What is the integral of-3csc^2(x) ?

The integral of-3csc^2(x) is 3cot(x)+C

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integral of-3csc^2(x)

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

3 cot (x) + C

Solution steps

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

Take the constant out:

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