991. a) f(x) = -1/x^2 + x; 6) f(x) = 1/(2√x) - 1/x^2; B) f(x) = -1/x^2 + x^3; r) f(x) = 1/(2√x) + 1.

Краткое пояснение:

Пошаговое решение:

1. a) f(x) = -1/x² + x = -x^-2 + x
   Первообразная F(x) = \( -\frac{x^{-2+1}}{-2+1} + \frac{x^{1+1}}{1+1} \) = \( -\frac{x^{-1}}{-1} + \frac{x^2}{2} \) = \( x^{-1} + \frac{x^2}{2} \) = \( \frac{1}{x} + \frac{x^2}{2} \).
2. 6) f(x) = 1/(2√x) - 1/x² = 1/2 * x^-1/2 - x^-2
   Первообразная F(x) = \( \frac{1}{2} \frac{x^{-1/2+1}}{-1/2+1} - \frac{x^{-2+1}}{-2+1} \) = \( \frac{1}{2} \frac{x^{1/2}}{1/2} - \frac{x^{-1}}{-1} \) = \( x^{1/2} + x^{-1} \) = \( \sqrt{x} + \frac{1}{x} \).
3. B) f(x) = -1/x² + x³ = -x^-2 + x³
   Первообразная F(x) = \( -\frac{x^{-2+1}}{-2+1} + \frac{x^{3+1}}{3+1} \) = \( -\frac{x^{-1}}{-1} + \frac{x^4}{4} \) = \( x^{-1} + \frac{x^4}{4} \) = \( \frac{1}{x} + \frac{x^4}{4} \).
4. r) f(x) = 1/(2√x) + 1 = 1/2 * x^-1/2 + 1
   Первообразная F(x) = \( \frac{1}{2} \frac{x^{-1/2+1}}{-1/2+1} + \frac{x^{0+1}}{0+1} \) = \( \frac{1}{2} \frac{x^{1/2}}{1/2} + x \) = \( x^{1/2} + x \) = \( \sqrt{x} + x \).

Ответ: a) \( \frac{1}{x} + \frac{x^2}{2} \); 6) \( \sqrt{x} + \frac{1}{x} \); B) \( \frac{1}{x} + \frac{x^4}{4} \); r) \( \sqrt{x} + x \)