What is the integral of-cot(x)csc(x) ?

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

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integral of-cot(x)csc(x)

\int - cot (x) csc (x) d x

csc (x) + C

Solution steps

\int - cot (x) csc (x) d x

Take the constant out:

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

= - \int cot (x) csc (x) d x

Apply u-substitution

= - \int - 1 d u

Integral of a constant:

\int a d x = a x

= - (- 1) u

Substitute back

u = csc (x)

= - (- 1) csc (x)

Simplify

= csc (x)

Add a constant to the solution

= csc (x) + C