What is the integral of cot(11x) ?

The integral of cot(11x) is 1/11 ln|sin(11x)|+C

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integral of cot(11x)

\int cot (11 x) d x

\frac{1}{11} ln ∣ sin (11 x) ∣ + C

Solution steps

\int cot (11 x) d x

Rewrite using trig identities

= \int \frac{cos ( 11 x )}{sin ( 11 x )} d x

Apply u-substitution

: \int \frac{1}{11 u} d u

= \int \frac{1}{11 u} d u

Take the constant out:

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

= \frac{1}{11} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{11} ln ∣ u ∣

Substitute back

u = sin (11 x)

= \frac{1}{11} ln ∣ sin (11 x) ∣

Add a constant to the solution

= \frac{1}{11} ln ∣ sin (11 x) ∣ + C

\frac{d}{d x} (\frac{2}{1 + 4 x})

(16, - 2), (15, 86)

- \frac{200}{( t + 2 ) ^{2}}

\frac{d}{d x} (\frac{3}{x} + 5 sin (x))

\frac{3}{2 ( s + 1 ) ^{2} + 32}

What is the integral of cot(11x) ?
The integral of cot(11x) is 1/11 ln|sin(11x)|+C