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

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

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

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

ln ∣ 2 + sin (x) ∣ + C

Solution steps

\int \frac{cos ( x )}{2 + sin ( 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 + sin (x)

= ln ∣ 2 + sin (x) ∣

Add a constant to the solution

= ln ∣ 2 + sin (x) ∣ + C

\int r (cos (θ)) z^{3}

\frac{d y}{d x}, sin (x y) = 5 x^{4} y^{2} + 6

x \to 1 lim (x e^{- x})

\frac{d}{d x} (\frac{16}{x})

\frac{\partial}{\partial x} (y^{2} e^{x y})

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