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Solving integrals/ sqrt((1+cot^(2)x))

Integral of sqrt((1+cot^(2)x)) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
 pi                    
 --                    
 2                     
  /                    
 |                     
 |     _____________   
 |    /        2       
 |  \/  1 + cot (x)  dx
 |                     
/                      
pi                     
--                     
6
∫π6π2cot⁡2(x)+1 dx\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{2}} \sqrt{\cot^{2}{\left(x \right)} + 1}\, dx 
Integral(sqrt(1 + cot(x)^2), (x, pi/6, pi/2))
The answer (Indefinite) [src]
−log⁡(sin⁡2x+cos⁡2x+2 cos⁡x+1)−log⁡(sin⁡2x+cos⁡2x−2 cos⁡x+1)2-{{\log \left(\sin ^2x+\cos ^2x+2\,\cos x+1\right)-\log \left(\sin ^2x+\cos ^2x-2\,\cos x+1\right)}\over{2}}
Simplify
The answer [src] 
 pi                    
 --                    
 2                     
  /                    
 |                     
 |     _____________   
 |    /        2       
 |  \/  1 + cot (x)  dx
 |                     
/                      
pi                     
--                     
6
∫π6π2cot⁡2(x)+1 dx\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{2}} \sqrt{\cot^{2}{\left(x \right)} + 1}\, dx 
=
= 
 pi                    
 --                    
 2                     
  /                    
 |                     
 |     _____________   
 |    /        2       
 |  \/  1 + cot (x)  dx
 |                     
/                      
pi                     
--                     
6
∫π6π2cot⁡2(x)+1 dx\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{2}} \sqrt{\cot^{2}{\left(x \right)} + 1}\, dx
Simplify
Numerical answer [src] 
1.31695789692482
1.31695789692482

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

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