sinx除以x的广义积分什么?

Question

sinx除以x的广义积分什么?

Answer 1

级数sinx=x-x^3/3!+x^5/5!+...+(-1)^(n+1) *x^(2n-1)/(2n-1)!sinx/x=1/x-x^2/3+x^4/5+..+(-1)^(n+1)*x^(2n-2)/(2n-1)!逐项积分∫sinxdx/x= ln|x|-x^3/3*3!+x^5/5*5!+...+(-1)^(n+1)x^(2n-1)/[(2n-1)(2n-1)!]