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Integral of dx/x(lnx+3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1              
  /              
 |               
 |  log(x) + 3   
 |  ---------- dx
 |      x        
 |               
/                
0                
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)} + 3}{x}\, dx$$
Integral((log(x) + 3)/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 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:

    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 a constant times a function is the constant times the integral of the function:

        1. The integral of is .

        So, the result is:

      The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                 
 |                                 2
 | log(x) + 3          (3 + log(x)) 
 | ---------- dx = C + -------------
 |     x                     2      
 |                                  
/                                   
$$\int \frac{\log{\left(x \right)} + 3}{x}\, dx = C + \frac{\left(\log{\left(x \right)} + 3\right)^{2}}{2}$$
The answer [src]
-oo
$$-\infty$$
=
=
-oo
$$-\infty$$
-oo
Numerical answer [src]
-839.692525013348
-839.692525013348

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