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1/((1+4x^2)*arctg(2x))
Solving integrals/ 1/((1+4x^2)*arctg(2x))

Integral of 1/((1+4x^2)*arctg(2x)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1/2                          
   /                           
  |                            
  |              1             
  |   1*-------------------- dx
  |     /       2\             
  |     \1 + 4*x /*atan(2*x)   
  |                            
 /                             
  ___                          
\/ 3                           
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  2
∫32121⋅1(4x2+1)atan⁡(2x) dx\int\limits_{\frac{\sqrt{3}}{2}}^{\frac{1}{2}} 1 \cdot \frac{1}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}}\, dx 
Integral(1/((1 + 4*x^2)*atan(2*x)), (x, sqrt(3)/2, 1/2))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=tan(_theta)/2, rewritten=1/(2*atan(tan(_theta))), substep=ConstantTimesRule(constant=1/2, other=1/atan(tan(_theta)), substep=URule(u_var=_u, u_func=atan(tan(_theta)), constant=1, substep=ReciprocalRule(func=_u, context=1/_u, symbol=_u), context=1/atan(tan(_theta)), symbol=_theta), context=1/(2*atan(tan(_theta))), symbol=_theta), restriction=True, context=1/((4*x**2 + 1)*atan(2*x)), symbol=x)

  1. Add the constant of integration:

    log⁡(atan⁡(2x))2+constant\frac{\log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{2}+ \mathrm{constant}

The answer is:

log⁡(atan⁡(2x))2+constant\frac{\log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                              
 |                                               
 |            1                    log(atan(2*x))
 | 1*-------------------- dx = C + --------------
 |   /       2\                          2       
 |   \1 + 4*x /*atan(2*x)                        
 |                                               
/
log⁡arctan⁡(2 x)2{{\log \arctan \left(2\,x\right)}\over{2}}
Simplify
The graph
0.500.550.600.650.700.750.800.851.0-1.0
Plot the graph f(x)
The answer [src] 
   /pi\      /pi\
log|--|   log|--|
   \4 /      \3 /
------- - -------
   2         2
log⁡(π4)2−log⁡(π3)2{{\log \left({{\pi}\over{4}}\right)}\over{2}}-{{\log \left({{\pi }\over{3}}\right)}\over{2}} 
=
= 
   /pi\      /pi\
log|--|   log|--|
   \4 /      \3 /
------- - -------
   2         2
log⁡(π4)2−log⁡(π3)2\frac{\log{\left(\frac{\pi}{4} \right)}}{2} - \frac{\log{\left(\frac{\pi}{3} \right)}}{2}
Упростить
Numerical answer [src] 
-0.14384103622589
-0.14384103622589
The graph
Integral of 1/((1+4x^2)*arctg(2x)) dx

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

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