1. Jul 11, 2008

### golriz

1. The problem statement, all variables and given/known data

hi
does the following integral converge or diverge?
∫_2^∞▒ln⁡〖x 〗/(e^x+1) dx
thanks

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 11, 2008

### Dick

What have you tried?

3. Jul 11, 2008

### HallsofIvy

First, as Dick said, we need to know what you know and what you have tried before we can make any suggestions. Second, you seem to have used several "special" characters that do not show up on my internet reader. Could you please restate the integral without them?

4. Jul 11, 2008

### golriz

oh i have showed you my question.
my question is:
"Use the coparison test to determine if the following integral converge or diverge:
integral of [ ln x/ e^x + 1 ]dx from 2 to infinity "
i don't know can you understand my question now?

5. Jul 11, 2008

### Dick

I understood the question to begin with. The question was do you understand it. If you are going to use a comparison test you first have to take a guess as to whether it converges or diverges. What's your opinion? If you think it converges find another function thats greater than the given function and show it converges. If you think it diverges find another function that's less than the given function and show it diverges. What's your choice?

6. Jul 11, 2008

### golriz

i know the comparison test but i don't know the solution of this problem.
because i should choose a function greater or less than the given function that converging or diverging of these functions be obvious for me, so i don't know these functions.
do you understand my mean?

7. Jul 12, 2008

### Dick

I understand your meaning. I'm just asking for your opinion on how to start. ln(x) grows really slowly, e^x grows awfully fast. Do you guess it will converge or diverge? I.e. should we look for a lower bound or an upper bound?

8. Jul 12, 2008

### golriz

i think it converges and we should look for upper bound

9. Jul 12, 2008

### Dick

Good, I agree. So we have to look for something larger than ln(x) to put in the numerator and something smaller than e^x+1 to put in the denominator. The resulting integral should be something that i) we can integrate and ii) converges. Any guesses?

10. Jul 12, 2008

### golriz

i'm not sure but can i suggest x/e^x we can integrate it by parts

11. Jul 12, 2008

### Dick

That's exactly what I would have suggested. It converges and it's larger than ln(x)/(e^x+1). Well done.

12. Jul 12, 2008

### golriz

oh really thank u so much because of your help
so no need to proving the converging of x/e^x?

13. Jul 12, 2008

### Dick

Yes, you have to prove it. Don't be silly. I know it converges because I've done this stuff before. If the person who is grading your work knows it does and knows that you know it does and you have an agreement that you don't have to show it, then you don't. It's not hard is it?

14. Jul 12, 2008

### golriz

no not hard
thanks a lot again
bye

15. Jul 12, 2008

### Dick

No problem. You are pretty good at this. You take hints well. I didn't really tell you much you didn't already know. Bye.