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

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

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

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

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

Solution steps

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

Apply u-substitution

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

Apply the Power Rule

= - \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

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