Question

I need to know if the improper integral from 1 to + infinity ( ln x / ( x + ln (x + 1) ) dx converges. Help?

Answer 1

use limit x -> inf and rewrite the integral, solve using limits and then integrate the result

Answer 2

\[\int\limits_{1}^{+\infty} \left( \frac{ \ln }{ x + \ln x } \right)\]

Answer 3

Even if the boundaries are 1 and c, I still can't integrate.

Answer 4

\[\int_1^\infty\frac{\ln xdx}{x+\ln(x+1)}\]?

Answer 5

Hmm I can't figure this one out, are you suppose to use power series or something? :\

Answer 6

you wrote two different things

Answer 7

I was thinking perhaps we could use a comparison test if we are clever, but is the problem as you typed it in the post, or as you typed it below?

Answer 8

Turing test, yes, what you wrote.

Answer 9

use concept of improper integrals,

Answer 10

As I typed it in the problem.

Answer 11

\[\lim_{t \rightarrow \infty} \int\limits_{1}^{t} f(x)dx\]

Answer 12

i have modified the formula, but put value of f(x)=function you typed in the question

Answer 13

yeah, and how do you integrate that sucker?

Answer 14

...

Answer 15

multiple ways, try adding 1 and taking away one from numerator

or double substitutiion

Answer 16

@TuringTest , clearly you use the concept of integration to integrate it.

Answer 17

double sub is a long method but will get you the answer, if you want to avoid the former method

Answer 18

how about a demonstration? what substitution

Answer 19

yeah show us your method @psi9epsilon

Answer 20

I say we look for a comparison, but I can't think of one...
I have to leave unfortunately

Answer 21

try comparing to the integral of ln(x) /2x

Answer 22

nice @Algebraic! that should do the trick :)