Paneer Definite Masala 6

Calculus Level 3

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

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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