ГДЗ по алгебре и начала математического анализа 10 класс Алимов Задание 1027

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\[1)\ y^{'} = 3 - 4x;\]

\[y(x) = 3 \bullet \frac{x^{1}}{1} - 4 \bullet \frac{x^{2}}{2} =\]

\[= 3x - 2x^{2} + C.\]

\[2)\ y^{'} = 6x^{2} - 8x + 1;\]

\[y(x) = 6 \bullet \frac{x^{3}}{3} - 8 \bullet \frac{x^{2}}{2} + 1 \bullet \frac{x^{1}}{1} =\]

\[= 2x^{3} - 4x^{2} + x + C.\]

\[3)\ y^{'} = 3e^{2x};\]

\[y(x) = 3 \bullet \frac{1}{2} \bullet e^{2x} = \frac{3}{2}e^{2x} + C.\]

\[4)\ y^{'} = 4\cos{2x};\]

\[y(x) = 4 \bullet \frac{1}{2} \bullet \sin{2x} =\]

\[= 2\sin{2x} + C.\]

\[5)\ y^{'} = 3\sin x;\]

\[y(x) = 3 \bullet \left( - \cos x \right) =\]

\[= - 3\cos x + C.\]

\[6)\ y^{'} = \cos x - \sin x;\]

\[y(x) = \sin x - \left( - \cos x \right) =\]

\[= \sin x + \cos x + C.\]