Mister Exam

Integral of dx/x(1+lnx) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                    
  /                    
 |                     
 |    1                
 |  1*-*(1 + log(x)) dx
 |    x                
 |                     
/                      
0                      
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{x} \left(\log{\left(x \right)} + 1\right)\, dx$$
Integral(1*(1 + log(x))/x, (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. The integral of is when :

        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. 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:

      1. The integral of is .

      The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                        
 |                                        2
 |   1                       (-1 - log(x)) 
 | 1*-*(1 + log(x)) dx = C + --------------
 |   x                             2       
 |                                         
/                                          
$$\int 1 \cdot \frac{1}{x} \left(\log{\left(x \right)} + 1\right)\, dx = C + \frac{\left(- \log{\left(x \right)} - 1\right)^{2}}{2}$$
The answer [src]
-oo
$$-\infty$$
=
=
-oo
$$-\infty$$
Numerical answer [src]
-927.873417281334
-927.873417281334

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