tlng siii lg butuh bgt tlng yg baik

InTegraL Parsial

∫x³ cos x dx
= x³ sin x - (3x² . -cos x) + (6x . -sin x) - (6 . cos x) + C
= x³ sin x + 3x² cos x - 6x sin x - 6 cos x + C
= (x sin x)(x² - 6) + (3x cos x)(x - 2) + C

Int parsial
dengan  ∫ u dv = uv - ∫ v du

u = x³ → du = 3x²
dv = cos x dx → v = sin x
∫x³ cos x dx  = x³ sin x - ∫ 3x² sin x dx.

u = 3x² → du = 6x
dv = sin x dx → v = - cos x
∫3x² sin x dx = 3x² (-cos x) - ∫ 6x (-cos x)  dx

u = 6x → du = 6
dx = - cos x → v = - sin x
∫6x  cos x dx = 6x (-sin x) - ∫ 6 (-sin x) dx

u = 6 → du = 0
dv = -sin  x dx → v = cos x
∫6 (-sin x) dx = 6 (cos x)
.
∫x³ cos x dx =
= x³ sin x - ∫3x² sinx dx
= x³ sin x - (- 3x² cos x - ∫6x cos x dx )
= x³ sin x + 3x² cos x  + ( -6x sin x - ∫6(-sin x) dx)
= x³ sin x + 3x² cos x  - 6x sin x - 6 cos x + c
= (x³ - 6x) sin x  + (3x² - 6) cos x + c
= x(x² -6) sin x + 3(x² -2) cos x + c