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Integral of ln(1/(5-3*cos(x))) dx

Limits of integration:

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The solution

You have entered [src]
 2*pi                    
   /                     
  |                      
  |     /     1      \   
  |  log|------------| dx
  |     \5 - 3*cos(x)/   
  |                      
 /                       
 0                       
$$\int\limits_{0}^{2 \pi} \log{\left(\frac{1}{5 - 3 \cos{\left(x \right)}} \right)}\, dx$$
Integral(log(1/(5 - 3*cos(x))), (x, 0, 2*pi))
The answer (Indefinite) [src]
  /                               /                                      
 |                               |                                       
 |    /     1      \             |    x*sin(x)             /     1      \
 | log|------------| dx = C - 3* | ------------- dx + x*log|------------|
 |    \5 - 3*cos(x)/             | -5 + 3*cos(x)           \5 - 3*cos(x)/
 |                               |                                       
/                               /                                        
$$\int \log{\left(\frac{1}{5 - 3 \cos{\left(x \right)}} \right)}\, dx = C + x \log{\left(\frac{1}{5 - 3 \cos{\left(x \right)}} \right)} - 3 \int \frac{x \sin{\left(x \right)}}{3 \cos{\left(x \right)} - 5}\, dx$$
The answer [src]
 2*pi                    
   /                     
  |                      
  |     /     1      \   
  |  log|------------| dx
  |     \5 - 3*cos(x)/   
  |                      
 /                       
 0                       
$$\int\limits_{0}^{2 \pi} \log{\left(\frac{1}{5 - 3 \cos{\left(x \right)}} \right)}\, dx$$
=
=
 2*pi                    
   /                     
  |                      
  |     /     1      \   
  |  log|------------| dx
  |     \5 - 3*cos(x)/   
  |                      
 /                       
 0                       
$$\int\limits_{0}^{2 \pi} \log{\left(\frac{1}{5 - 3 \cos{\left(x \right)}} \right)}\, dx$$
Integral(log(1/(5 - 3*cos(x))), (x, 0, 2*pi))
Numerical answer [src]
-9.45039700028561
-9.45039700028561

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