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1/(sin(x)-cos(x))

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

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |  sin(x) - cos(x)   
 |                    
/                     
0                     
$$\int\limits_{0}^{1} \frac{1}{\sin{\left(x \right)} - \cos{\left(x \right)}}\, dx$$
Integral(1/(sin(x) - cos(x)), (x, 0, 1))
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. Now simplify:

  4. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                           ___    /      ___      /x\\     ___    /      ___      /x\\
 |                          \/ 2 *log|1 - \/ 2  + tan|-||   \/ 2 *log|1 + \/ 2  + tan|-||
 |        1                          \               \2//            \               \2//
 | --------------- dx = C + ----------------------------- - -----------------------------
 | sin(x) - cos(x)                        2                               2              
 |                                                                                       
/                                                                                        
$$\int \frac{1}{\sin{\left(x \right)} - \cos{\left(x \right)}}\, dx = C - \frac{\sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{2} + \frac{\sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{2}$$
The graph
Numerical answer [src]
1.02684047752354
1.02684047752354
The graph
Integral of 1/(sin(x)-cos(x)) dx

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