If \( \int_{1}^{2} e^{x^{2}} d x=a \), then \( \int_{e}^{e^{4}} \sqrt{\ln x} d x \) is equal to

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If \( \int_{1}^{2} e^{x^{2}} d x=a \), then \( \int_{e}^{e^{4}} \sqrt{\ln x} d x \) is equal to
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