What is the integral of cot(θ)csc(θ) ?

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

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integral of cot(θ)csc(θ)

\int cot (θ) csc (θ) d θ

- csc (θ) + C

Solution steps

\int cot (θ) csc (θ) d θ

Apply u-substitution

: \int - 1 d u

= \int - 1 d u

Integral of a constant:

\int a d x = a x

= (- 1) u

Substitute back

u = csc (θ)

= (- 1) csc (θ)

Simplify

= - csc (θ)

Add a constant to the solution

= - csc (θ) + C

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What is the integral of cot(θ)csc(θ) ?
The integral of cot(θ)csc(θ) is -csc(θ)+C