Fourier transform

try to take x=2t and use the symmetry or duality property and then the scaling property

 

Use the fact that your expression can be expressed as [tex]\int{\frac{f(t)}{g(t)}dx}[/tex], where [tex]f(t) = e^{-j\omega t}, g(t)=1+4t^{2}[/tex] and proceed as stated by the rule. If i remember it correctly it goes something like [tex]\frac{f'(t)g(t)-g'(t)f(t)}{g(t)^{2}}[/tex]

 

You've mixed up differentiation and integration...

 

manchot is right ... so complicated ... i think the properties of the fourier transformation is better

 

damn.... you're right ;)

 

check the scaling and the symmetry property ... sorry i can't tell the answer ... it is the rules ...