How to calculate $\int_{0}^{\infty} \frac{e^{itx}}{(1+x^{c})^{k+1}} \, \mathrm{d}x $?

Question

I was calculating a characteristic function and I couldn't compute this integral: $$\int_{0}^{\infty} \frac{e^{itx}}{(1+x^{c})^{k+1}} \, \mathrm{d}x $$ Where $k,c>0$, any hint would be of great help.