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Integral of arctan(1/(x-1)) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src]
  2               
  /               
 |                
 |      /  1  \   
 |  atan|-----| dx
 |      \x - 1/   
 |                
/                 
-2                
$$\int\limits_{-2}^{2} \operatorname{atan}{\left(\frac{1}{x - 1} \right)}\, dx$$
Integral(atan(1/(x - 1)), (x, -2, 2))
The answer (Indefinite) [src]
                           /       2    \      /   2    \                      
  /                     log|2 + --------|   log|--------|                      
 |                         |           2|      |       2|                      
 |     /  1  \             \    (x - 1) /      \(x - 1) /               /  1  \
 | atan|-----| dx = C + ----------------- - ------------- + (x - 1)*atan|-----|
 |     \x - 1/                  2                 2                     \x - 1/
 |                                                                             
/                                                                              
$$\int \operatorname{atan}{\left(\frac{1}{x - 1} \right)}\, dx = C + \left(x - 1\right) \operatorname{atan}{\left(\frac{1}{x - 1} \right)} + \frac{\log{\left(2 + \frac{2}{\left(x - 1\right)^{2}} \right)}}{2} - \frac{\log{\left(\frac{2}{\left(x - 1\right)^{2}} \right)}}{2}$$
The graph
The answer [src]
log(2)                 log(10)   pi
------ - 3*atan(1/3) - ------- + --
  2                       2      4 
$$- \frac{\log{\left(10 \right)}}{2} - 3 \operatorname{atan}{\left(\frac{1}{3} \right)} + \frac{\log{\left(2 \right)}}{2} + \frac{\pi}{4}$$
=
=
log(2)                 log(10)   pi
------ - 3*atan(1/3) - ------- + --
  2                       2      4 
$$- \frac{\log{\left(10 \right)}}{2} - 3 \operatorname{atan}{\left(\frac{1}{3} \right)} + \frac{\log{\left(2 \right)}}{2} + \frac{\pi}{4}$$
log(2)/2 - 3*atan(1/3) - log(10)/2 + pi/4
Numerical answer [src]
-0.929529371656556
-0.929529371656556

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