Initial program 59.9
\[\frac{1}{x} - \frac{1}{\tan x}\]
Applied taylor 0.3
\[\leadsto \frac{1}{45} \cdot {x}^{3} + \left(\frac{2}{945} \cdot {x}^{5} + \frac{1}{3} \cdot x\right)\]
Taylor expanded around 0 0.3
\[\leadsto \color{blue}{\frac{1}{45} \cdot {x}^{3} + \left(\frac{2}{945} \cdot {x}^{5} + \frac{1}{3} \cdot x\right)}\]
- Using strategy
rm
Applied add-cube-cbrt 1.5
\[\leadsto \frac{1}{45} \cdot {x}^{3} + \left(\frac{2}{945} \cdot {x}^{5} + \color{blue}{\left(\sqrt[3]{\frac{1}{3} \cdot x} \cdot \sqrt[3]{\frac{1}{3} \cdot x}\right) \cdot \sqrt[3]{\frac{1}{3} \cdot x}}\right)\]
Applied taylor 33.9
\[\leadsto \frac{1}{45} \cdot {x}^{3} + \left(\frac{2}{945} \cdot {x}^{5} + {\left(e^{\frac{1}{3} \cdot \left(\log \frac{1}{3} + \log x\right)}\right)}^{2} \cdot \sqrt[3]{\frac{1}{3} \cdot x}\right)\]
Taylor expanded around 0 33.9
\[\leadsto \frac{1}{45} \cdot {x}^{3} + \left(\frac{2}{945} \cdot {x}^{5} + \color{blue}{{\left(e^{\frac{1}{3} \cdot \left(\log \frac{1}{3} + \log x\right)}\right)}^{2}} \cdot \sqrt[3]{\frac{1}{3} \cdot x}\right)\]
Applied simplify 1.5
\[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{1}{3} \cdot x}\right)}^{3} + \left(\left(x \cdot x\right) \cdot \left(x \cdot \frac{1}{45}\right) + \frac{2}{945} \cdot {x}^{5}\right)}\]
Applied simplify 0.3
\[\leadsto \color{blue}{x \cdot \frac{1}{3}} + \left(\left(x \cdot x\right) \cdot \left(x \cdot \frac{1}{45}\right) + \frac{2}{945} \cdot {x}^{5}\right)\]
- Removed slow pow expressions
