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Identical expressions
x^ two +3xy^ two
x squared plus 3xy squared
x to the power of two plus 3xy to the power of two
x2+3xy2
x²+3xy²
x to the power of 2+3xy to the power of 2
x^2+3xy^2dx
Similar expressions
x^2-3xy^2

Integral of x^2+3xy^2 dx

The solution

You have entered [src]

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

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

Integral(x^2 + (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 $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 3 x y^{2}\, dx = y^{2} \int 3 x\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 3 x\, dx = 3 \int x\, dx$
    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: $\frac{3 x^{2}}{2}$
  So, the result is: $\frac{3 x^{2} y^{2}}{2}$
The result is: $\frac{x^{3}}{3} + \frac{3 x^{2} y^{2}}{2}$
Now simplify:

$\frac{x^{2} \left(2 x + 9 y^{2}\right)}{6}$
Add the constant of integration:

$\frac{x^{2} \left(2 x + 9 y^{2}\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(2 x + 9 y^{2}\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

       2
1   3*y 
- + ----
3    2

$$\frac{3 y^{2}}{2} + \frac{1}{3}$$

       2
1   3*y 
- + ----
3    2

$$\frac{3 y^{2}}{2} + \frac{1}{3}$$

1/3 + 3*y^2/2

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

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Integral of x^2+3xy^2 dx

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The solution