# Is the following system time-invariant or time-varying?

I was wondering if the following system is time-invariant or time-varying $$y(t)=e^{-t}\int_{0}^{t}e^{\sigma}x(\sigma+1)d\sigma$$ I know that it's not causal, and I think it's time-varying because of that $$\e^{-t}\$$ before the integral that makes the input delay and the delay of the output not equal, I am not sure if I am right.

Thank you.

• $e^{-t}$ is not a delay, and does not render the system time variant (confusing with $e^{-sT}$)? What function of $\sigma$ is $x(\sigma +1)$? – Chu Apr 19 at 9:32
• @Chu x(t) is the input, the variable is formally changed to a dummy integration variable to avoid double meanings. Variable t is used as integration limit. – user287001 Apr 19 at 10:16