`f(x) = e^2` Find the most general antiderivative of the function. (Check your answer by differentiation.)

Textbook Question

Chapter 4, 4.9 - Problem 10 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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`e^2` isn't depend on x, so its antiderivative is `x*e^2.` The general antiderivative is

`x*e^2+C,`

where C is any constant.

Let's check:

`(x*e^2+C)'=x'*e^2+C'=1*e^2+0=e^2.`

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