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

The integral of cos^2(x)*sin^2(x) is 1/8 (x-1/4 sin(4x))+C

Popular >

integral of cos^2(x)*sin^2(x)

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

\frac{1}{8} (x - \frac{1}{4} sin (4 x)) + C

Solution steps

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

Rewrite using trig identities

= \int \frac{1 - cos ( 4 x )}{8} d x

Take the constant out:

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

= \frac{1}{8} \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}{8} (\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}{8} (x - \frac{1}{4} sin (4 x))

Add a constant to the solution

= \frac{1}{8} (x - \frac{1}{4} sin (4 x)) + C

\frac{\partial}{\partial x} (\frac{2}{x ^{2} + 1})

2 x y^{3} + x y = 18, (6, 1)

\frac{1}{e ^{j t}}

\frac{d}{d x} (e^{x} (x - 9))

\frac{d}{d x} (\frac{x ^{5} + 5}{x ^{3}})

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