Initial program 47.5
\[\frac{2}{\left(\left(\frac{{t}^{3}}{{\ell}^2} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^2\right) - 1\right)}\]
- Using strategy
rm
Applied add-cube-cbrt 47.6
\[\leadsto \frac{2}{\left(\left(\frac{{t}^{3}}{{\ell}^2} \cdot \sin k\right) \cdot \tan k\right) \cdot \color{blue}{{\left(\sqrt[3]{\left(1 + {\left(\frac{k}{t}\right)}^2\right) - 1}\right)}^3}}\]
Applied add-cube-cbrt 47.6
\[\leadsto \frac{2}{\left(\left(\frac{{t}^{3}}{{\ell}^2} \cdot \sin k\right) \cdot \color{blue}{{\left(\sqrt[3]{\tan k}\right)}^3}\right) \cdot {\left(\sqrt[3]{\left(1 + {\left(\frac{k}{t}\right)}^2\right) - 1}\right)}^3}\]
Applied add-cube-cbrt 47.6
\[\leadsto \frac{2}{\left(\left(\frac{{t}^{3}}{{\ell}^2} \cdot \color{blue}{{\left(\sqrt[3]{\sin k}\right)}^3}\right) \cdot {\left(\sqrt[3]{\tan k}\right)}^3\right) \cdot {\left(\sqrt[3]{\left(1 + {\left(\frac{k}{t}\right)}^2\right) - 1}\right)}^3}\]
Applied add-cube-cbrt 47.6
\[\leadsto \frac{2}{\left(\left(\frac{{t}^{3}}{\color{blue}{{\left(\sqrt[3]{{\ell}^2}\right)}^3}} \cdot {\left(\sqrt[3]{\sin k}\right)}^3\right) \cdot {\left(\sqrt[3]{\tan k}\right)}^3\right) \cdot {\left(\sqrt[3]{\left(1 + {\left(\frac{k}{t}\right)}^2\right) - 1}\right)}^3}\]
Applied add-cube-cbrt 47.6
\[\leadsto \frac{2}{\left(\left(\frac{\color{blue}{{\left(\sqrt[3]{{t}^{3}}\right)}^3}}{{\left(\sqrt[3]{{\ell}^2}\right)}^3} \cdot {\left(\sqrt[3]{\sin k}\right)}^3\right) \cdot {\left(\sqrt[3]{\tan k}\right)}^3\right) \cdot {\left(\sqrt[3]{\left(1 + {\left(\frac{k}{t}\right)}^2\right) - 1}\right)}^3}\]
Applied cube-undiv 47.6
\[\leadsto \frac{2}{\left(\left(\color{blue}{{\left(\frac{\sqrt[3]{{t}^{3}}}{\sqrt[3]{{\ell}^2}}\right)}^3} \cdot {\left(\sqrt[3]{\sin k}\right)}^3\right) \cdot {\left(\sqrt[3]{\tan k}\right)}^3\right) \cdot {\left(\sqrt[3]{\left(1 + {\left(\frac{k}{t}\right)}^2\right) - 1}\right)}^3}\]
Applied cube-unprod 47.6
\[\leadsto \frac{2}{\left(\color{blue}{{\left(\frac{\sqrt[3]{{t}^{3}}}{\sqrt[3]{{\ell}^2}} \cdot \sqrt[3]{\sin k}\right)}^3} \cdot {\left(\sqrt[3]{\tan k}\right)}^3\right) \cdot {\left(\sqrt[3]{\left(1 + {\left(\frac{k}{t}\right)}^2\right) - 1}\right)}^3}\]
Applied cube-unprod 47.6
\[\leadsto \frac{2}{\color{blue}{{\left(\left(\frac{\sqrt[3]{{t}^{3}}}{\sqrt[3]{{\ell}^2}} \cdot \sqrt[3]{\sin k}\right) \cdot \sqrt[3]{\tan k}\right)}^3} \cdot {\left(\sqrt[3]{\left(1 + {\left(\frac{k}{t}\right)}^2\right) - 1}\right)}^3}\]
Applied cube-unprod 47.2
\[\leadsto \frac{2}{\color{blue}{{\left(\left(\left(\frac{\sqrt[3]{{t}^{3}}}{\sqrt[3]{{\ell}^2}} \cdot \sqrt[3]{\sin k}\right) \cdot \sqrt[3]{\tan k}\right) \cdot \sqrt[3]{\left(1 + {\left(\frac{k}{t}\right)}^2\right) - 1}\right)}^3}}\]
Applied simplify 31.1
\[\leadsto \frac{2}{{\color{blue}{\left(\left(\sqrt[3]{\tan k} \cdot \sqrt[3]{\sin k}\right) \cdot \left(\sqrt[3]{{\left(\frac{k}{t}\right)}^2} \cdot \frac{t}{\sqrt[3]{\ell \cdot \ell}}\right)\right)}}^3}\]
- Using strategy
rm
Applied square-mult 31.1
\[\leadsto \frac{2}{{\left(\left(\sqrt[3]{\tan k} \cdot \sqrt[3]{\sin k}\right) \cdot \left(\sqrt[3]{\color{blue}{\frac{k}{t} \cdot \frac{k}{t}}} \cdot \frac{t}{\sqrt[3]{\ell \cdot \ell}}\right)\right)}^3}\]
Applied cbrt-prod 22.5
\[\leadsto \frac{2}{{\left(\left(\sqrt[3]{\tan k} \cdot \sqrt[3]{\sin k}\right) \cdot \left(\color{blue}{\left(\sqrt[3]{\frac{k}{t}} \cdot \sqrt[3]{\frac{k}{t}}\right)} \cdot \frac{t}{\sqrt[3]{\ell \cdot \ell}}\right)\right)}^3}\]
Applied associate-*l* 22.5
\[\leadsto \frac{2}{{\left(\left(\sqrt[3]{\tan k} \cdot \sqrt[3]{\sin k}\right) \cdot \color{blue}{\left(\sqrt[3]{\frac{k}{t}} \cdot \left(\sqrt[3]{\frac{k}{t}} \cdot \frac{t}{\sqrt[3]{\ell \cdot \ell}}\right)\right)}\right)}^3}\]
- Using strategy
rm
Applied cbrt-prod 10.9
\[\leadsto \frac{2}{{\left(\left(\sqrt[3]{\tan k} \cdot \sqrt[3]{\sin k}\right) \cdot \left(\sqrt[3]{\frac{k}{t}} \cdot \left(\sqrt[3]{\frac{k}{t}} \cdot \frac{t}{\color{blue}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\right)\right)\right)}^3}\]
- Removed slow pow expressions
