1/(x^2-x+1)^2的积分推导

题目详情

1/(x^2-x+1)^2的积分推导

▼优质解答

答案和解析

1/(x^2-x+1)^2=1/[(x-1/2)^2+3/4]^2
令x=√3/2tanθ+1/2,则上式=1/[3/4(tanθ)^2+3/4]^2=1/[3/4(secθ)^2]^2=16/9(cosθ)^4
cosθ=1/√[4/3(x-1/2)^2+1]
所以原函数=16/9(cosθ)^4=16/[4(x-1/2)^2+3]^2

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