Integral of xye^x+y dx

The solution

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  1                
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 |  /     x    \   
 |  \x*y*E  + y/ dx
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/                  
0

$$\int\limits_{0}^{1} \left(e^{x} x y + y\right)\, dx$$

Integral((x*y)*E^x + y, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\left(x y - y\right) e^{x}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int y\, dx = x y$
The result is: $x y + \left(x y - y\right) e^{x}$
Now simplify:

$y \left(x + \left(x - 1\right) e^{x}\right)$
Add the constant of integration:

$y \left(x + \left(x - 1\right) e^{x}\right)+ \mathrm{constant}$

The answer is:

$y \left(x + \left(x - 1\right) e^{x}\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                          
 | /     x    \                            x
 | \x*y*E  + y/ dx = C + x*y + (-y + x*y)*e 
 |                                          
/

$$\int \left(e^{x} x y + y\right)\, dx = C + x y + \left(x y - y\right) e^{x}$$

Simplify

The answer [src]

2*y

$$2 y$$

2*y

$$2 y$$

2*y

Use the examples entering the upper and lower limits of integration.

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Integral of xye^x+y dx

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The solution