What is the integral of x^2e^{x-3} ?

The integral of x^2e^{x-3} is x^2e^{x-3}-2(e^{x-3}x-e^{x-3})+C

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integral of x^2e^{x-3}

\int x^{2} e^{x - 3} d x

x^{2} e^{x - 3} - 2 (e^{x - 3} x - e^{x - 3}) + C

Solution steps

\int x^{2} e^{x - 3} d x

Apply Integration By Parts

: x^{2} e^{x - 3} - \int 2 x e^{x - 3} d x

= x^{2} e^{x - 3} - \int 2 x e^{x - 3} d x

\int 2 x e^{x - 3} d x = 2 (e^{x - 3} x - e^{x - 3})

= x^{2} e^{x - 3} - 2 (e^{x - 3} x - e^{x - 3})

Add a constant to the solution

= x^{2} e^{x - 3} - 2 (e^{x - 3} x - e^{x - 3}) + C

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What is the integral of x^2e^{x-3} ?
The integral of x^2e^{x-3} is x^2e^{x-3}-2(e^{x-3}x-e^{x-3})+C