The question:
$\displaystyle \int \frac{dx}{4 + x^2}$
I'm fairly sure I have to use some sort of substitution for this question. But I can't seem to get it to work. >_<
This is just a formula for the indefinite integral
here is where it comes from
$\displaystyle \displaystyle \int \frac{a}{x^2+a^2}dx$
let $\displaystyle x=a\tan(\theta) \implies dx=a\sec^2{\theta}d\theta$ this gives
$\displaystyle \displaystyle \int \frac{a}{a^2\tan^2(\theta)+a^2}a\sec^2{\theta}d\th eta=\int d\theta =\theta=\tan^{-1}\left(\frac{x}{a} \right)+c$