Using integration by parts, ∫x eˣ dx equals:

Using integration by parts, ∫x eˣ dx equals:

• A. x eˣ − eˣ + C
• B. eˣ + C
• C. x eˣ + eˣ + C
• D. eˣ(x − 1) + C

Answer: A) x eˣ − eˣ + C

Explanation: ILATE rule: u = x (algebraic), dv = eˣ dx. du = dx, v = eˣ. ∫x eˣ dx = x eˣ − ∫eˣ dx = x eˣ − eˣ + C. Option 3 is also equivalent but option 0 is the direct result.