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

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

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

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

ln ∣ 2 - cos (x) ∣ + C

Solution steps

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

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 (x)

= ln ∣ 2 - cos (x) ∣

Add a constant to the solution

= ln ∣ 2 - cos (x) ∣ + C

y = 2 x^{2}, y = 3 - x, 0, 3

y^{^{''}} + (10 + 5) y = \frac{( 10 - 5 )}{2}

\frac{( x + x ^{2} + 8 )}{2}

x \cdot sin (x) + x \cdot cos (x)

\int 2 x^{- 1} d x

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