请问∫1/(x3(x4+1)dx等于多少啊

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▼优质解答

答案和解析

∫dx/[x^3(x^4+1)]
let
x^2 = tany
2xdx = (secy)^2 dy
∫dx/[x^3(x^4+1)]
= (1/2)∫ (coty)^2 dy
= (1/2)∫ [(cscy)^2-1] dy
= (1/2)( -coty -y) + C
= (1/2)( -1/x^2 -arctan(x^2) ) + C

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