令t=x³ => dt=3x²dx
∫x²/(a^6-x^6) dx
= ∫x²/(a^6-t²) * 1/(3x²) dt
= (1/3)∫dt/(a^6-t²)
= (1/3)∫dt/[(a³)²-(t)²]
= (1/3) * 1/(2a³) * ln|(a³+t)/(a³-t)| + C
= 1/(6a³) * ln|(a³+x³)/(a³-x³)| + C
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
/ x^6 dx 代x = a*sinz，dx = a*cosz dz (a -x )^(3/2) = (a -a sin x)^(3/2) = (a cos x)^(3/2) = a cos x 原式 =
2l
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