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Solving integrals/ (dx)/(3x-2)

Integral of (dx)/(3x-2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  3           
  /           
 |            
 |     1      
 |  ------- dx
 |  3*x - 2   
 |            
/             
2
$$\int\limits_{2}^{3} \frac{1}{3 x - 2}\, dx$$ 
Integral(1/(3*x - 2), (x, 2, 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 .

      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             log(3*x - 2)
 | ------- dx = C + ------------
 | 3*x - 2               3      
 |                              
/
$$\int \frac{1}{3 x - 2}\, dx = C + \frac{\log{\left(3 x - 2 \right)}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  log(4)   log(7)
- ------ + ------
    3        3
$$- \frac{\log{\left(4 \right)}}{3} + \frac{\log{\left(7 \right)}}{3}$$ 
=
= 
  log(4)   log(7)
- ------ + ------
    3        3
$$- \frac{\log{\left(4 \right)}}{3} + \frac{\log{\left(7 \right)}}{3}$$ 
-log(4)/3 + log(7)/3
Numerical answer [src] 
0.186538595978474
0.186538595978474

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

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