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Integral of (log(x)-1)/x^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1              
  /              
 |               
 |  log(x) - 1   
 |  ---------- dx
 |       2       
 |      x        
 |               
/                
0                
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)} - 1}{x^{2}}\, dx$$
Integral((log(x) - 1)/x^2, (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. Let .

        Then let and substitute :

        1. Integrate term-by-term:

          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. The integral of the exponential function is itself.

          1. The integral of the exponential function is itself.

          The result is:

        Now substitute back in:

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. Let .

        Then let and substitute :

        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. The integral of the exponential function is itself.

          Now substitute back in:

        Now substitute back in:

      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:

      The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                          
 |                           
 | log(x) - 1          log(x)
 | ---------- dx = C - ------
 |      2                x   
 |     x                     
 |                           
/                            
$$\int \frac{\log{\left(x \right)} - 1}{x^{2}}\, dx = C - \frac{\log{\left(x \right)}}{x}$$
The answer [src]
-oo
$$-\infty$$
=
=
-oo
$$-\infty$$
-oo
Numerical answer [src]
-6.0760804301603e+20
-6.0760804301603e+20

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