What is the integral of cot(17x) ?

The integral of cot(17x) is 1/17 ln|sin(17x)|+C

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integral of cot(17x)

\int cot (17 x) d x

\frac{1}{17} ln ∣ sin (17 x) ∣ + C

Solution steps

\int cot (17 x) d x

Rewrite using trig identities

= \int \frac{cos ( 17 x )}{sin ( 17 x )} d x

Apply u-substitution

: \int \frac{1}{17 u} d u

= \int \frac{1}{17 u} d u

Take the constant out:

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

= \frac{1}{17} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{17} ln ∣ u ∣

Substitute back

u = sin (17 x)

= \frac{1}{17} ln ∣ sin (17 x) ∣

Add a constant to the solution

= \frac{1}{17} ln ∣ sin (17 x) ∣ + C

\int (cos (x) + \frac{1}{3} x) d x

\int e^{x - 1} + x^{- 2} d x

\int - x^{2} + 3 x d x

\frac{d}{d x} (\frac{x - cos ( x )}{x ^{2} + cot ( x )})

\frac{d}{d x} (\frac{9 x ^{2}}{x})

What is the integral of cot(17x) ?
The integral of cot(17x) is 1/17 ln|sin(17x)|+C