Question

How do you evaluate `\int \frac { 1} { x ^ { 2} + y ^ { 2} }`?

Answer 1

`int dx/(x^2+y^2) = 1/yarctan(x/y) +C`

Explanation:

You should really specify which is the variable of integration. However, as the expression is symmetric in `x` and `y`, it makes little difference:

`int dx/(x^2+y^2) = 1/y int (d(x/y))/(1+(x/y)^2) = 1/yarctan(x/y) +C`

and of course:

`int dy/(x^2+y^2) = 1/xarctan(y/x) + C`