What is the integral of-e^xx^2 ?

The integral of-e^xx^2 is -e^xx^2+2e^xx-2e^x+C

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integral of-e^xx^2

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \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}))

Simplify

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

= - e^{x} x^{2} + 2 e^{x} x - 2 e^{x}

Add a constant to the solution

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

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