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ln^2(x)

Integral of ln^2(x) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1           
  /           
 |            
 |     2      
 |  log (x) dx
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$$\int\limits_{0}^{1} \log{\left(x \right)}^{2}\, dx$$
Integral(log(x)^2, (x, 0, 1))
Detail solution
  1. Let .

    Then let and substitute :

    1. Use integration by parts:

      Let and let .

      Then .

      To find :

      1. The integral of the exponential function is itself.

      Now evaluate the sub-integral.

    2. Use integration by parts:

      Let and let .

      Then .

      To find :

      1. The integral of the exponential function is itself.

      Now evaluate the sub-integral.

    3. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of the exponential function is itself.

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                             
 |                                              
 |    2                        2                
 | log (x) dx = C + 2*x + x*log (x) - 2*x*log(x)
 |                                              
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$$\int \log{\left(x \right)}^{2}\, dx = C + x \log{\left(x \right)}^{2} - 2 x \log{\left(x \right)} + 2 x$$
The graph
The answer [src]
2
$$2$$
=
=
2
$$2$$
2
Numerical answer [src]
2.0
2.0
The graph
Integral of ln^2(x) dx

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