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Solving integrals/ 6*x*y

Integral of 6xy dx

The solution

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$$\int\limits_{0}^{1} 6 x y\, dx$$

Integral((6*x)*y, (x, 0, 1))

Detail solution

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

$\int 6 x y\, dx = y \int 6 x\, dx$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 6 x\, dx = 6 \int x\, dx$
  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: $3 x^{2}$
So, the result is: $3 x^{2} y$
Add the constant of integration:

$3 x^{2} y+ \mathrm{constant}$

The answer is:

$3 x^{2} y+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | 6*x*y dx = C + 3*y*x 
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$$\int 6 x y\, dx = C + 3 x^{2} y$$

Simplify

The answer [src]

3*y

$$3 y$$

=

3*y

$$3 y$$

3*y

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