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

1 Answer
Jun 17, 2016

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