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

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

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integral of x^2e^{-x/a}

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

- a e^{- \frac{x}{a}} x^{2} + 2 a (- a e^{- \frac{x}{a}} x - a^{2} e^{- \frac{x}{a}}) + C

Solution steps

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

Apply Integration By Parts

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

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

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

= - a e^{- \frac{x}{a}} x^{2} - (- 2 a (- a e^{- \frac{x}{a}} x - a^{2} e^{- \frac{x}{a}}))

Simplify

= - a e^{- \frac{x}{a}} x^{2} + 2 a (- a e^{- \frac{x}{a}} x - a^{2} e^{- \frac{x}{a}})

Add a constant to the solution

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

\int (cos (y) cos (z)) d y

\frac{d}{d x} (5 + 2 x^{2})

x^{2} - 2 x + 2, g (3) = 2 x - 2, [0, 3]

b^{2}

\frac{1}{x ^{2} + 1}

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