Question Detail

To evaluate ∫ Cos³ x dx, we first rewrite Cos³ x as Cos² x * Cos x.∫ Cos³ x dx = ∫ Cos² x * Cos x dxNow, use the trigonometric identity Cos² x = 1 - Sin² x:= ∫ (1 - Sin² x) Cos x dxNext, use a substitution. Let u = sin x. Then, du = d/dx(sin x) dx = cos x dx.Substitute u and du into the integral:= ∫ (1 - u²) duIntegrate with respect to u:= u - (u³/3) + CFinally, substitute back u = sin x:= sin x - (sin³ x)/3 + C.This matches option A.