Integral of xcosxydy dy

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  2              
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 |  x*cos(x)*y dy
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1

$$\int\limits_{1}^{2} y x \cos{\left(x \right)}\, dy$$

Integral((x*cos(x))*y, (y, 1, 2))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                       2       
 |                     x*y *cos(x)
 | x*cos(x)*y dy = C + -----------
 |                          2     
/

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

Simplify

The answer [src]

3*x*cos(x)
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    2

$$\frac{3 x \cos{\left(x \right)}}{2}$$

3*x*cos(x)
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    2

$$\frac{3 x \cos{\left(x \right)}}{2}$$

3*x*cos(x)/2

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

Integral of x*cosx*ydy dy