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

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

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integral of 1/(cos(θ)-1)

\int \frac{1}{cos ( θ ) - 1} d θ

cot (\frac{θ}{2}) + C

Solution steps

\int \frac{1}{cos ( θ ) - 1} d θ

Apply u-substitution

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

= \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

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

Apply the Power Rule

: - \frac{1}{u}

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

Substitute back

u = tan (\frac{θ}{2})

= - (- \frac{1}{tan ( \frac{θ}{2} )})

Simplify

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

= cot (\frac{θ}{2})

Add a constant to the solution

= cot (\frac{θ}{2}) + C

\frac{d}{d x} (cos (0.5 x))

y^{^{'''}} - 9 y^{^{''}} + 15 y^{^{'}} + 25 y = 0

\frac{\partial}{\partial x} (\frac{x}{v})

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

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

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