求积分 ∫ x/(a-x)^2 dx ,a是常数.

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求积分 ∫ x/(a-x)^2 dx ,a是常数.

∫ x/(a - x)² dx
= ∫ [a - (a - x)]/(a - x)² dx
= ∫ [a * 1/(a - x)² - 1/(a - x)] dx
= - ∫ [a * 1/(a - x)² - 1/(a - x)] d(a - x)
= ln|a - x| - a * [- 1/(a - x)] + C
= ln|a - x| + a/(a - x) + C