ГДЗ по алгебре и начала математического анализа 11 класс Колягин Задание 358

\[1)\ f(x) = (x + 1)^{3};\]

\[F(x) = \frac{(x + 1)^{4}}{4} + C.\]

\[2)\ f(x) = (x - 2)^{4};\]

\[F(x) = \frac{(x - 2)^{5}}{5} + C.\]

\[3)\ f(x) = \frac{2}{\sqrt{x - 2}} = 2(x - 2)^{- \frac{1}{2}};\]

\[F(x) = 2 \bullet (x - 2)^{\frac{1}{2}}\ :\frac{1}{2} + C =\]

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

\[4)\ f(x) = \frac{3}{\sqrt[3]{x + 3}} = 3(x + 3)^{- \frac{1}{3}};\]

\[F(x) = 3 \bullet (x + 3)^{\frac{2}{3}}\ :\frac{2}{3} + C =\]

\[= \frac{9}{2}(x + 3)^{\frac{2}{3}} + C.\]

\[5)\ f(x) = \frac{1}{x - 1} + 4\cos(x + 2);\]

\[F(x) = \ln|x - 1| + 4\sin(x + 2) + C.\]

\[6)\ f(x) = \frac{3}{x - 3} - 2\sin(x - 1);\]

\[F(x) =\]

\[= 3\ln|x - 3| + 2\cos(x - 1) + C.\]