Integral of xdy+y dx

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  2           
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 |  (x + y) dy
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3

$$\int\limits_{3}^{2} \left(x + y\right)\, dy$$

Integral(x + y, (y, 3, 2))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int x\, dy = x y$
1. The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int y\, dy = \frac{y^{2}}{2}$
The result is: $x y + \frac{y^{2}}{2}$
Now simplify:

$\frac{y \left(2 x + y\right)}{2}$
Add the constant of integration:

$\frac{y \left(2 x + y\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{y \left(2 x + y\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                  2      
 |                  y       
 | (x + y) dy = C + -- + x*y
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$$\int \left(x + y\right)\, dy = C + x y + \frac{y^{2}}{2}$$

Simplify

The answer [src]

-5/2 - x

$$- x - \frac{5}{2}$$

-5/2 - x

$$- x - \frac{5}{2}$$

-5/2 - x

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