What is the integral of (72)/(1-cos(8x)) ?

The integral of (72)/(1-cos(8x)) is -9cot(4x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (72)/(1-cos(8x))

\int \frac{72}{1 - cos ( 8 x )} d x

- 9 cot (4 x) + C

Solution steps

\int \frac{72}{1 - cos ( 8 x )} d x

Take the constant out:

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

= 72 \cdot \int \frac{1}{1 - cos ( 8 x )} d x

Apply u-substitution

: \int \frac{1}{8 ( 1 - cos ( u ) )} d u

= 72 \cdot \int \frac{1}{8 ( 1 - cos ( u ) )} d u

Take the constant out:

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

= 72 \cdot \frac{1}{8} \cdot \int \frac{1}{1 - cos ( u )} d u

Apply u-substitution

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

= 72 \cdot \frac{1}{8} \cdot \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= 72 \cdot \frac{1}{8} (- \frac{1}{v})

Substitute back

= 72 \cdot \frac{1}{8} (- \frac{1}{tan ( \frac{8 x}{2} )})

Simplify

72 \cdot \frac{1}{8} (- \frac{1}{tan ( \frac{8 x}{2} )}) : - 9 cot (4 x)

= - 9 cot (4 x)

Add a constant to the solution

= - 9 cot (4 x) + C

e^{- x^{4}}

\int \frac{1}{( 8 x + 9 ) ^{2}} d x

n = 1 \sum \infty (- 4)^{n}

\int sec (x) tan (x) - 4 e^{x} d x

\int sinh (4 x) d x

What is the integral of (72)/(1-cos(8x)) ?
The integral of (72)/(1-cos(8x)) is -9cot(4x)+C