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

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

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integral of (cos(θ))/(sin(θ)+2)

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

ln ∣ sin (θ) + 2 ∣ + C

Solution steps

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

Apply u-substitution

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = sin (θ) + 2

= ln ∣ sin (θ) + 2 ∣

Add a constant to the solution

= ln ∣ sin (θ) + 2 ∣ + C

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