lrs7595
幼苗
共回答了21个问题采纳率:85.7% 举报
1/(x^3+1)=1/(x+1)(x^2+1-x)=1/3(x+1)+(-x/3+2/3)/(x^2-x+1) ∫dx/(x^3+1)=1/3ln(x+1)-1/3∫(x-1/2-3/2)/[(x-1/2)^2+3/4]dx =1/3ln(x+1)-1/6ln[(x-1/2)^2+3/4]+1/2∫1/(x-1/2)^2+3/4]dx =1/3ln[(x+1)/√(x^2-x+1)]+√3/3arctan[2√3(x-1/2)/3]+c
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