Thread: Help with an multiple integral

I'm a little rusty when it comes to these kind of integrals. Any help would be appreciated.

Find the indefinite integral of [(x^2 + y^2 - 2y^2)/(x^2 + y^2)^2]dx, that is, integrate with respect to x. I understand that I need to treat y as a constant, it's the integral itself that I'm having trouble with. Sorry if that's difficult to read, I still need to learn latex.

Originally Posted by spoon737

I'm a little rusty when it comes to these kind of integrals. Any help would be appreciated.

Find the indefinite integral of [(x^2 + y^2 - 2y^2)/(x^2 + y^2)^2]dx, that is, integrate with respect to x. I understand that I need to treat y as a constant, it's the integral itself that I'm having trouble with. Sorry if that's difficult to read, I still need to learn latex.

i believe you have a typo or something here. they would not say y^2 - 2y^2, they'd just write -y^2

Oops, you're right, that should read -y^2 instead of y^2 - 2y^2. This isn't how the actual problem was presented, I had to do some work to get to this point. I just forgot to simplify that one part. Still, I could use help in solving that integral.

Originally Posted by spoon737

Oops, you're right, that should read -y^2 instead of y^2 - 2y^2. This isn't how the actual problem was presented, I had to do some work to get to this point. I just forgot to simplify that one part. Still, I could use help in solving that integral.

Sorry for taking so long, here:

I will start you off (remember, we are treating y as a constant throughout the entire problem)




We employ the method of partial fractions:



...i think you know how to solve this, let's get to the meat of the matter





now just find the integrals on the right: factor out the on the bottom of the first so you will get it in the form to use arctan, for the second, use trig substitution,

If you get stuck you can check back with me