If I_m = int[0, e] (log(x))^m dx, show that I_m + m I_m-1 | < 3

[shaswata tripathy]

\(\displaystyle \mbox{If }\, I_m\, =\, \displaystyle{\int_0^e}\, \left(\log(x)\right)^m\, dx,\, \mbox{ show that }\, I_m\, +\, m\, \left. I_{m-1}\right|\, <\, 3\)

Please help me.

 

[stapel]

\(\displaystyle \mbox{If }\, I_m\, =\, \displaystyle{\int_0^e}\, \left(\log(x)\right)^m\, dx,\, \mbox{ show that }\, I_m\, +\, m\, \left. I_{m-1}\right|\, <\, 3\)

Please help me.

We'll be glad to help. Of course, "helping" doesn't mean "doing it for you"; that would be called "cheating". :lol:

Please reply with an explanation of the "pipe" character to the left of the "less than" sign in the exercise, so we have a better chance of understanding what is going on here. When you reply, please include a clear listing of your efforts, showing what you've tried and where you ground to a halt. Thank you!

 

[shaswata tripathy]

reply to stapel

that pipe character to left of the less than sign is nothing we can ignore that. just a typo