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設lnx=a0+a1x+a2x(2)+…anx(n)+… y=xlnx-x於是就有y=0+(a0-1)x+a1x(2)+… 求導a0-1+2a1x(1)+3a2x(2)+… 對比發現第一項無解.所以不能展開成x的級數.倒是ln(1+x)可以展開 求導得到1/(1+x)=1-x+x(2)+(-x)(n)+.. 再積分ln(1+x)=(-1)(n)*n!*x(n)
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