Question

What is `f(x) = int x^2e^(x-1)-x^3e^-x dx` if `f(2) = 7`?

Answer 1

your integral is given by
`x^3e^-x+x^2e^(x-1)+3x^2e^(-x)-2xe^(x-1)+6e^(-x)x+2e^(x-1)+6e^(-x)+C`

Explanation:

I have got this after several times integrating by parts.
We get `C` by the following equation
`38e^(-2)+2e+C=7`