( int x e^{-x} d x )

Question

Accepted Answer

Step:1 ：Perform integration by parts: let (u=x) and (dv=e^{-x}dx), then (du=dx) and (v=-e^{-x})Step:2 ：Apply the integration by parts formula: (int x e^{-x} d x = -x e^{-x} - int(-e^{-x})dx)Step:3 ：Evaluate the integral: (int x e^{-x} d x = -x e^{-x} + e^{-x} + C)

Answer

Step: 1 ：Perform integration by parts: let (u=x) and (dv=e^{-x}dx), then (du=dx) and (v=-e^{-x})Step: 2 ：Apply the integration by parts formula: (int x e^{-x} d x = -x e^{-x} - int(-e^{-x})dx)Step: 3 ：Evaluate the integral: (int x e^{-x} d x = -x e^{-x} + e^{-x} + C)

\( \int x e^{-x} d x \)

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