int (-1 0) (x^2 + 2 * x + 1) * sin 3x dx = int (-1 0) (x^2 + 2 * x + 1) d(-1/3 * cos 3x) =
= -1/3 * int (-1 0) (x^2 + 2 * x + 1) d(cos 3x) =
= -1/3 * ((x^2 + 2 * x + 1) * cos 3x)_{-1}^{0} +
+ 1/3 * int (-1 0) cos 3x d(x^2 + 2 * x + 1) =
= -1/3 * ((0^2 + 2 * 0 + 1) * cos 0 - ((-1)^2 + 2 * (-1) + 1) * cos (-3)) +
+ 1/3 * int (-1 0) (2 * x + 2) * cos 3x dx =
= -1/3 + 1/3 * int (-1 0) (2 * x + 2) d(1/3 * sin 3x) =
= -1/3 + 1/9 * int (-1 0) (2 * x + 2) d(sin 3x) =
= -1/3 + 1/9 * ((2 * x + 2) * sin 3x)_{-1}^{0} - 1/9 * int (-1 0) sin 3x d(2 * x + 2) =
= -1/3 + 1/9 * ((2 * 0 + 2) * sin 0 - (2 * (-1) + 2) * sin (-3)) - 2/9 * int (-1 0) sin 3x dx =
= -1/3 - 2/9 * int (-1 0) sin 3x dx = -1/3 - 2/9 * (-1/3 * cos 3x)_{-1}^{0} =
= -1/3 - 2/9 * (-1/3 * cos 0 + 1/3 * cos (-3)) = -1/3 - 2/9 * (-1/3 + 1/3 * cos 3) =
= -1/3 + 2/27 - 2/27 * cos 3 = -9/27 + 2/27 - 2/27 * cos 3 =
= -7/27 - 2/27 * cos 3 = 1/27 * (-7 - 2 * cos 3)