Let I_n =∫_1^e x^19( log |x|)^n d x, where n ∈ N. If (20) I_10=α I_9+β I_8, for natural numbers α and β, then α-β equals to \ \ \ \.

Let $\displaystyle \mathrm{I}_{\mathrm{n}}=\int_1^{\mathrm{e}} x^{19}(\log |x|)^{\mathrm{n}} \mathrm{d} x$, where $\displaystyle \mathrm{n} \in \mathrm{N}$. If $\displaystyle (20) \mathrm{I}_{10}=\alpha \mathrm{I}_9+\beta \mathrm{I}_8$, for natural numbers $\displaystyle \alpha$ and $\displaystyle \beta$, then $\displaystyle \alpha-\beta$ equals to \_\_\_\_.