Solving retreat formulas
If you unroll the formulae you get:
$$T(n) = T(n-1) + c \cdot log(n) = \sum_{i=2}^{n} c\cdot log(i) + d = O(n \cdot log(n)) $$

Last equality is true from the following fact:
$$\sum_{i=1}^n log(i) \ge \sum_{i=\frac{n}{2}}^n log(i) \ge \frac{n}{2} \cdot log(\frac{n}{2}) = O(n \cdot log(n))$$
$$\sum_{i=1}^n log(i) = log(n!) \le log(n^n) = n\cdot log(n) = O(n\cdot log(n))$$