Mister Exam

Integral of xlog(x-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  3                
  /                
 |                 
 |  x*log(x - 1) dx
 |                 
/                  
2                  
$$\int\limits_{2}^{3} x \log{\left(x - 1 \right)}\, dx$$
Integral(x*log(x - 1*1), (x, 2, 3))
Detail solution
  1. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. The integral of is when :

    Now evaluate the sub-integral.

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

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. The integral of is when :

      1. The integral of a constant is the constant times the variable of integration:

      1. Let .

        Then let and substitute :

        1. The integral of is .

        Now substitute back in:

      The result is:

    So, the result is:

  3. Now simplify:

  4. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                         2    2           
 |                       x   log(-1 + x)   x    x *log(x - 1)
 | x*log(x - 1) dx = C - - - ----------- - -- + -------------
 |                       2        2        4          2      
/                                                            
$${{\log \left(x-1\right)\,x^2}\over{2}}-{{{{x^2+2\,x}\over{2}}+\log \left(x-1\right)}\over{2}}$$
The graph
The answer [src]
-7/4 + 4*log(2)
$$4\,\log 2-{{7}\over{4}}$$
=
=
-7/4 + 4*log(2)
$$- \frac{7}{4} + 4 \log{\left(2 \right)}$$
Numerical answer [src]
1.02258872223978
1.02258872223978
The graph
Integral of xlog(x-1) dx

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