What is the integral of cot(18x) ?

The integral of cot(18x) is 1/18 ln|sin(18x)|+C

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integral of cot(18x)

\int cot (18 x) d x

\frac{1}{18} ln ∣ sin (18 x) ∣ + C

Solution steps

\int cot (18 x) d x

Rewrite using trig identities

= \int \frac{cos ( 18 x )}{sin ( 18 x )} d x

Apply u-substitution

: \int \frac{1}{18 u} d u

= \int \frac{1}{18 u} d u

Take the constant out:

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

= \frac{1}{18} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{18} ln ∣ u ∣

Substitute back

u = sin (18 x)

= \frac{1}{18} ln ∣ sin (18 x) ∣

Add a constant to the solution

= \frac{1}{18} ln ∣ sin (18 x) ∣ + C

\frac{d}{d x} (x^{2} + 10 x)

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

\frac{d}{d s} (s^{3})

n = 0 \sum \infty \frac{5 ^{n}}{6 ^{n}}

x^{2} y^{^{'}} + 3 x y = 1

What is the integral of cot(18x) ?
The integral of cot(18x) is 1/18 ln|sin(18x)|+C