Is this intergral inequality valid? [closed]

Question

Does the inequality $\int_2^{\infty} \dfrac{\sqrt x(\log x)^3 + (1+ \log x^2) x}{x(\log x)^2(x^2 - 1)} \,\mathrm {d}x > \ln \dfrac{17}{10}$ hold ?

Answer 1

Mathematica says that

NIntegrate[ (Sqrt[x] Log[x]^3 + x (1 + 2 Log[x]))/( 
     x Log[x]^2 (x^2 - 1) ), {x, 2, Infinity}] - Log[17/10] // N

is about $1.08424$, so yes.