- #1

Tanishq Nandan

- 122

- 5

## Homework Statement

Integrate: 4cos(x/2).cos(x).sin(21x/2)

## Homework Equations

▪sin(A+B)=sinAcosB+sinBcosA

▪2sinAcosA=sin2A

And obviously,

▪Integration of sinx is (-cosx)

▪Integration of cosx is (sinx)

## 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..