What is the integral of (sin(2y))/(1-3cos(2y)) ?

The integral of (sin(2y))/(1-3cos(2y)) is 1/6 ln|1-3cos(2y)|+C

Popular >

integral of (sin(2y))/(1-3cos(2y))

\int \frac{sin ( 2 y )}{1 - 3 cos ( 2 y )} d y

\frac{1}{6} ln ∣ 1 - 3 cos (2 y) ∣ + C

Solution steps

\int \frac{sin ( 2 y )}{1 - 3 cos ( 2 y )} d y

Apply u-substitution

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

= \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 = 1 - 3 cos (2 y)

= \frac{1}{6} ln ∣ 1 - 3 cos (2 y) ∣

Add a constant to the solution

= \frac{1}{6} ln ∣ 1 - 3 cos (2 y) ∣ + C

\int \frac{x ^{2}}{x ^{2} - 5} d x

\int 3 x^{2} (x^{3} + 7)^{7} d x

\int 5^{x} - e^{x} + 6 d x

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

\int 10 cos (5 x) sin^{5} (5 x) d x

What is the integral of (sin(2y))/(1-3cos(2y)) ?
The integral of (sin(2y))/(1-3cos(2y)) is 1/6 ln|1-3cos(2y)|+C