Given the following integral:
$$ \int_0^2 \frac{1}{\ln(x)} dx $$
Does it converge?
Iv'e gone this far: $$ \int_0^2 \frac{1}{\ln(x)} dx = \int_0^1 \frac{1}{\ln(x)} dx + \int_1^2 \frac{1}{\ln(x)} dx $$
Now I'm having trouble calculating each. I can only tell that: $ \int \frac{1}{\ln(x)} dx \gt \int\frac1x dx $