1. The problem statement, all variables and given/known data Evaluate integral dx/(x^4-10x^2+9) 2. Relevant equations 3. 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.