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Identical expressions
x+xy^ two
x plus xy squared
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x+xy^2dx
Similar expressions
x-xy^2

Integral of x+xy^2 dx

The solution

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

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

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

Detail solution

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

$\frac{x^{2} \left(y^{2} + 1\right)}{2}$
Add the constant of integration:

$\frac{x^{2} \left(y^{2} + 1\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(y^{2} + 1\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

$$\frac{y^{2}}{2} + \frac{1}{2}$$

$$\frac{y^{2}}{2} + \frac{1}{2}$$

1/2 + y^2/2

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

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Integral of x+xy^2 dx

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The solution