What is the integral of 2/(cos(x)-1) ?

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

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integral of 2/(cos(x)-1)

\int \frac{2}{cos ( x ) - 1} d x

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

Solution steps

\int \frac{2}{cos ( x ) - 1} d x

Take the constant out:

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

= 2 \cdot \int \frac{1}{cos ( x ) - 1} d x

Apply u-substitution

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

= 2 \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

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

Apply the Power Rule

: - \frac{1}{u}

= 2 (- (- \frac{1}{u}))

Substitute back

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

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{y - 1}{y} d y

\frac{d}{d x} (lo g_{2} (2 x + 1))

x^{2} + 2, x + 2

6 e^{- 3 x}

\int_{- \infty}^{0} \frac{1}{4 - 6 x} d x

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