Задача 80804 ...

626fab9a354ab65fb2f43abb

2/26/2026 11:27:34 AM

★

[m]\int (x^3 + \frac{1}{\sqrt{x}} + 2a^{x}) dx = \int (x^3 + x^{-1/2} + 2a^{x}) dx =[/m]
[m]\large = \frac{x^4}{4} + \frac{x^{1/2}}{1/2} + \frac{2a^{x}}{\ln a} + C = \frac{x^4}{4} + 2\sqrt{x} + \frac{2a^{x}}{\ln a} + C [/m]

[m](\sin 2x + \frac{1}{x^3} - a^{3x})' = (\sin 2x + x^{-3} - a^{3x})' = [/m]
[m]= \cos 2x \cdot 2 + (-3)x^{-4} - a^{3x} \ln a \cdot 3 = 2\cos 2x - \frac{3}{x^4} - 3\ln a \cdot a^{3x}[/m]