\(\frac{(e^{\log_* (1 + \left({\left({\left(\sqrt{(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*}\right)}^2\right)}^2 - {\left((N * \left(\log N\right) + 1)_*\right)}^2\right))} - 1)^*}{(N * \left(\log N\right) + 1)_* + (N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*}\)
- Started with
\[\left(\left(N + 1\right) \cdot \log \left(N + 1\right) - N \cdot \log N\right) - 1\]
31.0
- Applied simplify to get
\[\color{red}{\left(\left(N + 1\right) \cdot \log \left(N + 1\right) - N \cdot \log N\right) - 1} \leadsto \color{blue}{(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_* - (N * \left(\log N\right) + 1)_*}\]
30.0
- Using strategy
rm 30.0
- Applied add-sqr-sqrt to get
\[\color{red}{(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*} - (N * \left(\log N\right) + 1)_* \leadsto \color{blue}{{\left(\sqrt{(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*}\right)}^2} - (N * \left(\log N\right) + 1)_*\]
30.1
- Using strategy
rm 30.1
- Applied flip-- to get
\[\color{red}{{\left(\sqrt{(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*}\right)}^2 - (N * \left(\log N\right) + 1)_*} \leadsto \color{blue}{\frac{{\left({\left(\sqrt{(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*}\right)}^2\right)}^2 - {\left((N * \left(\log N\right) + 1)_*\right)}^2}{{\left(\sqrt{(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*}\right)}^2 + (N * \left(\log N\right) + 1)_*}}\]
30.1
- Applied simplify to get
\[\frac{{\left({\left(\sqrt{(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*}\right)}^2\right)}^2 - {\left((N * \left(\log N\right) + 1)_*\right)}^2}{\color{red}{{\left(\sqrt{(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*}\right)}^2 + (N * \left(\log N\right) + 1)_*}} \leadsto \frac{{\left({\left(\sqrt{(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*}\right)}^2\right)}^2 - {\left((N * \left(\log N\right) + 1)_*\right)}^2}{\color{blue}{(N * \left(\log N\right) + 1)_* + (N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*}}\]
30.1
- Using strategy
rm 30.1
- Applied expm1-log1p-u to get
\[\frac{\color{red}{{\left({\left(\sqrt{(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*}\right)}^2\right)}^2 - {\left((N * \left(\log N\right) + 1)_*\right)}^2}}{(N * \left(\log N\right) + 1)_* + (N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*} \leadsto \frac{\color{blue}{(e^{\log_* (1 + \left({\left({\left(\sqrt{(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*}\right)}^2\right)}^2 - {\left((N * \left(\log N\right) + 1)_*\right)}^2\right))} - 1)^*}}{(N * \left(\log N\right) + 1)_* + (N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_*}\]
29.7
