Thread: Integration by partial fractions

Hey, I was wondering if somebody could check over the following integration problem for me.

Int (x^2 + 1 ) / (X^2 - 3x + 2) dx

I used partial fractions (disregard title)

for an answer I got ln absolute value (x-2) - ln absolute value (x-1) + c

gracias !!!!!

edit: i originally thought you did int. by parts, but partial fractions makes more sense.

Why is there division in the integral. Do you mean perhaps to say * insteand of /

It is written as

integrate: (x^2 + 1 ) (divided by) (X^2 - 3x + 2) dx

If you were talking about why is there a / instead * in relation to my original comment of int. by parts, I wrote down the wrong method. (my bad )

it is indeed supposed to be divided by, sorry for any confusion.

If you check your answer by differenciating you get,
1/(x-2)-1/(x-1)=1/(x^2-3x+2)

Which is clearly wrong.
How did you express it as partial fractions?

Why I didn't check it before it beyond me and you are clearly right, the answer doesn't even come close. Upon looking over my work though I think I have found the problem. If you express it as partial fractions from the start, you'll have it set equal to x^2 + 1, but there won't be anything (once you do out the actual fractions) to set the x^2 part equal to. In other words there won't be any variables (A, b etc) to set equal to x^2. I think you actually have to do synthethetc division first, then from that answer you can move forward with partial fractions. I'm going to check that out.

Thanks for checking my answer.