What is the integral of (cos(x))/(5+sin(x)) ?

The integral of (cos(x))/(5+sin(x)) is ln|5+sin(x)|+C

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integral of (cos(x))/(5+sin(x))

\int \frac{cos ( x )}{5 + sin ( x )} d x

ln ∣ 5 + sin (x) ∣ + C

Solution steps

\int \frac{cos ( x )}{5 + 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 = 5 + sin (x)

= ln ∣ 5 + sin (x) ∣

Add a constant to the solution

= ln ∣ 5 + sin (x) ∣ + C

11 t^{2} + 9

\int_{0}^{3} \frac{1}{x ^{2} - 6 x + 5} d x

\frac{6 x}{( x ^{2} + 3 ) ^{2}}

y = 7^{x + a r c c o s (x)}

x^{2} - 4 x, 2 x - x^{2}

What is the integral of (cos(x))/(5+sin(x)) ?
The integral of (cos(x))/(5+sin(x)) is ln|5+sin(x)|+C