What is the integral of cot(1/8 x) ?

The integral of cot(1/8 x) is 8ln|sin(x/8)|+C

integral of cot(1/8 x)

\int cot (\frac{1}{8} x) d x

8 ln sin (\frac{x}{8}) + C

Solution steps

\int cot (\frac{1}{8} x) d x

Rewrite using trig identities

= \int \frac{cos ( \frac{x}{8} )}{sin ( \frac{x}{8} )} d x

Apply u-substitution

= \int \frac{8}{u} d u

Take the constant out:

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

= 8 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 8 ln ∣ u ∣

Substitute back

u = sin (\frac{x}{8})

= 8 ln sin (\frac{x}{8})

Add a constant to the solution

= 8 ln sin (\frac{x}{8}) + C

\frac{d}{d x} (\frac{1}{2 x - 1})

\int \frac{3 y}{( 2 + 3 y ^{2} ) ^{3}} d y

\frac{d}{d x} (cos^{2} (3 x + 1) - sin^{2} (3 x + 1))

\int 1 + sin (x) d x

d er i v a t i v e f (x) = 5 + 4 e^{3 x}

What is the integral of cot(1/8 x) ?
The integral of cot(1/8 x) is 8ln|sin(x/8)|+C