Задача 65564 напишите общий вид первообразных функции...
Условие
математика 10-11 класс
90
Решение
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[m]F (x^{n}) = \frac{x^{n+1}}{n+1} + C[/m]
1) [m]F(x) = \frac{x^{\sqrt{5}}}{\sqrt{5}} + \frac{x^{3,5}}{3,5} + C = \frac{\sqrt{5}x^{\sqrt{5}}}{5} + \frac{2x^{3,5}}{7} + C[/m]
2) [m]F(x) = \frac{-2x^{-52}}{-52} + \frac{x^{3/2}}{3/2} + C = \frac{1}{26x^{52}} + \frac{2x^{3/2}}{3} + C[/m]
3) [m]F(x) = \frac{x^{4+\sqrt{2}}}{4+\sqrt{2}} + \frac{x^{7/4}}{7/4} + C = \frac{(4-\sqrt{2})x^{4+\sqrt{2}}}{14} + \frac{4x^{7/4}}{7} + C[/m]
[m](4-\sqrt{2})(4+\sqrt{2}) = 4^2 - (\sqrt{2})^2 = 16 - 2 = 14[/m]
4) [m]F(x) = \frac{5x^{-\sqrt{6}}}{-\sqrt{6}} - \frac{x^{7/5}}{7/5}+ C =\frac{-5\sqrt{6}x^{-\sqrt{6}}}{6} - \frac{5x^{7/5}}{7}+ C[/m]