Mister Exam

You entered:

∫(lnx)²/xdx

What you mean?

Integral of ∫(lnx)²/xdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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