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Question
Integrate the function:
`cos x/sqrt(4 - sin^2 x)`
Solution
Let I = `int (cos x)/sqrt(4 - sin^2 x)`dx
Substituting sin x = 2t
cos x dx = 2 dt
Hence, `I = int (2 dt)/sqrt(4 - 4t^2)`
`= int (2 dt)/(2sqrt(1 - t^2))`
`= int 1/sqrt(1 - t^2) dt = sin^-1 t + C`
`= sin^-1 ((sin x)/2) + C ....[(because sin x = 2 t), (=> t = (sin x)/2)]`
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