Evaluate: \( \int x \cdot \sqrt{\frac{2 \sin \left(x^{2}+1\right)-\sin 2\left(x^{2}+1\right)}{2 ...

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Evaluate: \( \int x \cdot \sqrt{\frac{2 \sin \left(x^{2}+1\right)-\sin 2\left(x^{2}+1\right)}{2 \sin \left(x^{2}+1\right)+\sin 2\left(x^{2}+1\right)}} d x \)
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