Question

This integral diverges or converges and why?

Answer 1

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

Answer 2

@AriPotta or @campbell_st please help @ASAAD123 :) Thank you :)

Answer 3

No one solve this?

Answer 4

@phi

Answer 5

@amistre64

Answer 6

@experimentX

Answer 7

@eliassaab

Answer 8

@jagatuba

Answer 9

@LonelyandForgotten

Answer 10

@Agent_Sniffles

Answer 11

in a pinch, you can always use the wolf:

http://www.wolframalpha.com/

Answer 12

@amistre64 wolf shows last answer, the steps does not show it and it and it converges ,but how get it.

Answer 13

just as a cursory note, the bottom appears to grow larger, faster, than the top

what methods have yo been taught so far to work thru this problem?

Answer 14

comparison test
compare to other function ,but l did that and I get the bigger function diverges !!!??

Answer 15

can you show me what you did?

Answer 16

for large values of x, the bottom can simplify to xln^3(x)

\[\frac{ln(x)}{xln^3(x)}=\frac{1}{xln^2(x)}\]
can we compare that?

Answer 17

but this diverges and it is the bigger!!!

Answer 18

\[\frac{ lnx }{ xln^3x }\] diverges and is bigger than\[\frac{ lnx }{ x^{1/3}+xln^3x }\]

Answer 19

\[\frac{ lnx }{ x+xln^3x }\] converges and is smaller than \[\frac{ lnx }{ x ^{1/3}+xln^3 x }\]