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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of y^2e^{-y}

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

y = \frac{10}{x}

\frac{d}{d x} (tan (\frac{x}{2}) - cot (\frac{x}{2}))

\int (2 x - 3) (4 x^{2} + 1) d x

\frac{d}{d x} (\frac{5 x}{x - 2})

x \to - 2 lim (\frac{7}{x ^{2}})

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