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I'm trying to transform this: $$n \log n + n \log(n^{\log n})$$ into big O notation.

I can't get to reduce the right part of the addition...

Neither of these work: $$n^{\log n} \log(n)\qquad\text{nor}\qquad n \log(\log n * n)$$

I was planning to get them to multiply together, and then I would have only 1 small function.

How do I reduce the right part ?

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I can't quite see your formatting –  Rustyn Feb 10 '13 at 18:23
thanks, I fixed the formating a bit. –  Dave Feb 10 '13 at 18:24

1 Answer 1

up vote 5 down vote accepted

Notice that $n\log(n^{\log n}) = n (\log n)^2$. So $$ n\log n + n \log(n^{\log n}) = n\log n + n \log^2 n $$ $$ = n \log n(1+\log n) = n (\log n) O(\log n) = O(n \log^2 n) $$

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