求定积分(1nx/√x)*dx上限4下限1

Question

求定积分 (1n x/√x)*dx 上限4 下限1

Answer 1

分步积分
∫[1,4] (1n x/√x)*dx
=2∫[1,4] 1n xd√x
=2√xlnx[1,4] -2∫[1,4] √xd1n x
=8ln2-2∫[1,4] √x/xd x
=8ln2-2∫[1,4] d√x
=8ln2-4√x[1,4]
=8ln2-4