Initial program 44.7
\[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
- Using strategy
rm Applied add-log-exp44.7
\[\leadsto {\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - \color{blue}{\log \left(e^{{x}^{\left(\frac{1}{n}\right)}}\right)}\]
Applied add-log-exp44.7
\[\leadsto \color{blue}{\log \left(e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}\right)} - \log \left(e^{{x}^{\left(\frac{1}{n}\right)}}\right)\]
Applied diff-log44.7
\[\leadsto \color{blue}{\log \left(\frac{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}}{e^{{x}^{\left(\frac{1}{n}\right)}}}\right)}\]
Applied simplify44.7
\[\leadsto \log \color{blue}{\left(e^{{\left(1 + x\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}\right)}\]
- Using strategy
rm Applied sub-neg44.7
\[\leadsto \log \left(e^{\color{blue}{{\left(1 + x\right)}^{\left(\frac{1}{n}\right)} + \left(-{x}^{\left(\frac{1}{n}\right)}\right)}}\right)\]
Applied exp-sum44.7
\[\leadsto \log \color{blue}{\left(e^{{\left(1 + x\right)}^{\left(\frac{1}{n}\right)}} \cdot e^{-{x}^{\left(\frac{1}{n}\right)}}\right)}\]
Taylor expanded around inf 33.3
\[\leadsto \color{blue}{\left(\log \left(e^{-1} \cdot e\right) + \frac{1}{n \cdot x}\right) - \frac{1}{2} \cdot \frac{1}{n \cdot {x}^{2}}}\]
Applied simplify32.6
\[\leadsto \color{blue}{\left(\frac{\frac{1}{n}}{x} + \left(-1 + 1\right)\right) - \frac{\frac{\frac{1}{2}}{x}}{x \cdot n}}\]
- Using strategy
rm Applied add-log-exp32.6
\[\leadsto \left(\frac{\frac{1}{n}}{x} + \left(-1 + 1\right)\right) - \color{blue}{\log \left(e^{\frac{\frac{\frac{1}{2}}{x}}{x \cdot n}}\right)}\]
Initial program 6.5
\[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
- Using strategy
rm Applied add-log-exp6.9
\[\leadsto {\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - \color{blue}{\log \left(e^{{x}^{\left(\frac{1}{n}\right)}}\right)}\]
Applied add-log-exp6.9
\[\leadsto \color{blue}{\log \left(e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}\right)} - \log \left(e^{{x}^{\left(\frac{1}{n}\right)}}\right)\]
Applied diff-log6.9
\[\leadsto \color{blue}{\log \left(\frac{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}}{e^{{x}^{\left(\frac{1}{n}\right)}}}\right)}\]
Applied simplify6.8
\[\leadsto \log \color{blue}{\left(e^{{\left(1 + x\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}\right)}\]
- Using strategy
rm Applied sub-neg6.8
\[\leadsto \log \left(e^{\color{blue}{{\left(1 + x\right)}^{\left(\frac{1}{n}\right)} + \left(-{x}^{\left(\frac{1}{n}\right)}\right)}}\right)\]
Applied exp-sum6.9
\[\leadsto \log \color{blue}{\left(e^{{\left(1 + x\right)}^{\left(\frac{1}{n}\right)}} \cdot e^{-{x}^{\left(\frac{1}{n}\right)}}\right)}\]
- Using strategy
rm Applied add-log-exp7.0
\[\leadsto \log \left(e^{{\left(1 + x\right)}^{\left(\frac{1}{n}\right)}} \cdot \color{blue}{\log \left(e^{e^{-{x}^{\left(\frac{1}{n}\right)}}}\right)}\right)\]
