I am to find out whether the following Improper Integral converges:
$$\int_2^\infty \frac{e^{x/4}}{x^3{ln}^5x}\,dx\quad$$
Things that I've tried: Comparison with $$\frac{1}{x^3{ln}^5x}$$ Or with:(Which is impossible since it's not a "Decreasing" function) $$\frac{e^{x/4}}{x^3}$$ Or: $$\frac{{1}}{x}$$ Thanks in advance.
Hint
The integral is divergent since
$$ \frac{e^{x/4}}{x^3{\ln}^5x}\ge\frac 1 x\quad \text{for $x$ large enough}$$