Integral of 1/(3x-4) dx

The solution

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  1             
  /             
 |              
 |       1      
 |  1*------- dx
 |    3*x - 4   
 |              
/               
0

$$\int\limits_{0}^{1} 1 \cdot \frac{1}{3 x - 4}\, dx$$

Simplify

Detail solution

Let $u = 3 x - 4$ .

Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :

$\int \frac{1}{9 u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{3 u}\, du = \frac{\int \frac{1}{u}\, du}{3}$
  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:

$\frac{\log{\left(3 x - 4 \right)}}{3}$
Now simplify:

$\frac{\log{\left(3 x - 4 \right)}}{3}$
Add the constant of integration:

$\frac{\log{\left(3 x - 4 \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(3 x - 4 \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                                
 |      1             log(3*x - 4)
 | 1*------- dx = C + ------------
 |   3*x - 4               3      
 |                                
/

$${{\log \left(3\,x-4\right)}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-log(4) 
--------
   3

$$-{{\log 4}\over{3}}$$

-log(4) 
--------
   3

$$- \frac{\log{\left(4 \right)}}{3}$$

Simplify

Numerical answer [src]

-0.462098120373297

-0.462098120373297

The graph

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

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Integral of 1/(3x-4) dx

Limits of integration:

The graph:

Piecewise:

The solution