I have to solve the following recurrence :$\displaystyle T(n)=2T(n/2)+T(n/3)+\theta(n^2)$
I have done the whole tree analyses and now I have to prove that $\displaystyle T(n) \leq dn^{2}\log_{2}(n)$ but I can not find mathematical way to prove that, is there any trick with logarithms that I can use?