\(\left(\frac{e^{\log \left(\sqrt{{N}^2 - 1}\right)} \cdot \sqrt{\log \left(N + 1\right)}}{\sqrt{N - 1}} + \sqrt{N \cdot \log N}\right) \cdot \left(\frac{\sqrt{{N}^2 - 1} \cdot \sqrt{\log \left(N + 1\right)}}{\sqrt{N - 1}} - \sqrt{N \cdot \log N}\right) - 1\)
- Started with
\[\left(\left(N + 1\right) \cdot \log \left(N + 1\right) - N \cdot \log N\right) - 1\]
31.0
- Using strategy
rm 31.0
- Applied flip-+ to get
\[\left(\color{red}{\left(N + 1\right)} \cdot \log \left(N + 1\right) - N \cdot \log N\right) - 1 \leadsto \left(\color{blue}{\frac{{N}^2 - {1}^2}{N - 1}} \cdot \log \left(N + 1\right) - N \cdot \log N\right) - 1\]
30.1
- Applied associate-*l/ to get
\[\left(\color{red}{\frac{{N}^2 - {1}^2}{N - 1} \cdot \log \left(N + 1\right)} - N \cdot \log N\right) - 1 \leadsto \left(\color{blue}{\frac{\left({N}^2 - {1}^2\right) \cdot \log \left(N + 1\right)}{N - 1}} - N \cdot \log N\right) - 1\]
29.9
- Applied simplify to get
\[\left(\frac{\color{red}{\left({N}^2 - {1}^2\right) \cdot \log \left(N + 1\right)}}{N - 1} - N \cdot \log N\right) - 1 \leadsto \left(\frac{\color{blue}{\left({N}^2 - 1\right) \cdot \log \left(N + 1\right)}}{N - 1} - N \cdot \log N\right) - 1\]
29.9
- Using strategy
rm 29.9
- Applied add-sqr-sqrt to get
\[\left(\frac{\left({N}^2 - 1\right) \cdot \log \left(N + 1\right)}{N - 1} - \color{red}{N \cdot \log N}\right) - 1 \leadsto \left(\frac{\left({N}^2 - 1\right) \cdot \log \left(N + 1\right)}{N - 1} - \color{blue}{{\left(\sqrt{N \cdot \log N}\right)}^2}\right) - 1\]
29.9
- Applied add-sqr-sqrt to get
\[\left(\frac{\left({N}^2 - 1\right) \cdot \log \left(N + 1\right)}{\color{red}{N - 1}} - {\left(\sqrt{N \cdot \log N}\right)}^2\right) - 1 \leadsto \left(\frac{\left({N}^2 - 1\right) \cdot \log \left(N + 1\right)}{\color{blue}{{\left(\sqrt{N - 1}\right)}^2}} - {\left(\sqrt{N \cdot \log N}\right)}^2\right) - 1\]
29.9
- Applied add-sqr-sqrt to get
\[\left(\frac{\left({N}^2 - 1\right) \cdot \color{red}{\log \left(N + 1\right)}}{{\left(\sqrt{N - 1}\right)}^2} - {\left(\sqrt{N \cdot \log N}\right)}^2\right) - 1 \leadsto \left(\frac{\left({N}^2 - 1\right) \cdot \color{blue}{{\left(\sqrt{\log \left(N + 1\right)}\right)}^2}}{{\left(\sqrt{N - 1}\right)}^2} - {\left(\sqrt{N \cdot \log N}\right)}^2\right) - 1\]
29.9
- Applied add-sqr-sqrt to get
\[\left(\frac{\color{red}{\left({N}^2 - 1\right)} \cdot {\left(\sqrt{\log \left(N + 1\right)}\right)}^2}{{\left(\sqrt{N - 1}\right)}^2} - {\left(\sqrt{N \cdot \log N}\right)}^2\right) - 1 \leadsto \left(\frac{\color{blue}{{\left(\sqrt{{N}^2 - 1}\right)}^2} \cdot {\left(\sqrt{\log \left(N + 1\right)}\right)}^2}{{\left(\sqrt{N - 1}\right)}^2} - {\left(\sqrt{N \cdot \log N}\right)}^2\right) - 1\]
29.9
- Applied square-unprod to get
\[\left(\frac{\color{red}{{\left(\sqrt{{N}^2 - 1}\right)}^2 \cdot {\left(\sqrt{\log \left(N + 1\right)}\right)}^2}}{{\left(\sqrt{N - 1}\right)}^2} - {\left(\sqrt{N \cdot \log N}\right)}^2\right) - 1 \leadsto \left(\frac{\color{blue}{{\left(\sqrt{{N}^2 - 1} \cdot \sqrt{\log \left(N + 1\right)}\right)}^2}}{{\left(\sqrt{N - 1}\right)}^2} - {\left(\sqrt{N \cdot \log N}\right)}^2\right) - 1\]
29.9
- Applied square-undiv to get
\[\left(\color{red}{\frac{{\left(\sqrt{{N}^2 - 1} \cdot \sqrt{\log \left(N + 1\right)}\right)}^2}{{\left(\sqrt{N - 1}\right)}^2}} - {\left(\sqrt{N \cdot \log N}\right)}^2\right) - 1 \leadsto \left(\color{blue}{{\left(\frac{\sqrt{{N}^2 - 1} \cdot \sqrt{\log \left(N + 1\right)}}{\sqrt{N - 1}}\right)}^2} - {\left(\sqrt{N \cdot \log N}\right)}^2\right) - 1\]
29.9
- Applied difference-of-squares to get
\[\color{red}{\left({\left(\frac{\sqrt{{N}^2 - 1} \cdot \sqrt{\log \left(N + 1\right)}}{\sqrt{N - 1}}\right)}^2 - {\left(\sqrt{N \cdot \log N}\right)}^2\right)} - 1 \leadsto \color{blue}{\left(\frac{\sqrt{{N}^2 - 1} \cdot \sqrt{\log \left(N + 1\right)}}{\sqrt{N - 1}} + \sqrt{N \cdot \log N}\right) \cdot \left(\frac{\sqrt{{N}^2 - 1} \cdot \sqrt{\log \left(N + 1\right)}}{\sqrt{N - 1}} - \sqrt{N \cdot \log N}\right)} - 1\]
29.9
- Using strategy
rm 29.9
- Applied add-exp-log to get
\[\left(\frac{\color{red}{\sqrt{{N}^2 - 1}} \cdot \sqrt{\log \left(N + 1\right)}}{\sqrt{N - 1}} + \sqrt{N \cdot \log N}\right) \cdot \left(\frac{\sqrt{{N}^2 - 1} \cdot \sqrt{\log \left(N + 1\right)}}{\sqrt{N - 1}} - \sqrt{N \cdot \log N}\right) - 1 \leadsto \left(\frac{\color{blue}{e^{\log \left(\sqrt{{N}^2 - 1}\right)}} \cdot \sqrt{\log \left(N + 1\right)}}{\sqrt{N - 1}} + \sqrt{N \cdot \log N}\right) \cdot \left(\frac{\sqrt{{N}^2 - 1} \cdot \sqrt{\log \left(N + 1\right)}}{\sqrt{N - 1}} - \sqrt{N \cdot \log N}\right) - 1\]
29.9
- Removed slow pow expressions
