x/(x^8-1)的不定积分

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x/(x^8-1)的不定积分x/(x^8-1)的不定积分x/(x^8-1)的不定积分设t=x^2则dt=2xdx∴xdx/(x^8-1)=dt/2(t^4-1)1/(t^4-1)=(1/2)*[1/(

x/(x^8-1)的不定积分
x/(x^8-1)的不定积分

x/(x^8-1)的不定积分
设t=x^2 则dt=2xdx
∴xdx/(x^8-1)=dt/2(t^4-1)
1/(t^4-1)=(1/2)*[1/(t^2-1)-1/(t^2+1)]
=(1/4)*[1/(t-1)-1/(t+1)]-(1/2)*[1/(t^2+1)]
∴∫xdx/(x^8-1)
=(1/8)*In(|t-1|/|t+1|)-(1/4)*arctant+C
=(1/8)*In(|x^2-1|/|x^2+1|)-(1/4)*arctan(x^2)+C