Initial program 53.1
\[\frac{2}{e^{x} + e^{-x}}\]
Initial simplification53.1
\[\leadsto \frac{2}{e^{x} + e^{-x}}\]
Taylor expanded around 0 53.0
\[\leadsto \color{blue}{\left(\frac{5}{24} \cdot {x}^{4} + 1\right) - \frac{1}{2} \cdot {x}^{2}}\]
- Using strategy
rm Applied add-cube-cbrt53.0
\[\leadsto \color{blue}{\left(\sqrt[3]{\left(\frac{5}{24} \cdot {x}^{4} + 1\right) - \frac{1}{2} \cdot {x}^{2}} \cdot \sqrt[3]{\left(\frac{5}{24} \cdot {x}^{4} + 1\right) - \frac{1}{2} \cdot {x}^{2}}\right) \cdot \sqrt[3]{\left(\frac{5}{24} \cdot {x}^{4} + 1\right) - \frac{1}{2} \cdot {x}^{2}}}\]
Taylor expanded around 0 53.0
\[\leadsto \color{blue}{\left(\left(\frac{1}{9} \cdot {x}^{4} + 1\right) - \frac{1}{3} \cdot {x}^{2}\right)} \cdot \sqrt[3]{\left(\frac{5}{24} \cdot {x}^{4} + 1\right) - \frac{1}{2} \cdot {x}^{2}}\]
- Using strategy
rm Applied add-cube-cbrt53.0
\[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\frac{1}{9} \cdot {x}^{4}} \cdot \sqrt[3]{\frac{1}{9} \cdot {x}^{4}}\right) \cdot \sqrt[3]{\frac{1}{9} \cdot {x}^{4}}} + 1\right) - \frac{1}{3} \cdot {x}^{2}\right) \cdot \sqrt[3]{\left(\frac{5}{24} \cdot {x}^{4} + 1\right) - \frac{1}{2} \cdot {x}^{2}}\]
Final simplification53.0
\[\leadsto \left(\left(\sqrt[3]{{x}^{4} \cdot \frac{1}{9}} \cdot \left(\sqrt[3]{{x}^{4} \cdot \frac{1}{9}} \cdot \sqrt[3]{{x}^{4} \cdot \frac{1}{9}}\right) + 1\right) - {x}^{2} \cdot \frac{1}{3}\right) \cdot \sqrt[3]{\left(1 + \frac{5}{24} \cdot {x}^{4}\right) - \frac{1}{2} \cdot {x}^{2}}\]
