Question

How do you integrate [(x^2-2x-1)]/[((x-1)^2)(x^2+1)] dx. I know you have to use partial fractions...but im kind of stuck. =[

Answer 1

you're looking for a decomposition of the form:
[x^2 - 2x - 1][((x-1)^2)(x^2 + 1)]^-1 = A[x-1]^-1 + B[x -1]^-2 + [Cx + D][x^2 + 1]
if you equate the denominators and substitute convenient values of x you'll get those coefficiants

Answer 2

@deejbrya90 did you understand?

Answer 3

yea......i have that, but i don't know where to go from there. That's the thing. Like how do i find A, B, and C with so many variables?

Answer 4

@lgbasallote would you please help here. I gotta leave now:)
@deejbrya90 @lgbasallote will help you

Answer 5

if you find a common denominator, you can make the numerator of the left equal the numerator of the right. you can then substitute any value of x you'd like (some choices better than others) and get 4 equations with 4 unknowns which will give you your coefficients:)

Answer 6

ohhhhh ok. thank you!! ^_^