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Solving integrals/ dx:x*sqrt(2x+1)

Integral of dx:x*sqrt(2x+1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |    _________   
 |  \/ 2*x + 1    
 |  ----------- dx
 |       x        
 |                
/                 
0
$$\int\limits_{0}^{1} \frac{\sqrt{2 x + 1}}{x}\, dx$$ 
Integral(sqrt(2*x + 1)/x, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                 
 |                                                                                  
 |   _________                                                                      
 | \/ 2*x + 1              /      _________\       _________      /       _________\
 | ----------- dx = C - log\1 + \/ 1 + 2*x / + 2*\/ 1 + 2*x  + log\-1 + \/ 1 + 2*x /
 |      x                                                                           
 |                                                                                  
/
$$\int \frac{\sqrt{2 x + 1}}{x}\, dx = C + 2 \sqrt{2 x + 1} + \log{\left(\sqrt{2 x + 1} - 1 \right)} - \log{\left(\sqrt{2 x + 1} + 1 \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
            /  ___\
oo - 2*acoth\\/ 3 /
$$- 2 \operatorname{acoth}{\left(\sqrt{3} \right)} + \infty$$ 
=
= 
            /  ___\
oo - 2*acoth\\/ 3 /
$$- 2 \operatorname{acoth}{\left(\sqrt{3} \right)} + \infty$$ 
oo - 2*acoth(sqrt(3))
Numerical answer [src] 
44.9307370327658
44.9307370327658

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

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