Pyramid 341
Preview $$U_{341}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right) \left(- 2 x - \sqrt{1 - 4 x} + 1\right)}{4 x^{2} y}$$
Pyramid 342
Preview $$U_{342}(x, y) = \frac{2 y \left(x + \frac{1 - \sqrt{1 - 4 y}}{2 y}\right)^{2}}{1 - \sqrt{1 - 4 y}}$$
Pyramid 343
Preview $$U_{343}(x, y) = \frac{y}{3} - \frac{- \frac{2 x}{3} - \frac{\left(y + 1\right)^{2}}{9}}{\sqrt[3]{\frac{x^{2}}{2 y + 2} + \frac{\sqrt{3} x \sqrt{x \left(27 x + 4 \left(y + 1\right)^{2}\right)}}{18 y + 18} + \frac{x \left(y + 1\right)}{3} + \frac{\left(y + 1\right)^{3}}{27}}} + \sqrt[3]{\frac{x^{2}}{2 y + 2} + \frac{\sqrt{3} x \sqrt{x \left(27 x + 4 \left(y + 1\right)^{2}\right)}}{18 y + 18} + \frac{x \left(y + 1\right)}{3} + \frac{\left(y + 1\right)^{3}}{27}} + \frac{1}{3}$$
Pyramid 344
Preview $$U_{344}(x, y) = \frac{\frac{2 x}{3} + \frac{1}{9 \left(1 - y\right)^{2}}}{\sqrt[3]{\frac{x^{2} \left(1 - y\right)}{2} + \frac{\sqrt{3} x \sqrt{x \left(27 x + \frac{4}{\left(1 - y\right)^{2}}\right)} \left(1 - y\right)}{18} + \frac{x}{3 - 3 y} + \frac{1}{27 \left(1 - y\right)^{3}}}} + \sqrt[3]{\frac{x^{2} \left(1 - y\right)}{2} + \frac{\sqrt{3} x \sqrt{x \left(27 x + \frac{4}{\left(1 - y\right)^{2}}\right)} \left(1 - y\right)}{18} + \frac{x}{3 - 3 y} + \frac{1}{27 \left(1 - y\right)^{3}}} + \frac{1}{3 - 3 y}$$
Pyramid 345
Preview $$U_{345}(x, y) = \frac{\frac{2 x}{3} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{36 y^{2}}}{\sqrt[3]{\frac{x^{2} y}{1 - \sqrt{1 - 4 y}} + \frac{\sqrt{3} x y \sqrt{x \left(27 x + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{y^{2}}\right)}}{9 - 9 \sqrt{1 - 4 y}} + \frac{x \left(1 - \sqrt{1 - 4 y}\right)}{6 y} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3}}{216 y^{3}}}} + \sqrt[3]{\frac{x^{2} y}{1 - \sqrt{1 - 4 y}} + \frac{\sqrt{3} x y \sqrt{x \left(27 x + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{y^{2}}\right)}}{9 - 9 \sqrt{1 - 4 y}} + \frac{x \left(1 - \sqrt{1 - 4 y}\right)}{6 y} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3}}{216 y^{3}}} + \frac{1 - \sqrt{1 - 4 y}}{6 y}$$
Pyramid 346
Preview $$U_{346}(x, y) = \frac{\left(- 2 x - \sqrt{1 - 4 x} + 1\right) \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{4 x^{2} y^{2}}$$
Pyramid 347
Preview $$U_{347}(x, y) = \frac{2 y^{2} \left(x + \frac{- 2 y - \sqrt{1 - 4 y} + 1}{2 y^{2}}\right)^{2}}{- 2 y - \sqrt{1 - 4 y} + 1}$$
Pyramid 348
Preview $$U_{348}(x, y) = \frac{\frac{2 x}{3} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{36 y^{4}}}{\sqrt[3]{\frac{x^{2} y^{2}}{- 2 y - \sqrt{1 - 4 y} + 1} + \frac{\sqrt{3} x y^{2} \sqrt{x \left(27 x + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{y^{4}}\right)}}{- 18 y - 9 \sqrt{1 - 4 y} + 9} + \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{6 y^{2}} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{216 y^{6}}}} + \sqrt[3]{\frac{x^{2} y^{2}}{- 2 y - \sqrt{1 - 4 y} + 1} + \frac{\sqrt{3} x y^{2} \sqrt{x \left(27 x + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{y^{4}}\right)}}{- 18 y - 9 \sqrt{1 - 4 y} + 9} + \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{6 y^{2}} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{216 y^{6}}} + \frac{- 2 y - \sqrt{1 - 4 y} + 1}{6 y^{2}}$$
Pyramid 349
Preview $$U_{349}(x, y) = \frac{- 2 x - \sqrt{1 - 4 x} + 1}{2 x^{2} \left(1 - y\right)^{2}}$$
Pyramid 350
Preview $$U_{350}(x, y) = \left(x \left(1 - y\right) + \frac{1}{1 - y}\right)^{2}$$
Pyramid 351
Preview $$U_{351}(x, y) = \frac{\frac{2 x}{3} + \frac{1}{9 \left(1 - y\right)^{4}}}{\sqrt[3]{\frac{x^{2} \left(1 - y\right)^{2}}{2} + \frac{\sqrt{3} x \sqrt{x \left(27 x + \frac{4}{\left(1 - y\right)^{4}}\right)} \left(1 - y\right)^{2}}{18} + \frac{x}{3 \left(1 - y\right)^{2}} + \frac{1}{27 \left(1 - y\right)^{6}}}} + \sqrt[3]{\frac{x^{2} \left(1 - y\right)^{2}}{2} + \frac{\sqrt{3} x \sqrt{x \left(27 x + \frac{4}{\left(1 - y\right)^{4}}\right)} \left(1 - y\right)^{2}}{18} + \frac{x}{3 \left(1 - y\right)^{2}} + \frac{1}{27 \left(1 - y\right)^{6}}} + \frac{1}{3 \left(1 - y\right)^{2}}$$
Pyramid 352
Preview $$U_{352}(x, y) = \frac{- 2 x - \sqrt{1 - 4 x} + 1}{2 x^{2} \left(1 - y\right)^{3}}$$
Pyramid 353
Preview $$U_{353}(x, y) = \left(1 - y\right)^{3} \left(x + \frac{1}{\left(1 - y\right)^{3}}\right)^{2}$$
Pyramid 354
Preview $$U_{354}(x, y) = \frac{1 - \sqrt{1 - 4 x}}{2 x \left(1 - y\right)^{3}}$$
Pyramid 355
Preview $$U_{355}(x, y) = - \frac{1}{\left(1 - y\right)^{6} \left(x - \frac{1}{\left(1 - y\right)^{3}}\right)}$$
Pyramid 356
Preview $$U_{356}(x, y) = \frac{y}{2} - \frac{\sqrt{4 x + \left(y + 1\right)^{2}}}{2} + \frac{1}{2}$$
Pyramid 357
Preview $$U_{357}(x, y) = \frac{\left(y + 1\right)^{2}}{1 - x}$$
Pyramid 358
Preview $$U_{358}(x, y) = \frac{1 - \sqrt{- 4 x y^{2} - 8 x y - 4 x + 1}}{2 x}$$
Pyramid 359
Preview $$U_{359}(x, y) = \frac{- x - 2 y - \sqrt{x^{2} - 2 x + y \left(4 x - 4\right) + 1} + 1}{2 y^{2}}$$
Pyramid 360
Preview $$U_{360}(x, y) = x + y^{2} + 2 y + 1$$
Page: 1 ... 15 16 17 18 19 20 21 ... 76
or
expand_less