The arctan function has the following property: if x is positive, then
arctan(1/x) + arctan(x) = π/2
This means

For the remaining integral, integrate by parts with




We have arctan(1) = π/4 and arctan(1/√3) = π/6, and

which gives

so that

Alternatively, you can integrate by parts immediately:


so that

You'll end up with the same result either way.