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

\int tan^{3} (2 x) sec^{4} (2 x) d x

\int_{x}^{x + 2} (4 t + 1) d t

\frac{\partial}{\partial x} (2 cos (x y))

y = 2 x^{3} - 5 x, (1, - 3)

f (x) = 2 x^{3}, (- 1, - 2)

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