Are you told to let ? because if so, your substitution into the two pdfs is wrong.
You can prove that the integral exists, by taking the limit of the integrand as x tends to 0, and noting that the function is continuous on (0,b). Then in order to solve for the integral, find the power series of and hence simplify
Under certain circumstances (which I suck at stating), you can reverse the integral and the sum signs and it becomes easy to compute.