What is the integral of cos(2x)-1 ?

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

\int cos (2 x) - 1 d x

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

Solution steps

\int cos (2 x) - 1 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) d x - \int 1 d x

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

\int 1 d x = x

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

Add a constant to the solution

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

\frac{d y}{d x} = \frac{( x - y )}{( x + 2 y )}

\frac{\partial}{\partial x} (x^{2} + z^{2})

\frac{d}{d x} (\frac{3 x ^{2} + 2 x}{4 x - 3})

g (x) = 3 e^{x} x

\frac{d}{d x} (cos (x) + x cos (y) - y)

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