Question

What is `f(x) = int x^2e^x-x^2 dx` if `f(-1) = 5`?

Answer 1

`f(x)=(x^2-2x+2)*e^x-(x^3)/3+14/3-5e^(-1)`

Explanation:

`f(x)=int x^2*e^x*dx`-`int x^2*dx`

=`(x^2-2x+2)*e^x-(x^3)/3+C`

After imposing `f(-1)=5` condition,

`5e^(-1)+1/3+C=5`

Hence `C=14/3-5e^(-1)`

Thus, `f(x)=(x^2-2x+2)*e^x-(x^3)/3+14/3-5e^(-1)`

Note: I used tabular integration for first integral.