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Solving integrals/ arctg√(4x+1)

Integral of arctg√(4x+1) 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\\/ 4*x + 1 / dx
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∫02atan⁡(4x+1) dx\int\limits_{0}^{2} \operatorname{atan}{\left(\sqrt{4 x + 1} \right)}\, dx 
Integral(atan(sqrt(4*x + 1)), (x, 0, 2))
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             
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∫atan⁡(4x+1) dx=C−4x+14+(4x+1)atan⁡(4x+1)4+atan⁡(4x+1)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
0.02.00.20.40.60.81.01.21.41.61.80.02.5
Plot the graph f(x)
The answer [src] 
  1   pi   5*atan(3)
- - - -- + ---------
  2   8        2
−12−π8+5atan⁡(3)2- \frac{1}{2} - \frac{\pi}{8} + \frac{5 \operatorname{atan}{\left(3 \right)}}{2} 
=
= 
  1   pi   5*atan(3)
- - - -- + ---------
  2   8        2
−12−π8+5atan⁡(3)2- \frac{1}{2} - \frac{\pi}{8} + \frac{5 \operatorname{atan}{\left(3 \right)}}{2} 
-1/2 - pi/8 + 5*atan(3)/2
Numerical answer [src] 
2.22991534929691
2.22991534929691

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

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