What is the integral of 2xye^{x+y} ?

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

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integral of 2xye^{x+y}

\int 2 x y e^{x + y} d x

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

Solution steps

\int 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 e^{y + x} x d x

Apply Integration By Parts

: e^{y + x} x - \int e^{y + x} d x

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

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

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

Add a constant to the solution

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

y^{^{'}} = - y t + 0.1 y^{^{'}} t + 4

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

\int 8 x (x^{7} - \frac{1}{8}) d x

x \to \frac{π}{3} lim (sin (x))

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