Initial program 29.8
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
- Using strategy
rm
Applied add-exp-log 30.0
\[\leadsto {\color{blue}{\left(e^{\log \left(x + 1\right)}\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
Applied pow-exp 30.0
\[\leadsto \color{blue}{e^{\log \left(x + 1\right) \cdot \frac{1}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
Applied simplify 29.7
\[\leadsto e^{\color{blue}{\frac{\log \left(x + 1\right)}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
- Using strategy
rm
Applied flip3-- 29.7
\[\leadsto \color{blue}{\frac{{\left(e^{\frac{\log \left(x + 1\right)}{3}}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}}{{\left(e^{\frac{\log \left(x + 1\right)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log \left(x + 1\right)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}}\]
Applied simplify 29.5
\[\leadsto \frac{\color{blue}{\left(x + 1\right) - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^3}}{{\left(e^{\frac{\log \left(x + 1\right)}{3}}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + e^{\frac{\log \left(x + 1\right)}{3}} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}\]
Applied simplify 29.6
\[\leadsto \frac{\left(x + 1\right) - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^3}{\color{blue}{{x}^{\left(\frac{1}{3}\right)} \cdot \left({x}^{\left(\frac{1}{3}\right)} + \sqrt[3]{x + 1}\right) + {\left(\sqrt[3]{x + 1}\right)}^2}}\]
Applied taylor 29.6
\[\leadsto \frac{\left(1 + x\right) - {\left({x}^{\frac{1}{3}}\right)}^3}{{x}^{\left(\frac{1}{3}\right)} \cdot \left({x}^{\left(\frac{1}{3}\right)} + \sqrt[3]{x + 1}\right) + {\left(\sqrt[3]{x + 1}\right)}^2}\]
Taylor expanded around 0 29.6
\[\leadsto \frac{\color{blue}{\left(1 + x\right) - {\left({x}^{\frac{1}{3}}\right)}^3}}{{x}^{\left(\frac{1}{3}\right)} \cdot \left({x}^{\left(\frac{1}{3}\right)} + \sqrt[3]{x + 1}\right) + {\left(\sqrt[3]{x + 1}\right)}^2}\]
Applied simplify 2.6
\[\leadsto \color{blue}{\frac{1}{{\left(\sqrt[3]{1 + x}\right)}^2 + {x}^{\left(\frac{1}{3}\right)} \cdot \left({x}^{\left(\frac{1}{3}\right)} + \sqrt[3]{1 + x}\right)}}\]
- Removed slow pow expressions
