What is the integral of (cos(u))/(sin(u)) ?

The integral of (cos(u))/(sin(u)) is ln|sin(u)|+C

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integral of (cos(u))/(sin(u))

\int \frac{cos ( u )}{sin ( u )} d u

ln ∣ sin (u) ∣ + C

Solution steps

\int \frac{cos ( u )}{sin ( u )} d u

Apply u-substitution

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

v = sin (u)

= ln ∣ sin (u) ∣

Add a constant to the solution

= ln ∣ sin (u) ∣ + C

What is the integral of (cos(u))/(sin(u)) ?
The integral of (cos(u))/(sin(u)) is ln|sin(u)|+C