What is the integral of cos(4x)cos(-3x) ?

The integral of cos(4x)cos(-3x) is 1/2 (sin(x)+1/7 sin(7x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(4x)cos(-3x)

\int cos (4 x) cos (- 3 x) d x

\frac{1}{2} (sin (x) + \frac{1}{7} sin (7 x)) + C

Solution steps

\int cos (4 x) cos (- 3 x) d x

Simplify

cos (4 x) cos (- 3 x) : cos (3 x) cos (4 x)

= \int cos (3 x) cos (4 x) d x

Rewrite using trig identities

= \int \frac{1}{2} (cos (7 x) + cos (- 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 (7 x) + cos (- x) d x

Simplify

cos (7 x) + cos (- x) : cos (x) + cos (7 x)

= \frac{1}{2} \cdot \int cos (x) + cos (7 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 (x) d x + \int cos (7 x) d x)

\int cos (x) d x = sin (x)

\int cos (7 x) d x = \frac{1}{7} sin (7 x)

= \frac{1}{2} (sin (x) + \frac{1}{7} sin (7 x))

Add a constant to the solution

= \frac{1}{2} (sin (x) + \frac{1}{7} sin (7 x)) + C

\int x sin (\frac{n x}{2}) d x

\int \frac{3}{( w - 3 ) 4 w ^{2} - 24 w + 20} d w

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

\int 4 x - 3 3 x d x

\int \frac{2 x ^{3} + 4 x}{x ^{4} + 4 x ^{2} + 9} d x

What is the integral of cos(4x)cos(-3x) ?
The integral of cos(4x)cos(-3x) is 1/2 (sin(x)+1/7 sin(7x))+C