Initial program 15.0
\[\tan^{-1} \left(N + 1\right) - \tan^{-1} N\]
- Using strategy
rm Applied diff-atan13.8
\[\leadsto \color{blue}{\tan^{-1}_* \frac{\left(N + 1\right) - N}{1 + \left(N + 1\right) \cdot N}}\]
Simplified0.4
\[\leadsto \tan^{-1}_* \frac{\color{blue}{1}}{1 + \left(N + 1\right) \cdot N}\]
Simplified0.4
\[\leadsto \tan^{-1}_* \frac{1}{\color{blue}{(N \cdot \left(N + 1\right) + 1)_*}}\]
- Using strategy
rm Applied expm1-log1p-u0.9
\[\leadsto \color{blue}{(e^{\log_* (1 + \tan^{-1}_* \frac{1}{(N \cdot \left(N + 1\right) + 1)_*})} - 1)^*}\]
- Using strategy
rm Applied add-cube-cbrt0.7
\[\leadsto \color{blue}{\left(\sqrt[3]{(e^{\log_* (1 + \tan^{-1}_* \frac{1}{(N \cdot \left(N + 1\right) + 1)_*})} - 1)^*} \cdot \sqrt[3]{(e^{\log_* (1 + \tan^{-1}_* \frac{1}{(N \cdot \left(N + 1\right) + 1)_*})} - 1)^*}\right) \cdot \sqrt[3]{(e^{\log_* (1 + \tan^{-1}_* \frac{1}{(N \cdot \left(N + 1\right) + 1)_*})} - 1)^*}}\]
Final simplification0.7
\[\leadsto \sqrt[3]{(e^{\log_* (1 + \tan^{-1}_* \frac{1}{(N \cdot \left(N + 1\right) + 1)_*})} - 1)^*} \cdot \left(\sqrt[3]{(e^{\log_* (1 + \tan^{-1}_* \frac{1}{(N \cdot \left(N + 1\right) + 1)_*})} - 1)^*} \cdot \sqrt[3]{(e^{\log_* (1 + \tan^{-1}_* \frac{1}{(N \cdot \left(N + 1\right) + 1)_*})} - 1)^*}\right)\]
