Using integration by parts, evaluate integral( x * e^x dx ).
Answer and explanation
Correct answer: C. x * e^x - e^x + C
- Step 1: Formula: integral(u dv) = uv - integral(v du). Let u = x => du = dx; dv = e^x dx => v = e^x. Step 2. integral(x e^x dx) = x e^x - integral(e^x dx) = x e^x - e^x + C = (x - 1)e^x + C. *Answer: x e^x - e^x + C. Why not the others:** Integrating factors separately violates the product rule of differentiation.
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