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

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Answer 1 · 2016-11-14T12:46:59

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

We have # f(x)=int5e^(2x)-2e^x-xdx #

Integrating gives us:

# f(x) = 5/2e^(2x) - 2e^x - x^2/2 + C #

We know #f(4)=1#, so

# 5/2e^8 - 2e^4 - 16/2 + C = 1 #
# :. C = 9 - 5/2e^8 + 2e^4 #

Hence,

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