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Integral of dx/x√1-ln^2x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  E                     
  /                     
 |                      
 |  /  ___          \   
 |  |\/ 1       2   |   
 |  |----- - log (x)| dx
 |  \  x            /   
 |                      
/                       
1                       
$$\int\limits_{1}^{e} \left(- \log{\left(x \right)}^{2} + \frac{\sqrt{1}}{x}\right)\, dx$$
Integral(sqrt(1)/x - log(x)^2, (x, 1, E))
Detail solution
  1. Integrate term-by-term:

    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. 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:

      So, the result is:

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

      1. Don't know the steps in finding this integral.

        But the integral is

      So, the result is:

    The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                                
 |                                                                 
 | /  ___          \                                               
 | |\/ 1       2   |                     2                         
 | |----- - log (x)| dx = C - 2*x - x*log (x) + 2*x*log(x) + log(x)
 | \  x            /                                               
 |                                                                 
/                                                                  
$$\int \left(- \log{\left(x \right)}^{2} + \frac{\sqrt{1}}{x}\right)\, dx = C - x \log{\left(x \right)}^{2} + 2 x \log{\left(x \right)} - 2 x + \log{\left(x \right)}$$
The graph
The answer [src]
3 - E
$$3 - e$$
=
=
3 - E
$$3 - e$$
3 - E
Numerical answer [src]
0.281718171540955
0.281718171540955

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