题目

积分1/(x^14-x^2)^1/2

提问时间：2021-04-01

答案

令 x=1/u,则 dx=-du/u^2,∫dx/(x^14-x^2)^(1/2) = ∫-du/{u^2[(u^(-14)-u^(-2)]^(1/2)}= -∫u^5du/(1-u^12)^(1/2)= -(1/6)∫du^6/(1-u^12)^(1/2)= -(1/6)arcsinu^6 + C= -(1/6)arcsin(1/x^6)+C