Initial program 29.4
\[\left(e^{x} - 2\right) + e^{-x}\]
Simplified29.4
\[\leadsto \color{blue}{\left(e^{x} - 2\right) - \frac{-1}{e^{x}}}\]
Taylor expanded around 0 0.7
\[\leadsto \color{blue}{{x}^{2} + \left(\frac{1}{12} \cdot {x}^{4} + \frac{1}{360} \cdot {x}^{6}\right)}\]
Simplified0.7
\[\leadsto \color{blue}{(\left({x}^{6}\right) \cdot \frac{1}{360} + \left((\left({x}^{4}\right) \cdot \frac{1}{12} + \left(x \cdot x\right))_*\right))_*}\]
- Using strategy
rm Applied add-sqr-sqrt0.7
\[\leadsto (\left({x}^{6}\right) \cdot \frac{1}{360} + \color{blue}{\left(\sqrt{(\left({x}^{4}\right) \cdot \frac{1}{12} + \left(x \cdot x\right))_*} \cdot \sqrt{(\left({x}^{4}\right) \cdot \frac{1}{12} + \left(x \cdot x\right))_*}\right)})_*\]
- Using strategy
rm Applied pow10.7
\[\leadsto (\left({x}^{6}\right) \cdot \frac{1}{360} + \left(\sqrt{(\left({x}^{4}\right) \cdot \frac{1}{12} + \left(x \cdot x\right))_*} \cdot \color{blue}{{\left(\sqrt{(\left({x}^{4}\right) \cdot \frac{1}{12} + \left(x \cdot x\right))_*}\right)}^{1}}\right))_*\]
Applied pow10.7
\[\leadsto (\left({x}^{6}\right) \cdot \frac{1}{360} + \left(\color{blue}{{\left(\sqrt{(\left({x}^{4}\right) \cdot \frac{1}{12} + \left(x \cdot x\right))_*}\right)}^{1}} \cdot {\left(\sqrt{(\left({x}^{4}\right) \cdot \frac{1}{12} + \left(x \cdot x\right))_*}\right)}^{1}\right))_*\]
Applied pow-prod-down0.7
\[\leadsto (\left({x}^{6}\right) \cdot \frac{1}{360} + \color{blue}{\left({\left(\sqrt{(\left({x}^{4}\right) \cdot \frac{1}{12} + \left(x \cdot x\right))_*} \cdot \sqrt{(\left({x}^{4}\right) \cdot \frac{1}{12} + \left(x \cdot x\right))_*}\right)}^{1}\right)})_*\]
Simplified0.7
\[\leadsto (\left({x}^{6}\right) \cdot \frac{1}{360} + \left({\color{blue}{\left((x \cdot x + \left({x}^{4} \cdot \frac{1}{12}\right))_*\right)}}^{1}\right))_*\]
Final simplification0.7
\[\leadsto (\left({x}^{6}\right) \cdot \frac{1}{360} + \left((x \cdot x + \left({x}^{4} \cdot \frac{1}{12}\right))_*\right))_*\]
