Mister Exam

Integral of arctg(2x-3) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  2                 
  /                 
 |                  
 |  atan(2*x - 3) dx
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3/2                 
$$\int\limits_{\frac{3}{2}}^{2} \operatorname{atan}{\left(2 x - 3 \right)}\, dx$$
The answer (Indefinite) [src]
  /                          /             2\                          
 |                        log\1 + (2*x - 3) /   (2*x - 3)*atan(2*x - 3)
 | atan(2*x - 3) dx = C - ------------------- + -----------------------
 |                                 4                       2           
/                                                                      
$${{\left(2\,x-3\right)\,\arctan \left(2\,x-3\right)-{{\log \left( \left(2\,x-3\right)^2+1\right)}\over{2}}}\over{2}}$$
The graph
The answer [src]
  log(2)   pi
- ------ + --
    4      8 
$$-{{2\,\log 2-\pi}\over{8}}$$
=
=
  log(2)   pi
- ------ + --
    4      8 
$$- \frac{\log{\left(2 \right)}}{4} + \frac{\pi}{8}$$
Numerical answer [src]
0.219412286558738
0.219412286558738
The graph
Integral of arctg(2x-3) dx

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