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- Is the integral of e to the t the same as the derivative?

If I take the exponential function e^t and take the derivative, I think I get the same e^t. Even if I keep doing it over and over, second, third derivative, etc. My admittedly naive question, though, is this symmetric? Meaning...if I take the the integral of e^t, do I just get the reverse or do I have t deal with an infinity of constants because it is an indefinite integral?