# How to calculate the following expectation

I have a problem to find the expectation of the following expression,
$$E\left[W_T e^{\int_0^T(W_s)ds}\right].$$
Here, $W_T$ is a Brownian motion. Any suggestions as to how to proceed with it? Many thanks for the help!

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calculate $E(exp^{\int^T W_s ds})$ by using that exponent is gaussian, then differentiate result wrt $T$...I'm assuming $W_t$ is brownian motion, and that you wanted $W_T$ out front –  mike Dec 13 '12 at 21:10
Got it, many thanks!!! –  user53013 Dec 14 '12 at 6:23