What is the integral of cot(y) ?

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

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integral of cot(y)

\int cot (y) d y

ln ∣ sin (y) ∣ + C

Solution steps

\int cot (y) d y

Rewrite using trig identities

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

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 (y)

= ln ∣ sin (y) ∣

Add a constant to the solution

= ln ∣ sin (y) ∣ + C

x \to 0 + lim (x (1 - cos (\frac{1}{x})))

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