Initial program 30.5
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
- Using strategy
rm Applied flip3--30.4
\[\leadsto \color{blue}{\frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + \left({x}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)} + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}}\]
Applied simplify30.4
\[\leadsto \frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}}{\color{blue}{{\left(1 + x\right)}^{\left(\frac{1}{3}\right)} \cdot {\left(1 + x\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)} \cdot \left({\left(1 + x\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right)}}\]
- Using strategy
rm Applied add-sqr-sqrt30.5
\[\leadsto \frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\color{blue}{\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}} \cdot \sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}}^{3}}{{\left(1 + x\right)}^{\left(\frac{1}{3}\right)} \cdot {\left(1 + x\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)} \cdot \left({\left(1 + x\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right)}\]
- Using strategy
rm Applied pow-to-exp30.5
\[\leadsto \frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}} \cdot \sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^{3}}{{\left(1 + x\right)}^{\left(\frac{1}{3}\right)} \cdot {\left(1 + x\right)}^{\left(\frac{1}{3}\right)} + \color{blue}{e^{\log x \cdot \frac{1}{3}}} \cdot \left({\left(1 + x\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right)}\]
Applied simplify30.5
\[\leadsto \frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}} \cdot \sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^{3}}{{\left(1 + x\right)}^{\left(\frac{1}{3}\right)} \cdot {\left(1 + x\right)}^{\left(\frac{1}{3}\right)} + e^{\color{blue}{\frac{\log x}{3}}} \cdot \left({\left(1 + x\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right)}\]
- Using strategy
rm Applied add-cube-cbrt30.5
\[\leadsto \frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}} \cdot \sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^{3}}{{\left(1 + x\right)}^{\left(\frac{1}{3}\right)} \cdot {\left(1 + x\right)}^{\left(\frac{1}{3}\right)} + e^{\color{blue}{\left(\sqrt[3]{\frac{\log x}{3}} \cdot \sqrt[3]{\frac{\log x}{3}}\right) \cdot \sqrt[3]{\frac{\log x}{3}}}} \cdot \left({\left(1 + x\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right)}\]
Applied exp-prod30.5
\[\leadsto \frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}} \cdot \sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^{3}}{{\left(1 + x\right)}^{\left(\frac{1}{3}\right)} \cdot {\left(1 + x\right)}^{\left(\frac{1}{3}\right)} + \color{blue}{{\left(e^{\sqrt[3]{\frac{\log x}{3}} \cdot \sqrt[3]{\frac{\log x}{3}}}\right)}^{\left(\sqrt[3]{\frac{\log x}{3}}\right)}} \cdot \left({\left(1 + x\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right)}\]
