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Integral of 1/(1-cos(6*x)) dx

Limits of integration:

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Piecewise:

The solution

You have entered [src]
  p                
  -                
  4                
  /                
 |                 
 |       1         
 |  ------------ dx
 |  1 - cos(6*x)   
 |                 
/                  
p                  
-                  
6                  
$$\int\limits_{\frac{p}{6}}^{\frac{p}{4}} \frac{1}{1 - \cos{\left(6 x \right)}}\, dx$$
Integral(1/(1 - cos(6*x)), (x, p/6, p/4))
Detail solution
  1. Rewrite the integrand:

  2. 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:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                
 |                                 
 |      1                    1     
 | ------------ dx = C - ----------
 | 1 - cos(6*x)          6*tan(3*x)
 |                                 
/                                  
$$\int \frac{1}{1 - \cos{\left(6 x \right)}}\, dx = C - \frac{1}{6 \tan{\left(3 x \right)}}$$
The answer [src]
      1           1    
- ---------- + --------
       /3*p\        /p\
  6*tan|---|   6*tan|-|
       \ 4 /        \2/
$$- \frac{1}{6 \tan{\left(\frac{3 p}{4} \right)}} + \frac{1}{6 \tan{\left(\frac{p}{2} \right)}}$$
=
=
      1           1    
- ---------- + --------
       /3*p\        /p\
  6*tan|---|   6*tan|-|
       \ 4 /        \2/
$$- \frac{1}{6 \tan{\left(\frac{3 p}{4} \right)}} + \frac{1}{6 \tan{\left(\frac{p}{2} \right)}}$$
-1/(6*tan(3*p/4)) + 1/(6*tan(p/2))

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