integral 6 cos² 1/3x dx

2 cos² (1/3 x) = 1 + cos 2(1/3 x)
3 . 2 cos² (1/3 x) = 3(1 + cos (2/3 x))
6cos² (1/3 x) = 3(1 + cos (2/3 x))

∫6cos² (1/3 x) dx
= 3 ∫(1 + cos (2/3 x)) dx
= 3(x + 3/2 ∫dsin (2/3 x))
= 3x + 9/2 sin (2/3 x) + C

INtegral TriGonmerI

∫ 6 cos² (1/3 x) dx =
= 3 ∫ 2 cos² (1/3 x) dx
= 3 ∫ cos 2(1/3 x) + 1  dx
= 3 ∫ cos (2/3 x)  + 1 dx
= 3 { 3/2  sin (2/3 x) + x} + c
= 9/2 sin (2/3 x )  +  3x + c