Mister Exam

Integral of lnxdx/x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |  log(x)   
 |  ------ dx
 |    x      
 |           
/            
0            
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{x}\, dx$$
Integral(log(x)/x, (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. The integral of is when :

      Now substitute back in:

    Method #2

    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. 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 when :

            So, the result is:

          Now substitute back in:

        So, the result is:

      Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                       
 |                    2   
 | log(x)          log (x)
 | ------ dx = C + -------
 |   x                2   
 |                        
/                         
$$\int \frac{\log{\left(x \right)}}{x}\, dx = C + \frac{\log{\left(x \right)}^{2}}{2}$$
The answer [src]
-oo
$$-\infty$$
=
=
-oo
$$-\infty$$
-oo
Numerical answer [src]
-971.963863415327
-971.963863415327

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