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Identical expressions
x^ three +xy^ two
x cubed plus xy squared
x to the power of three plus xy to the power of two
x3+xy2
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x^3+xy^2dx
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x^3-xy^2

Integral of x^3+xy^2 dx

The solution

You have entered [src]

  1               
  /               
 |                
 |  / 3      2\   
 |  \x  + x*y / dx
 |                
/                 
0

$$\int\limits_{0}^{1} \left(x^{3} + x y^{2}\right)\, dx$$

Integral(x^3 + x*y^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{3}\, dx = \frac{x^{4}}{4}$
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: $\frac{x^{2} y^{2}}{2}$
The result is: $\frac{x^{4}}{4} + \frac{x^{2} y^{2}}{2}$
Now simplify:

$\frac{x^{2} \left(x^{2} + 2 y^{2}\right)}{4}$
Add the constant of integration:

$\frac{x^{2} \left(x^{2} + 2 y^{2}\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(x^{2} + 2 y^{2}\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                       4    2  2
 | / 3      2\          x    x *y 
 | \x  + x*y / dx = C + -- + -----
 |                      4      2  
/

$${{x^2\,y^2}\over{2}}+{{x^4}\over{4}}$$

Simplify

The answer [src]

$${{2\,y^2+1}\over{4}}$$

$$\frac{y^{2}}{2} + \frac{1}{4}$$

Simplify

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

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Integral of x^3+xy^2 dx

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The solution