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

The integral of 8/(cos(x)-1) is 8cot(x/2)+C

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

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

8 cot (\frac{x}{2}) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int - \frac{1}{u ^{2}} d u

= 8 \cdot \int - \frac{1}{u ^{2}} d u

Take the constant out:

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

= 8 (- \int \frac{1}{u ^{2}} d u)

Apply the Power Rule

: - \frac{1}{u}

= 8 (- (- \frac{1}{u}))

Substitute back

u = tan (\frac{x}{2})

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

Simplify

8 (- (- \frac{1}{tan ( \frac{x}{2} )})) : 8 cot (\frac{x}{2})

= 8 cot (\frac{x}{2})

Add a constant to the solution

= 8 cot (\frac{x}{2}) + C

y = x^{3}, x = - 2, x = 2

x \to 3 lim (\frac{x ^{2} + 4}{x - 5})

13 x

\frac{d}{d x} ((7 x^{3} - 5)^{9})

f (x) = \frac{2 csc ( x )}{x}

What is the integral of 8/(cos(x)-1) ?
The integral of 8/(cos(x)-1) is 8cot(x/2)+C