Integral of x+y+1 dx

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

Integral(x + y + 1, (x, 0, 1))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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$$\int \left(\left(x + y\right) + 1\right)\, dx = C + \frac{x^{2}}{2} + x y + x$$

Simplify

The answer [src]

3/2 + y

$$y + \frac{3}{2}$$

3/2 + y

$$y + \frac{3}{2}$$

3/2 + y

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