积分1/(x^14-x^2)^1/2

题目详情

积分1/(x^14-x^2)^1/2

▼优质解答

答案和解析

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

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