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Integral of (sin(2021)x)/(pi*sin(x)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 pi               
  /               
 |                
 |  sin(2021)*x   
 |  ----------- dx
 |   pi*sin(x)    
 |                
/                 
0                 
$$\int\limits_{0}^{\pi} \frac{x \sin{\left(2021 \right)}}{\pi \sin{\left(x \right)}}\, dx$$
Integral(sin(2021)*x/((pi*sin(x))), (x, 0, pi))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Don't know the steps in finding this integral.

      But the integral is

    So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
                          /                   
                         |                    
                         |   x                
                         | ------ dx*sin(2021)
  /                      | sin(x)             
 |                       |                    
 | sin(2021)*x          /                     
 | ----------- dx = C + ----------------------
 |  pi*sin(x)                     pi          
 |                                            
/                                             
$$-{{\sin 2021\,\left(x\,\log \left(\sin ^2x+\cos ^2x+2\,\cos x+1 \right)-x\,\log \left(\sin ^2x+\cos ^2x-2\,\cos x+1\right)+2\,i\,x\, {\rm atan2}\left(\sin x , \cos x+1\right)+2\,i\,x\,{\rm atan2}\left( \sin x , 1-\cos x\right)+2\,i\,{\it li}_{2}(e^{i\,x})-2\,i\,{\it li} _{2}(-e^{i\,x})\right)}\over{2\,\pi}}$$
The answer [src]
 pi                    
  /                    
 |                     
 |    x                
 |  ------ dx*sin(2021)
 |  sin(x)             
 |                     
/                      
0                      
-----------------------
           pi          
$$\frac{\sin{\left(2021 \right)} \int\limits_{0}^{\pi} \frac{x}{\sin{\left(x \right)}}\, dx}{\pi}$$
=
=
 pi                    
  /                    
 |                     
 |    x                
 |  ------ dx*sin(2021)
 |  sin(x)             
 |                     
/                      
0                      
-----------------------
           pi          
$$\frac{\sin{\left(2021 \right)} \int\limits_{0}^{\pi} \frac{x}{\sin{\left(x \right)}}\, dx}{\pi}$$
Numerical answer [src]
-30.4929541152786
-30.4929541152786

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