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Kaylis [27]
2 years ago
9

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">
Mathematics
1 answer:
givi [52]2 years ago
3 0

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}

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