integral of sin(13x) — step-by-step solution

Let's integrate:

\int(\sin (13 x))dx

To use the known integral of

\sin (u)

, let

u = 13 x

. Then

du = 13 dx

, so

dx = \frac{1}{13} \cdot du

We use

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

, then substitute

u = 13 x

back

- \frac{\cos (13 x)}{13}

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

- \frac{\cos (13 x)}{13} + C