What is the integral of 3/(tan(x)) ?

The integral of 3/(tan(x)) is 3ln|sin(x)|+C

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integral of 3/(tan(x))

\int \frac{3}{tan ( x )} d x

3 ln ∣ sin (x) ∣ + C

Solution steps

\int \frac{3}{tan ( x )} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{tan ( x )} d x

Rewrite using trig identities

= 3 \cdot \int \frac{cos ( x )}{sin ( x )} d x

Apply u-substitution

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

= 3 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 ln ∣ u ∣

Substitute back

u = sin (x)

= 3 ln ∣ sin (x) ∣

Add a constant to the solution

= 3 ln ∣ sin (x) ∣ + C

\int ln (tan (x)) sec^{2} (x) d x

\int \frac{1}{y} d y

\int x ln (x^{- 1}) d x

\int \frac{x ^{3} - 1}{x ^{2} + x} d x

\int (6 x^{2} + 2 x) d x

What is the integral of 3/(tan(x)) ?
The integral of 3/(tan(x)) is 3ln|sin(x)|+C