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Solving integrals/ x*arctg(sqrt4x-1)

Integral of x*arctg(sqrt4x-1) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                       
  /                       
 |                        
 |        /  _____    \   
 |  x*atan\\/ 4*x  - 1/ dx
 |                        
/                         
0
$$\int\limits_{0}^{1} x \operatorname{atan}{\left(\sqrt{4 x} - 1 \right)}\, dx$$ 
Integral(x*atan(sqrt(4*x) - 1), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                         
 |                                    ___    3/2       /         ___\    2     /  _____    \
 |       /  _____    \          x   \/ x    x      atan\-1 + 2*\/ x /   x *atan\\/ 4*x  - 1/
 | x*atan\\/ 4*x  - 1/ dx = C - - - ----- - ---- + ------------------ + --------------------
 |                              8     8      12            8                     2          
/
$$\int x \operatorname{atan}{\left(\sqrt{4 x} - 1 \right)}\, dx = C - \frac{x^{\frac{3}{2}}}{12} - \frac{\sqrt{x}}{8} + \frac{x^{2} \operatorname{atan}{\left(\sqrt{4 x} - 1 \right)}}{2} - \frac{x}{8} + \frac{\operatorname{atan}{\left(2 \sqrt{x} - 1 \right)}}{8}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  1   3*pi
- - + ----
  3    16
$$- \frac{1}{3} + \frac{3 \pi}{16}$$ 
=
= 
  1   3*pi
- - + ----
  3    16
$$- \frac{1}{3} + \frac{3 \pi}{16}$$ 
-1/3 + 3*pi/16
Numerical answer [src] 
0.255715289214753
0.255715289214753

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

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