Does $$\int^{\infty}_2 {e^{x/4} \over x^3({\ln x})^5}dx $$ converge?
I don't know how to start - What can I compare it to? It seems too complicated.
How do you approach to this kind of problems?
2026-05-05 16:58:55.1778000335
Does $\int^{\infty}_2 {e^{x/4} \over x^3({\ln x})^5} $ converge?
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We have for all $n$:
$$\lim_{x \to \infty} \frac{e^x}{x^n} = \infty$$
By applying L'hopital's rule $n$-times.
Also: $\log x \le x$ holds for all $x$.
Can you combine these facts to get something useful?