Setting the function you have to integrate becomes...

(1)

Now is...

(2)

... and the two fractional terms in (2) can be written as series in the following manner...

(3)

Now you insert (3) in (2), then multiply by and obtain (1) , then set in (1) and [finally!...] at this point you can integrate 'term by term'... a little tedious job ...

Kind regards

A little p.s. : the series expansions (3) are possible only for , so that the procedure is correct only for , i.e. only for ...