What is the integral of cos^2(2aθ) ?

The integral of cos^2(2aθ) is θ-θ/2+1/(8a)sin(4aθ)+C

Popular >

integral of cos^2(2aθ)

\int cos^{2} (2 a θ) d θ

θ - \frac{θ}{2} + \frac{1}{8 a} sin (4 a θ) + C

Solution steps

\int cos^{2} (2 a θ) d θ

Rewrite using trig identities

= \int 1 - sin^{2} (2 a 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

= \int 1 d θ - \int sin^{2} (2 a θ) d θ

\int 1 d θ = θ

\int sin^{2} (2 a θ) d θ = \frac{θ}{2} - \frac{1}{8 a} sin (4 a θ)

= θ - (\frac{θ}{2} - \frac{1}{8 a} sin (4 a θ))

Simplify

= θ - \frac{θ}{2} + \frac{1}{8 a} sin (4 a θ)

Add a constant to the solution

= θ - \frac{θ}{2} + \frac{1}{8 a} sin (4 a θ) + C

\frac{\partial}{\partial x} (5 \cdot (x - 4) \cdot y^{3})

\frac{d}{d x} ((2 x - 1)^{\frac{1}{2}})

\int \frac{3}{5 x ^{2} + 5} d x

(9 x + 0.8 x^{2} + 0.07 x^{3})^{^{'}}

What is the integral of cos^2(2aθ) ?
The integral of cos^2(2aθ) is θ-θ/2+1/(8a)sin(4aθ)+C