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

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

integral of cos^2(4t)

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

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

Solution steps

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

Rewrite using trig identities

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

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 t) d t

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 t + \int cos (8 t) d t)

\int 1 d t = t

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

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

Add a constant to the solution

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

t a y l or x^{- 2}, 5

\frac{d}{d x} (sin (x^{12}))

x \to 0 lim (\frac{- 1}{x})

p a r i t y x^{2} sin (x) tan (x)

d er i v a t i v e 5 sin (2 x)

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