e^xdx
The expression “e^xdx” represents an integral
The expression “e^xdx” represents an integral. Specifically, it represents the indefinite integral of the exponential function e^x with respect to the variable x.
To find the antiderivative (or primitive) of e^x, we can use a basic property of the exponential function. The derivative of e^x with respect to x is simply e^x itself. Hence, the antiderivative of e^x is also e^x.
Therefore, the integral of e^xdx is equal to e^x plus a constant of integration (C):
∫e^xdx = e^x + C
This equation means that if you differentiate e^x + C with respect to x, you will get e^x.
It is important to note that indefinite integrals are not unique, as they have an infinite number of solutions differing by a constant value. Hence, the inclusion of the constant of integration (C) accounts for all possible solutions.
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