evaluation of function gave a result of wrong length in integrate function

Question

I have some trouble with my functions. I tried the Vectorize function but it doesn't work,too. I couldn't solve the problem . Could anyone please help me on this matter?

a<-function(t){ 
     b<-function(x){
       c1<-function(x){
exp(2*t*cos(x)-(2*t))
 }
      c2<-function(x){
 cos(0) - cos(2*x)
 }
  c3<-function(x){
  2 - 2*cos(x)
                }
      (c1(x)*c2(x))/c3(x)
         }

exp(0)-(1/pi)*integrate(Vectorize(b), lower = 0, upper =pi)$value

      }

Thanks