Mister Exam

Integral of 1/(4x-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1           
  /           
 |            
 |     1      
 |  ------- dx
 |  4*x - 1   
 |            
/             
0             
$$\int\limits_{0}^{1} \frac{1}{4 x - 1}\, dx$$
Integral(1/(4*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 .

      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(4*x - 1)
 | ------- dx = C + ------------
 | 4*x - 1               4      
 |                              
/                               
$$\int \frac{1}{4 x - 1}\, dx = C + \frac{\log{\left(4 x - 1 \right)}}{4}$$
The graph
The answer [src]
nan
$$\text{NaN}$$
=
=
nan
$$\text{NaN}$$
nan
Numerical answer [src]
-4.49069862441201
-4.49069862441201

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