Question

How do you evaluate the integral `int (dx)/(x(lnx)^(1/5)` from `1/2` to `oo`?

Answer 1

`int_(1/2)^oo (dx)/(x(lnx)^(1/5)) = oo`

Explanation:

`int (dx)/(x(lnx)^(1/5)) = 5/4(log_e x)^(4/5)+C`

but

`log_e x` is a monotonic increasing function with `x` so

`int_(1/2)^oo (dx)/(x(lnx)^(1/5)) = oo`