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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(3x)cos(x)

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

\frac{1}{2} (\frac{1}{4} sin (4 x) + \frac{1}{2} sin (2 x)) + C

Solution steps

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

Rewrite using trig identities

= \int \frac{1}{2} (cos (4 x) + cos (2 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 (4 x) + cos (2 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 (4 x) d x + \int cos (2 x) d x)

\int cos (4 x) d x = \frac{1}{4} sin (4 x)

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

= \frac{1}{2} (\frac{1}{4} sin (4 x) + \frac{1}{2} sin (2 x))

Add a constant to the solution

= \frac{1}{2} (\frac{1}{4} sin (4 x) + \frac{1}{2} sin (2 x)) + C

3 (1 + x^{2}) y^{^{'}} = 2 x y (y^{3} - 1)

f (t) = 2 - \frac{4}{t}, (4, 1)

\frac{d}{d x} (x^{2} + \frac{a ^{4}}{x ^{2}})

\frac{d y}{d x} = \frac{x - 1}{y - 4}

\frac{d}{d x} (\frac{x - 4}{x})

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