Initial program 30.6
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
Initial simplification30.6
\[\leadsto \sqrt[3]{1 + x} - \sqrt[3]{x}\]
- Using strategy
rm Applied add-cbrt-cube30.7
\[\leadsto \sqrt[3]{1 + x} - \color{blue}{\sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}\]
- Using strategy
rm Applied flip3--30.6
\[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{1 + x}\right)}^{3} - {\left(\sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\right)}^{3}}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \left(\sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \sqrt[3]{1 + x} \cdot \sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\right)}}\]
Taylor expanded around 0 0.6
\[\leadsto \frac{\color{blue}{1}}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \left(\sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \sqrt[3]{1 + x} \cdot \sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\right)}\]
- Using strategy
rm Applied add-cbrt-cube0.6
\[\leadsto \frac{1}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \left(\sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \color{blue}{\sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}} + \sqrt[3]{1 + x} \cdot \sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\right)}\]
Final simplification0.6
\[\leadsto \frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{\sqrt[3]{x} \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x + 1} + \sqrt[3]{\sqrt[3]{x} \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{\sqrt[3]{x} \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)}}\right)}\]
