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Similar expressions
x^2-2*y

Integral of x^2+2*y dx

The solution

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

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

Integral(x^2 + 2*y, (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 is the constant times the variable of integration:
  
  $\int 2 y\, dx = 2 x y$
The result is: $\frac{x^{3}}{3} + 2 x y$
Now simplify:

$\frac{x \left(x^{2} + 6 y\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} + 6 y\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} + 6 y\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

1/3 + 2*y

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

1/3 + 2*y

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

1/3 + 2*y

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

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Integral of x^2+2*y dx

Limits of integration:

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Piecewise:

The solution