What is the integral of 3/(sec(x)-1) ?

The integral of 3/(sec(x)-1) is 3(-cot(x/2)-x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3/(sec(x)-1)

\int \frac{3}{sec ( x ) - 1} d x

3 (- cot (\frac{x}{2}) - x) + C

Solution steps

\int \frac{3}{sec ( x ) - 1} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int \frac{1}{sec ( x ) - 1} d x

\frac{1}{sec ( x ) - 1} = \frac{sec ( x )}{sec ( x ) - 1} - 1

= 3 \cdot \int \frac{sec ( x )}{sec ( x ) - 1} - 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

= 3 (\int \frac{sec ( x )}{sec ( x ) - 1} d x - \int 1 d x)

\int \frac{sec ( x )}{sec ( x ) - 1} d x = - cot (\frac{x}{2})

\int 1 d x = x

= 3 (- cot (\frac{x}{2}) - x)

Add a constant to the solution

= 3 (- cot (\frac{x}{2}) - x) + C

x \to a lim (2 f (x))

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

t^{2} \frac{d y}{d t} = - y

\frac{d}{d x} (6 x y + 5 x^{2})

\int \frac{1}{( x - 43 ) ^{0.92}} d x

What is the integral of 3/(sec(x)-1) ?
The integral of 3/(sec(x)-1) is 3(-cot(x/2)-x)+C