\(1 - \frac{\frac{\left(\frac{\frac{1.421413741}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \left(\frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1} + 0.254829592\right)\right) + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1} + -1.453152027}{{\left(\left|x\right| \cdot 0.3275911 + 1\right)}^3}}{\left|x\right| \cdot 0.3275911 + 1}}{e^{\left|x\right| \cdot \left|x\right|}}\)
- Started with
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
13.8
- Using strategy
rm 13.8
- Applied add-cbrt-cube to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \color{red}{\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)}\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \color{blue}{\sqrt[3]{{\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}^3}}\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
13.8
- Applied taylor to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \sqrt[3]{{\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}^3}\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \sqrt[3]{{\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}^3}\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
13.8
- Taylor expanded around 0 to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \sqrt[3]{{\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \color{red}{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}} \cdot 1.061405429\right)\right)\right)}^3}\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \sqrt[3]{{\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \color{blue}{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}} \cdot 1.061405429\right)\right)\right)}^3}\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
13.8
- Applied simplify to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \sqrt[3]{{\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}^3}\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \frac{\left(\left(0.254829592 + \frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1}\right) + \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \frac{1.421413741}{\left|x\right| \cdot 0.3275911 + 1}\right) + {\left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1}\right)}^3 \cdot \left(\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1} + -1.453152027\right)}{e^{\left|x\right| \cdot \left|x\right|}}\]
13.8
- Applied final simplification
- Applied simplify to get
\[\color{red}{1 - \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \frac{\left(\left(0.254829592 + \frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1}\right) + \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \frac{1.421413741}{\left|x\right| \cdot 0.3275911 + 1}\right) + {\left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1}\right)}^3 \cdot \left(\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1} + -1.453152027\right)}{e^{\left|x\right| \cdot \left|x\right|}}} \leadsto \color{blue}{1 - \frac{\frac{\left(\frac{\frac{1.421413741}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \left(\frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1} + 0.254829592\right)\right) + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1} + -1.453152027}{{\left(\left|x\right| \cdot 0.3275911 + 1\right)}^3}}{\left|x\right| \cdot 0.3275911 + 1}}{e^{\left|x\right| \cdot \left|x\right|}}}\]
13.8
