Examine the integrals below. Consider the multiple tools you have available for integrating and use the best one. After evaluating each integral, write a short description of the method you used.

1. $\int _ { - \infty } ^ { \infty } \frac { 1 } { x ^ { 2 } + 25 } d x$

2. $\int _ { 0 } ^ { 4 } \frac { x } { \sqrt { 16 - x ^ { 2 } } } d x$

3. $\int _ { - \infty } ^ { - 1 } \frac { 1 } { x ^ { 3 } } d x$

4. $\int _ { 0 } ^ { 4 } \frac { 1 } { x ^ { 2 } - 2 x - 3 } d x$