Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 354

\[1)\ f(x) = x^{6};\]

\[F(x) = \frac{x^{6 + 1}}{6 + 1} + C = \frac{x^{7}}{7} + C.\]

\[2)\ f(x) = x^{5};\]

\[F(x) = \frac{x^{5 + 1}}{5 + 1} + C = \frac{x^{6}}{6} + C.\]

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

\[F(x) = \frac{x^{- \frac{1}{3} + 1}}{- \frac{1}{3} + 1} + C = \frac{3x^{\frac{2}{3}}}{2} + C =\]

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

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

\[F(x) = \frac{x^{\frac{1}{4} + 1}}{\frac{1}{4} + 1} + C = \frac{4x^{\frac{5}{4}}}{5} + C =\]

\[= \frac{4\sqrt[4]{x^{5}}}{5} + C.\]

\[5)\ f(x) = x^{\frac{2}{3}};\]

\[F(x) = \frac{x^{\frac{2}{3} + 1}}{\frac{2}{3} + 1} + C = \frac{3x^{\frac{5}{3}}}{5} + C.\]

\[6)\ f(x) = x^{- \frac{3}{4}};\]

\[F(x) = \frac{x^{- \frac{3}{4} + 1}}{- \frac{3}{4} + 1} + C = 4x^{\frac{1}{4}} + C.\]