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Identical expressions
(6dx)/(3x- one)
(6dx) divide by (3x minus 1)
(6dx) divide by (3x minus one)
6dx/3x-1
(6dx) divide by (3x-1)
Similar expressions
(6dx)/(3x+1)

Integral of (6dx)/(3x-1) dx

The solution

You have entered [src]

  1           
  /           
 |            
 |     6      
 |  ------- dx
 |  3*x - 1   
 |            
/             
0

$$\int\limits_{0}^{1} \frac{6}{3 x - 1}\, dx$$

Integral(6/(3*x - 1), (x, 0, 1))

Detail solution

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

$\int \frac{6}{3 x - 1}\, dx = 6 \int \frac{1}{3 x - 1}\, dx$
1. Let $u = 3 x - 1$ .
  
  Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :
  
  $\int \frac{1}{3 u}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{3}$
    1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
    So, the result is: $\frac{\log{\left(u \right)}}{3}$
  Now substitute $u$ back in:
  
  $\frac{\log{\left(3 x - 1 \right)}}{3}$
So, the result is: $2 \log{\left(3 x - 1 \right)}$
Now simplify:

$2 \log{\left(3 x - 1 \right)}$
Add the constant of integration:

$2 \log{\left(3 x - 1 \right)}+ \mathrm{constant}$

The answer is:

$2 \log{\left(3 x - 1 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                                
 |    6                           
 | ------- dx = C + 2*log(3*x - 1)
 | 3*x - 1                        
 |                                
/

$$\int \frac{6}{3 x - 1}\, dx = C + 2 \log{\left(3 x - 1 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

nan

$$\text{NaN}$$

nan

$$\text{NaN}$$

nan

Numerical answer [src]

235.199781775798

235.199781775798

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

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Identical expressions

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Integral of (6dx)/(3x-1) dx

Limits of integration:

The graph:

Piecewise:

The solution