What is the integral of 1/(-csc(x)) ?

The integral of 1/(-csc(x)) is cos(x)+C

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integral of 1/(-csc(x))

\int \frac{1}{- csc ( x )} d x

cos (x) + C

Solution steps

\int \frac{1}{- csc ( x )} d x

Take the constant out:

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

= - \int \frac{1}{csc ( x )} d x

Rewrite using trig identities

= - \int sin (x) d x

Use the common integral:

\int sin (x) d x = - cos (x)

= - (- cos (x))

Simplify

= cos (x)

Add a constant to the solution

= cos (x) + C

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