Just in case you are not sure what to do after the substitution:
u^4/(u^2 + 3u + 2)
Now, use long division to get a more standard integral:
u^2 - 3u + 7 - (15u + 14)/(u^2 + 3u + 2)
Since the denominator is factorable, you can use partial fractions to finish it up.