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

1 Answer
Dec 9, 2017

f(x)=e^(2x-1)/2+e^(3-x)+e^x+3-e^3/2+e+e^2
f(x)=e^(2x-1)/2+e^(3-x)+e^x+3.06456947

Explanation:

Using inte^(ax+b)dx=e^(ax+b)/a

Our integration gives us:
f(x)=e^(2x-1)/2+e^(3-x)+e^x+C

We also know that e^(2(2)-1)/2+e^(3-2)+e^2+C=3

e^3/2+e+e^2+C=3

C=3-e^3/2+e+e^2~~3.06456947

f(x)=e^(2x-1)/2+e^(3-x)+e^x+3-e^3/2+e+e^2
f(x)=e^(2x-1)/2+e^(3-x)+e^x+3.06456947