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Similar expressions
5/sin(x-pi/3)^2

Integral of 5/sin(x+pi/3)^2 dx

The solution

You have entered [src]

 pi                
 --                
 3                 
  /                
 |                 
 |       5         
 |  ------------ dx
 |     2/    pi\   
 |  sin |x + --|   
 |      \    3 /   
 |                 
/                  
0

$$\int\limits_{0}^{\frac{\pi}{3}} \frac{5}{\sin^{2}{\left(x + \frac{\pi}{3} \right)}}\, dx$$

Integral(5/sin(x + pi/3)^2, (x, 0, pi/3))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{5}{\sin^{2}{\left(x + \frac{\pi}{3} \right)}}\, dx = 5 \int \frac{1}{\sin^{2}{\left(x + \frac{\pi}{3} \right)}}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{\tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{2} - \frac{1}{2 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}$
So, the result is: $\frac{5 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{2} - \frac{5}{2 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}$
Add the constant of integration:

$\frac{5 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{2} - \frac{5}{2 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}+ \mathrm{constant}$

The answer is:

$\frac{5 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{2} - \frac{5}{2 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                           /x   pi\
 |                                       5*tan|- + --|
 |      5                      5              \2   6 /
 | ------------ dx = C - ------------- + -------------
 |    2/    pi\               /x   pi\         2      
 | sin |x + --|          2*tan|- + --|                
 |     \    3 /               \2   6 /                
 |                                                    
/

$$\int \frac{5}{\sin^{2}{\left(x + \frac{\pi}{3} \right)}}\, dx = C + \frac{5 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{2} - \frac{5}{2 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

     ___
10*\/ 3 
--------
   3

$$\frac{10 \sqrt{3}}{3}$$

     ___
10*\/ 3 
--------
   3

$$\frac{10 \sqrt{3}}{3}$$

10*sqrt(3)/3

Numerical answer [src]

5.77350269189626

5.77350269189626

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

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Integral of 5/sin(x+pi/3)^2 dx

Limits of integration:

The graph:

Piecewise:

The solution