Integral of dx/(1-sinx) dx

The solution

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

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

Integral(1/(1 - sin(x)), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{1}{1 - \sin{\left(x \right)}} = - \frac{1}{\sin{\left(x \right)} - 1}$
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     
 | ---------- dx = C - -----------
 | 1 - sin(x)                  /x\
 |                     -1 + tan|-|
/                              \2/

$$\int \frac{1}{1 - \sin{\left(x \right)}}\, dx = C - \frac{2}{\tan{\left(\frac{x}{2} \right)} - 1}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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

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

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

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

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

Numerical answer [src]

2.40822344233583

2.40822344233583

The graph

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

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Identical expressions

Similar expressions

Integral of dx/(1-sinx) dx

Limits of integration:

The graph:

Piecewise:

The solution