$\int_0^\infty\frac{x^{a-1}}{1+x^n}\,dx$ and $\int_0^\infty\frac{\log x}{(1+x^2)^2}\,dx$

Compute the following integrals. (i) \(\int _ { 0 } ^ { \infty } { \frac { x ^ { a - 1 } } { 1 + x ^ { n } } } d x , 0 < a < n\)

\[ { \mathrm { ( i i ) } } \int _ { 0 } ^ { \infty } { \frac { \log x } { ( 1 + x ^ { 2 } ) ^ { 2 } } } d x \]