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Interesting but tricky integration problem

  • Thread starter grignard
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  • #1
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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
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Use polynomial division to divide x^2+3x-8 by x^2+16 first.
 
  • #3
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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.
 

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