determine whether the integral converges or diverges
integral of 1/ x*(lnx)^2 in the range of e to infinity
help me please
thanks a lot
2007-01-25 17:08:03 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Use u substitution. I can't say how I picked it - just guess some stuff and see what works. I tried u = ln(x) and u = 1/x and then u = 1/ln(x) (which works).
u = 1/ln(x) so du = -1/x(ln(x))^2
Thus you must integrate (-1)du, which is -u + C.
Switching back to x,
-u + C = -1/ln(x) + C and evaluating this at at e and infinity gives 0 - (-1) = 1.
Hence it converges.
2007-01-25 17:26:36 · answer #1 · answered by chiggitychaunce2 2 · 0⤊ 0⤋
Is this supposed to be (1/x) * (ln x)^2?
If so the integral is [(ln x)^3] / 3
The integral diverges because the natural log of infinity is infinite.
2007-01-26 01:15:47 · answer #2 · answered by z_o_r_r_o 6 · 1⤊ 0⤋
Wow, i was trying to make sense of it for a while and zorro is completely correct
2007-01-26 01:17:53 · answer #3 · answered by maxroth@pacbell.net 2 · 0⤊ 0⤋
aww man I thought that said Integra like acura integra...the l ruined it....
2007-01-26 01:11:51 · answer #4 · answered by 2zero9 2 · 0⤊ 0⤋