Is the following valid? $|x(t)|^2$

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$x(t)=\int_{-\infty} ^{\infty} X(jw)e^{jwt}dw$.

Where $X(jw)$ is the fourier transform of $x(t)$.

What is $|x(t)|^2$?

Can I say, it is $|\int_{-\infty} ^{\infty} X(jw)e^{jwt}dw|^2$, which is again, equal to $\int_{-\infty} ^{\infty}| X(jw)|^2|e^{jwt}|^2dw$= $\int_{-\infty} ^{\infty} |X(jw)|^2dw$

Is this valid?