晕 看错题了
∫x^2/(a^6-x^6) dx
= 1/3∫dx^3 /(a^6-x^3)
= (1/3)∫dx^3 /[(a^3)^3-(x^3 )^2]
= (1/3) * 1/(2a^3) * ln|(a^3+x^3 )/(a^3-x^3 )| + C
= 1/(6a^3) * ln|(a^3+x^3)/(a^3-x^3)| + C