What is the integral of cot(26x) ?

The integral of cot(26x) is 1/26 ln|sin(26x)|+C

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integral of cot(26x)

\int cot (26 x) d x

\frac{1}{26} ln ∣ sin (26 x) ∣ + C

Solution steps

\int cot (26 x) d x

Rewrite using trig identities

= \int \frac{cos ( 26 x )}{sin ( 26 x )} d x

Apply u-substitution

= \int \frac{1}{26 u} d u

Take the constant out:

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

= \frac{1}{26} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{26} ln ∣ u ∣

Substitute back

u = sin (26 x)

= \frac{1}{26} ln ∣ sin (26 x) ∣

Add a constant to the solution

= \frac{1}{26} ln ∣ sin (26 x) ∣ + C

What is the integral of cot(26x) ?
The integral of cot(26x) is 1/26 ln|sin(26x)|+C