Initial program 1.0
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
Initial simplification0.0
\[\leadsto \frac{\frac{\frac{\frac{4}{3}}{\pi}}{1 - v \cdot v}}{\sqrt{(\left(v \cdot 6\right) \cdot \left(-v\right) + 2)_*}}\]
- Using strategy
rm Applied add-cbrt-cube0.0
\[\leadsto \frac{\frac{\frac{\frac{4}{3}}{\pi}}{\color{blue}{\sqrt[3]{\left(\left(1 - v \cdot v\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \left(1 - v \cdot v\right)}}}}{\sqrt{(\left(v \cdot 6\right) \cdot \left(-v\right) + 2)_*}}\]
Applied add-cbrt-cube0.0
\[\leadsto \frac{\frac{\color{blue}{\sqrt[3]{\left(\frac{\frac{4}{3}}{\pi} \cdot \frac{\frac{4}{3}}{\pi}\right) \cdot \frac{\frac{4}{3}}{\pi}}}}{\sqrt[3]{\left(\left(1 - v \cdot v\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \left(1 - v \cdot v\right)}}}{\sqrt{(\left(v \cdot 6\right) \cdot \left(-v\right) + 2)_*}}\]
Applied cbrt-undiv0.0
\[\leadsto \frac{\color{blue}{\sqrt[3]{\frac{\left(\frac{\frac{4}{3}}{\pi} \cdot \frac{\frac{4}{3}}{\pi}\right) \cdot \frac{\frac{4}{3}}{\pi}}{\left(\left(1 - v \cdot v\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \left(1 - v \cdot v\right)}}}}{\sqrt{(\left(v \cdot 6\right) \cdot \left(-v\right) + 2)_*}}\]
Simplified0.0
\[\leadsto \frac{\sqrt[3]{\color{blue}{{\left(\frac{\frac{4}{\pi \cdot 3}}{1 - v \cdot v}\right)}^{3}}}}{\sqrt{(\left(v \cdot 6\right) \cdot \left(-v\right) + 2)_*}}\]
Final simplification0.0
\[\leadsto \frac{\sqrt[3]{{\left(\frac{\frac{4}{3 \cdot \pi}}{1 - v \cdot v}\right)}^{3}}}{\sqrt{(\left(6 \cdot v\right) \cdot \left(-v\right) + 2)_*}}\]
