∫1/（(x-2)^2*(x-3)）dx

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答案和解析

∫dx/[(x-2)^2(x-3)]
=∫[(x-2)-(x-3)]dx/[(x-2)^2(x-3)]
=∫[(x-2)-(x-3)]dx/[(x-2)(x-3) -∫dx/(x-2)^2
=∫dx/(x-2)-∫dx/(x-3)+1/(x-2) +C
=ln|(x-2)/(x-3)| +1/(x-2)+C

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