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Integral of sqrt(3x-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  3               
  /               
 |                
 |    _________   
 |  \/ 3*x - 1  dx
 |                
/                 
0                 
$$\int\limits_{0}^{3} \sqrt{3 x - 1}\, dx$$
Integral(sqrt(3*x - 1), (x, 0, 3))
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*(3*x - 1)   
 | \/ 3*x - 1  dx = C + --------------
 |                            9       
/                                     
$$\int \sqrt{3 x - 1}\, dx = C + \frac{2 \left(3 x - 1\right)^{\frac{3}{2}}}{9}$$
The graph
The answer [src]
           ___
2*I   32*\/ 2 
--- + --------
 9       9    
$$\frac{32 \sqrt{2}}{9} + \frac{2 i}{9}$$
=
=
           ___
2*I   32*\/ 2 
--- + --------
 9       9    
$$\frac{32 \sqrt{2}}{9} + \frac{2 i}{9}$$
2*i/9 + 32*sqrt(2)/9
Numerical answer [src]
(5.02811796336524 + 0.222582701002079j)
(5.02811796336524 + 0.222582701002079j)

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