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Solving integrals/ sqrt((6*x)-1)

Integral of sqrt((6*x)-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |    _________   
 |  \/ 6*x - 1  dx
 |                
/                 
0
$$\int\limits_{0}^{1} \sqrt{6 x - 1}\, dx$$ 
Integral(sqrt(6*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
 |   _________          (6*x - 1)   
 | \/ 6*x - 1  dx = C + ------------
 |                           9      
/
$$\int \sqrt{6 x - 1}\, dx = C + \frac{\left(6 x - 1\right)^{\frac{3}{2}}}{9}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
        ___
I   5*\/ 5 
- + -------
9      9
$$\frac{5 \sqrt{5}}{9} + \frac{i}{9}$$ 
=
= 
        ___
I   5*\/ 5 
- + -------
9      9
$$\frac{5 \sqrt{5}}{9} + \frac{i}{9}$$ 
i/9 + 5*sqrt(5)/9
Numerical answer [src] 
(1.24236102619322 + 0.111210057208727j)
(1.24236102619322 + 0.111210057208727j)

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

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