a$.$ Determine the type of improper integral for

${\displaystyle \underset{0}{\overset{}{}}}\frac{arctan(x)}{1+x^2}dx$

explain why it is of that type, and compute its value. $(15$ points$)$

b$.$ Determine the type of improper integral for

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

explain why it is of that type, and use the Limit Comparison Test to check for convergence or divergence. $(15$ points$)$