What is the integral of cot(23x) ?

The integral of cot(23x) is 1/23 ln|sin(23x)|+C

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integral of cot(23x)

\int cot (23 x) d x

\frac{1}{23} ln ∣ sin (23 x) ∣ + C

Solution steps

\int cot (23 x) d x

Rewrite using trig identities

= \int \frac{cos ( 23 x )}{sin ( 23 x )} d x

Apply u-substitution

: \int \frac{1}{23 u} d u

= \int \frac{1}{23 u} d u

Take the constant out:

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

= \frac{1}{23} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{23} ln ∣ u ∣

Substitute back

u = sin (23 x)

= \frac{1}{23} ln ∣ sin (23 x) ∣

Add a constant to the solution

= \frac{1}{23} ln ∣ sin (23 x) ∣ + C

x \to 3 lim (x^{2} - x + 1)

x \to 2 - lim (\frac{x + 1}{x - 2})

\int 9 t sin^{2} (t) d t

y^{^{'}} = \frac{6 x sec ( \frac{y}{x} ) + y}{x}

\frac{d}{d x} (- \frac{8 x}{x ^{2} + 1})

What is the integral of cot(23x) ?
The integral of cot(23x) is 1/23 ln|sin(23x)|+C