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Integral of log(x)^2/x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1           
  /           
 |            
 |     2      
 |  log (x)   
 |  ------- dx
 |     x      
 |            
/             
0             
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)}^{2}}{x}\, dx$$
Integral(log(x)^2/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                3   
 | log (x)          log (x)
 | ------- dx = C + -------
 |    x                3   
 |                         
/                          
$$\int \frac{\log{\left(x \right)}^{2}}{x}\, dx = C + \frac{\log{\left(x \right)}^{3}}{3}$$
The answer [src]
oo
$$\infty$$
=
=
oo
$$\infty$$
oo
Numerical answer [src]
28568.3797156332
28568.3797156332

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