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Solving integrals/ Ctg^4(x)dx

Integral of Ctg^4(x)dx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
 pi           
 --           
 2            
  /           
 |            
 |     4      
 |  cot (x) dx
 |            
/             
pi            
--            
4
∫π4π2cot⁡4(x) dx\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{2}} \cot^{4}{\left(x \right)}\, dx 
Integral(cot(x)^4, (x, pi/4, pi/2))
The answer (Indefinite) [src] 
  /                                       
 |                                   3    
 |    4                 cos(x)    cos (x) 
 | cot (x) dx = C + x + ------ - ---------
 |                      sin(x)        3   
/                                3*sin (x)
∫cot⁡4(x) dx=C+x+cos⁡(x)sin⁡(x)−cos⁡3(x)3sin⁡3(x)\int \cot^{4}{\left(x \right)}\, dx = C + x + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{3}{\left(x \right)}}{3 \sin^{3}{\left(x \right)}}
Simplify
The graph
0.800.850.900.951.001.051.101.151.201.251.301.351.401.451.501.5502
Plot the graph f(x)
The answer [src] 
  2   pi
- - + --
  3   4
−23+π4- \frac{2}{3} + \frac{\pi}{4} 
=
= 
  2   pi
- - + --
  3   4
−23+π4- \frac{2}{3} + \frac{\pi}{4} 
-2/3 + pi/4
Numerical answer [src] 
0.118731496730782
0.118731496730782

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

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