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Solving integrals/ cos5xcos3x

Integral of cos5xcos3x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                     
 --                     
 2                      
  /                     
 |                      
 |  cos(5*x)*cos(3*x) dx
 |                      
/                       
pi                      
--                      
8
$$\int\limits_{\frac{\pi}{8}}^{\frac{\pi}{2}} \cos{\left(3 x \right)} \cos{\left(5 x \right)}\, dx$$ 
Integral(cos(5*x)*cos(3*x), (x, pi/8, pi/2))
The answer (Indefinite) [src] 
  /                                              
 |                            sin(2*x)   sin(8*x)
 | cos(5*x)*cos(3*x) dx = C + -------- + --------
 |                               4          16   
/
$$\int \cos{\left(3 x \right)} \cos{\left(5 x \right)}\, dx = C + \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(8 x \right)}}{16}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
      ___________      ___________ 
     /       ___      /       ___  
    /  1   \/ 2      /  1   \/ 2   
-  /   - - ----- *  /   - + -----  
 \/    2     4    \/    2     4    
-----------------------------------
                 2
$$- \frac{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2}$$ 
=
= 
      ___________      ___________ 
     /       ___      /       ___  
    /  1   \/ 2      /  1   \/ 2   
-  /   - - ----- *  /   - + -----  
 \/    2     4    \/    2     4    
-----------------------------------
                 2
$$- \frac{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2}$$ 
-sqrt(1/2 - sqrt(2)/4)*sqrt(1/2 + sqrt(2)/4)/2
Numerical answer [src] 
-0.176776695296637
-0.176776695296637

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

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