I know that the following integration is convergent but have not known its value. Can you help me? Thank you very much.
$\displaystyle \int_3^{+\infty}\frac{dx}{x^3-3x-1}$
It's not going to be easy! That cubic can be factored into three linear terms and then you can use "partial fractions". The difficulty is that the cubic has no simple (i.e. rational) roots. They are approximately -1.503, -0.3827, and 1.8802.