∫ dx/√(3 + 2x - x²)
= ∫ dx/√[- (x² - 2x + 1 - 1) + 3]
= ∫ dx/√[4 - (x - 1)²]
= ∫ d(x - 1)/√[2² - (x - 1)²]
= arcsin[(x - 1)/2] + C