Hi, today in such a case I try first Maple to find a cliose form expression. If Maple gives me such a form I come back later to books in order to write properly the things mathematically. 

Thank you for you reply

do you mean using  symbolic integration?

Yes, using symbolic tools as MAPLE, to can obtain the close form when it exists.

I think it is a good practice, thanks

However,  I found the answer to my question in the book itself :)

they actually have made some ordering technique based on classification large expressions to inner and outer functions