What is the integral of cos^2(4x) ?

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

Popular >

integral of cos^2(4x)

\int cos^{2} (4 x) d x

\frac{1}{2} (x + \frac{1}{8} sin (8 x)) + C

Solution steps

\int cos^{2} (4 x) d x

Rewrite using trig identities

= \int \frac{1}{2} (1 + cos (8 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 (8 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 (8 x) d x)

\int 1 d x = x

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

= \frac{1}{2} (x + \frac{1}{8} sin (8 x))

Add a constant to the solution

= \frac{1}{2} (x + \frac{1}{8} sin (8 x)) + C

y = (\frac{x}{3.3} + \frac{3.3}{x}) (x^{2} + 1)

x \to + 2 lim (2 + 3)

\int (1 + 20 w) w d w

\int \frac{x ^{2}}{( 16 - x ^{2} ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (e^{3 x} \cdot 3)

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