1. The problem statement, all variables and given/known data Integrate: 4cos(x/2).cos(x).sin(21x/2) 2. Relevant equations ▪sin(A+B)=sinAcosB+sinBcosA ▪2sinAcosA=sin2A And obviously, ▪Integration of sinx is (-cosx) ▪Integration of cosx is (sinx) 3. The attempt at a solution ○I multiplied the numerator and denominator with sin(x/2) ○The numerator simplified to sin(2x)sin(21x/2) and in the denominator,we have sin(x/2). ○Now,I expanded sin(21x/2) by breaking 21x/2 into 10x and x/2 and using the above specified formula,which,on simplifying gives two terms. ○Now,the first term comes out to be sin2xcos10x,which can be integrated easily (well,maybe not one step but at least it can be done),but the second term is: sin(2x).sin(10x).cot(x/2) How to integrate this term,it just eludes me..