How to determine values of $p$ making the integral
$$\int_{x=2}^{\infty}\frac{(x+1)^{p}\sin(x)}{\log(x)}\mathrm{d}x$$
converges absolutely or conditionally? Comparison $\log(x)$ with $x$ where $x\to\infty$ gives divergence for $1-p<1$. Am I right and what to do next?