# Math Help - Exponential of a Brownian motion

1. ## Exponential of a Brownian motion

How do I calculate the expectation of the exponential of a Brownian motion in an easy way, I mean this:

$E[Exp(a W_{t})]$

With $W_{t}$ a Brownian motion

Thx for the help

2. Write it out in integral form
$
\int e^{a x} (2\pi t)^{-1/2}e^{-\frac{x^2}{2t}} dx.
$