Find all antiderivatives of the following function.
\[
f(x)=e^{-7 x}
\]
\[
\int f(x) d x=
\]

Step 1 ：We are asked to find the antiderivative of the function \(f(x) = e^{-7x}\).

Step 2 ：The antiderivative of \(e^{ax}\), where \(a\) is a constant, is \(\frac{1}{a}e^{ax}\). Therefore, the antiderivative of \(e^{-7x}\) should be \(-\frac{1}{7}e^{-7x}\).

Step 3 ：However, the antiderivative is not unique. The general antiderivative of a function includes a constant of integration, usually denoted as \(C\). Therefore, the general antiderivative of \(e^{-7x}\) should be \(-\frac{1}{7}e^{-7x} + C\).

Step 4 ：Final Answer: The general antiderivative of the function \(f(x) = e^{-7x}\) is \(\boxed{-\frac{1}{7}e^{-7x} + C}\).