Question

Integral Trigonometri.. tolong dibantu

Answer 1

1) ∫ cos 2x - 2 sin x dx = 1/2 sin 2x + 2(-cos x) + c
= 1/2 sin 2zx - 2 cos x + c

2) ∫3 - 6 sin² x dx= ∫ 3(1 - 2 sin² x) dx = 3∫ cos 2x dx
= 3/2 sin 2x + c

3) ∫4 sin 5x cos 3x dx = 2∫2 sin 5x cos 3 dx =
= 2∫ ( sin 8x + sin 2x) dx
= 2 (-1/8 cos 8x - 1/2 cos 2x)
= -1/4 cos 8x - cos 2x + c

4) ∫ sin(1/2 x - π) cos (1/2x - π)
= 1/2 ∫ 2 sin(1/2x - π) cos(1/2x - π)
= 1/2 ∫  sin 2(1/2x - π)
= 1/2 {- cos (2(1/2x - π))
= - 1/2 cos (x - 2π) + c

5) ∫ 6 sec² 3x dx = 6 tan 3x + C