What is the integral of 3/(1-cos(x)) ?

The integral of 3/(1-cos(x)) is -3cot(x/2)+C

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integral of 3/(1-cos(x))

\int \frac{3}{1 - cos ( x )} d x

- 3 cot (\frac{x}{2}) + C

Solution steps

\int \frac{3}{1 - cos ( x )} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{1 - cos ( x )} d x

Apply u-substitution

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

= 3 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 3 (- \frac{1}{u})

Substitute back

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

= 3 (- \frac{1}{tan ( \frac{x}{2} )})

Simplify

3 (- \frac{1}{tan ( \frac{x}{2} )}) : - 3 cot (\frac{x}{2})

= - 3 cot (\frac{x}{2})

Add a constant to the solution

= - 3 cot (\frac{x}{2}) + C

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What is the integral of 3/(1-cos(x)) ?
The integral of 3/(1-cos(x)) is -3cot(x/2)+C