Fourier transform of $f(x)=-2e^{-x}+3e^{-2x}$

Question

I am trying to find FT of the function $$f(x)=-2e^{-x}+3e^{-2x}$$. we have $$F(w)=\int_{-\infty}^{\infty}\left(-2 e^{-x}+3 e^{-2 x}\right) e^{-i \omega x} d x$$ $\implies$ $$F(w)=-2 \int_{-\infty}^{\infty} e^{-(1+i \omega) x} d x+3 \int_{-\infty}^{\infty} e^{-(2+i \omega) x} d x$$ But after integration, the lower limits are bothering me?