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Integral of 1/(sin(x+pi/3)^2) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
 pi                
 --                
 6                 
  /                
 |                 
 |       1         
 |  ------------ dx
 |     2/    pi\   
 |  sin |x + --|   
 |      \    3 /   
 |                 
/                  
0                  
$$\int\limits_{0}^{\frac{\pi}{6}} \frac{1}{\sin^{2}{\left(x + \frac{\pi}{3} \right)}}\, dx$$
Integral(1/(sin(x + pi/3)^2), (x, 0, pi/6))
The answer (Indefinite) [src]
  /                         /x   pi\                
 |                       tan|- + --|                
 |      1                   \2   6 /         1      
 | ------------ dx = C + ----------- - -------------
 |    2/    pi\               2             /x   pi\
 | sin |x + --|                        2*tan|- + --|
 |     \    3 /                             \2   6 /
 |                                                  
/                                                   
$$\int \frac{1}{\sin^{2}{\left(x + \frac{\pi}{3} \right)}}\, dx = C + \frac{\tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{2} - \frac{1}{2 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}$$
The graph
The answer [src]
  ___
\/ 3 
-----
  3  
$$\frac{\sqrt{3}}{3}$$
=
=
  ___
\/ 3 
-----
  3  
$$\frac{\sqrt{3}}{3}$$
sqrt(3)/3
Numerical answer [src]
0.577350269189626
0.577350269189626

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