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sqrt(2x+1)

Integral of 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
 |                
/                 
0                 
$$\int\limits_{0}^{1} \sqrt{2 x + 1}\, dx$$
Integral(sqrt(2*x + 1), (x, 0, 1))
Detail solution
  1. Let .

    Then let and substitute :

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is when :

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                 
 |                               3/2
 |   _________          (2*x + 1)   
 | \/ 2*x + 1  dx = C + ------------
 |                           3      
/                                   
$$\int \sqrt{2 x + 1}\, dx = C + \frac{\left(2 x + 1\right)^{\frac{3}{2}}}{3}$$
The graph
The answer [src]
  1     ___
- - + \/ 3 
  3        
$$- \frac{1}{3} + \sqrt{3}$$
=
=
  1     ___
- - + \/ 3 
  3        
$$- \frac{1}{3} + \sqrt{3}$$
-1/3 + sqrt(3)
Numerical answer [src]
1.39871747423554
1.39871747423554
The graph
Integral of sqrt(2x+1) dx

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