Evaluate the integral using integration by parts: integral of x * e^x dx.
Answer and explanation
Correct answer: D. x * e^x - e^x + C
- Step 1: Set u = x, dv = e^x dx. Then du = dx and v = e^x.
- Step 2: Formula: integral u dv = uv - integral v du = xe^x - integral e^x dx = x*e^x - e^x + C.
Answer
x * e^x - e^x + C.
Why not the others: 'x e^x + e^x + C' adds instead of subtracting the second integral; '0.5 x^2 e^x + C' integrates both factors simultaneously; 'e^x - x * e^x + C' reverses the sign of the terms.
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