Question

show whether the integral converges or diverges

is the integral finite?
\[\int_1^\infty \frac{1}{2x - 1} \mathrm{d}x\]

Answer 1

diverges for sure

Answer 2

in order for it to converge, the degree of the denominator must be larger than the degree of the numerator by more than one

Answer 3

if you integrate that thing, you will get the log of something
when you take the limit as \(x\to \infty\) of the log of whatever, it will go to infinity

Answer 4

\[log_{something} ( \inf ) = \inf\]

Answer 5

for example
\[\int_1^{\infty}\frac{x+1}{x^2-2}dx\] diverges, whereas \[\int_1^{\infty}\frac{x+1}{x^3-2}dx\] converges

Answer 6

I see

Answer 7

\[anybase^{\inf} = \inf\]is what the logarithm x->inf is about?

Answer 8

^
"when you take the limit as x→∞ of the log of whatever, it will go to infinity"

Answer 9

\[\lim_{x \rightarrow \inf} log_{whatever} ( x) = \inf\]is the same statement as
\[whatever^{\inf} = x,x\rightarrow \inf\]?