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xarcctg^2x
Solving integrals/ xarcctg^2x

Integral of xarcctg^2x dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |        2      
 |  x*acot (x) dx
 |               
/                
0
$$\int\limits_{0}^{1} x \operatorname{acot}^{2}{\left(x \right)}\, dx$$ 
Integral(x*acot(x)^2, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                    
 |                         2         /     2\                2     2   
 |       2             acot (x)   log\1 + x /               x *acot (x)
 | x*acot (x) dx = C + -------- + ----------- + x*acot(x) + -----------
 |                        2            2                         2     
/
$${{\log \left(x^2+1\right)-\arctan ^2x}\over{2}}+{\rm arccot}\; x\, \left(x-\arctan x\right)+{{x^2\,\left({\rm arccot}\; x\right)^2 }\over{2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
           2     
log(2)   pi    pi
------ - --- + --
  2       16   4
$${{8\,\log 2-\pi^2+4\,\pi}\over{16}}$$ 
=
= 
           2     
log(2)   pi    pi
------ - --- + --
  2       16   4
$$- \frac{\pi^{2}}{16} + \frac{\log{\left(2 \right)}}{2} + \frac{\pi}{4}$$
Упростить
Numerical answer [src] 
0.515121478609336
0.515121478609336
The graph
Integral of xarcctg^2x dx

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

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