# What is #f(x) = int e^(2x-1)-e^(3-x)+e^-x dx# if #f(2) = 3 #?

First we have to integrate

the integral is

so, it follows

Solving for C integration constant

Our final answer

God bless....I hope the explanation is useful.

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The function ( f(x) = \int e^{2x-1} - e^{3-x} + e^{-x} , dx ) satisfies ( f(2) = 3 ).

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