$$\int_{-\infty}^{+\infty}xe^{-\lambda}(x-a)^2\ \text{d}x = e^{-\lambda}\int_{-\infty}^{+\infty}(x^3 + a^2 x - 2ax^2)\ \text{d}x$$
And you easily can integrate it, but it will diverge.
So I think you wrote wrong, and the real integral is
$$\int_{-\infty}^{+\infty}x e^{-\lambda(x-a)^2}\ \text{d}x$$
At this point you can use
$$\sqrt{\lambda}(x-a) = y ~~~~~~~ \text{d}y = \sqrt{\lambda}\ \text{d}x ~~~~~~~ x = \frac{y}{\sqrt{\lambda}}+a$$
Can you proceed?
