What is the integral of 1/(sin(1/2)xcot(1/2)x) ?

The integral of 1/(sin(1/2)xcot(1/2)x) is -1/(sin(1/2)cot(1/2)x)+C

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integral of 1/(sin(1/2)xcot(1/2)x)

\int \frac{1}{sin ( \frac{1}{2} ) x cot ( \frac{1}{2} ) x} d x

- \frac{1}{sin ( \frac{1}{2} ) cot ( \frac{1}{2} ) x} + C

Solution steps

\int \frac{1}{sin ( \frac{1}{2} ) x cot ( \frac{1}{2} ) x} d x

Take the constant out:

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

= \frac{1}{sin ( \frac{1}{2} ) cot ( \frac{1}{2} )} \cdot \int \frac{1}{xx} d x

xx = x^{2}

= \frac{1}{sin ( \frac{1}{2} ) cot ( \frac{1}{2} )} \cdot \int \frac{1}{x ^{2}} d x

Apply the Power Rule

: - \frac{1}{x}

= \frac{1}{sin ( \frac{1}{2} ) cot ( \frac{1}{2} )} (- \frac{1}{x})

Simplify

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

= - \frac{1}{sin ( \frac{1}{2} ) cot ( \frac{1}{2} ) x}

Add a constant to the solution

= - \frac{1}{sin ( \frac{1}{2} ) cot ( \frac{1}{2} ) x} + C

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