give the smallest possible big o estimate for the following

give the smallest possible big o estimate for the following functions (n*log(n) +1)(n+5) +n^3

Solution

Answer:

We have given: (nlogn +1)(n+5) + n^3

=> n^2logn +n + 5nlogn + 5 +n^3

=> n^3 + n^2logn + 5nlogn + 5

If we check the function now , the dominating is n^3 , therefore big o estimate for this function is O(n^3).