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arctg(sqrt(4x-1))
Solving integrals/ arctg(sqrt(4x-1))

Integral of arctg(sqrt(4x-1)) dx

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The solution

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  1                     
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 |  atan\\/ 4*x - 1 / dx
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0
$$\int\limits_{0}^{1} \operatorname{atan}{\left(\sqrt{4 x - 1} \right)}\, dx$$ 
Integral(atan(sqrt(4*x - 1)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                        
 |                              _________       /  _________\                 /  _________\
 |     /  _________\          \/ 4*x - 1    atan\\/ 4*x - 1 /   (4*x - 1)*atan\\/ 4*x - 1 /
 | atan\\/ 4*x - 1 / dx = C - ----------- + ----------------- + ---------------------------
 |                                 4                4                        4             
/
$$\int \operatorname{atan}{\left(\sqrt{4 x - 1} \right)}\, dx = C - \frac{\sqrt{4 x - 1}}{4} + \frac{\left(4 x - 1\right) \operatorname{atan}{\left(\sqrt{4 x - 1} \right)}}{4} + \frac{\operatorname{atan}{\left(\sqrt{4 x - 1} \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  1                      
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 |  atan\\/ -1 + 4*x / dx
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$$\int\limits_{0}^{1} \operatorname{atan}{\left(\sqrt{4 x - 1} \right)}\, dx$$ 
=
= 
  1                      
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 |      /  __________\   
 |  atan\\/ -1 + 4*x / dx
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0
$$\int\limits_{0}^{1} \operatorname{atan}{\left(\sqrt{4 x - 1} \right)}\, dx$$ 
Integral(atan(sqrt(-1 + 4*x)), (x, 0, 1))
Numerical answer [src] 
(0.61385564943587 + 0.249964776813378j)
(0.61385564943587 + 0.249964776813378j)
The graph
Integral of arctg(sqrt(4x-1)) dx

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

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