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Solving integrals/ arctan((2x+1)/sqrt(3))

Integral of arctan((2x+1)/sqrt(3)) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |      /2*x + 1\   
 |  atan|-------| dx
 |      |   ___ |   
 |      \ \/ 3  /   
 |                  
/                   
0
∫01atan⁡(2x+13) dx\int\limits_{0}^{1} \operatorname{atan}{\left(\frac{2 x + 1}{\sqrt{3}} \right)}\, dx 
Integral(atan((2*x + 1)/sqrt(3)), (x, 0, 1))
The answer (Indefinite) [src] 
                                /     /             2\                                \
                                |     |    (2*x + 1) |                                |
                                |  log|1 + ----------|     ___                        |
                            ___ |     \        3     /   \/ 3                /2*x + 1\|
  /                       \/ 3 *|- ------------------- + -----*(2*x + 1)*atan|-------||
 |                              |           2              3                 |   ___ ||
 |     /2*x + 1\                \                                            \ \/ 3  //
 | atan|-------| dx = C + -------------------------------------------------------------
 |     |   ___ |                                        2                              
 |     \ \/ 3  /                                                                       
 |                                                                                     
/
∫atan⁡(2x+13) dx=C+3(33(2x+1)atan⁡(2x+13)−log⁡((2x+1)23+1)2)2\int \operatorname{atan}{\left(\frac{2 x + 1}{\sqrt{3}} \right)}\, dx = C + \frac{\sqrt{3} \left(\frac{\sqrt{3}}{3} \left(2 x + 1\right) \operatorname{atan}{\left(\frac{2 x + 1}{\sqrt{3}} \right)} - \frac{\log{\left(\frac{\left(2 x + 1\right)^{2}}{3} + 1 \right)}}{2}\right)}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.02.0
Plot the graph f(x)
The answer [src] 
         ___       
5*pi   \/ 3 *log(3)
---- - ------------
 12         4
−3log⁡(3)4+5π12- \frac{\sqrt{3} \log{\left(3 \right)}}{4} + \frac{5 \pi}{12} 
=
= 
         ___       
5*pi   \/ 3 *log(3)
---- - ------------
 12         4
−3log⁡(3)4+5π12- \frac{\sqrt{3} \log{\left(3 \right)}}{4} + \frac{5 \pi}{12} 
5*pi/12 - sqrt(3)*log(3)/4
Numerical answer [src] 
0.833283863547574
0.833283863547574

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

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