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Integral of log(x)^3/x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1           
  /           
 |            
 |     3      
 |  log (x)   
 |  ------- dx
 |     x      
 |            
/             
0             
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)}^{3}}{x}\, dx$$
Integral(log(x)^3/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]
  /                        
 |                         
 |    3                4   
 | log (x)          log (x)
 | ------- dx = C + -------
 |    x                4   
 |                         
/                          
$$\int \frac{\log{\left(x \right)}^{3}}{x}\, dx = C + \frac{\log{\left(x \right)}^{4}}{4}$$
The answer [src]
-oo
$$-\infty$$
=
=
-oo
$$-\infty$$
-oo
Numerical answer [src]
-944636.568261642
-944636.568261642

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