You don't use integration by parts. Here, since the numerator is of greater degree than the denominator, you first have to long divide.
Then you need to factorise the denominator of the proper fraction and apply the partial fractions technique.
I know I have done something very wrong, but not sure where.
We have just learnt how to integrate by parts.
I have uploaded a scan of my working in this link :
(It gave me an error when I tried to insert image into this post)
Thank you very much .