1) -4∫cos x sin 3x cos 3x dx ? 2) ∫4x (3x-2)³ dx ?

Integral Tak Tentu

1) -4 ∫ cos x  sin 3x  cos 3x dx
= - 4∫ cos x { 1/2 ( 2 sin 3x cos 3x)} dx
= - 4(1/2) ∫ cos x . sin 6x dx
= - 2 ∫ 1/2( 2 sin 6x cos x) dx
= - 2(1/2) ∫ sin 7/2x + sin 5/2 x
= - ∫sin 7/2 x + sin 5/2 x
= -[ (-2/7) cos 7/2 x - 2/5 cos 5/2 x ]
= 2/7 cos 7/2 x + 2/5 cos 5/2 x + c

2) ∫4x (3x-2)³ dx
parsial.....
def...........int
4x........ ...(3x-2)³
4...........1/3 (1/4)(3x-2)⁴
0...........1/3. 1/4. 1/3. 1/5. (3x-2)⁵
=
= 4x(1/3)(1/4)(3x-2)⁴ - 4(1/3)(1/4)(1/3)(1/5)(3x-2)⁵ + c
= 1/3 x(3x-2)⁴ - 1/45 (3x-2)⁵ + c
= 1/45 (3x-2)⁴ { 15x  - (3x-2)} + c
= 1/45 (3x-2)⁴ (15x - 3x +2) + c
= 1/45 (3x-2)⁴ (12x +2) + c
= 1/45 (3x-2)⁴ (2)(6x +1) + c
= 2/45 (3x-2)⁴ (6x +1) + c