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Evaluate: int(cosx)/(1/4-cos^2x)\ dx...

Evaluate: `int(cosx)/(1/4-cos^2x)\ dx`

Text Solution

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`=int frac{cosx}{1/4-(1-sin^2x)}dx`
`sinx=t=> cosx dx=dt`
`=int frac{dt}{1/4-(1-t^2)}`
`=4 int frac{1}{(2t)^2-(sqrt 3)^2}dt`
`2/(sqrt 3) log frac{2 sinx- sqrt 3}{2 sinx+ sqrt 3}+C`
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