What is the integral of x^2e^{1-x} ?

The integral of x^2e^{1-x} is -e^{1-x}x^2+2(-e^{1-x}x-e^{1-x})+C

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integral of x^2e^{1-x}

\int x^{2} e^{1 - x} d x

- e^{1 - x} x^{2} + 2 (- e^{1 - x} x - e^{1 - x}) + C

Solution steps

\int x^{2} e^{1 - x} d x

Apply Integration By Parts

= - e^{1 - x} x^{2} - \int - 2 e^{1 - x} x d x

\int - 2 e^{1 - x} x d x = - 2 (- e^{1 - x} x - e^{1 - x})

= - e^{1 - x} x^{2} - (- 2 (- e^{1 - x} x - e^{1 - x}))

Simplify

= - e^{1 - x} x^{2} + 2 (- e^{1 - x} x - e^{1 - x})

Add a constant to the solution

= - e^{1 - x} x^{2} + 2 (- e^{1 - x} x - e^{1 - x}) + C

What is the integral of x^2e^{1-x} ?
The integral of x^2e^{1-x} is -e^{1-x}x^2+2(-e^{1-x}x-e^{1-x})+C