2007-07-30 00:22:05 · 5 answers · asked by 5 2 in Science & Mathematics ➔ Mathematics
Can someone give me DETAILED working explaining each step of the way. Not just the name of the method. The way you would present in an exam, without leaving out any details. Thank you!
2007-07-30 00:58:29 · update #1
u=ln x, du=1/x dx, so you get the integral of u du which leads to (1/2)(ln x)^2 +C.
2007-07-30 00:25:15 · answer #1 · answered by mathematician 7 · 3⤊ 0⤋
You convert ln x into log,by dividing log e.... log e is constant which will come out of the integration sign..Then you are left over with log x divided by x..this you integrate by parts(product rule)..
2007-07-30 07:50:01 · answer #2 · answered by srikanta 2 · 0⤊ 0⤋
I = â« (ln x) / x dx
Let u = ln x
du = (1 / x) dx
I = ⫠u du = u ² / 2 + C = (1/2) ln ² x + C
2007-08-03 01:56:36 · answer #3 · answered by Como 7 · 1⤊ 1⤋
integ (ln x)/x = (1/x)^2 / 2 = 1 / (2x^2) + c
2007-07-30 08:04:08 · answer #4 · answered by CPUcate 6 · 0⤊ 2⤋
put y = lnx then dy = ln x dx then dx =dy/lnx =dy/y
then integration y/e^y dy/y= integ e^-y dy= -e^-y + c
= - e^-lnx= -!/ e^lnx +c
2007-07-30 09:11:55 · answer #5 · answered by mramahmedmram 3 · 0⤊ 1⤋