Question

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

Answer 1

`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`