Integral of 1/(1-sinx) dx

The solution

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  1                
  /                
 |                 
 |        1        
 |  1*---------- dx
 |    1 - sin(x)   
 |                 
/                  
0

$$\int\limits_{0}^{1} 1 \cdot \frac{1}{- \sin{\left(x \right)} + 1}\, dx$$

Simplify

Detail solution

Rewrite the integrand:

$1 \cdot \frac{1}{1 - \sin{\left(x \right)}} = - \frac{1}{\sin{\left(x \right)} - 1}$
The integral of a constant times a function is the constant times the integral of the function:

$\int \left(- \frac{1}{\sin{\left(x \right)} - 1}\right)\, dx = - \int \frac{1}{\sin{\left(x \right)} - 1}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{2}{\tan{\left(\frac{x}{2} \right)} - 1}$
So, the result is: $- \frac{2}{\tan{\left(\frac{x}{2} \right)} - 1}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                 
 |                                  
 |       1                    2     
 | 1*---------- dx = C - -----------
 |   1 - sin(x)                  /x\
 |                       -1 + tan|-|
/                                \2/

$$-{{2}\over{{{\sin x}\over{\cos x+1}}-1}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

           2      
-2 - -------------
     -1 + tan(1/2)

$$-{{2\,\cos 1}\over{\sin 1-\cos 1-1}}-{{2}\over{\sin 1-\cos 1-1}}-2$$

           2      
-2 - -------------
     -1 + tan(1/2)

$$-2 - \frac{2}{-1 + \tan{\left(\frac{1}{2} \right)}}$$

Simplify

Numerical answer [src]

2.40822344233583

2.40822344233583

The graph

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

Other calculators

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Identical expressions

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Integral of 1/(1-sinx) dx

Limits of integration:

The graph:

Piecewise:

The solution