Ok, so polynomial long division, use need it to make the degree of the polynom. in the numerator smaller than the one in denominator.
**See here for the long division steps, can't make it work on here
Long division polynomial.doc
The numbers in red on the attachment are the numbers you use in your new integral:
I was wrong about needing partial fractions for this one. You can just integrate it normally. Some long division polynomial problems you will want to combine your answers into a new rational integral with a smaller polynomial in the numerator and then use partial fractions.
*Sorry this took me so long to get to you!
Let me know if you still need help!