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arctg(2x-3)
Solving integrals/ arctg(2x-3)

Integral of arctg(2x-3) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  2                 
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 |  atan(2*x - 3) dx
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3/2
∫322atan⁡(2x−3) dx\int\limits_{\frac{3}{2}}^{2} \operatorname{atan}{\left(2 x - 3 \right)}\, dx
Simplify
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           
/
(2 x−3) arctan⁡(2 x−3)−log⁡((2 x−3)2+1)22{{\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}}
Simplify
The graph
1.502.001.551.601.651.701.751.801.851.901.950.01.0
Plot the graph f(x)
The answer [src] 
  log(2)   pi
- ------ + --
    4      8
−2 log⁡2−π8-{{2\,\log 2-\pi}\over{8}} 
=
= 
  log(2)   pi
- ------ + --
    4      8
−log⁡(2)4+π8- \frac{\log{\left(2 \right)}}{4} + \frac{\pi}{8}
Simplify
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.

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