Question

How does the integral of (du/(u^2+4)) become 1/2 arctan (x+1/2) + C?

Answer 1

Using Trig substituion

Answer 2

u=tan(x)
du=sec(x)^2 du

Answer 3

How did u become over two, what happened to the four in the equation?

Answer 4

substituting
u=2tan(x)
du=2sec(x)^2dx
so
u^2+4 is
4tan(x)^2+4
4(tan(x)^2 +1)
\[1/4*2\int\limits \sec(x)^2/\sec(x)^2 d(x)\]