根号下(1+u^2)/(1-u^2)求积分

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根号下(1+u^2)/(1-u^2)求积分根号下(1+u^2)/(1-u^2)求积分根号下(1+u^2)/(1-u^2)求积分∫(1+u^2)/(1-u^2)du=∫(-1+2/(1-u^2))du=

根号下(1+u^2)/(1-u^2)求积分
根号下(1+u^2)/(1-u^2)求积分

根号下(1+u^2)/(1-u^2)求积分
∫ (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