Exploring the Indefinite Integral of e^U | Integration Rule and Solution Explanation

∫ e^U dU

The integral ∫ e^U dU represents the anti-derivative or the indefinite integral of the function e^U with respect to U

The integral ∫ e^U dU represents the anti-derivative or the indefinite integral of the function e^U with respect to U.

To integrate ∫ e^U dU, we can use a simple rule of integration. The integral of e^U is simply e^U, so the anti-derivative of e^U is e^U, plus a constant C.

Therefore, the solution to the integral ∫ e^U dU is e^U + C, where C is the constant of integration.

It’s important to note that adding the constant C is necessary because when we differentiate e^U, we get back e^U. However, there could be infinitely many functions whose derivative is e^U, and by adding the constant C, we are capturing all possible solutions.

So, in summary:
∫ e^U dU = e^U + C

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