∫2x+3/x^2+2x+2dx求解

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∫2x+3/x^2+2x+2dx求解∫2x+3/x^2+2x+2dx求解∫2x+3/x^2+2x+2dx求解∫(2x+3)/(x²+2x+2)dx,注意d(x²+2x+2)=(2x

∫2x+3/x^2+2x+2dx求解
∫2x+3/x^2+2x+2dx求解

∫2x+3/x^2+2x+2dx求解
∫ (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