Integrating 1/(x^2+1): Attempting to Solve an Integration Problem

[thereddevils]

Homework Statement

evaluate $$\int \frac{1}{x^2+1} dx$$

Homework Equations

The Attempt at a Solution

This can't be $$\frac{\ln x^2+1}{2x}$$ , my first thought on this .

Then , i tried partial fraction , it didn't work either .

 

[Mark44]

Homework Statement

evaluate $$\int \frac{1}{x^2+1} dx$$

Homework Equations

The Attempt at a Solution

This can't be $$\frac{\ln x^2+1}{2x}$$ , my first thought on this .

Then , i tried partial fraction , it didn't work either .

Your first thought led you to try an ordinary substitution, u = x^2 + 1. This won't work, though, because du = 2xdx, so there's no way to change the given integrand to du/u.

If you know a derivative formula for which d/dx(something) = 1/(x^2 + 1) then that will be helpful in this problem. If you don't know or don't remember such a formula, a trig substitution will be the way to go, with tan u = x/1.