Ответ:
Найти первообразную функции .
[tex]\displaystyle f(x)=\dfrac{1}{2\sqrt{x} }-\dfrac{2}{x^3}\\\\\\F(x)=\int \Big(\dfrac{1}{2\sqrt{x} }-\dfrac{2}{x^3}\Big)\, dx=\int \Big(\dfrac{1}{2}\, x^{-\frac{1}{2}}-2x^{-3}\Big)\m dx=\frac{1}{2}\cdot \frac{x^{\frac{1}{2}}}{\frac{1}{2}}-2\cdot \frac{x^{-2}}{-2}+C=\\\\\\=\sqrt{x}+\frac{1}{x^2}+C[/tex]
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Ответ:
Найти первообразную функции .
[tex]\displaystyle f(x)=\dfrac{1}{2\sqrt{x} }-\dfrac{2}{x^3}\\\\\\F(x)=\int \Big(\dfrac{1}{2\sqrt{x} }-\dfrac{2}{x^3}\Big)\, dx=\int \Big(\dfrac{1}{2}\, x^{-\frac{1}{2}}-2x^{-3}\Big)\m dx=\frac{1}{2}\cdot \frac{x^{\frac{1}{2}}}{\frac{1}{2}}-2\cdot \frac{x^{-2}}{-2}+C=\\\\\\=\sqrt{x}+\frac{1}{x^2}+C[/tex]