Neither have closed form solutions, so unless you know about Exponential Integrals, Hypergeometric functions and the Gamma Function, I would advise looking for a series solution to these.
Yeah that doesn't make sense. We wouldn't be asked to solve integrals of this form. I must've made some mistake the in the steps to obtain the integrals. But anyway, thanks for the help, and thanks for that link. Will be handy in the future.