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Integral of 3x+3y dx

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 3/2              
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 |  (3*x + 3*y) dx
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0

$$\int\limits_{0}^{\frac{3}{2}} \left(3 x + 3 y\right)\, dx$$

Integral(3*x + 3*y, (x, 0, 3/2))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 3 x\, dx = 3 \int x\, dx$
  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: $\frac{3 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 3 y\, dx = 3 x y$
The result is: $\frac{3 x^{2}}{2} + 3 x y$
Now simplify:

$\frac{3 x \left(x + 2 y\right)}{2}$
Add the constant of integration:

$\frac{3 x \left(x + 2 y\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{3 x \left(x + 2 y\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        2        
 |                      3*x         
 | (3*x + 3*y) dx = C + ---- + 3*x*y
 |                       2          
/

$$\int \left(3 x + 3 y\right)\, dx = C + \frac{3 x^{2}}{2} + 3 x y$$

Simplify

The answer [src]

27   9*y
-- + ---
8     2

$$\frac{9 y}{2} + \frac{27}{8}$$

27   9*y
-- + ---
8     2

$$\frac{9 y}{2} + \frac{27}{8}$$

27/8 + 9*y/2

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

Integral of 3*x+3*y dx