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

Limits of integration:

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The solution

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

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