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xctg^2x

Integral of xctg^2x dx

Limits of integration:

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The solution

You have entered [src]
  1             
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 |       2      
 |  x*cot (x) dx
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01xcot2(x)dx\int\limits_{0}^{1} x \cot^{2}{\left(x \right)}\, dx
Integral(x*cot(x)^2, (x, 0, 1))
The answer (Indefinite) [src]
  /                                                               
 |                     2      /       2   \                       
 |      2             x    log\1 + tan (x)/     x                 
 | x*cot (x) dx = C - -- - ---------------- - ------ + log(tan(x))
 |                    2           2           tan(x)              
/                                                                 
(sin2(2x)+cos2(2x)2cos(2x)+1)log(sin2x+cos2x+2cosx+1)+(sin2(2x)+cos2(2x)2cos(2x)+1)log(sin2x+cos2x2cosx+1)x2sin2(2x)4xsin(2x)x2cos2(2x)+2x2cos(2x)x22sin2(2x)+2cos2(2x)4cos(2x)+2{{\left(\sin ^2\left(2\,x\right)+\cos ^2\left(2\,x\right)-2\,\cos \left(2\,x\right)+1\right)\,\log \left(\sin ^2x+\cos ^2x+2\,\cos x+1 \right)+\left(\sin ^2\left(2\,x\right)+\cos ^2\left(2\,x\right)-2\, \cos \left(2\,x\right)+1\right)\,\log \left(\sin ^2x+\cos ^2x-2\, \cos x+1\right)-x^2\,\sin ^2\left(2\,x\right)-4\,x\,\sin \left(2\,x \right)-x^2\,\cos ^2\left(2\,x\right)+2\,x^2\,\cos \left(2\,x\right) -x^2}\over{2\,\sin ^2\left(2\,x\right)+2\,\cos ^2\left(2\,x\right)-4 \,\cos \left(2\,x\right)+2}}
The graph
0.001.000.100.200.300.400.500.600.700.800.90-500010000
The answer [src]
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Numerical answer [src]
43.7757497717895
43.7757497717895
The graph
Integral of xctg^2x dx

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