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Solving integrals/ (x^2+2xy)

Integral of (x^2+2xy) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Integrate term-by-term:

    1. The integral of is when :

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

      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:

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                               
 |                        3       
 | / 2        \          x       2
 | \x  + 2*x*y/ dx = C + -- + y*x 
 |                       3        
/
$$\int \left(x^{2} + 2 x y\right)\, dx = C + \frac{x^{3}}{3} + x^{2} y$$
Simplify
The answer [src] 
19/3 + 5*y
$$5 y + \frac{19}{3}$$ 
=
= 
19/3 + 5*y
$$5 y + \frac{19}{3}$$ 
19/3 + 5*y

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

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