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∫2x+3⼀x^2+2x+2dx求解

2025-04-08 07:37:26

推荐回答（1个）

回答1：

∫ (2x + 3)/(x² + 2x + 2) dx，注意d(x² + 2x + 2) = (2x + 2) dx
= ∫ (2x + 2)/(x² + 2x + 2) dx + ∫ dx/(x² + 2x + 2)
= ∫ d(x² + 2x + 2)/(x² + 2x + 2) + ∫ dx/[(x + 1)² + 1]，公式∫ dx/(x² + a²) = (1/a)arctan(x/a) + C
= ln| x² + 2x + 2 | + arctan(x + 1) + C

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