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Similar expressions
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Integral of tan^2x÷(1-sinx) dx

The solution

You have entered [src]

  1              
  /              
 |               
 |      2        
 |   tan (x)     
 |  ---------- dx
 |  1 - sin(x)   
 |               
/                
0

$$\int\limits_{0}^{1} \frac{\tan^{2}{\left(x \right)}}{1 - \sin{\left(x \right)}}\, dx$$

Integral(tan(x)^2/(1 - sin(x)), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{\tan^{2}{\left(x \right)}}{1 - \sin{\left(x \right)}} = - \frac{\tan^{2}{\left(x \right)}}{\sin{\left(x \right)} - 1}$
The integral of a constant times a function is the constant times the integral of the function:

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

$- \int \frac{\tan^{2}{\left(x \right)}}{\sin{\left(x \right)} - 1}\, dx+ \mathrm{constant}$

The answer is:

$- \int \frac{\tan^{2}{\left(x \right)}}{\sin{\left(x \right)} - 1}\, dx+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

   1               
   /               
  |                
  |       2        
  |    tan (x)     
- |  ----------- dx
  |  -1 + sin(x)   
  |                
 /                 
 0

$$- \int\limits_{0}^{1} \frac{\tan^{2}{\left(x \right)}}{\sin{\left(x \right)} - 1}\, dx$$

   1               
   /               
  |                
  |       2        
  |    tan (x)     
- |  ----------- dx
  |  -1 + sin(x)   
  |                
 /                 
 0

$$- \int\limits_{0}^{1} \frac{\tan^{2}{\left(x \right)}}{\sin{\left(x \right)} - 1}\, dx$$

-Integral(tan(x)^2/(-1 + sin(x)), (x, 0, 1))

Numerical answer [src]

2.18835955652192

2.18835955652192

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

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Integral of tan^2x÷(1-sinx) dx

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The graph:

Piecewise:

The solution