Evaluate: \( \int_{0}^{1} \frac{d x}{\left(5+2 x-2 x^{2}\right)\left(1+c^{2-4 x}\right)} \)

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Evaluate: \( \int_{0}^{1} \frac{d x}{\left(5+2 x-2 x^{2}\right)\left(1+c^{2-4 x}\right)} \)
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