integral of cos(2θ) — step-by-step solution

Let's integrate:

\int(\cos (2 θ))dθ

Let u =

2 θ

. Then du =

2

*dθ, so dθ =

\frac{1}{2}

*du

We use

\int(\cos (u))du

\sin (u)

, then substitute u =

2 θ

back

\frac{\sin (2 θ)}{2}

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

\frac{\sin (2 θ)}{2} + C