求不定积分x^2/(a^6-x^6)dx

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求不定积分x^2/(a^6-x^6)dx求不定积分x^2/(a^6-x^6)dx求不定积分x^2/(a^6-x^6)dx∫x^2/(a^6-x^6)dxletx^3=a^3siny3x^2dx=a^3

求不定积分x^2/(a^6-x^6)dx
求不定积分x^2/(a^6-x^6)dx

求不定积分x^2/(a^6-x^6)dx
∫ x^2/(a^6-x^6) dx
let
x^3= a^3 siny
3x^2 dx= a^3.cosy dy
∫ x^2/(a^6-x^6) dx
= [1/(3a^3)]∫ (1/cosy) dy
=[1/(3a^3)] ln|secy + tany | +C
=[1/(3a^3)] ln| a^3/√(a^6-x^6) + x^3/√(a^6-x^6) | +C

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