Definite Integration

Let \({J_{n,m}} = \int\limits_0^{{1 \over 2}} {{{{x^n}} \over {{x^m} - 1}}dx}\), \(\forall\) n > m and n, m \(\in\) N. Consider a matrix \(A = {[{a_{ij}}]_{3 \times 3}}\) where \({a_{ij}} = \left\{ {\matrix{ {{j_{6 + i,3}} - {j_{i + 3,3}},} & {i \le j} \cr {0,} & {i > j} \cr } } \right.\). Then \(\left| {adj{A^{ - 1}}} \right|\) is :