Mister Exam

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Integral of d{x}:
Integral of x^2*dx
Integral of x²dx
Integral of csc(x)
Integral of arctan(1/x)
Identical expressions
- two xy^2
minus 2xy squared
minus two xy squared
-2xy2
-2xy²
-2xy to the power of 2
-2xy^2dx
Similar expressions
2xy^2

Solving integrals/ -2xy^2

Integral of -2xy^2 dx

The solution

You have entered [src]

  1           
  /           
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 |        2   
 |  -2*x*y  dx
 |            
/             
0

$$\int\limits_{0}^{1} - 2 x y^{2}\, dx$$

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

Detail solution

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

$\int - 2 x y^{2}\, dx = y^{2} \int \left(- 2 x\right)\, dx$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 2 x\right)\, dx = - 2 \int x\, dx$
  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: $- x^{2}$
So, the result is: $- x^{2} y^{2}$
Add the constant of integration:

$- x^{2} y^{2}+ \mathrm{constant}$

The answer is:

$- x^{2} y^{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int - 2 x y^{2}\, dx = C - x^{2} y^{2}$$

Simplify

The answer [src]

  2
-y

$$- y^{2}$$

=

  2
-y

$$- y^{2}$$

-y^2

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