If $\int_0^1 4 \cot ^{-1}\left(1-2 x+4 x^2\right) \mathrm{d} x=\operatorname{atan}^{-1}(2)-\operatorname{blog}_{\mathrm{e}}(5)$, where $\mathrm{a}, \mathrm{b} \in \mathbf{N}$, then $(2 \mathrm{a}+\mathrm{b})$ is equal to
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