What is the integral of-4/(sin^2(r)) ?

The integral of-4/(sin^2(r)) is 4cot(r)+C

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integral of-4/(sin^2(r))

\int - \frac{4}{sin ^{2} ( r )} d r

4 cot (r) + C

Solution steps

\int - \frac{4}{sin ^{2} ( r )} d r

Take the constant out:

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

= - 4 \cdot \int \frac{1}{sin ^{2} ( r )} d r

Use the common integral:

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

= - 4 (- cot (r))

Simplify

= 4 cot (r)

Add a constant to the solution

= 4 cot (r) + C

What is the integral of-4/(sin^2(r)) ?
The integral of-4/(sin^2(r)) is 4cot(r)+C