What is the integral of 7/(cos(x)-1) ?

The integral of 7/(cos(x)-1) is 7cot(x/2)+C

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integral of 7/(cos(x)-1)

\int \frac{7}{cos ( x ) - 1} d x

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

Solution steps

\int \frac{7}{cos ( x ) - 1} d x

Take the constant out:

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

= 7 \cdot \int \frac{1}{cos ( x ) - 1} d x

Apply u-substitution

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

= 7 \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

= 7 (- \int \frac{1}{u ^{2}} d u)

Apply the Power Rule

: - \frac{1}{u}

= 7 (- (- \frac{1}{u}))

Substitute back

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

= 7 (- (- \frac{1}{tan ( \frac{x}{2} )}))

Simplify

7 (- (- \frac{1}{tan ( \frac{x}{2} )})) : 7 cot (\frac{x}{2})

= 7 cot (\frac{x}{2})

Add a constant to the solution

= 7 cot (\frac{x}{2}) + C

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What is the integral of 7/(cos(x)-1) ?
The integral of 7/(cos(x)-1) is 7cot(x/2)+C