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The general antiderivative of $\cos x$ is $\sin x + C$, and the general antiderivative of $e^x$ is $e^x + C$. In both cases, $C$ represents an arbitrary constant, indicating that any vertical shift of these base functions is also a valid antiderivative.

Conditions: The variable is $x$.; The domain is all real numbers (or a connected interval thereof).

The general antiderivative of $\cos x$ is $\sin x + C$, and the general antiderivative of $e^x$ is $e^x + C$. In both cases, $C$ represents an arbitrary constant, indicating that any vertical shift of these base functions is also a valid antiderivative.

Conditions: The variable is $x$.; The domain is all real numbers (or a connected interval thereof).