Вычислить неопределенный интеграл x3sin2x dx

U = x3
dv = sin2xdx
du = 3x2 dx
v = - 12 cos 2x
x3sin2x dx = - 12x3cos 2x+32*x2cos2x dx
Для интеграла x2cos2x dx:
u = x2
dv = cos2xdx
du = 2x dx
v = 12 sin 2x
- 12x3cos 2x+32*x2cos2x dx = - 12x3cos 2x + 34x2sin2x-32*xsin2x dx
Для интеграла xsin2x dx:
u = x
dv = sin2xdx
du = dx
v = -12 cos 2x
- 12x3cos 2x + 34x2sin2x-32*xsin2x dx =- 12x3cos 2x + 34x2sin2x+ 34xcos2x - 34 *cos 2x dx = - 12x3cos 2x++ 34x2sin2x+34xcos2x-38sin2x+c
5.2