Integral of y+x dx

The solution

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      ____          
 -2*\/ -x           
     /              
    |               
    |     (y + x) dx
    |               
   /                
   -4

$$\int\limits_{-4}^{- 2 \sqrt{- x}} \left(x + y\right)\, dx$$

Integral(y + x, (x, -4, -2*sqrt(-x)))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                  2      
 |                  x       
 | (y + x) dx = C + -- + x*y
 |                  2       
/

$$\int \left(x + y\right)\, dx = C + \frac{x^{2}}{2} + x y$$

Simplify

The answer [src]

                       ____
-8 - 2*x + 4*y - 2*y*\/ -x

$$- 2 x - 2 y \sqrt{- x} + 4 y - 8$$

                       ____
-8 - 2*x + 4*y - 2*y*\/ -x

$$- 2 x - 2 y \sqrt{- x} + 4 y - 8$$

-8 - 2*x + 4*y - 2*y*sqrt(-x)

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

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Integral of y+x dx

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