integration

∫ 2cos(3+π/2) dx

I.

If you mean :

$$\small{\text{ $ \begin{array}{rcl} \hline \int 2\cos{ (3+ \frac{\pi}{2} ) } \ dx \\ = 2\cos{ (3+ \frac{\pi}{2} ) } \int{dx} \\ = 2\cos{ (3+ \frac{\pi}{2} ) } x + c \\ \hline \end{array} $ }}$$

II.

If you mean :

$$\small{\text{ $ \begin{array}{rcl} \hline \int 2 \cos{ (x ) } \ dx \\ = 2 \int \cos{(x)} \ dx \\ = 2 \sin{(x)} +c\\ \hline \end{array} $ }}$$

III.

If you mean:

$$\small{\text{ $ \begin{array}{rcl} \hline \int 2 \cos{ (x + \frac{\pi}{2} ) } \ dx \\ = 2 \int \cos{ (x + \frac{\pi}{2} ) } \ dx \quad | \quad u=x+\frac{\pi}{2} \quad du=dx \\ = 2 \int \cos{(u)} \ du \\ = 2 \sin{(u)} +c\\ = 2 \sin{(x+\frac{\pi}{2} )} +c\\ \hline \end{array} $ }}$$

It's the top one. Great, thank you!