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Solving integrals/ xarcctg(x/3)

Integral of xarcctg(x/3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ___            
 \/ 3             
   /              
  |               
  |         /x\   
  |   x*acot|-| dx
  |         \3/   
  |               
 /                
 0
$$\int\limits_{0}^{\sqrt{3}} x \operatorname{acot}{\left(\frac{x}{3} \right)}\, dx$$ 
Integral(x*acot(x/3), (x, 0, sqrt(3)))
The answer (Indefinite) [src] 
  /                               /x\    2     /x\
 |                          9*acot|-|   x *acot|-|
 |       /x\          3*x         \3/          \3/
 | x*acot|-| dx = C + --- + --------- + ----------
 |       \3/           2        2           2     
 |                                                
/
$$\int x \operatorname{acot}{\left(\frac{x}{3} \right)}\, dx = C + \frac{x^{2} \operatorname{acot}{\left(\frac{x}{3} \right)}}{2} + \frac{3 x}{2} + \frac{9 \operatorname{acot}{\left(\frac{x}{3} \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
           ___
  pi   3*\/ 3 
- -- + -------
  4       2
$$- \frac{\pi}{4} + \frac{3 \sqrt{3}}{2}$$ 
=
= 
           ___
  pi   3*\/ 3 
- -- + -------
  4       2
$$- \frac{\pi}{4} + \frac{3 \sqrt{3}}{2}$$ 
-pi/4 + 3*sqrt(3)/2
Numerical answer [src] 
1.81267804795587
1.81267804795587

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

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