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(x+arctg2x)/(1+4x^2)
Solving integrals/ (x+arctg2x)/(1+4x^2)

Integral of (x+arctg2x)/(1+4x^2) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |  x + atan(2*x)   
 |  ------------- dx
 |            2     
 |     1 + 4*x      
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{x + \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1}\, dx$$ 
Integral((x + atan(2*x))/(1 + 4*x^2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                 
 |                            2           /       2\
 | x + atan(2*x)          atan (2*x)   log\1 + 4*x /
 | ------------- dx = C + ---------- + -------------
 |           2                4              8      
 |    1 + 4*x                                       
 |                                                  
/
$$\int \frac{x + \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1}\, dx = C + \frac{\log{\left(4 x^{2} + 1 \right)}}{8} + \frac{\operatorname{atan}^{2}{\left(2 x \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
Numerical answer [src] 
0.507624309882537
0.507624309882537
The graph
Integral of (x+arctg2x)/(1+4x^2) dx

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

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