Question

Найдите первообразную! Даю 70 баллов​

Answer 1

1) f(x) = x + 3

F(x) = x²/2 + 3x + C

2) f(x) = x²+4x -1

F(x) = x³/3 + 4x²/2 - x + C = x³ + 2x² - x + C

3) f(x) = (x³ + x)/(x² + 1) = x(x² + 1)/(x² +1) = x

x² + 1 ≠ 0

f(x) = x

F(x) = x²/2 + C

4) f(x) = 6x² -2x⁻²

F(x) = 6x³/3 -2x⁻¹+ C = 2x³ -2/x + C

5) f(x) = 9/x¹⁰ + 2/x⁹ = 9x⁻¹⁰ + 2x⁻⁹

F(x) = 9x⁻⁹/-9 + 2x⁻⁸/-8 + C = -1/x⁹ -1/(4x⁸) + C