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Problem To evaluate ∫ d x ( x − 1 ) − x 2 + 3 x − 2 \int\frac{dx}{(x-1)\sqrt{-x^2+3x-2}} ∫ ( x − 1 ) − x 2 + 3 x − 2 d x − x 2 + 3 x − 2 = u \sqrt{-x^2+3x-2}=u − x 2 + 3 x − 2 = u − x 2 + 3 x − 2 = u x − 2 \sqrt{-x^2+3x-2}=ux-\sqrt{2} − x 2 + 3 x − 2 = ux − 2 − x 2 + 3 x − 2 = u ( 1 − x ) \sqrt{-x^2+3x-2}=u(1-x) − x 2 + 3 x − 2 = u ( 1 − x ) − x 2 + 3 x − 2 = u ( x + 2 ) \sqrt{-x^2+3x-2}=u(x+2) − x 2 + 3 x − 2 = u ( x + 2 ) Browse the problem library