`f(x) = 5e^x - 3cosh(x)` Find the most general antiderivative of the function. (Check your answer by differentiation.)

Textbook Question

Chapter 4, 4.9 - Problem 19 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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Integrating f gives (both integrals are well-known)

`5e^x-3sinh(x)+C,`

where `C` is any constant. This is the answer.

Checking by differentiation:

`(5e^x-3sinh(x)+C)'=(5e^x)'-(3sinh(x))'+C'=5e^x-3cosh(x).`

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