cos 4x - cos 4a = ( 2cos^2 (2x) -1 - 2cos^2 (2a) +1)
=2(cos^2(2x)-cos^2(2a))
=2(cos2x+cos2a)(cos2x-cos2a)
=2(cos2x+cos2a)(2cos^2(x)-1 -2cos^2(a)+1)
=4(cos2x+cos2a)(cos^2 x - cos^2 a)
=(cos2x+cos2a) ( cos x + cos a)(cos x - cos a)

I =4* int [ 0 ,pi] (cos2x+cos2a) ( cos x + cos a) dx
I =4* int [ 0 ,pi] (cos 2x cosx +cos 2x cos a + cos 2a cos x + cos 2a cos a ) dx
I =4* int [ 0 ,pi] (0.5 cos 3x - 0.5 cosx +cos 2x cos a + cos 2a cos x + cos 2a cos a ) dx

but cos 2a cos a is a constant ===>
int [0,pi] cos 2a cos a dx= cos 2a cos a x fromx=0 to x = pi
= cos 2a cos a * pi - cos 2a cos a *0= pi * cos 2a cos a

int [0.pi] (0.5(cos 3x )=0.5 /3 sin 3x from x = 0 to x = pi
= 0.5/3 ( sin 3pi - sin 0)=0
so we find int[0,pi] for cos n x = 0 ===>

I = 4 * ( pi * cos 2a cos a ) .