复变函数 积分计算∫上+无穷下0 1/(1+x^4)dx
问题描述:
复变函数 积分计算∫上+无穷下0 1/(1+x^4)dx
答
∫dx/(1+x^4)=∫dx/[x^2+1)^2-(√2x)^2]=∫dx/[x^2+√2x+1)(x^2-√2x+1)]
=(1/2√2)∫[(x^2+√2x+1)-(x^2-√2x+1)]dx/[x(x^2+√2x+1)(x^2-√2x+1)]
=1/√8∫dx/x(x^2-√2x+1)-1/√8∫dx/x(x^2+√2x+1)