What is the integral of cos(16x)cos(7x) ?

The integral of cos(16x)cos(7x) is 1/2 (1/23 sin(23x)+1/9 sin(9x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of cos(16x)cos(7x)

\int cos (16 x) cos (7 x) d x

\frac{1}{2} (\frac{1}{23} sin (23 x) + \frac{1}{9} sin (9 x)) + C

Solution steps

\int cos (16 x) cos (7 x) d x

Rewrite using trig identities

= \int \frac{1}{2} (cos (23 x) + cos (9 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 cos (23 x) + cos (9 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 cos (23 x) d x + \int cos (9 x) d x)

\int cos (23 x) d x = \frac{1}{23} sin (23 x)

\int cos (9 x) d x = \frac{1}{9} sin (9 x)

= \frac{1}{2} (\frac{1}{23} sin (23 x) + \frac{1}{9} sin (9 x))

Add a constant to the solution

= \frac{1}{2} (\frac{1}{23} sin (23 x) + \frac{1}{9} sin (9 x)) + C

What is the integral of cos(16x)cos(7x) ?
The integral of cos(16x)cos(7x) is 1/2 (1/23 sin(23x)+1/9 sin(9x))+C