2007-09-30 05:51:58 · 4 answers · asked by Random_girl 2 in Science & Mathematics ➔ Mathematics
Y'all are great! Thank you so much = )
2007-09-30 06:12:40 · update #1
Make a substitution:
u = ln x.
Then
du = dx/x
So your problem is ∫ udu = u²/2 = (ln x)²/2 + C
2007-09-30 05:58:04 · answer #1 · answered by steiner1745 7 · 2⤊ 0⤋
Use u-substitution to solve this problem. We do not know the integral of lnx, so set u = lnx.
Then take the derivative, and you get du = 1/x dx.
Here, you notice that (ln x)(1/x) is the same thing as lnx/x. So here, in terms of u, you have the integral of u du.
Take the integral as you normally would and you'll get:
1/2 u^2 + C.
You want to get this back in terms of x, so plug u back into the problem:
(1/2)(ln u)^2 + C
2007-09-30 13:04:32 · answer #2 · answered by Anonymous · 2⤊ 0⤋
use u substitution. u=lnx du=1/x I believe that is right its been a while.
sorry, du=1/xdx simple mistake.
2007-09-30 12:54:20 · answer #3 · answered by Anonymous · 2⤊ 0⤋
â«lnx/x dx
= â«lnx dlnx
= (1/2)(lnx)^2+c
2007-09-30 12:55:42 · answer #4 · answered by sahsjing 7 · 2⤊ 1⤋