Q:

Trigonometric Written Confustion

I am currently doing trig integration and have come across trig functions which are written as:
cos2(x) or 2cos(x).
I was wondering whether they are the same thing.Or are they just written differently as in the case of  1/tan(x) being the same as cot(x).
Further clarification:
Integral ( 4cos^2(x) dx)
Integral ( 2(1 + cos2x) dx 
= 2x + sin2x + C

A:

There is a trigonometric identity that states
$$
    \cos^2 \theta = \frac{1 + \cos 2\theta}{2}
$$
That's what's being employed in your integral

$$ \int 4\cos^2x\,dx = \int 2 (1+\cos 2x)\,dx = 2x + \sin 2x + C$$ 

Like Simple Art, I've never seen $\cos 2(x)$ used in a formula.  I would take it to mean $\cos(2x)$, but it could also be, as Emilio suggested, an incorrect transcription of $\cos^2(x)$.  Best avoided, either way.

