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Question
Integrate the function in `x^2e^x`.
Solution
Let `I = int x^2 e^x dx`
Put u = x2, v = ex
`int uv dx = u int v dx - int( (du)/dx int v dx) dx`
`= x^2 int e^x dx - int (2x).e^x dx`
`= x^2 e^x - 2 int xe^x dx`
We define the first function by integrating multiple parts.
`I = x^2 e^x - 2 [x int e^x dx - int (d/dx x. int e^x dx)]`
`= x^2 e^x - 2 [xe^x - 2 int 1.e^x dx]`
`= x^2 e^x - 2x e^x + 2e^x + C`
`= e^x (x^2 - 2x + 2) + C`
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