What is the integral of (1/(tan(x))) ?

The integral of (1/(tan(x))) is ln|sin(x)|+C

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integral of (1/(tan(x)))

\int (\frac{1}{tan ( x )}) d x

ln ∣ sin (x) ∣ + C

Solution steps

\int \frac{1}{tan ( x )} d x

Rewrite using trig identities

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

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = sin (x)

= ln ∣ sin (x) ∣

Add a constant to the solution

= ln ∣ sin (x) ∣ + C

What is the integral of (1/(tan(x))) ?
The integral of (1/(tan(x))) is ln|sin(x)|+C