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Integral of 1/(sin(4x-1)^2) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |     2            
 |  sin (4*x - 1)   
 |                  
/                   
0                   
$$\int\limits_{0}^{1} \frac{1}{\sin^{2}{\left(4 x - 1 \right)}}\, dx$$
Integral(1/(sin(4*x - 1)^2), (x, 0, 1))
The answer (Indefinite) [src]
  /                                                          
 |                                                           
 |       1                        1           tan(-1/2 + 2*x)
 | ------------- dx = C - ----------------- + ---------------
 |    2                   8*tan(-1/2 + 2*x)          8       
 | sin (4*x - 1)                                             
 |                                                           
/                                                            
$$\int \frac{1}{\sin^{2}{\left(4 x - 1 \right)}}\, dx = C + \frac{\tan{\left(2 x - \frac{1}{2} \right)}}{8} - \frac{1}{8 \tan{\left(2 x - \frac{1}{2} \right)}}$$
The graph
The answer [src]
  1                  
  /                  
 |                   
 |        1          
 |  -------------- dx
 |     2             
 |  sin (-1 + 4*x)   
 |                   
/                    
0                    
$$\int\limits_{0}^{1} \frac{1}{\sin^{2}{\left(4 x - 1 \right)}}\, dx$$
=
=
  1                  
  /                  
 |                   
 |        1          
 |  -------------- dx
 |     2             
 |  sin (-1 + 4*x)   
 |                   
/                    
0                    
$$\int\limits_{0}^{1} \frac{1}{\sin^{2}{\left(4 x - 1 \right)}}\, dx$$
Integral(sin(-1 + 4*x)^(-2), (x, 0, 1))
Numerical answer [src]
2393.84009872817
2393.84009872817

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