Initial program 30.1
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
- Using strategy
rm
Applied add-exp-log 30.3
\[\leadsto {\color{blue}{\left(e^{\log \left(x + 1\right)}\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
Applied pow-exp 30.3
\[\leadsto \color{blue}{e^{\log \left(x + 1\right) \cdot \frac{1}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
Applied simplify 30.0
\[\leadsto e^{\color{blue}{\frac{\log \left(x + 1\right)}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
- Using strategy
rm
Applied flip3-- 30.0
\[\leadsto \color{blue}{\frac{{\left(e^{\frac{\log \left(x + 1\right)}{3}}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}}{{\left(e^{\frac{\log \left(x + 1\right)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log \left(x + 1\right)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}}\]
Applied simplify 29.8
\[\leadsto \frac{\color{blue}{\left(x + 1\right) - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^3}}{{\left(e^{\frac{\log \left(x + 1\right)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log \left(x + 1\right)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}\]
Applied simplify 29.8
\[\leadsto \frac{\left(x + 1\right) - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^3}{\color{blue}{\left({x}^{\left(\frac{1}{3}\right)} + \sqrt[3]{x + 1}\right) \cdot \sqrt[3]{x + 1} + {x}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}}}\]
Applied taylor 29.8
\[\leadsto \frac{\left(x + 1\right) - {\left({x}^{\frac{1}{3}}\right)}^3}{\left({x}^{\left(\frac{1}{3}\right)} + \sqrt[3]{x + 1}\right) \cdot \sqrt[3]{x + 1} + {x}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}}\]
Taylor expanded around 0 29.8
\[\leadsto \frac{\left(x + 1\right) - {\color{blue}{\left({x}^{\frac{1}{3}}\right)}}^3}{\left({x}^{\left(\frac{1}{3}\right)} + \sqrt[3]{x + 1}\right) \cdot \sqrt[3]{x + 1} + {x}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}}\]
Applied simplify 2.6
\[\leadsto \color{blue}{\frac{1}{{x}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)} + \sqrt[3]{x + 1} \cdot \left({x}^{\left(\frac{1}{3}\right)} + \sqrt[3]{x + 1}\right)}}\]
Applied simplify 2.6
\[\leadsto \frac{1}{\color{blue}{\left({x}^{\left(\frac{1}{3}\right)} + \sqrt[3]{x + 1}\right) \cdot \sqrt[3]{x + 1} + {\left({x}^{\left(\frac{1}{3}\right)}\right)}^2}}\]
- Removed slow pow expressions
