Помогите, пожалуйста, вычислить интеграл:
int (-pi 0) (x^2 - x + 1) * cos x dx

int (-pi 0) (x^2 - x + 1) * cos x dx = int (-pi 0) (x^2 - x + 1) d(sin x) =
= ((x^2 - x + 1) * sin x)_{-pi}^{0} - int (-pi 0) sin x d(x^2 - x + 1) =
= ((0^2 - 0 + 1) * sin 0 - ((-pi)^2 - (-pi) + 1) * sin (-pi)) -
- int (-pi 0) (2 * x - 1) * sin x dx = int (-pi 0) (2 * x - 1) d(cos x) dx =
= ((2 * x - 1) * cos x)_{-pi}^{0} - int (-pi 0) cos x d(2 * x - 1) =
= ((2 * 0 - 1) * cos 0 - (2 * (-pi) - 1) * cos (-pi)) - 2 * int (-pi 0) cos x dx =
= (-1 + 2 * (-pi) - 1) - 2 * (sin x)_{-pi}^{0} =
= -2 - 2 * pi - 2 * (sin 0 - sin (-pi)) = -2 - 2 * pi