What is f(x) if derivative is f'(x)=sin2x/(sin^2 x-4)?

Expert Answers

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We need to find f(x) given that f'(x) = sin 2x /((sin x)^2 - 4)

let ((sin x)^2 - 4) = y

dy = 2*sin x * cos x  dx

=>dy = sin 2x dx

Int [ sin 2x /((sin x)^2 - 4) dx]

=> Int [ 1/y dy]

=> ln |y | + C

substitute y = ((sin x)^2 - 4)

=> ln |((sin x)^2 - 4)| + C

The function f(x)  = ln |((sin x)^2 - 4)| + C

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