What is the integral of (lnsqrtx)/x?
2 Answers
Explanation:
Let
int (lnsqrtx)/xdx = 1/2 int(lnx)/xdx = 1/4ln^2x + C
or,
You were on the right track. It is more simple than it seems; we know that
int lnsqrtx/xdx
= 1/2int (lnx)/xdx
Let
=> 1/2 int udu
= 1/2 u^2/2 + C
= 1/2 ln^2x/2 + C
= color(blue)(1/4 ln^2x + C)
Or, we could rewrite this as:
= (1/2lnx)^2 + C
= color(blue)(ln^2(sqrtx) + C)