What is the integral of cot(24x) ?

The integral of cot(24x) is 1/24 ln|sin(24x)|+C

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integral of cot(24x)

\int cot (24 x) d x

\frac{1}{24} ln ∣ sin (24 x) ∣ + C

Solution steps

\int cot (24 x) d x

Rewrite using trig identities

= \int \frac{cos ( 24 x )}{sin ( 24 x )} d x

Apply u-substitution

: \int \frac{1}{24 u} d u

= \int \frac{1}{24 u} d u

Take the constant out:

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

= \frac{1}{24} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{24} ln ∣ u ∣

Substitute back

u = sin (24 x)

= \frac{1}{24} ln ∣ sin (24 x) ∣

Add a constant to the solution

= \frac{1}{24} ln ∣ sin (24 x) ∣ + C

13 sin (x), 13 cos (x), 0, π

x \to \infty lim ([0, x])

t \to 0 - lim (2 t - 4)

x \to 0 - lim (- 2 + \frac{18}{x ^{2}})

x \to 6 + lim (\frac{3}{x - 6})

What is the integral of cot(24x) ?
The integral of cot(24x) is 1/24 ln|sin(24x)|+C