What is the integral of #int (lnx) / (x^(1/2)) dx #?

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Answer 1 · 2017-02-21T16:32:39

The answer is #=2sqrtxlnx-4sqrtx+C#

#intu'vdx=uv-intuv'dx#

Here,

#u'=1/sqrtx#, #=>#, #u=2sqrtx#

#v=lnx#, #=>#, #v'=1/x#

Therefore,

#int(lnxdx)/sqrtx=2sqrtxlnx-int(2sqrtxdx)/x#

#=2sqrtxlnx-2int(dx)/sqrtx#

#=2sqrtxlnx-4sqrtx+C#