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

User Nelstaar
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1 Answer

12 votes
12 votes

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}

User Letin
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