高数，求不定积分
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∫dx/[x(x^4+1)] = ∫xdx/[x^2(x^4+1)]
= (1/2)∫dx^2/[x^2(x^4+1)] = (1/2)∫du/[u(u^2+1)]
= (1/2)∫[1/u - u/(1+u^2)]du = (1/2)lnu - (1/4)ln(1+u^2) + C
= (1/2)ln(x^2) - (1/4)ln(1+x^4) + C
= ln|x| - (1/4)ln(1+x^4) + C
= (1/2)∫dx^2/[x^2(x^4+1)] = (1/2)∫du/[u(u^2+1)]
= (1/2)∫[1/u - u/(1+u^2)]du = (1/2)lnu - (1/4)ln(1+u^2) + C
= (1/2)ln(x^2) - (1/4)ln(1+x^4) + C
= ln|x| - (1/4)ln(1+x^4) + C
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