Another Convergent/Divergent Problem?

Question

Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as "divergent."

Integral: 7 to Infinite= (ln(x))/x dx

Answer 1

The integral to infinity of f(x) = 1/x is divergent, therefore the integral of f(x) = ln(x)/x has to be divergent.

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LOL, helpful link in the previous post. The answer to your question is bound to be in there somewhere....

Answer 2

EDIT: You're absolutely right zanti3, I made an error in applying the comparison test. Convergent series was a long time ago for me, haha. This integral diverges as you said.

Answer 3

Zantie's answwer is absolutely right and is probaly the simplest way to conclude the integral diverges. .Anyway, we can come to this same conclusion directly, because

Integral (7 to oo) ln(x)/x dx = [1/2 (ln(x))^2] (7 to oo) = oo, becauseln(x) - and so ln(x)^2 - goes to oo when x -> oo.

This remains true if, instead of 7, the inferior integration limit is any a> 0.

Answer 4

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Answer 5

http://www.mathworld.wolfram.com