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

Take the constant out:

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

= - \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

f (x) = (x^{2} + 15) (2 x + 18)

\int \frac{16}{1 + x ^{2}} d x

\frac{d y}{d x} = 2 (1 - y)

\frac{\partial}{\partial y} (\frac{- 1}{x ^{2} + y ^{2}})

\frac{\partial}{\partial x} (e^{(4 x y)})

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