Question

Show that `intx²( e^x -1 )dx = x²e^x -2xe^x +2e^x -(x^3)/3 + c`?

Answer 1

Voilá

Explanation:

`I = intx^2(e^x-1)dx`

Rewriting it

`I = intx^2e^x - x^2dx`

`I = intx^2e^xdx - x^3/3`

For the first integral say `u = x^2` so `du = 2x` and `dv = v = e^x`

`I = x^2e^x - 2intxe^xdx - x^3/3`

Say that `u = x` so `du = 1` and `dv = v = e^x`

`I = x^2e^x - 2(xe^x - inte^xdx) - x^3/3`

`I = x^2e^x - 2xe^x + 2e^x - x^3/3 + c`