DB45
∫ 6x sin(2x - π) dx = 6 ∫ x (- sin 2x) dx = -6 ∫ x sin 2x dx
def .......int x ...........sin (2x) 1 .......-1/2 cos 2x 0 ......-1/4 sin 2x = -1/2x cos 2x + 1/4 sin 2x = -1/2 cos 2x + 1/4 (2) sin x cos x = -1/2 cos 2x + 1/2 sin x cos x - 6∫ x sin 2x dx = -6 {-1/2 x cos 2x + 1/2 sin x cos x) = 3x cos x - 3 sin x cos x + c
= -6 ∫ x sin 2x dx
def .......int
x ...........sin (2x)
1 .......-1/2 cos 2x
0 ......-1/4 sin 2x
= -1/2x cos 2x + 1/4 sin 2x
= -1/2 cos 2x + 1/4 (2) sin x cos x
= -1/2 cos 2x + 1/2 sin x cos x
- 6∫ x sin 2x dx = -6 {-1/2 x cos 2x + 1/2 sin x cos x)
= 3x cos x - 3 sin x cos x + c