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

Let's compute the integral:

\int \sin (2 x) d x

To use the known integral of

\sin (u)

, let

u = 2 x

. Then

du = 2 dx

, so

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

We use

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

, then substitute

u = 2 x

back

ⓘ The derivative of

- \frac{\cos (2 x)}{2}

\sin (2 x)

, so

- \frac{\cos (2 x)}{2}

is an antiderivative of

\sin (2 x)

\int \sin (2 x) d x

- \frac{\cos (2 x)}{2}

- \frac{\cos (2 x)}{2}

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

- \frac{\cos (2 x)}{2} + C