\[ \begin{eqnarray} && \int_{-100}^{101}\dfrac1{(5+2x-2x^2)(1+e^{2-4x})}\, dx \\ && \int_{-100}^{101}\dfrac1{5+2x-2x^2}\,dx\end{eqnarray} \]

Let \(I_1\) and \(I_2\) denote the Cauchy Principal Value of the first and second integral above. Find \( \dfrac{I_1}{I_2} \).

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