第1个回答 2018-06-16
ln^2x是(lnx)²吗?
原式=∫√x (lnx)²dx
=2/3 ∫(lnx)²d[x^(3/2)]
=2/3 (lnx)²x^(3/2)-2/3 ∫x^(3/2)·2lnx ·1/x dx
=2/3 (lnx)²x^(3/2)-4/3 ∫xlnxdx
=2/3 (lnx)²x^(3/2)-2/3 ∫lnx dx²
=2/3 (lnx)²x^(3/2)-2/3 x²lnx +4/3 ∫1dx
=2/3 (lnx)²x^(3/2)-2/3 x²lnx +4x/3+C本回答被网友采纳