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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int \frac{7}{x ^{2} x ^{2} + 36} d x

\int \frac{1}{x} e^{x} d x

\frac{d}{d x} (\frac{x}{3 x - 4 \cdot ln ( x )})

f (x) = x^{2} 16 - x^{2}

\frac{\partial}{\partial x} (x \cdot e^{x^{2} y})

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