Question

Найти первообразную
1) f(x) =3x^2+x-1
2) f(x) = sin (П/3-2x)
3) f(x) =e^2x

Answer 1

1.

$f(x) = 3 {x}^{2} +x - 1$

$f'(x) = 3 \times 2x + 1 = 6x + 1$

2.

$f(x) = \sin( \frac{\pi}{3} - 2x ) \\$

$f'(x) = \cos( \frac{\pi}{3} - 2x ) \times ( \frac{\pi}{3} - 2x)' = \\ = - 2 \cos( \frac{\pi}{3} - 2x)$

3.

$f(x) = {e}^{2x}$

$f'(x) = {e}^{2x} \times (2x) '= 2 {e}^{2x} \\$