5-16 Find the general indefinite integral. 16. \int (\sin 2 x)/(\sin x) d x

Question

5-16 Find the general indefinite integral.
16.
`\int (\sin 2 x)/(\sin x) d x`

Answer 1

I assume the integral is

`\displaystyle \int(\sin(2x))/(\sin(x)) \, dx`

Simplify the integrand:

`\sin(2x) = 2\sin(x)\cos(x) \implies (\sin(2x))/(\sin(x)) = 2\cos(x)`

Then the indefinite integral is

`\displaystyle \int(\sin(2x))/(\sin(x)) \, dx = 2 \int \cos(x) \, dx = \boxed{2 \sin(x) + C}`