I assume you mean . This pdf is incomplete as you do not include the interval over which this expression is defined (the support).
You should know that you need to calculate (and I have not included the integral terminals since you did not completely define the pdf). So please show all your working and clearly state where you are stuck.
Your mgf is OK: - Wolfram|Alpha
I assume at this level you can correctly differentiate and substitute t = 0. You can check your own answer using the definition of E(X): Calculate .