Mister Exam

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How to use it?
Integral of d{x}:
Integral of x^5/(x^2+1)
Integral of cos(3x)dx
Integral of (4-x^2)^0.5
Integral of 2x/(x^2+1)^2
x*(y^2)
Identical expressions
x*(y^ two)
x multiply by (y squared )
x multiply by (y to the power of two)
x*(y2)
x*y2
x*(y²)
x*(y to the power of 2)
x(y^2)
x(y2)
xy2
xy^2
x*(y^2)dx
Similar expressions
(2xy^2-2x^3)

Solving integrals/ x*(y^2)

Integral of x*(y^2) dy

The solution

You have entered [src]

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

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

Detail solution

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

$\int x y^{2}\, dy = x \int y^{2}\, dy$
1. The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int y^{2}\, dy = \frac{y^{3}}{3}$
So, the result is: $\frac{x y^{3}}{3}$
Add the constant of integration:

$\frac{x y^{3}}{3}+ \mathrm{constant}$

The answer is:

$\frac{x y^{3}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                  
 |                  3
 |    2          x*y 
 | x*y  dy = C + ----
 |                3  
/

$$\int x y^{2}\, dy = C + \frac{x y^{3}}{3}$$

Simplify

The answer [src]

x
-
3

$$\frac{x}{3}$$

=

x
-
3

$$\frac{x}{3}$$

x/3

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