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2x^2+2y^2
Identical expressions
two x^ two +2y^2
2x squared plus 2y squared
two x to the power of two plus 2y squared
2x2+2y2
2x²+2y²
2x to the power of 2+2y to the power of 2
2x^2+2y^2dx
Similar expressions
2x^2-2y^2

Integral of 2x^2+2y^2 dx

The solution

You have entered [src]

  x                 
  /                 
 |                  
 |  /   2      2\   
 |  \2*x  + 2*y / dx
 |                  
/                   
 2                  
x

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

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

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

     6      3                   
  2*x    2*x       2  2        2
- ---- + ---- - 2*x *y  + 2*x*y 
   3      3

$$- \frac{2 x^{6}}{3} + \frac{2 x^{3}}{3} - 2 x^{2} y^{2} + 2 x y^{2}$$

     6      3                   
  2*x    2*x       2  2        2
- ---- + ---- - 2*x *y  + 2*x*y 
   3      3

$$- \frac{2 x^{6}}{3} + \frac{2 x^{3}}{3} - 2 x^{2} y^{2} + 2 x y^{2}$$

-2*x^6/3 + 2*x^3/3 - 2*x^2*y^2 + 2*x*y^2

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

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Integral of 2x^2+2y^2 dx

Limits of integration:

The graph:

Piecewise:

The solution