What is the integral of cot(27x) ?

The integral of cot(27x) is 1/27 ln|sin(27x)|+C

Popular >

integral of cot(27x)

\int cot (27 x) d x

\frac{1}{27} ln ∣ sin (27 x) ∣ + C

Solution steps

\int cot (27 x) d x

Rewrite using trig identities

= \int \frac{cos ( 27 x )}{sin ( 27 x )} d x

Apply u-substitution

: \int \frac{1}{27 u} d u

= \int \frac{1}{27 u} d u

Take the constant out:

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

= \frac{1}{27} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{27} ln ∣ u ∣

Substitute back

u = sin (27 x)

= \frac{1}{27} ln ∣ sin (27 x) ∣

Add a constant to the solution

= \frac{1}{27} ln ∣ sin (27 x) ∣ + C

\int \frac{x ^{2} + 3 x + 1}{x ^{4}} d x

\int p (p + 3)^{8} d p

\int 9 y^{2} y^{3} + 1 d y

\int \frac{e ^{x}}{sec ( x )} d x

\int (\frac{1}{( 1 + x ^{2} )}) d x

What is the integral of cot(27x) ?
The integral of cot(27x) is 1/27 ln|sin(27x)|+C