$\mathrm{J}_{6 + i, 3}-\mathrm{J}_{i+3,3} ; \mathrm{i} \leq \mathrm{j}$

$\Rightarrow \int_{0}^{\frac{1}{2}} \frac{\mathrm{x}^{6+\mathrm{i}}}{\mathrm{x}^{3}-1}-\int_{0}^{\frac{1}{2}} \frac{\mathrm{x}^{\mathrm{i}+3}}{\mathrm{x}^{3}-1}$

$\Rightarrow \int_{0}^{1 / 2} \frac{\mathrm{x}^{\mathrm{i}+3}\left(\mathrm{x}^{3}-1\right)}{\mathrm{x}^{3}-1}$

$\Rightarrow \frac{\mathrm{x}^{3+\mathrm{i}+1}}{3+\mathrm{i}+1}=\left(\frac{\mathrm{x}^{4+\mathrm{i}}}{4+\mathrm{i}}\right)^{1 / 2}$

$\mathrm{a}_{\mathrm{ij}}=\mathrm{j}_{6+\mathrm{i}, 3}-\mathrm{j}_{\mathrm{i}+3,3}=\frac{\left(\frac{1}{2}\right)^{4+\mathrm{i}}}{4+\mathrm{i}}$

$\mathrm{a}_{11}=\frac{\left(\frac{1}{2}\right)^{5}}{5}=\frac{1}{5.2^{5}}$

$\mathrm{a}_{12}=\frac{1}{5.2^{5}}$

$\mathrm{a}_{13}=\frac{1}{5.2^{5}}$

$\mathrm{a}_{22}=\frac{1}{6.2^{6}}$

$\mathrm{a}_{23}=\frac{1}{6.2^{6}}$

$\mathrm{a}_{33}=\frac{1}{7.2^{7}}$

$\mathrm{A}=\left[\begin{array}{ccc}\frac{1}{5.2^{5}} & \frac{1}{5.2^{5}} & \frac{1}{5.2^{5}} \\ 0 & \frac{1}{6.2^{6}} & \frac{1}{6.2^{6}} \\ 0 & 0 & \frac{1}{7.2^{7}}\end{array}\right]$

$|\mathrm{A}|=\frac{1}{5.2^{5}}\left[\frac{1}{6.2^{6}} \times \frac{1}{7.2^{7}}\right]$

$|A|=\frac{1}{210.2^{18}}$

$\left|\operatorname{adj} A^{-1}\right|=\left|A^{-1}\right|^{n-1}=\left|A^{-1}\right|^{2}=\frac{1}{(|A|)^{2}}$

$\Rightarrow\left(210.2^{18}\right)^{2}$

$(105)^{2} \times 2^{38}$