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Solving integrals/ 1/(5x-2)

Integral of 1/(5x-2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  b           
  /           
 |            
 |     1      
 |  ------- dx
 |  5*x - 2   
 |            
/             
a
$$\int\limits_{a}^{b} \frac{1}{5 x - 2}\, dx$$ 
Integral(1/(5*x - 2), (x, a, b))
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(5*x - 2)
 | ------- dx = C + ------------
 | 5*x - 2               5      
 |                              
/
$$\int \frac{1}{5 x - 2}\, dx = C + \frac{\log{\left(5 x - 2 \right)}}{5}$$
Simplify
The answer [src] 
  log(-2 + 5*a)   log(-2 + 5*b)
- ------------- + -------------
        5               5
$$- \frac{\log{\left(5 a - 2 \right)}}{5} + \frac{\log{\left(5 b - 2 \right)}}{5}$$ 
=
= 
  log(-2 + 5*a)   log(-2 + 5*b)
- ------------- + -------------
        5               5
$$- \frac{\log{\left(5 a - 2 \right)}}{5} + \frac{\log{\left(5 b - 2 \right)}}{5}$$ 
-log(-2 + 5*a)/5 + log(-2 + 5*b)/5

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

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