Question

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

Answer 1

`f(x)=1/4x^4-1/2x^2+xe^x-e^x+11/4`

Explanation:

`f(x)=intx^3-x+xe^x` `dx`

Integrate each term separately:

`f(x)=1/4x^4-1/2x^2+xe^x-e^x+"c"`

`f(1)=1/4(1)^4-1/2(1)^2+1e^1-e^1+"c"=3`

`"c"=11/4`

`f(x)=1/4x^4-1/2x^2+xe^x-e^x+11/4`