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Solving integrals/ 1/sqrt(3*x+1)

Integral of 1/sqrt(3*x+1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |       1        
 |  ----------- dx
 |    _________   
 |  \/ 3*x + 1    
 |                
/                 
0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{3 x + 1}}\, dx$$ 
Integral(1/(sqrt(3*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 a constant is the constant times the variable of integration:

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                  
 |                          _________
 |      1               2*\/ 3*x + 1 
 | ----------- dx = C + -------------
 |   _________                3      
 | \/ 3*x + 1                        
 |                                   
/
$$\int \frac{1}{\sqrt{3 x + 1}}\, dx = C + \frac{2 \sqrt{3 x + 1}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
2/3
$$\frac{2}{3}$$ 
=
= 
2/3
$$\frac{2}{3}$$ 
2/3
Numerical answer [src] 
0.666666666666667
0.666666666666667

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

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