Interesting but tricky integration problem

[grignard]

Homework Statement

Evaluate the integral, (x^2+3x-8/x^2+16)dx, without using partial fraction expansion. Now this has really confused me. I know that partial fraction expansion is not viable because the mumerator has a higher power overall than the denominator

The Attempt at a Solution

S x^2 /(x^2 + 16) dx + S 3x /(x^2 + 16) dx - S 8 /(x^2 + 16) dx

i have split it up like this, but i am not sure if this counts as a partial fracion expansion?

Next id use the rule, that the integral of (dx/a^2+x^2)=1/a tan(-1) x/a +c. But there are several x^2 on top, so how this does fit in.
It probably easier than it looks, any help would be much appreciaed. Thanks

 

[Dick]

Use polynomial division to divide x^2+3x-8 by x^2+16 first.

 

[Mark44]

I know that partial fraction expansion is not viable because the mumerator has a higher power overall than the denominator

Minor point -- the numerator does NOT have a higher power than the denominator. The degree of each is 2.