Question

What is `f(x) = int 3x^2+xe^(x)dx` if `f(0)=3`?

Answer 1

I found: `f(x)=x^3+e^x(x-1)+4`

Explanation:

Let us solve the integral first:
`int(3x^2+xe^x)dx=3x^3/3+xe^x-int1e^xdx=`
`=x^3+xe^x-e^x+c`

let us use the condition `f(0)=3` so that for `x=0` we have:

`3=0^3+0e^0-e^0+c`
`3=-1+c`

so that:

`c=4`

finally:
`f(x)=x^3+xe^x-e^x+4=x^3+e^x(x-1)+4`