Evaluate: \( \int \frac{2 e^{5 x}+e^{4 x}-4 e^{3 x}+4 e^{2 x}+2 e^{x}}{\left(e^{2 x}+4\right)\le...

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Evaluate: \( \int \frac{2 e^{5 x}+e^{4 x}-4 e^{3 x}+4 e^{2 x}+2 e^{x}}{\left(e^{2 x}+4\right)\left(e^{2 x}-1\right)^{2}} d x \)
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