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

Feb 3, 2018

$\int 1 - \cos \left(x\right) \mathrm{dx} = x - \sin \left(x\right) + \text{C}$

#### Explanation:

Given: $\int 1 - \cos \left(x\right)$

Using the following properties:

$\int c \mathrm{dx} = c x$

$\int - \cos x \left(x\right) \mathrm{dx} \implies - \int \cos \left(x\right) \mathrm{dx} = - \sin \left(x\right)$

$\therefore \int 1 - \cos \left(x\right) \mathrm{dx} = x - \sin \left(x\right) + \text{C} \leftarrow$ Don't forget the constant