$$\int x \sqrt{\frac{2 \sin \left(x^2+1\right)-\sin 2\left(x^2+1\right)}{2 \sin \left(x^2+1\right)+\sin 2\left(x^2+1\right)}} d x=$$

$$\text { For all real } x \text {, the minimum value of } \frac{1-x+x^2}{1+x+x^2} \text { is }$$

If $$\bar{a}=\hat{i}+4 \hat{j}+2 \hat{k}, \bar{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}, \bar{c}=2 \hat{i}-\hat{j}+4 \hat{k}$$, then a vector $$\overline{\mathrm{d}}$$ which is parallel to vector $$\overline{\mathrm{a}} \times \overline{\mathrm{b}}$$ and which $$\overline{\mathrm{c}} \cdot \overline{\mathrm{d}}=15$$, is