Question

∫√ (1+Inx) / (xInx) dx

Answer 1

∫√ (1+Inx) / (xInx) dx

let

y= lnx

dy = (1/x) dx

∫√ (1+Inx) / (xInx) dx

=∫ [√ (1+y) / y] dy

let

y= (tana)^2

dy = 2(tana)^2(seca)da

∫ [√ (1+y) / y] dy

=∫ (seca / (tana)^2).2(tana)^2(seca)da

=2∫ (seca)^2 da

= 2tana+ C

= 2√y + C

=2√lnx + C