# Thread: Integral w.r.t y alone

1. ## Integral w.r.t y alone

Im working on a problem an this comes up $\frac{d\psi}{dy}=\frac{2a(y^2-x^2+a^2)}{((x-a)^2 +y^2)((x-a)^2 +y^2)}$ ho do i integrate something like that to get $atan(\frac{y}{x+a}) - atan(\frac{y}{x-a})$ ? It seems at the very least unfriendly to partial fractions and just looks tedious

2. Originally Posted by phycdude
Im working on a problem an this comes up $\frac{d\psi}{dy}=\frac{2a(y^2-x^2+a^2)}{((x-a)^2 +y^2)((x-a)^2 +y^2)}$ ho do i integrate something like that to get $atan(\frac{y}{x+a}) - atan(\frac{y}{x-a})$ ? It seems at the very least unfriendly to partial fractions and just looks tedious
Actually it splits very nicely

$
\frac{d\psi}{dy}= \frac{2a(y^2-x^2+a^2)}{((x-a)^2 +y^2)((x-a)^2 +y^2)} = \;\; \frac{x+a}{(x+a)^2+y^2} - \frac{x-a}{(x-a)^2+y^2}
$
.

3. Originally Posted by Danny
Actually it splits very nicely

$
\frac{d\psi}{dy}= \frac{2a(y^2-x^2+a^2)}{((x-a)^2 +y^2)((x-a)^2 +y^2)} = \;\; \frac{x+a}{(x+a)^2+y^2} - \frac{x-a}{(x-a)^2+y^2}
$
.

how did u do that?

4. Originally Posted by Danny
Actually it splits very nicely

$
\frac{d\psi}{dy}= \frac{2a(y^2-x^2+a^2)}{((x-a)^2 +y^2)((x-a)^2 +y^2)} = \;\; \frac{x+a}{(x+a)^2+y^2} - \frac{x-a}{(x-a)^2+y^2}
$
.
well there seems to be a typo in the denominator, my bad heres the correction
$
\frac{d\psi}{dy}= \frac{2a(y^2-x^2+a^2)}{((x+a)^2 +y^2)((x-a)^2 +y^2)}$