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