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

1 Answer
Nov 14, 2016

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

Explanation:

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