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1/(1-cos(x))
Solving integrals/ 1/(1-cos(x))

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

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The solution

You have entered [src] 
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 |      1        
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 |  1 - cos(x)   
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∫0111−cos⁡(x) dx\int\limits_{0}^{1} \frac{1}{1 - \cos{\left(x \right)}}\, dx 
Integral(1/(1 - cos(x)), (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

    11−cos⁡(x)=−1cos⁡(x)−1\frac{1}{1 - \cos{\left(x \right)}} = - \frac{1}{\cos{\left(x \right)} - 1}

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

    ∫(−1cos⁡(x)−1) dx=−∫1cos⁡(x)−1 dx\int \left(- \frac{1}{\cos{\left(x \right)} - 1}\right)\, dx = - \int \frac{1}{\cos{\left(x \right)} - 1}\, dx

    1. Don't know the steps in finding this integral.

      But the integral is

      1tan⁡(x2)\frac{1}{\tan{\left(\frac{x}{2} \right)}}

    So, the result is: −1tan⁡(x2)- \frac{1}{\tan{\left(\frac{x}{2} \right)}}

  3. Add the constant of integration:

    −1tan⁡(x2)+constant- \frac{1}{\tan{\left(\frac{x}{2} \right)}}+ \mathrm{constant}

The answer is:

−1tan⁡(x2)+constant- \frac{1}{\tan{\left(\frac{x}{2} \right)}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                          
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 | 1 - cos(x)             /x\
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∫11−cos⁡(x) dx=C−1tan⁡(x2)\int \frac{1}{1 - \cos{\left(x \right)}}\, dx = C - \frac{1}{\tan{\left(\frac{x}{2} \right)}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-200000000200000000
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The answer [src] 
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The graph
Integral of 1/(1-cos(x)) dx

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

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