Integrate : ∫x2ex dx – InterviewSolution

1.

Integrate : ∫x2ex dx

Answer»

Let I = ∫x²e^x dx

= x²∫e^x dx - ∫{(dx²/dx) ∫x²e^x} dx

= x²e^x - ∫2x e^x dx

= x²e^x - 2∫xe^x dx

= x²e^x - 2[x∫e^x dx - ∫(dx/dx) x (e^x) dx

= x²e^x - 2[xe^x- ∫e^x] dx

= x²e^x - 2[xe^x - e^x] + c

= x²e^x - 2xe^x - e^x + c

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