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Integral of (sinx*dx)/(1-cosx) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  0              
  /              
 |               
 |    sin(x)     
 |  ---------- dx
 |  1 - cos(x)   
 |               
/                
0                
$$\int\limits_{0}^{0} \frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\, dx$$
Integral(sin(x)/(1 - cos(x)), (x, 0, 0))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. The integral of is .

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. The integral of a constant times a function is the constant times the integral of the function:

      1. Let .

        Then let and substitute :

        1. The integral of a constant times a function is the constant times the integral of the function:

          1. The integral of is .

          So, the result is:

        Now substitute back in:

      So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                   
 |                                    
 |   sin(x)                           
 | ---------- dx = C + log(1 - cos(x))
 | 1 - cos(x)                         
 |                                    
/                                     
$$\int \frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\, dx = C + \log{\left(1 - \cos{\left(x \right)} \right)}$$
The graph
The answer [src]
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Numerical answer [src]
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    Use the examples entering the upper and lower limits of integration.