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Similar expressions
y(x^2-y^2)

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

The solution

You have entered [src]

  1               
  /               
 |                
 |    / 2    2\   
 |  y*\x  + y / dx
 |                
/                 
0

$$\int\limits_{0}^{1} y \left(x^{2} + y^{2}\right)\, dx$$

Integral(y*(x^2 + y^2), (x, 0, 1))

Detail solution

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

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

 3   y
y  + -
     3

$$y^{3} + \frac{y}{3}$$

 3   y
y  + -
     3

$$y^{3} + \frac{y}{3}$$

y^3 + y/3

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

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

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The solution