\({\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)}^3 - {e}^{\left(\frac{\log x}{3}\right)}\)
- Started with
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
13.2
- Using strategy
rm 13.2
- Applied pow-to-exp to get
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{{x}^{\left(\frac{1}{3}\right)}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{e^{\log x \cdot \frac{1}{3}}}\]
13.5
- Applied simplify to get
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - e^{\color{red}{\log x \cdot \frac{1}{3}}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - e^{\color{blue}{\frac{\log x}{3}}}\]
13.2
- Using strategy
rm 13.2
- Applied *-un-lft-identity to get
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - e^{\color{red}{\frac{\log x}{3}}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - e^{\color{blue}{1 \cdot \frac{\log x}{3}}}\]
13.2
- Applied exp-prod to get
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{e^{1 \cdot \frac{\log x}{3}}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{{\left(e^{1}\right)}^{\left(\frac{\log x}{3}\right)}}\]
13.2
- Applied simplify to get
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {\color{red}{\left(e^{1}\right)}}^{\left(\frac{\log x}{3}\right)} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {\color{blue}{e}}^{\left(\frac{\log x}{3}\right)}\]
13.2
- Using strategy
rm 13.2
- Applied add-cube-cbrt to get
\[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}} - {e}^{\left(\frac{\log x}{3}\right)} \leadsto \color{blue}{{\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\right)}^3} - {e}^{\left(\frac{\log x}{3}\right)}\]
13.3
