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Identical expressions
one /(one -cos(six *x))
1 divide by (1 minus co sinus of e of (6 multiply by x))
one divide by (one minus co sinus of e of (six multiply by x))
1/(1-cos(6x))
1/1-cos6x
1 divide by (1-cos(6*x))
1/(1-cos(6*x))dx
Similar expressions
1/(1-cos6x)
1/(1+cos(6*x))

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

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

Rewrite the integrand:

$\frac{1}{1 - \cos{\left(6 x \right)}} = - \frac{1}{\cos{\left(6 x \right)} - 1}$
The integral of a constant times a function is the constant times the integral of the function:

$\int \left(- \frac{1}{\cos{\left(6 x \right)} - 1}\right)\, dx = - \int \frac{1}{\cos{\left(6 x \right)} - 1}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{1}{6 \tan{\left(3 x \right)}}$
So, the result is: $- \frac{1}{6 \tan{\left(3 x \right)}}$
Add the constant of integration:

$- \frac{1}{6 \tan{\left(3 x \right)}}+ \mathrm{constant}$

The answer is:

- \frac{1}{6 \tan{\left(3 x \right)}}+ \mathrm{constant}

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)}}

Simplify

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.

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

Limits of integration:

The graph:

Piecewise:

The solution