What is the integral of cos(2x-4) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(2x-4)

\int cos (2 x - 4) d x

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

Solution steps

\int cos (2 x - 4) d x

Rewrite using trig identities

= \int cos (2 x) cos (4) + sin (2 x) sin (4) 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

= \int cos (2 x) cos (4) d x + \int sin (2 x) sin (4) d x

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

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

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

Use the Angle Difference identity:

sin (s) cos (t) - cos (s) sin (t) = sin (s - t)

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

Add a constant to the solution

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

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

\int 15 x (x + 1) d x

\int (6 x^{2} - 5) e^{2 x^{3} - 5 x} d x

\int sin (x + a) d x

\int (5 x + 16)^{4} d x

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