Calculus II - Partial Fractions - Evaluate integral dx/(x^4-10x^2+9)

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Homework Statement



Evaluate integral dx/(x^4-10x^2+9)

Homework Equations





The Attempt at a Solution



Ok so I'm trying to solve this problem for my calculus II course as a homework problem and am lost.

The first attachment you'll see how I attempted to evaluate the integral by setting u = x^2, which resulted in

1/2 integral dx/(sqrt(u)(u^2-16u+9))

I then factored u^2-16u+9 by finding the solution of what u is equal to using the quadratic formula and got this as my new resulting integral

1/2 integral du/(sqrt(u)(u-8+sqrt(55))(u-8-sqrt(55)))

I then tried to result this into partial fractions in order to evaluate the integral in form

A/sqrt(u) + B/(u-8+sqrt(55)) + C/(u-8-sqrt(55))

When I solved for A, B, and C, I got

A = 1/9
B = -1/(2 sqrt(55) sqrt(8+sqrt(55)) )
C = 1/(2 sqrt(55) sqrt(8 + sqrt(55) )

When I then tried to evaluate each separate integral I got

x/9 - 1/(4 sqrt(55) sqrt(8 + sqrt(55))) ln|x^2 - 8 + sqrt(55)| + 1/(4 sqrt(55) sqrt(8 + sqrt(55) ) ) ln|x^2 - 8 - sqrt(55)| + c

I guess I did something wrong...

I than tried to evaluate the integral using trig substitution as you will see in the the second attachment, i crossed off my first attempt and just got to the point were i decided it was getting to complicated for calculus II I had to make two trig substitutions using two different triangles.

I'm lost thanks for any help.
 

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Answers and Replies

  • #2
Dick
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Factor x^4-10*x^2+9. It splits completely into linear factors. Then use partial fractions.
 
  • #3
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Factor x^4-10*x^2+9. It splits completely into linear factors. Then use partial fractions.
oh wow thanks =) i over complicated it a bit much
 

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