What is the integral of cos^2(3θ) ?

The integral of cos^2(3θ) is 1/2 (θ+1/6 sin(6θ))+C

Popular >

integral of cos^2(3θ)

\int cos^{2} (3 θ) d θ

\frac{1}{2} (θ + \frac{1}{6} sin (6 θ)) + C

Solution steps

\int cos^{2} (3 θ) d θ

Rewrite using trig identities

= \int \frac{1}{2} (1 + cos (6 θ)) d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int 1 + cos (6 θ) d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int 1 d θ + \int cos (6 θ) d θ)

\int 1 d θ = θ

\int cos (6 θ) d θ = \frac{1}{6} sin (6 θ)

= \frac{1}{2} (θ + \frac{1}{6} sin (6 θ))

Add a constant to the solution

= \frac{1}{2} (θ + \frac{1}{6} sin (6 θ)) + C

\frac{\partial}{\partial x} (e^{z^{2}} + y ln (x^{2} + 5))

\frac{d y}{d x} = \frac{y}{x} + 2 x + 3

\frac{d y}{d t} = (y + 1) (y - 3), y (0) = 1

x \to \frac{4}{3} lim (2 x^{2} - 4 x + 5)

\int x (3^{- x^{2}}) d x

What is the integral of cos^2(3θ) ?
The integral of cos^2(3θ) is 1/2 (θ+1/6 sin(6θ))+C