In the book "Signals and Systems" by Alan V. Oppenheim, it proves that the Inverse Fourier Transform
$$x(t) = \frac{1}{2\pi}\int_{-\infty}^{+\infty} X(jw)e^{jwt}dw,$$
is the derived from Fourier Series when $T\rightarrow \infty$. However, for some reason, the Inverse Fourier Transform is used for periodic signals. Why? Since $T\rightarrow \infty$ is for aperiodic signals.