What is the integral of cot(15x) ?

The integral of cot(15x) is 1/15 ln|sin(15x)|+C

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integral of cot(15x)

\int cot (15 x) d x

\frac{1}{15} ln ∣ sin (15 x) ∣ + C

Solution steps

\int cot (15 x) d x

Rewrite using trig identities

= \int \frac{cos ( 15 x )}{sin ( 15 x )} d x

Apply u-substitution

: \int \frac{1}{15 u} d u

= \int \frac{1}{15 u} d u

Take the constant out:

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

= \frac{1}{15} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{15} ln ∣ u ∣

Substitute back

u = sin (15 x)

= \frac{1}{15} ln ∣ sin (15 x) ∣

Add a constant to the solution

= \frac{1}{15} ln ∣ sin (15 x) ∣ + C

\frac{\partial}{\partial s} (s^{2} + t^{2})

n = 0 \sum \infty n sin (n \cdot π)

\frac{s + 1}{( s ( s ^{2} + s + 1 ) )}

\frac{\partial}{\partial x} (e^{c o s (x)})

\frac{d}{d x} ((8 x + 9) (9 x - 10))

What is the integral of cot(15x) ?
The integral of cot(15x) is 1/15 ln|sin(15x)|+C