第2008题:积化和差公式
计算不定积分 ∫cos(x)cos(2x)cos(3x)dx\int \cos (x) \cos (2x) \cos (3x) dx∫cos(x)cos(2x)cos(3x)dx .
A. −cos2x4−cos4x8-\dfrac{\cos 2x}{4}-\dfrac{\cos 4x}{8}−4cos2x−8cos4x −cos6x12−x3+C-\dfrac{\cos 6x}{12}-\dfrac{x}{3}+C−12cos6x−3x+C
B. −cos2x8−cos4x16-\dfrac{\cos 2x}{8}-\dfrac{\cos 4x}{16}−8cos2x−16cos4x −cos6x24−x4+C-\dfrac{\cos 6x}{24}-\dfrac{x}{4}+C−24cos6x−4x+C
C. sin2x4+sin4x8\dfrac{\sin 2x}{4}+\dfrac{\sin 4x}{8}4sin2x+8sin4x +sin6x12+x3+C+\dfrac{\sin 6x}{12}+\dfrac{x}{3}+C+12sin6x+3x+C
D. sin2x8+sin4x16\dfrac{\sin 2x}{8}+\dfrac{\sin 4x}{16}8sin2x+16sin4x +sin6x24+x4+C\dfrac{\sin 6x}{24}+\dfrac{x}{4}+C24sin6x+4x+C