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

Question

6902 views around the world

You can reuse this answer
Creative Commons License

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,

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

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

$=2sqrtxlnx-4sqrtx+C$

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