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

Let's integrate:

\int \cos (2 x) d x

To use the known integral of

\cos (u)

, let

u = 2 x

. Then

du = 2 dx

, so

dx = \frac{1}{2} \cdot du

We use

\int \cos (u) d u = \sin (u)

, then substitute

u = 2 x

back

ⓘ The derivative of

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

\cos (2 x)

, so

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

is an antiderivative of

\cos (2 x)

\int \cos (2 x) d x

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

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

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

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