What is the integral of (x^2)/(e^{-x)} ?

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

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integral of (x^2)/(e^{-x)}

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

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

Solution steps

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

Simplify

\frac{x ^{2}}{e ^{- x}} : e^{x} x^{2}

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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