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Solving integrals/ 1/(2*sqrt(3x-2))

Integral of 1/(2*sqrt(3x-2)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |      _________   
 |  2*\/ 3*x - 2    
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{1}{2 \sqrt{3 x - 2}}\, dx$$ 
Integral(1/(2*sqrt(3*x - 2)), (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                \/ 3*x - 2 
 | ------------- dx = C + -----------
 |     _________               3     
 | 2*\/ 3*x - 2                      
 |                                   
/
$$\int \frac{1}{2 \sqrt{3 x - 2}}\, dx = C + \frac{\sqrt{3 x - 2}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
        ___
1   I*\/ 2 
- - -------
3      3
$$\frac{1}{3} - \frac{\sqrt{2} i}{3}$$ 
=
= 
        ___
1   I*\/ 2 
- - -------
3      3
$$\frac{1}{3} - \frac{\sqrt{2} i}{3}$$ 
1/3 - i*sqrt(2)/3
Numerical answer [src] 
(0.289181208372083 - 0.75640102155328j)
(0.289181208372083 - 0.75640102155328j)

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

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