allery∫ x e^x dx (by parts: u = x, dv = e^x dx):
Ae^x × x²
Bx e^x - e^x + C = e^x (x - 1) + C
Ce^x / x
Dx² e^x
Answer & Solution
Correct answer: B. x e^x - e^x + C = e^x (x - 1) + C
u = x, du = dx; dv = e^x dx, v = e^x.
We have ∫ x e^x dx = x e^x - ∫ e^x.
Then dx = x e^x - e^x + C.
So dx = (x - 1) e^x + C.
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