What is the integral of cot(48x) ?

The integral of cot(48x) is 1/48 ln|sin(48x)|+C

integral of cot(48x)

\int cot (48 x) d x

\frac{1}{48} ln ∣ sin (48 x) ∣ + C

Solution steps

\int cot (48 x) d x

Rewrite using trig identities

= \int \frac{cos ( 48 x )}{sin ( 48 x )} d x

Apply u-substitution

= \int \frac{1}{48 u} d u

Take the constant out:

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

= \frac{1}{48} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{48} ln ∣ u ∣

Substitute back

u = sin (48 x)

= \frac{1}{48} ln ∣ sin (48 x) ∣

Add a constant to the solution

= \frac{1}{48} ln ∣ sin (48 x) ∣ + C

\frac{d}{d x} (e^{c o s (2 x)} \cdot sin (2 x))

x \to \infty lim (xxxxx)

\frac{\partial}{\partial x} (\frac{1}{2} x)

ln (3) x^{4}

x^{\frac{2}{3}} (x - 5)

What is the integral of cot(48x) ?
The integral of cot(48x) is 1/48 ln|sin(48x)|+C