9.
$$I _ { n } = \int \left( x ^ { 2 } + 1 \right) ^ { - n } \mathrm {~d} x , \quad n > 0$$
- Show that, for \(n > 0\),
$$I _ { n + 1 } = \frac { x \left( x ^ { 2 } + 1 \right) ^ { - n } } { 2 n } + \frac { 2 n - 1 } { 2 n } I _ { n }$$
- Find \(I _ { 2 }\).