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Integral of 2x+y^2 dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src]
  2              
 y               
  /              
 |               
 |  /       2\   
 |  \2*x + y / dx
 |               
/                
 3               
y                
$$\int\limits_{y^{3}}^{y^{2}} \left(2 x + y^{2}\right)\, dx$$
Integral(2*x + y^2, (x, y^3, y^2))
Detail solution
  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is when :

      So, the result is:

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                             
 |                              
 | /       2\           2      2
 | \2*x + y / dx = C + x  + x*y 
 |                              
/                               
$$\int \left(2 x + y^{2}\right)\, dx = C + x^{2} + x y^{2}$$
The answer [src]
   5    6      4
- y  - y  + 2*y 
$$- y^{6} - y^{5} + 2 y^{4}$$
=
=
   5    6      4
- y  - y  + 2*y 
$$- y^{6} - y^{5} + 2 y^{4}$$
-y^5 - y^6 + 2*y^4

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