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

The integral of (csc^2(z))/(cot(z)) is -ln|cot(z)|+C

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integral of (csc^2(z))/(cot(z))

\int \frac{csc ^{2} ( z )}{cot ( z )} d z

- ln ∣ cot (z) ∣ + C

Solution steps

\int \frac{csc ^{2} ( z )}{cot ( z )} d z

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = cot (z)

= - ln ∣ cot (z) ∣

Add a constant to the solution

= - ln ∣ cot (z) ∣ + C

What is the integral of (csc^2(z))/(cot(z)) ?
The integral of (csc^2(z))/(cot(z)) is -ln|cot(z)|+C