\(\frac{e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2\right)}}{{x}^{\left(\frac{1}{3}\right)} + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}\)
- Started with
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
13.1
- Using strategy
rm 13.1
- Applied add-exp-log to get
\[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}} \leadsto \color{blue}{e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}}\]
13.1
- Using strategy
rm 13.1
- Applied add-sqr-sqrt to get
\[e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{{x}^{\left(\frac{1}{3}\right)}}\right)} \leadsto e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{{\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2}\right)}\]
13.2
- Using strategy
rm 13.2
- Applied flip-- to get
\[e^{\log \color{red}{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}} \leadsto e^{\log \color{blue}{\left(\frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2}\right)}}\]
13.2
- Applied log-div to get
\[e^{\color{red}{\log \left(\frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2}\right)}} \leadsto e^{\color{blue}{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2\right) - \log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}}\]
13.3
- Applied exp-diff to get
\[\color{red}{e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2\right) - \log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}} \leadsto \color{blue}{\frac{e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2\right)}}{e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}}}\]
13.3
- Applied simplify to get
\[\frac{e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2\right)}}{\color{red}{e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}}} \leadsto \frac{e^{\log \left({\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 - {\left({\left(\sqrt{{x}^{\left(\frac{1}{3}\right)}}\right)}^2\right)}^2\right)}}{\color{blue}{{x}^{\left(\frac{1}{3}\right)} + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)}}}\]
13.2
- Removed slow pow expressions
