Question

5-16 Find the general indefinite integral. 16. in%20x%7D%20d%20x" id="TexFormula1" title="\int \frac{\sin 2 x}{\sin x} d x" alt="\int \frac{\sin 2 x}{\sin x} d x" align="absmiddle" class="latex-formula">

Answer 1

I assume the integral is

$\displaystyle \int\frac{\sin(2x)}{\sin(x)} \, dx$

Simplify the integrand:

$\sin(2x) = 2\sin(x)\cos(x) \implies \dfrac{\sin(2x)}{\sin(x)} = 2\cos(x)$

Then the indefinite integral is

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