Question

计算定积分∫xlnxdx,（上限是e,下限是1）.请单的写一下计算步骤？

Answer 1

∫<1, e>xlnxdx = (1/2)∫<1, e>lnxd(x^2)
= (1/2){[x^2lnx]<1, e> - ∫<1, e>xdx}
= (1/2){e^2 - [x^2/2]<1, e>} = (1/4)(e^2+1)