Determine Whether Each Integral Is Convergent or Divergent $\int _ { 3 } ^ { \infty } \frac { 1 } { x ^ { 3 / 2 } } d x$

Essay

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.(a) $\int _ { 3 } ^ { \infty } \frac { 1 } { x ^ { 3 / 2 } } d x$ (b) $\int _ { e } ^ { \infty } \frac { 1 } { x ( \ln x ) } d x$ (c) $\int _ { 0 } ^ { \infty } \frac { x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } d x$