You don't use integration by parts. Here, since the numerator is of greater degree than the denominator, you first have to long divide.
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Then you need to factorise the denominator of the proper fraction and apply the partial fractions technique.
Hello.
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 :
http://imageshack.us/m/842/448/mhf.png
(It gave me an error when I tried to insert image into this post)
Thank you very much .