What is the integral of (cos(x))/(4+sin(x)) ?

The integral of (cos(x))/(4+sin(x)) is ln|4+sin(x)|+C

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integral of (cos(x))/(4+sin(x))

\int \frac{cos ( x )}{4 + sin ( x )} d x

ln ∣ 4 + sin (x) ∣ + C

Solution steps

\int \frac{cos ( x )}{4 + 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 = 4 + sin (x)

= ln ∣ 4 + sin (x) ∣

Add a constant to the solution

= ln ∣ 4 + sin (x) ∣ + C

\int \frac{2 - 5 x}{x ^{6}} d x

\frac{d y}{d x} + \frac{2 x y}{x ^{2} + 1} = x

\frac{3}{x ^{2}}

\int \frac{1}{x ^{2} x ^{2} + 9} d x

x \to 3 lim (7 x + ∣ x - 3 ∣)

What is the integral of (cos(x))/(4+sin(x)) ?
The integral of (cos(x))/(4+sin(x)) is ln|4+sin(x)|+C