What is the integral of (cos(6x))/(sin(6x)) ?

The integral of (cos(6x))/(sin(6x)) is 1/6 ln|sin(6x)|+C

integral of (cos(6x))/(sin(6x))

\int \frac{cos ( 6 x )}{sin ( 6 x )} d x

\frac{1}{6} ln ∣ sin (6 x) ∣ + C

Solution steps

\int \frac{cos ( 6 x )}{sin ( 6 x )} d x

Apply u-substitution

= \int \frac{1}{6 u} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{6} ln ∣ u ∣

Substitute back

u = sin (6 x)

= \frac{1}{6} ln ∣ sin (6 x) ∣

Add a constant to the solution

= \frac{1}{6} ln ∣ sin (6 x) ∣ + C

\int 2 x - 6 x^{3} d x

\frac{d}{d x} (2 π - x cos (x))

cos^{2} (x) sin (x) \frac{d y}{d x} cos^{3} (x) y = 1

l a pl a ce t r an s f or m H (t - 2 π) sin (t - 2 π)

\frac{d}{d x} (\frac{2 + x}{( 2 - x ) ^{5}})

What is the integral of (cos(6x))/(sin(6x)) ?
The integral of (cos(6x))/(sin(6x)) is 1/6 ln|sin(6x)|+C