Question

What is `f(x) = int 5x-2xe^(x)dx` if `f(0)=-2`?

Answer 1

`f(x)=int5x*dx-int2x*e^x*dx`

`=5/2*x^2-(2x*e^x-int2e^x*dx)`

`=5/2*x^2-(2x-2)*e^x+C`

Let `x=0`, `C+2=-2`, hence `C=-4`.

Thus, `f(x)=5/2*x^2-(2x-2)*e^x-4`

Explanation:

1) Take integral.

2) Impose `f(0)=-2` condition.