What is the integral of (56)/(1-cos(8x)) ?

The integral of (56)/(1-cos(8x)) is -7cot(4x)+C

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integral of (56)/(1-cos(8x))

\int \frac{56}{1 - cos ( 8 x )} d x

- 7 cot (4 x) + C

Solution steps

\int \frac{56}{1 - cos ( 8 x )} d x

Take the constant out:

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

= 56 \cdot \int \frac{1}{1 - cos ( 8 x )} d x

Apply u-substitution

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

= 56 \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

= 56 \cdot \frac{1}{8} \cdot \int \frac{1}{1 - cos ( u )} d u

Apply u-substitution

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

= 56 \cdot \frac{1}{8} \cdot \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= 56 \cdot \frac{1}{8} (- \frac{1}{v})

Substitute back

= 56 \cdot \frac{1}{8} (- \frac{1}{tan ( \frac{8 x}{2} )})

Simplify

56 \cdot \frac{1}{8} (- \frac{1}{tan ( \frac{8 x}{2} )}) : - 7 cot (4 x)

= - 7 cot (4 x)

Add a constant to the solution

= - 7 cot (4 x) + C

(- 1, 2), (4, 3)

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What is the integral of (56)/(1-cos(8x)) ?
The integral of (56)/(1-cos(8x)) is -7cot(4x)+C