What is the integral of 3(sin(x))^{-2} ?

The integral of 3(sin(x))^{-2} is -3cot(x)+C

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integral of 3(sin(x))^{-2}

\int 3 (sin (x))^{- 2} d x

- 3 cot (x) + C

Solution steps

\int 3 (sin (x))^{- 2} d x

Take the constant out:

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

= 3 \cdot \int (sin (x))^{- 2} d x

Simplify

(sin (x))^{- 2} : csc^{2} (x)

= 3 \cdot \int csc^{2} (x) d x

Use the common integral:

\int csc^{2} (x) d x = - cot (x)

= 3 (- cot (x))

Simplify

= - 3 cot (x)

Add a constant to the solution

= - 3 cot (x) + C

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What is the integral of 3(sin(x))^{-2} ?
The integral of 3(sin(x))^{-2} is -3cot(x)+C