I have the following recurrence relation, which I'm trying to solve using the Master Theorem:
T(n) = 2T(n/2) + n(2 + sin(n))
I compared this recurrence to the one of the following form:
T(n) = aT(n/b) + f(n)
Where a = 2, b = 2 and f(n) = n(2 + sin(n))
$n^{log_ba} = n^{log_22} = n$
Comparing f(n) and $n^{log_ba}$ asymptotically:
f(n) = n(2 + sin(n))
$n^{log_ba} = n$
Now this is the part where I am stuck. The dominating term in f(n) is n (as -1 <= sin(n) <= 1), which is the same as $n^{log_ba} = n$. Would this imply that this recurrence satisfies the second case of the Master Theorem?
The second case is: If $f(n) = Θ(n^{log_ba})$, then $T(n) = Θ(n^{log_ba}logn)$