(3)
∫(x-2)/√(3-2x-x^2) dx
=-(1/2)∫(-2x-2)/√(3-2x-x^2) dx -3∫dx/√(3-2x-x^2)
=-√(3-2x-x^2) -3∫dx/√(3-2x-x^2)
=-√(3-2x-x^2) -3arcsin[(x+1)/2] +C
---------
consider
3-2x-x^2 = 4-(x+1)^2
let
x+1 = 2sinu
dx =2cosu du
∫dx/√(3-2x-x^2)
=∫du
=u + C'
=arcsin[(x+1)/2] +C'
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