.quote=cron1003;494214]PLEASE HELP ME TO SOLVE THIS PROBLEM
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Try this
Using the formula
sinCsinD = 1/2[cos(C-D) -cos(C+D)]
cosCsinD = 1/2[sin(C+D) - sin(C-D)]
You get
sinx*sin2x*sin3x = 1/2*sin2x(cos2x - cos4x)
= 1/2[ sin2x*cos2x -sin2x*cos4x]
= 1/4[sin4x + sin2x - sin6x]
Now find the integration of each term.