How to prove convergence or divergence

[Stelyios]

∫(x*sin2(x))/(x3-1) over the terminals:
b= ∞ and a = 2

I have this improper integral and am absolutely stuck on how to approach it..

I need to prove its convergence or divergence

 

[Ishuda]

∫(x*sin2(x))/(x3-1) over the terminals:
b= ∞ and a = 2

I have this improper integral and am absolutely stuck on how to approach it..

I need to prove its convergence or divergence

Hint: Absolute convergence implies convergence and
\(\displaystyle |\frac{x\, sin^2(x)}{x^3\, -1}|\, \le\, \frac{x}{x^3\, -1}\, for\, x\, \ge\, 2\)