What is the integral from 0 to y of 2xye^{-x-y} ?

The integral from 0 to y of 2xye^{-x-y} is 2y(-ye^{-2y}-e^{-2y}+e^{-y})

integral from 0 to y of 2xye^{-x-y}

\int_{0}^{y} 2 x y e^{- x - y} d x

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

Solution steps

\int_{0}^{y} 2 x y e^{- x - y} d x

Take the constant out:

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

= 2 y \cdot \int_{0}^{y} e^{- y - x} x d x

Apply Integration By Parts

= 2 y [- e^{- y - x} x - \int - e^{- y - x} d x]_{0}^{y}

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

= 2 y [- e^{- y - x} x - e^{- y - x}]_{0}^{y}

Compute the boundaries:

- y e^{- 2 y} - e^{- 2 y} + e^{- y}

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

\int_{- 1}^{1} \frac{x ^{3}}{x + 2} d x

\int_{0}^{0.35} ln (1 + x^{2}) d x

\int_{0}^{l} x^{2} d x

\int_{- 2}^{2} \frac{1}{( 1 + x ) ^{2}} d x

\int_{2}^{5} \frac{1}{x x ^{2} + 1} d x

What is the integral from 0 to y of 2xye^{-x-y} ?
The integral from 0 to y of 2xye^{-x-y} is 2y(-ye^{-2y}-e^{-2y}+e^{-y})