求∫lnx / √x dx上限4下限1

答：
先算不定积分∫lnx/√x dx.
换元,令√x=t,则x=t²,dx=2tdt.
∫lnx/√x dx
=∫2tlnt²/t dt
=2∫lnt² dt
=2 tlnt² -2∫td(lnt²)
=2tlnt²-4t+C
=2√xlnx-4√x+C
=2√x(lnx-2)+C
所以定积分∫(1到4)lnx/√x dx
=2√x(lnx-2)|(1到4)
=4*(ln4-2)-2*(ln1-2)
=4(2ln2-2)+4
=8ln2-4