\((N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_* - {\left(\sqrt{\sqrt[3]{(N * \left(\log N\right) + 1)_*}}\right)}^2 \cdot {\left(\sqrt[3]{(N * \left(\log N\right) + 1)_*}\right)}^2\)
- 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-cube-cbrt to get
\[(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_* - \color{red}{(N * \left(\log N\right) + 1)_*} \leadsto (N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_* - \color{blue}{{\left(\sqrt[3]{(N * \left(\log N\right) + 1)_*}\right)}^3}\]
30.1
- Using strategy
rm 30.1
- Applied add-sqr-sqrt to get
\[(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_* - {\color{red}{\left(\sqrt[3]{(N * \left(\log N\right) + 1)_*}\right)}}^3 \leadsto (N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_* - {\color{blue}{\left({\left(\sqrt{\sqrt[3]{(N * \left(\log N\right) + 1)_*}}\right)}^2\right)}}^3\]
30.1
- Using strategy
rm 30.1
- Applied cube-mult to get
\[(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_* - \color{red}{{\left({\left(\sqrt{\sqrt[3]{(N * \left(\log N\right) + 1)_*}}\right)}^2\right)}^3} \leadsto (N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_* - \color{blue}{{\left(\sqrt{\sqrt[3]{(N * \left(\log N\right) + 1)_*}}\right)}^2 \cdot \left({\left(\sqrt{\sqrt[3]{(N * \left(\log N\right) + 1)_*}}\right)}^2 \cdot {\left(\sqrt{\sqrt[3]{(N * \left(\log N\right) + 1)_*}}\right)}^2\right)}\]
30.1
- Applied simplify to get
\[(N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_* - {\left(\sqrt{\sqrt[3]{(N * \left(\log N\right) + 1)_*}}\right)}^2 \cdot \color{red}{\left({\left(\sqrt{\sqrt[3]{(N * \left(\log N\right) + 1)_*}}\right)}^2 \cdot {\left(\sqrt{\sqrt[3]{(N * \left(\log N\right) + 1)_*}}\right)}^2\right)} \leadsto (N * \left(\log_* (1 + N)\right) + \left(\log_* (1 + N)\right))_* - {\left(\sqrt{\sqrt[3]{(N * \left(\log N\right) + 1)_*}}\right)}^2 \cdot \color{blue}{{\left(\sqrt[3]{(N * \left(\log N\right) + 1)_*}\right)}^2}\]
30.1
- Removed slow pow expressions
