Integral of (2x+y) df

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\int\limits_{0}^{2} \left(2 x + y\right)\, dy

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

Detail solution

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

$\frac{y \left(4 x + y\right)}{2}$
Add the constant of integration:

$\frac{y \left(4 x + y\right)}{2}+ \mathrm{constant}$

The answer is:

\frac{y \left(4 x + y\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src]

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

Simplify

The answer [src]

2 + 4*x

4 x + 2

2 + 4*x

4 x + 2

2 + 4*x

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