Pyramid 421
Preview $$U_{421}(x, y) = \frac{\sqrt{- 16 x y + 4 x + 1} + 1}{2 \sqrt{1 - 4 y}}$$
Pyramid 422
Preview $$U_{422}(x, y) = \frac{1 - \sqrt{- 16 x y + 4 x + 1}}{2 \sqrt{1 - 4 y}}$$
Pyramid 423
Preview $$U_{423}(x, y) = \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{4}{\left(1 - 4 y\right)^{\frac{3}{2}}}\right)}}{18} + \frac{1}{27 \left(1 - 4 y\right)^{\frac{3}{2}}}} + \frac{1}{\left(9 - 36 y\right) \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{4}{\left(1 - 4 y\right)^{\frac{3}{2}}}\right)}}{18} + \frac{1}{27 \left(1 - 4 y\right)^{\frac{3}{2}}}}} + \frac{1}{3 \sqrt{1 - 4 y}}$$
Pyramid 424
Preview $$U_{424}(x, y) = \frac{2 x y - x - \sqrt{x^{2} - 4 x y + 2 x + 1} - 1}{2 y - 2}$$
Pyramid 425
Preview $$U_{425}(x, y) = \frac{2 x y - x + \sqrt{x^{2} - 4 x y + 2 x + 1} - 1}{2 y - 2}$$
Pyramid 426
Preview $$U_{426}(x, y) = \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3}}{2 y^{3}}\right)}}{18} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3}}{216 y^{3}}} + \frac{1 - \sqrt{1 - 4 y}}{6 y} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{36 y^{2} \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3}}{2 y^{3}}\right)}}{18} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3}}{216 y^{3}}}}$$
Pyramid 427
Preview $$U_{427}(x, y) = \frac{\left(\frac{x}{1 - y} + 1\right)^{3}}{\left(1 - y\right)^{2}}$$
Pyramid 428
Preview $$U_{428}(x, y) = \frac{- 2 y - \sqrt{1 - 4 y} - \sqrt{2} \sqrt{8 x y^{4} + 2 y^{2} - 4 y + \sqrt{1 - 4 y} \left(2 y - 1\right) + 1} + 1}{4 y^{2}}$$
Pyramid 429
Preview $$U_{429}(x, y) = \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{2 y^{6}}\right)}}{18} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{216 y^{6}}} + \frac{- 2 y - \sqrt{1 - 4 y} + 1}{6 y^{2}} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{36 y^{4} \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{2 y^{6}}\right)}}{18} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{216 y^{6}}}}$$
Pyramid 430
Preview $$U_{430}(x, y) = \frac{\sqrt{3} \left(\sqrt{3 x y + \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}} + \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}\right)}{3 \sqrt{y}}$$
Pyramid 431
Preview $$U_{431}(x, y) = \frac{\sqrt{3} \left(- \sqrt{3 x y + \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}} + \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}\right)}{3 \sqrt{y}}$$
Pyramid 432
Preview $$U_{432}(x, y) = \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{32 \sqrt{3} \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{\frac{3}{2}}}\right)}}{18} + \frac{8 \sqrt{3} \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{243 y^{\frac{3}{2}}}} + \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{27 y \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{32 \sqrt{3} \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{\frac{3}{2}}}\right)}}{18} + \frac{8 \sqrt{3} \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{243 y^{\frac{3}{2}}}}} + \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 \sqrt{y}}$$
Pyramid 433
Preview $$U_{433}(x, y) = \frac{\sqrt{4 y + 1} + 1}{2 \left(1 - x\right)^{2}}$$
Pyramid 434
Preview $$U_{434}(x, y) = \frac{x^{2} - 2 x + y + 1}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1}$$
Pyramid 435
Preview $$U_{435}(x, y) = \frac{- x^{2} + 2 x - 1}{- x^{4} + 4 x^{3} - 6 x^{2} + 4 x + y - 1}$$
Pyramid 436
Preview $$U_{436}(x, y) = \frac{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + \left(x - 1\right) \sqrt{x^{6} - 6 x^{5} + 15 x^{4} - 20 x^{3} + 15 x^{2} - 6 x - 4 y + 1} + 1}{2 y}$$
Pyramid 437
Preview $$U_{437}(x, y) = x + \frac{\sqrt{4 y + 1}}{4} + \frac{\sqrt{2 x \left(\sqrt{4 y + 1} + 1\right) + \frac{\left(\sqrt{4 y + 1} + 1\right)^{2}}{4}}}{2} + \frac{1}{4}$$
Pyramid 438
Preview $$U_{438}(x, y) = x + \frac{\sqrt{4 y + 1}}{4} - \frac{\sqrt{2 x \left(\sqrt{4 y + 1} + 1\right) + \frac{\left(\sqrt{4 y + 1} + 1\right)^{2}}{4}}}{2} + \frac{1}{4}$$
Pyramid 439
Preview $$U_{439}(x, y) = x + \frac{y}{2} + \frac{\sqrt{4 x \left(y + 1\right) + \left(y + 1\right)^{2}}}{2} + \frac{1}{2}$$
Pyramid 440
Preview $$U_{440}(x, y) = x + \frac{y}{2} - \frac{\sqrt{4 x \left(y + 1\right) + \left(y + 1\right)^{2}}}{2} + \frac{1}{2}$$
Page: 1 ... 19 20 21 22 23 24 25 ... 76
or
expand_less