What is the integral of 4xye^{-(2x+y)} ?

The integral of 4xye^{-(2x+y)} is 4x(-e^{-y-2x}y-e^{-y-2x})+C

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integral of 4xye^{-(2x+y)}

\int 4 x y e^{- (2 x + y)} d y

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

Solution steps

\int 4 x y e^{- (2 x + y)} d y

Take the constant out:

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

= 4 x \cdot \int e^{- (y + 2 x)} y d y

Apply Integration By Parts

= 4 x (- e^{- y - 2 x} y - \int - e^{- y - 2 x} d y)

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

= 4 x (- e^{- y - 2 x} y - e^{- y - 2 x})

Add a constant to the solution

= 4 x (- e^{- y - 2 x} y - e^{- y - 2 x}) + C

y^{^{'}} = 6 x - y

\int_{0}^{0.1} k x d x

\frac{\partial}{\partial x} (arctan (x y))

\int 2 cos^{2} (x) d x

\frac{d}{d x} (cos (e^{x^{2} c o s (x)}))

What is the integral of 4xye^{-(2x+y)} ?
The integral of 4xye^{-(2x+y)} is 4x(-e^{-y-2x}y-e^{-y-2x})+C