What is the integral of (14)/(1-cos(7x)) ?

The integral of (14)/(1-cos(7x)) is -2cot((7x)/2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (14)/(1-cos(7x))

\int \frac{14}{1 - cos ( 7 x )} d x

- 2 cot (\frac{7 x}{2}) + C

Solution steps

\int \frac{14}{1 - cos ( 7 x )} d x

Take the constant out:

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

= 14 \cdot \int \frac{1}{1 - cos ( 7 x )} d x

Apply u-substitution

: \int \frac{1}{7 ( 1 - cos ( u ) )} d u

= 14 \cdot \int \frac{1}{7 ( 1 - cos ( u ) )} d u

Take the constant out:

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

= 14 \cdot \frac{1}{7} \cdot \int \frac{1}{1 - cos ( u )} d u

Apply u-substitution

: \int \frac{1}{v ^{2}} d v

= 14 \cdot \frac{1}{7} \cdot \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= 14 \cdot \frac{1}{7} (- \frac{1}{v})

Substitute back

= 14 \cdot \frac{1}{7} (- \frac{1}{tan ( \frac{7 x}{2} )})

Simplify

14 \cdot \frac{1}{7} (- \frac{1}{tan ( \frac{7 x}{2} )}) : - 2 cot (\frac{7 x}{2})

= - 2 cot (\frac{7 x}{2})

Add a constant to the solution

= - 2 cot (\frac{7 x}{2}) + C

y^{^{''}} + 2 y = cos (t) - 2 \cdot sin (2 t)

\int 3 e^{- 3 x} d x

y^{^{''}} - 2 y^{^{'}} + y = t^{- 3} e^{t}

\frac{d y}{d x} + \frac{3 y}{x} = \frac{e ^{x}}{x ^{3}}

\int - 2 x + 4 d x

What is the integral of (14)/(1-cos(7x)) ?
The integral of (14)/(1-cos(7x)) is -2cot((7x)/2)+C