What is the integral of cot(22x) ?

The integral of cot(22x) is 1/22 ln|sin(22x)|+C

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integral of cot(22x)

\int cot (22 x) d x

\frac{1}{22} ln ∣ sin (22 x) ∣ + C

Solution steps

\int cot (22 x) d x

Rewrite using trig identities

= \int \frac{cos ( 22 x )}{sin ( 22 x )} d x

Apply u-substitution

: \int \frac{1}{22 u} d u

= \int \frac{1}{22 u} d u

Take the constant out:

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

= \frac{1}{22} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{22} ln ∣ u ∣

Substitute back

u = sin (22 x)

= \frac{1}{22} ln ∣ sin (22 x) ∣

Add a constant to the solution

= \frac{1}{22} ln ∣ sin (22 x) ∣ + C

\int \frac{1}{x ^{4} x ^{2} - 64} d x

\frac{\partial}{\partial x} (x^{l n (x)})

\int_{- 2}^{2} 2 x^{2} - 6 x + 14 d x

\int x^{2} - 2 x + 8 d x

\frac{d}{d x} (\frac{2 x ^{2} + 6 x + 4}{x})

What is the integral of cot(22x) ?
The integral of cot(22x) is 1/22 ln|sin(22x)|+C