Question

The integral from -INF to 2 of 1/(x^2+1) dx. I've tried trig substitution, algebraic manipulation and L'Hôpital's rule to no avail. Please see attached screenshot. Thanks. :)

Answer 1

Well trig substitution should work here if you choose x=tan(u).

If what you've written there is truly the integral of 1/(1+x^2) then the derivative of it should be that. But check it, what's the derivative of: \[\frac{d}{dx} \frac{1}{2} \ln|x^2+1|=?\]

Answer 2

this is a standard form