求不定积分∫x ln^2xdx - 知识问答

求不定积分∫x ln^2xdx

1个回答

原式=1/2∫ln²xdx²
=1/2*x²ln²x-1/2∫x²dln²x
=1/2*x²ln²x-1/2∫x²*2lnx*1/xdx
=1/2*x²ln²x-1/2∫lnxdx²
=1/2*x²ln²x-1/2*x²lnx-1/2∫x²dlnx
=1/2*x²ln²x-1/2*x²lnx-1/2∫x²*1/xdx
=1/2*x²ln²x-1/2*x²lnx-1/2∫xdx
=1/2*x²ln²x-1/2*x²lnx-1/4*x²+C

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