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

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

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

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

ln ∣ 2 - cos (y) ∣ + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 2 - cos (y)

= ln ∣ 2 - cos (y) ∣

Add a constant to the solution

= ln ∣ 2 - cos (y) ∣ + C

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

\int_{0}^{3} x^{3} d x

x \to 2 lim (2 - x - 2)

f (x) = 0.4 x^{1.6}

(\frac{x - 2 ln ( x ) - 1}{x - 1})^{^{'}}

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