∫{x=0,-2}〔x+2〕/〔x^2+2x+2〕 dx
问题描述:
∫{x=0,-2}〔x+2〕/〔x^2+2x+2〕 dx
答
∫(-2,0)=(1/2)∫(-2,0)[2x+2]dx/[x^2+2x+2]+∫(-2,0)dx/[x^2+2x+2]
=(1/2)ln(x^2+2x+2)|(-2,0)+arctan(x+1)|(-2,0)
=π/2 这里上限为0,下限为-2