$(18$pts$)$ Evaluate the definite integral.

${\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{3}}{}}}\frac{x}{\sqrt[\phantom{2}]{x^2+1}}dx$

a$)$ Identify $u$ :

b$)$ Calculate $du$ :

c$)$ Rewrite the integral in terms of $u$ and evaluate the definite integral. Note you can go back to the original variable if you want to or keep the variable as $u.$