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

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

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
 pi                   
 --                   
 3                    
  /                   
 |                    
 |         1          
 |  --------------- dx
 |  cos(x) - sin(x)   
 |                    
/                     
0
$$\int\limits_{0}^{\frac{\pi}{3}} \frac{1}{- \sin{\left(x \right)} + \cos{\left(x \right)}}\, dx$$ 
Integral(1/(cos(x) - sin(x)), (x, 0, pi/3))
The answer (Indefinite) [src] 
  /                           ___    /      ___      /x\\     ___    /      ___      /x\\
 |                          \/ 2 *log|1 + \/ 2  + tan|-||   \/ 2 *log|1 - \/ 2  + tan|-||
 |        1                          \               \2//            \               \2//
 | --------------- dx = C + ----------------------------- - -----------------------------
 | cos(x) - sin(x)                        2                               2              
 |                                                                                       
/
$$\int \frac{1}{- \sin{\left(x \right)} + \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{2} - \frac{\sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
nan
$$\text{NaN}$$ 
=
= 
nan
$$\text{NaN}$$ 
nan
Numerical answer [src] 
-12.6679530080806
-12.6679530080806

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

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