Test the following integral for divergence:

Question

anonymous · Answer

$$\int\limits_{1}^{19}1/\ln(x)dx$$

experimentx · Answer

ln 1 = 0

experimentx · Answer

http://www.wolframalpha.com/input/?i=integrate+1%2Flnx+from+1+to+10 does not converge

turingtest · Answer

man, I have no idea how to show that

turingtest · Answer

Oh well, gotta go teach English
Later y'all!

anonymous · Answer

Maybe integral test using the limit of t as t goes to 0?

experimentx · Answer

no .. not really, at x=1, ln x = 0, so x=1 becomes asymptotic .. so it does not converge http://www.wolframalpha.com/input/?i=plot+lnx+%2C+1%2Flnx+from+0+to+19

experimentx · Answer

wow .. both fans of Death Note!! http://www.wolframalpha.com/input/?i=integrate+1%2Fln+x+from+2+to+19

experimentx · Answer

the above converges

anonymous · Answer

Yeah, I think you are correct. The integral is non trivial.

experimentx · Answer

correct term ..

anonymous · Answer

But maybe L will know better than me =)

experimentx · Answer

he's gone to leach English ... it's the successor's turn

rogue · Answer

Use the comparison test. Compare it would y = 1/(x-1). Since 1/ln x is larger than 1/(x-1) for all x on the interval (1, 19), and since the integral of 1/(x-1) from 1 to 19 diverges, the integral of 1/ln x from 1 to 19 also diverges.