What is the integral of (csc(θ)cot(θ))/2 ?

The integral of (csc(θ)cot(θ))/2 is -1/2 csc(θ)+C

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integral of (csc(θ)cot(θ))/2

\int \frac{csc ( θ ) cot ( θ )}{2} d θ

- \frac{1}{2} csc (θ) + C

Solution steps

\int \frac{csc ( θ ) cot ( θ )}{2} d θ

Take the constant out:

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

= \frac{1}{2} \cdot \int csc (θ) cot (θ) d θ

Apply u-substitution

: \int - 1 d u

= \frac{1}{2} \cdot \int - 1 d u

Integral of a constant:

\int a d x = a x

= \frac{1}{2} (- 1) u

Substitute back

u = csc (θ)

= \frac{1}{2} (- 1) csc (θ)

Simplify

= - \frac{1}{2} csc (θ)

Add a constant to the solution

= - \frac{1}{2} csc (θ) + C

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What is the integral of (csc(θ)cot(θ))/2 ?
The integral of (csc(θ)cot(θ))/2 is -1/2 csc(θ)+C