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!