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

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

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integral of xye^{x+y}

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

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

Solution steps

\int 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

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{( a x + b y ( x ) )}{( c x + d y )})

(x^{2} - 2) (x^{3} - 3 x)

\int \frac{tan ( 3 x )}{cos ( 3 x )} d x

5 y^{^{''}} + y^{^{'}} = - 10 x, y (0) = 0, y^{^{'}} (0) = - 15

f (x) = \frac{2 x + 1}{x + 2}, (1, 1)

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