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

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

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integral of 1/(-cos(u)+1)

\int \frac{1}{- cos ( u ) + 1} d u

- cot (\frac{u}{2}) + C

Solution steps

\int \frac{1}{- cos ( u ) + 1} d u

Apply u-substitution

: \int \frac{1}{v ^{2}} d v

= \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= - \frac{1}{v}

Substitute back

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

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

Use the basic trigonometric identity:

\frac{1}{tan ( x )} = cot (x)

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

Add a constant to the solution

= - cot (\frac{u}{2}) + C

\frac{\partial}{\partial y} ((2 x - 3 y)^{3})

\int - csc (x) cot (x) d x

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

(x + 6)^{2}

\frac{d}{d x} (\frac{5}{x ^{5}} + \frac{3}{x ^{2}})

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