根号下(1+u^2)/(1-u^2)求积分_数学解答

根号下(1+u^2)/(1-u^2)求积分

人气：260 ℃　时间：2020-05-19 03:44:53

解答

∫ (1+u^2)/(1-u^2)d u
= ∫ (-1+ 2/(1-u^2)) du
= -u +2∫ (1/(1-u^2)) du
= -u + ∫ (1/(1-u) + 1/(1+u)) du
= -u -ln|1-u| +ln|1+u| +C