Integral of 2x-y+1 dx

The solution

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 |  (2*x - y + 1) dx
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0

$$\int\limits_{0}^{1} \left(\left(2 x - y\right) + 1\right)\, dx$$

Integral(2*x - y + 1, (x, 0, 1))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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 2x-y+1 dx

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The solution