What is the integral of 5/(csc(x)) ?

The integral of 5/(csc(x)) is -5cos(x)+C

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integral of 5/(csc(x))

\int \frac{5}{csc ( x )} d x

- 5 cos (x) + C

Solution steps

\int \frac{5}{csc ( x )} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{csc ( x )} d x

Rewrite using trig identities

= 5 \cdot \int sin (x) d x

Use the common integral:

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

= 5 (- cos (x))

Simplify

= - 5 cos (x)

Add a constant to the solution

= - 5 cos (x) + C

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