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

The integral of (1-cos(x))/(1+cos(x)) is 2csc(x)-2cot(x)-x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1-cos(x))/(1+cos(x))

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

2 csc (x) - 2 cot (x) - x + C

Solution steps

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

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

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

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

\int 1 d x = x

= - 2 (- csc (x) + cot (x) + x) + x

Simplify

- 2 (- csc (x) + cot (x) + x) + x : 2 csc (x) - 2 cot (x) - x

= 2 csc (x) - 2 cot (x) - x

Add a constant to the solution

= 2 csc (x) - 2 cot (x) - x + C

\int e^{2 x - 7} d x

\frac{d}{d x} (4 arcsin (x^{3}))

\frac{d}{d x} (\frac{4 csc ( x )}{5 ^{x}})

x \to \infty lim (\frac{n}{n !})

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