Initial program 30.0
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
- Using strategy
rm Applied flip3--30.0
\[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x + 1}\right)}^{3} - {\left(\sqrt[3]{x}\right)}^{3}}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)}}\]
Taylor expanded around 0 0.5
\[\leadsto \frac{\color{blue}{1}}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)}\]
- Using strategy
rm Applied add-cube-cbrt0.6
\[\leadsto \frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\color{blue}{\left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)}\]
- Using strategy
rm Applied add-cbrt-cube0.6
\[\leadsto \frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) \cdot \color{blue}{\sqrt[3]{\left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}}} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)}\]
Final simplification0.6
\[\leadsto \frac{1}{\left(\sqrt[3]{\left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}} \cdot \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right) + \sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}}\]
