Solving a simple integral

[Mr Davis 97]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I know that I can convert this to the form $\displaystyle \int \frac{1}{x^2+(\pm \sqrt{a})^2} dx$ = $\displaystyle \frac{1}{\pm \sqrt{a}} \arctan (\frac{x}{\pm \sqrt{a}}) + C$, but I don't know whether to take the positive or the negative root.

 

[Orodruin]

Ask yourself whether it matters or not.

 

[Mr Davis 97]

Ask yourself whether it matters or not.

Does it not matter since $\arctan$ is an odd function, so in either case you get $\displaystyle \frac{1}{\sqrt{a}} \arctan (\frac{x}{\sqrt{a}}) + C$?

 

[Orodruin]

Indeed.