Question

integrate
-sinx/ã4+cos^2x dx

Answer 1

integrate
-sinx/square root 4+cos^2x dx

Answer 2

I assume you mean

sin x/√(4+cos^2 x)

let u = cos x
du = -sin x dx

and you have

-∫1/√(4+u^2) du
standard hyperbolic trig substitution is used to get

-arcsinh(u/2)
= -arcsinh(cosx / 2)