Interesting but tricky integration problem

  • Thread starter grignard
  • Start date
  • #1
1
0

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
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,260
619
Use polynomial division to divide x^2+3x-8 by x^2+16 first.
 
  • #3
34,825
6,568
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.
 

Related Threads on Interesting but tricky integration problem

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
13
Views
1K
Replies
11
Views
2K
Replies
8
Views
1K
Replies
2
Views
626
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
914
Top