Integral dari sin^3 2x dx

InTegraL

∫sin³ 2x dx
= ∫sin² 2x . sin 2x dx
= -1/2 ∫(1 - cos² 2x) dcos 2x
= -1/2 (cos 2x - 1/3 cos³ 2x) + C
= -1/6 (3 cos 2x - 2 cos³ 2x) + C

∫sin³ 2x dx
= ∫sin² 2x . sin 2x dx
= ∫(1 - cos² 2x) sin 2x dx

Mis u = cos 2x
du /dx = 2 (-sin 2x)
du/ ( -2 sin 2x)= dx

= ∫(1 - cos² 2x) sin 2x dx
= ∫(1 - u² ) sin 2x ×( du/ ( -2 sin 2x) )
= ∫(1 - u² )du / -2
=-1/2 ( u - 1/3 u³) +c
= -1/2 (cos 2x - 1/3 cos³ 2x) + C
= -1/2 cos 2x + 1/6 cos³ 2x + C