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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |       1        
 |  ----------- dx
 |    _________   
 |  \/ 2*x + 1    
 |                
/                 
0
∫0112x+1 dx\int\limits_{0}^{1} \frac{1}{\sqrt{2 x + 1}}\, dx 
Integral(1/(sqrt(2*x + 1)), (x, 0, 1))
Detail solution

  1. Let u=2x+1u = \sqrt{2 x + 1}.

    Then let du=dx2x+1du = \frac{dx}{\sqrt{2 x + 1}} and substitute dudu:

    ∫1 du\int 1\, du

    1. The integral of a constant is the constant times the variable of integration:

      ∫1 du=u\int 1\, du = u

    Now substitute uu back in:

    2x+1\sqrt{2 x + 1}

  2. Now simplify:

    2x+1\sqrt{2 x + 1}

  3. Add the constant of integration:

    2x+1+constant\sqrt{2 x + 1}+ \mathrm{constant}

The answer is:

2x+1+constant\sqrt{2 x + 1}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                
 |                                 
 |      1                 _________
 | ----------- dx = C + \/ 2*x + 1 
 |   _________                     
 | \/ 2*x + 1                      
 |                                 
/
∫12x+1 dx=C+2x+1\int \frac{1}{\sqrt{2 x + 1}}\, dx = C + \sqrt{2 x + 1}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
       ___
-1 + \/ 3
−1+3-1 + \sqrt{3} 
=
= 
       ___
-1 + \/ 3
−1+3-1 + \sqrt{3} 
-1 + sqrt(3)
Numerical answer [src] 
0.732050807568877
0.732050807568877

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

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