What is the integral of (sin^2(2x)) ?

The integral of (sin^2(2x)) is 1/2 (x-1/4 sin(4x))+C

Popular >

integral of (sin^2(2x))

\int (sin^{2} (2 x)) d x

\frac{1}{2} (x - \frac{1}{4} sin (4 x)) + C

Solution steps

\int sin^{2} (2 x) d x

Rewrite using trig identities

= \int \frac{1}{2} (1 - cos (4 x)) d x

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 (4 x) d x

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 x - \int cos (4 x) d x)

\int 1 d x = x

\int cos (4 x) d x = \frac{1}{4} sin (4 x)

= \frac{1}{2} (x - \frac{1}{4} sin (4 x))

Add a constant to the solution

= \frac{1}{2} (x - \frac{1}{4} sin (4 x)) + C

\frac{d y}{d x} = \frac{y ^{3}}{3 x - 2}

\int \frac{1}{2} x + 3 d x

x \to - 6 lim (\frac{2 x + 12}{x + 6})

x \to 0 lim (\frac{10}{x ( x + 1 )})

y = e^{- 2 x}

What is the integral of (sin^2(2x)) ?
The integral of (sin^2(2x)) is 1/2 (x-1/4 sin(4x))+C