What is the integral of cos^2(39x) ?

The integral of cos^2(39x) is 1/2 (x+1/78 sin(78x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos^2(39x)

\int cos^{2} (39 x) d x

\frac{1}{2} (x + \frac{1}{78} sin (78 x)) + C

Solution steps

\int cos^{2} (39 x) d x

Rewrite using trig identities

= \int \frac{1}{2} (1 + cos (78 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 (78 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 (78 x) d x)

\int 1 d x = x

\int cos (78 x) d x = \frac{1}{78} sin (78 x)

= \frac{1}{2} (x + \frac{1}{78} sin (78 x))

Add a constant to the solution

= \frac{1}{2} (x + \frac{1}{78} sin (78 x)) + C

\int 4^{5 t} d t

\int 2 cos (x) + 2 x d x

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

\int (x^{2} + 1) cos (3 x) d x

\int \frac{y}{1 + 3 y ^{2}} d y

What is the integral of cos^2(39x) ?
The integral of cos^2(39x) is 1/2 (x+1/78 sin(78x))+C