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Q.

∫cosx  cos2x  cos3x  dx  =

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a

14[16sin6x+12sin2x−14sin4x+x]+c

b

14[16sin6x−12sin2x−14sin4x−x]+c

c

14[16sin6x+12sin2x+14sin4x+x]+c

d

16sin6x+c

answer is C.

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Detailed Solution

∫cosx  cos2x  cos3x  dx  = 12∫2cosx.cos2x.cos3xdx                                           =12∫[cos3x+cosx]cos3xdx                                           =12∫cos23x+12∫cos3xcosxdx                                           =12∫1+cos6x2+14∫(cos4x+cos2x)dx                                         =14[x+16sin6x+sin4x4+12sin2x]+c
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