∫ (x-2)/ ((x+1)^2+4) dx

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∫(x-2)/((x+1)^2+4)dx∫(x-2)/((x+1)^2+4)dx∫(x-2)/((x+1)^2+4)dx令x+1=t,则x=t-1,dx=dt原式=∫(t-3)/(t^2+4)dx=∫

∫ (x-2)/ ((x+1)^2+4) dx
∫ (x-2)/ ((x+1)^2+4) dx

∫ (x-2)/ ((x+1)^2+4) dx
令x+1=t,则x=t-1,dx=dt
原式=∫ (t-3)/(t^2+4)dx =∫ t/(t^2+4)dt-3∫ 1/(t^2+4)d
=(1/2)∫ 1/(t^2+4)d(t^+4)-3arctan(t/2)+C
=(1/2)ln(t^2+4)-3arctan(t/2)+C
=(1/2)ln[(x+1)^2+4]-3arctan[(x+1)/2]+C

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