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Solving integrals/ cosx/(1-cosx)

Integral of cosx/(1-cosx) dx

The solution

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  1              
  /              
 |               
 |    cos(x)     
 |  ---------- dx
 |  1 - cos(x)   
 |               
/                
0

$$\int\limits_{0}^{1} \frac{\cos{\left(x \right)}}{1 - \cos{\left(x \right)}}\, dx$$

Integral(cos(x)/(1 - cos(x)), (x, 0, 1))

Detail solution

Rewrite the integrand:

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

$\int \left(- \frac{\cos{\left(x \right)}}{\cos{\left(x \right)} - 1}\right)\, dx = - \int \frac{\cos{\left(x \right)}}{\cos{\left(x \right)} - 1}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $x + \frac{1}{\tan{\left(\frac{x}{2} \right)}}$
So, the result is: $- x - \frac{1}{\tan{\left(\frac{x}{2} \right)}}$
Add the constant of integration:

$- x - \frac{1}{\tan{\left(\frac{x}{2} \right)}}+ \mathrm{constant}$

The answer is:

$- x - \frac{1}{\tan{\left(\frac{x}{2} \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                               
 |   cos(x)                  1   
 | ---------- dx = C - x - ------
 | 1 - cos(x)                 /x\
 |                         tan|-|
/                             \2/

$$\int \frac{\cos{\left(x \right)}}{1 - \cos{\left(x \right)}}\, dx = C - x - \frac{1}{\tan{\left(\frac{x}{2} \right)}}$$

Simplify

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Plot the graph f(x)

The answer [src]

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The graph

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

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Integral of cosx/(1-cosx) dx

Limits of integration:

The graph:

Piecewise:

The solution