let
2x-1= 2sint
2dx= 2cost dt
dx = cost dt
∫√[4-(2x-1)^2] dx
=4∫ (cost)^2 dt
=2∫ (1+cos2t) dt
=2 [ t + (1/2)sin2t ] + C
=2{ arcsin[(2x-1)/2] + (1/4)√[4-(2x-1)^2] } + C
where
t= arcsin[(2x-1)/2]
sin2t
= 2sint.cost
=2 [(2x-1)/2]. [√[4-(2x-1)^2] /2]
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