What is the integral of cot(19x) ?

The integral of cot(19x) is 1/19 ln|sin(19x)|+C

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integral of cot(19x)

\int cot (19 x) d x

\frac{1}{19} ln ∣ sin (19 x) ∣ + C

Solution steps

\int cot (19 x) d x

Rewrite using trig identities

= \int \frac{cos ( 19 x )}{sin ( 19 x )} d x

Apply u-substitution

: \int \frac{1}{19 u} d u

= \int \frac{1}{19 u} d u

Take the constant out:

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

= \frac{1}{19} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{19} ln ∣ u ∣

Substitute back

u = sin (19 x)

= \frac{1}{19} ln ∣ sin (19 x) ∣

Add a constant to the solution

= \frac{1}{19} ln ∣ sin (19 x) ∣ + C

\int x^{2} (3 x^{3} - 2)^{4} d x

\frac{d}{d x} (k^{x} + x^{k})

\int_{0}^{2} 2 π (x + 1) (12 - 6 x) d x

g (x) = 3^{(\frac{x}{2})}

x \to 2 lim (\frac{( 3 )}{x - 2})

What is the integral of cot(19x) ?
The integral of cot(19x) is 1/19 ln|sin(19x)|+C