<p>(-5 x^3-4 x^2+16)/(x^4+2 x^3)</p>
<p>So… I’m not sure but, tell me, can you integrate by parts if the denominator contains x^3?</p>
<p>If yes:
denominator of question = x^3(x+2)
Divide numerator by (x+2). it becomes solvable.</p>
<p>u substitution?</p>
<p>It cannot be solved if you actually try to divide the numerator by (x+2). Instead convert it into partial fractions and do it. Trust me I just solved it and it doesn’t take more than 5 min. If you want the whole working I shall post it.</p>
<p>Sorry, I meant integration by partial fractions after you divide it by (x+2) (not parts, so sorry!)
It does get solved if you divide by x+2, it’s maybe a bit long, but essentially we’re doing the same thing…</p>
<p>Are you in Calc BC? If you are, I would use partial fraction method.
So break it up into</p>
<p>(-5/x+2) + (-4/x^2) + (8/x^3)</p>
<p>Then integrate separately.</p>