Question

this integral diverges or converges and why?

Answer 1

First, what's the point of ln(x) in the numerator and the denominator? Simplify that.

Answer 2

Second, I'm going with "Relatively Obvious" as x increases without bound.

Answer 3

Your challenge is to address convergence as x approaches 1 from the positive side.

Answer 4

Sorry, too sleepy right now to attempt this one . . My guess is it converges based on intuitive feel (see "Relatively Obvious" above).

Answer 5

Only on one side, though.

Answer 6

@cliffsedge

Answer 7

\[\int\limits_{1}^{\infty}\frac{ lnx }{ x^{1/3}+x(\ln^3x) }dx\]

Answer 8

whoa was that ever wrong!!!!!

Answer 9

@satellite73 but if was (+) before x(ln^3x).