How do you evaluate the integral $\int \frac{sin θ}{2 - cos θ}$ $int sintheta/(2-costheta)$ ?

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How do you evaluate the integral $\int \frac{sin θ}{2 - cos θ}$ $int sintheta/(2-costheta)$ ?

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Answer 1 · 2017-03-22T23:18:38

$\int \frac{sin θ d θ}{2 - cos θ} = ln (2 - cos θ) + C$ $int (sinthetad theta)/(2-cos theta) = ln (2-costheta) + C$

Explanation:

Substitute:

$x = 2 - cos θ$ $x = 2-costheta$

$d x = sin θ d θ$ $dx = sintheta d theta$

and we have:

$\int \frac{sin θ d θ}{2 - cos θ} = \int \frac{d x}{x} = ln | x | + C = ln (2 - cos θ) + C$ $int (sinthetad theta)/(2-cos theta) = int dx/x= ln abs x+C = ln (2-costheta) + C$

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How do you evaluate the integral $\int \frac{sin θ}{2 - cos θ}$ $int sintheta/(2-costheta)$ ?

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