Find the integral of xe^(-2x) between the limits of 0 and 1 with respect to x.

We can identify xe^(-2x) as a product and hence we will most probably need to use integration by parts.

We then set u = x and v' = x^(-2x). It is important to do it this way round so that when we differentiate u we are left with u' = 1 which is what will make the second integral easier to solve.

Substitute these values into the formula for integration by parts being sure to be careful to avoid any sign errors. Finally substitute in the limits and you should get the answer of 0.25 - 0.75e^(-2)