Integral of xsinxydy dy

You have entered [src]

 pi              
  /              
 |               
 |  x*sin(x)*y dy
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/                
0

\int\limits_{0}^{\pi} y x \sin{\left(x \right)}\, dy

Integral((x*sin(x))*y, (y, 0, pi))

Detail solution

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

$\int y x \sin{\left(x \right)}\, dy = x \sin{\left(x \right)} \int y\, dy$
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: $\frac{x y^{2} \sin{\left(x \right)}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

    2       
x*pi *sin(x)
------------
     2

\frac{\pi^{2} x \sin{\left(x \right)}}{2}

    2       
x*pi *sin(x)
------------
     2

\frac{\pi^{2} x \sin{\left(x \right)}}{2}

x*pi^2*sin(x)/2

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