Integral of xy+1 dy

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  4             
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 |  (x*y + 1) dy
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2

$$\int\limits_{2}^{4} \left(x y + 1\right)\, dy$$

Integral(x*y + 1, (y, 2, 4))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                          2
 |                        x*y 
 | (x*y + 1) dy = C + y + ----
 |                         2  
/

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

Simplify

The answer [src]

2 + 6*x

$$6 x + 2$$

2 + 6*x

$$6 x + 2$$

2 + 6*x

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