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Solving integrals/ x*arcctg(x/5)

Integral of x*arcctg(x/5) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |        /x\   
 |  x*acot|-| dx
 |        \5/   
 |              
/               
0
∫01xacot⁡(x5) dx\int\limits_{0}^{1} x \operatorname{acot}{\left(\frac{x}{5} \right)}\, dx 
Integral(x*acot(x/5), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                /x\    2     /x\
 |                          25*acot|-|   x *acot|-|
 |       /x\          5*x          \5/          \5/
 | x*acot|-| dx = C + --- + ---------- + ----------
 |       \5/           2        2            2     
 |                                                 
/
∫xacot⁡(x5) dx=C+x2acot⁡(x5)2+5x2+25acot⁡(x5)2\int x \operatorname{acot}{\left(\frac{x}{5} \right)}\, dx = C + \frac{x^{2} \operatorname{acot}{\left(\frac{x}{5} \right)}}{2} + \frac{5 x}{2} + \frac{25 \operatorname{acot}{\left(\frac{x}{5} \right)}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90040
Plot the graph f(x)
The answer [src] 
5                  25*pi
- + 13*acot(1/5) - -----
2                    4
−25π4+52+13acot⁡(15)- \frac{25 \pi}{4} + \frac{5}{2} + 13 \operatorname{acot}{\left(\frac{1}{5} \right)} 
=
= 
5                  25*pi
- + 13*acot(1/5) - -----
2                    4
−25π4+52+13acot⁡(15)- \frac{25 \pi}{4} + \frac{5}{2} + 13 \operatorname{acot}{\left(\frac{1}{5} \right)} 
5/2 + 13*acot(1/5) - 25*pi/4
Numerical answer [src] 
0.719255885348998
0.719255885348998

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

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