\(\sqrt[3]{{\left(\sqrt{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^3}\right)}^2} - {x}^{\left(\frac{1}{3}\right)}\)
- Started with
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
30.4
- Using strategy
rm 30.4
- Applied add-exp-log to get
\[{\color{red}{\left(x + 1\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)} \leadsto {\color{blue}{\left(e^{\log \left(x + 1\right)}\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
30.7
- Applied pow-exp to get
\[\color{red}{{\left(e^{\log \left(x + 1\right)}\right)}^{\left(\frac{1}{3}\right)}} - {x}^{\left(\frac{1}{3}\right)} \leadsto \color{blue}{e^{\log \left(x + 1\right) \cdot \frac{1}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
30.7
- Applied simplify to get
\[e^{\color{red}{\log \left(x + 1\right) \cdot \frac{1}{3}}} - {x}^{\left(\frac{1}{3}\right)} \leadsto e^{\color{blue}{\frac{\log_* (1 + x)}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
30.4
- Using strategy
rm 30.4
- Applied add-cbrt-cube to get
\[\color{red}{e^{\frac{\log_* (1 + x)}{3}}} - {x}^{\left(\frac{1}{3}\right)} \leadsto \color{blue}{\sqrt[3]{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^3}} - {x}^{\left(\frac{1}{3}\right)}\]
30.4
- Using strategy
rm 30.4
- Applied add-sqr-sqrt to get
\[\sqrt[3]{\color{red}{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^3}} - {x}^{\left(\frac{1}{3}\right)} \leadsto \sqrt[3]{\color{blue}{{\left(\sqrt{{\left(e^{\frac{\log_* (1 + x)}{3}}\right)}^3}\right)}^2}} - {x}^{\left(\frac{1}{3}\right)}\]
30.4
