帮忙详细解一下这道题吧
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原积分 I = ∫[1/(x-1)+2/(x-1)^2+(x+2)/(x^2-x+5)]dx
= ln|x-1| - 2/(x-1) + (1/2)∫(2x-1+5)dx/(x^2-x+5)
= ln|x-1| - 2/(x-1) + (1/2)∫d(x^2-x+5)/(x^2-x+5)
+ (5/2)∫d(x-1/2)/[19/4+(x-1/2)^2]
= ln|x-1| - 2/(x-1) + (1/2)ln(x^2-x+5)
+ [5/(2√19)]arctan[(2x-1)/√19]+ C
= ln|x-1| - 2/(x-1) + (1/2)∫(2x-1+5)dx/(x^2-x+5)
= ln|x-1| - 2/(x-1) + (1/2)∫d(x^2-x+5)/(x^2-x+5)
+ (5/2)∫d(x-1/2)/[19/4+(x-1/2)^2]
= ln|x-1| - 2/(x-1) + (1/2)ln(x^2-x+5)
+ [5/(2√19)]arctan[(2x-1)/√19]+ C
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