Initial program 29.4
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
- Using strategy
rm
Applied flip3-- 29.2
\[\leadsto \color{blue}{\frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}}\]
Applied simplify 29.3
\[\leadsto \frac{\color{blue}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^3}}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}\]
Applied simplify 29.3
\[\leadsto \frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^3}{\color{blue}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + {x}^{\left(\frac{1}{3}\right)} \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right)}}\]
Applied taylor 3.0
\[\leadsto \frac{1}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + {x}^{\left(\frac{1}{3}\right)} \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right)}\]
Taylor expanded around 0 3.0
\[\leadsto \frac{\color{blue}{1}}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + {x}^{\left(\frac{1}{3}\right)} \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right)}\]
- Using strategy
rm
Applied pow-to-exp 2.9
\[\leadsto \frac{1}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \color{blue}{e^{\log x \cdot \frac{1}{3}}} \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right)}\]
Applied simplify 2.6
\[\leadsto \frac{1}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\color{blue}{\frac{\log x}{3}}} \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right)}\]
- Removed slow pow expressions
