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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

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

Simplify

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

Add a constant to the solution

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

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