the characteristic function of a random variable X is:
$$\Phi_X(\omega)=1-|\omega|\;\text{for}\;|\omega|<1$$ $$\Phi_X(\omega)=0\;\text{for}\;|\omega|>1$$
How to find the pdf of X?
I have started by using the Fourier transform inversion formula $$f_X(x)=\frac{1}{2\pi}\int\Phi_X(\omega)e^{-i\omega x}d\omega$$ how to do the rest? Thank you in advance.