integrate cos(2x) — step-by-step solution

Let's integrate:

\int(\cos (2 x))dx

For the math expression:

\cos (2 x)

, we know the derivative formula:

{(\sin (a))}^{'} = \cos (a)

, so we try differentiating with sin

Let's perform the differentiation:

{(\sin (2 x))}^{'}

We differentiate using:

{(\sin (f))}^{'} = {(f)}^{'} \cdot \cos (f)

(where f =

2 x

)

{(2 x)}^{'} \cdot \cos (2 x)

2 \cdot \cos (2 x)

You observe that the computed derivative and the original math expression are the same, except for a coefficient. So the integral is:

\frac{1}{2} \cdot \sin (2 x)

\frac{\sin (2 x)}{2}

Indefinite integrals are defined up to an additive constant C, so this yields:

\frac{\sin (2 x)}{2} + C

▷Result: $\frac{\sin (2 x)}{2} + C$ , with C being any constant