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

1 Answer
Mar 3, 2017

#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#