(define (integrate-series series)
  (define (aux series i)
    (cons-stream (/ (stream-car series) i)
                 (aux (stream-cdr series) (+ i 1))))
  (aux series 1))

; a)
; 1 ]=> (load "streams.txt")
; 
; ;Loading "streams.txt"... done
; ;Value: stream-prefix
; 
; 1 ]=> (stream-prefix (integrate-series integers) 10)
; 
; ;Value: (1 1 1 1 1 1 1 1 1 1)
; 
; 1 ]=> (stream-prefix (integrate-series ones) 10)
; 
; ;Value: (1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10)

(define exp-series
  (cons-stream 1 (integrate-series exp-series)))

; d(sin(x))/dx = cos(x)
; d(cos(x))/dx = -sin(x)
; => sin(x) = integrate cos(x)
; => cos(x) = integrate -sin(x)

(define cosine-series
  (cons-stream 1 (integrate-series (scale-stream sine-series -1))))

(define sine-series
  (cons-stream 0 (integrate-series cosine-series)))

; b)
; 1 ]=> (load "streams.txt")
; 
; ;Loading "streams.txt"... done
; ;Value: stream-prefix
; 
; 1 ]=> (stream-prefix exp-series 10)
; 
; ;Value: (1 1 1/2 1/6 1/24 1/120 1/720 1/5040 1/40320 1/362880)
; 
; 1 ]=> (stream-prefix cosine-series 10)
; 
; ;Value: (1 0 -1/2 0 1/24 0 -1/720 0 1/40320 0)
; 
; 1 ]=> (stream-prefix sine-series 10)
; 
; ;Value: (0 1 0 -1/6 0 1/120 0 -1/5040 0 1/362880)