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The value of \( \int_{\sqrt{\log 2}}^{\sqrt{\log 3}} \frac{x \sin x^{2}}{\sin x^{2}+\sin \left(\log 6-x^{2}\right)} d x \) is \( \quad \) (2011)
(a) \( \frac{1}{4} \log \frac{3}{2} \)
(b) \( \frac{1}{2} \log \frac{3}{2} \)
(c) \( \log \frac{3}{2} \)
(d) \( \frac{1}{6} \log \frac{3}{2} \)
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