The problem is t(x)=I(0)exp(-a(x)) which is also roughly equal to =I(0)[1-a(x)] but what if we have s(x)=t(xo-m*cos(wt))

find the fourier transform of s(x):

which is given by:

S(y)= int(s(x)*exp(-i*x*y))dx

= int(t(xo-m*cos(wt)*exp(-i*xo*y))dxo

and now is where i get lost the next line in the solution is:

= exp(-i*m*y*cos(wt))*int(t(xo)*exp(-i*xo*y))dxo

i dont understand how they took out the mcos(wt) from the integration, can someone help giving me direction to get to this line before continuing