What is the integral of cot(z) ?

The integral of cot(z) is ln|sin(z)|+C

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integral of cot(z)

\int cot (z) d z

ln ∣ sin (z) ∣ + C

Solution steps

\int cot (z) d z

Rewrite using trig identities

= \int \frac{cos ( z )}{sin ( z )} d z

Apply u-substitution

: \int \frac{1}{u} d u

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = sin (z)

= ln ∣ sin (z) ∣

Add a constant to the solution

= ln ∣ sin (z) ∣ + C

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