inverse fourier transform?

Question

X(jw)=2sin(w) / w(jw+2)

hint: 1/(jw+2) <---ft---> exp(-2t)

2sin(w)/w ---------- rect={ 1 absolute value of t <1

Answer 1

Another hint: Multiplication in Fourier domain corresponds to convolution in the time domain.

You can express X(jw) = A(w)B(w) using your hints.