Have a problem regarding the expected value of the Wiener process inside a function, namely:
Compute $E[cos(W_t)]$.
To extend my question, what is the general method of computing these E´s when it is wrapped up inside some function? For this I have a hunch of having to use some Taylor series for the cosine but how do I know? When do I need some special method apart from just using Ito´s?