What is $int ln x / sqrtx dx$ ?

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Answer 1 · 2018-05-03T23:32:13

$2sqrtx(lnx-2)+c$

$intlnx/sqrtxdx=intlnx/color(blue)(2sqrtx)(2color(blue)(dx))$

Substitute $sqrtx=u$

$=$ $intlnu^color(red)(2)/cancel(u)(2cancel(u)du)$ $=$

$int2*2lnudu$ $=$

$4intlnudu$ $=$

$4(u$ $lnu$ $-u)+c$ $=$

$4(sqrtxlnsqrtx-sqrtx)+c$ $=$

$4(1/2sqrtxlnx-sqrtx)+c$ $=$

$2sqrtx(lnx-2)+c$ ,

$c$ $in$ $RR$

What is int ln x / sqrtx dxint ln x / sqrtx dx?