Solve the following recurrences:

$($a$)T(n)=6T(\frac{n}{3})+n^{2}lgn+3n$

$($b$)T(n)=5T(\frac{n}{3})+7nlgn$

$($c$)T(n)=4T(\frac{n}{2})+n^{2}lgn+3nl{g}^{2}n$