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

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

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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

= \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{4 x ^{\frac{3}{2}} - x ^{3} + 8}{x})

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

\frac{d e}{d t}

\frac{2 - 5 s}{s ^{2} + 9}

\int \frac{1}{2} x^{2} d x

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