Determine whether $\int _{1}^{\infty}\frac{x\sin\left(x\right)}{\sqrt{1+x^5}}\,{\rm d}x$ is convergent or divergent My task is to determine if the following function is convergent or divergent.
$$
\int_{1}^{\infty}{x\sin\left(x\right) \over\sqrt{1 + x^{5}\,}\,}\,{\rm d}x$$
I have been trying to find a more easily integrable function which could be determined to belong in any of the two categories, but I have yet to succeed. Any help is appreciated!

Hint:$$ \left\vert\frac{x\sin{x}}{\sqrt{1+x^5}}\right\vert \leq\frac{x}{\sqrt{1+x^5}} $$
What does this bound tell us about the convergence?
