What is the integral of 1/(cot(3x)sin(3x)) ?

The integral of 1/(cot(3x)sin(3x)) is 1/3 ln|tan(3x)+sec(3x)|+C

Popular >

integral of 1/(cot(3x)sin(3x))

\int \frac{1}{cot ( 3 x ) sin ( 3 x )} d x

\frac{1}{3} ln ∣ tan (3 x) + sec (3 x) ∣ + C

Solution steps

\int \frac{1}{cot ( 3 x ) sin ( 3 x )} d x

Rewrite using trig identities

= \int sec (3 x) d x

Apply u-substitution

: \int sec (u) \frac{1}{3} d u

= \int sec (u) \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int sec (u) d u

Use the common integral:

\int sec (u) d u = ln ∣ tan (u) + sec (u) ∣

= \frac{1}{3} ln ∣ tan (u) + sec (u) ∣

Substitute back

u = 3 x

= \frac{1}{3} ln ∣ tan (3 x) + sec (3 x) ∣

Add a constant to the solution

= \frac{1}{3} ln ∣ tan (3 x) + sec (3 x) ∣ + C

\int \frac{1}{( 2 x - 5 ) ^{7}} d x

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

\int \frac{3 x ^{3}}{x ^{2} + 4 x + 5} d x

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

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

What is the integral of 1/(cot(3x)sin(3x)) ?
The integral of 1/(cot(3x)sin(3x)) is 1/3 ln|tan(3x)+sec(3x)|+C