What is the integral of 4/(cos(x)-1) ?

The integral of 4/(cos(x)-1) is 4cot(x/2)+C

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integral of 4/(cos(x)-1)

\int \frac{4}{cos ( x ) - 1} d x

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

Solution steps

\int \frac{4}{cos ( x ) - 1} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{cos ( x ) - 1} d x

Apply u-substitution

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

= 4 \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

= 4 (- \int \frac{1}{u ^{2}} d u)

Apply the Power Rule

: - \frac{1}{u}

= 4 (- (- \frac{1}{u}))

Substitute back

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

= 4 (- (- \frac{1}{tan ( \frac{x}{2} )}))

Simplify

4 (- (- \frac{1}{tan ( \frac{x}{2} )})) : 4 cot (\frac{x}{2})

= 4 cot (\frac{x}{2})

Add a constant to the solution

= 4 cot (\frac{x}{2}) + C

y^{^{''}} + 49 y = sin (7 t)

x \to 1 lim (\frac{x - 8 + 7}{x - 1})

y = \frac{x}{2 x + \frac{- 4}{x}}

9 y y^{^{'}} + 4 x = 0

e^{c o s (x)}

What is the integral of 4/(cos(x)-1) ?
The integral of 4/(cos(x)-1) is 4cot(x/2)+C