Question

The indefinite integral of [1]/[x^2 + 4] dx

Attempt:
Is this not arctan(x/2)*2?

Answer 1

divided by 2 not times 2

Answer 2

Why?

Answer 3

\[\frac{d}{dx}arctan(x/2)=\frac{1}{(x/2)^2+1}\frac{1}{2}\]

\[=\frac{1}{x^2/4+1}\frac{1}{2}=\frac{1}{x^2/2+2}\]

if we multiply by 1/2 we get the original integrand

Answer 4

I understand. Thank you.