Prove that for [latex]r>1[/latex] the improper integral [latex]$\displaystyle \int \frac{1}{(1+x^5))^(frac{r}{5})}dx$[/latex] exists. the boundaries for integration are infinity and one. (i don't know how to write that in code sorry)

And the hint is: Compare with the function [latex]$\displaystyle x\rightarrow \frac{1}{x^r}$[/latex].

Any help or answer very much appreciated.