Solution
: Step 1: Let u = x and dv = ex dx. We find that du = dx and v = ò dv = ò ex dx = ex.Step 2: Substitute these variables into the formula:
ò
xex dx = ò u dv = uv - ò v du = xex - ò ex dx.Step 3: Integrate the integral by using the eu Rule:
xex - ò ex dx = xex - ex + C.
Step 4: Check the result:
(xex - ex + C) = (1 ex + xex) - ex = xex.