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Solving integrals/ 1/(sinx-cosx-1)

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                       
 --                       
 2                        
  /                       
 |                        
 |           1            
 |  ------------------- dx
 |  sin(x) - cos(x) - 1   
 |                        
/                         
0
$$\int\limits_{0}^{\frac{\pi}{2}} \frac{1}{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) - 1}\, dx$$ 
Integral(1/(sin(x) - cos(x) - 1), (x, 0, pi/2))
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. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                             
 |                                              
 |          1                      /        /x\\
 | ------------------- dx = C + log|-1 + tan|-||
 | sin(x) - cos(x) - 1             \        \2//
 |                                              
/
$$\int \frac{1}{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) - 1}\, dx = C + \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
-oo - pi*I
$$-\infty - i \pi$$ 
=
= 
-oo - pi*I
$$-\infty - i \pi$$ 
-oo - pi*i
Numerical answer [src] 
-37.330070373877
-37.330070373877

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

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