# What is #f(x) = int 5e^(2x)-2e^x-x dx# if #f(4 ) = 1 #?

# f(x) = 5/2e^(2x) - 2e^x - x^2/2 + 9 - 5/2e^8 + 2e^4 #

Integrating gives us:

Hence,

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To find ( f(x) ) given ( f(4) = 1 ), integrate the function ( 5e^{2x} - 2e^x - x ) with respect to ( x ). Then, evaluate ( f(x) ) using the given condition ( f(4) = 1 ).

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