How do you integrate $3/(x^2+4)$ ?

Question

3996 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-02-20T18:44:21

I would start by factorizing $4$ from the denominator:

$int3/(x^2+4)dx=int3/4*1/(1+x^2/4)dx=$

Now I set:
$x^2/4=t^2$ and so $x=2t$ giving:

$dx=2dt$

Substituting in the integral:

$=int3/4*1/(1+t^2)2dt=3/2arctan(t)=$

Going back to $x$ :

$=3/2arctan(x/2)+c$

How do you integrate 3/(x^2+4)3/(x^2+4)?