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xdx/(x-1)(x-2)

Integral of xdx/(x-1)(x-2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

    Method #1

    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. 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 is .

          Now substitute back in:

        So, the result is:

      The result is:

    Method #2

    1. Rewrite the integrand:

    2. Rewrite the integrand:

    3. 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. 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 is .

          Now substitute back in:

        So, the result is:

      The result is:

    Method #3

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      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:

      1. 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 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:

      The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                           
 |                         2                  
 |   x                    x                   
 | -----*(x - 2) dx = C + -- - x - log(-1 + x)
 | x - 1                  2                   
 |                                            
/                                             
$$\int \frac{x}{x - 1} \left(x - 2\right)\, dx = C + \frac{x^{2}}{2} - x - \log{\left(x - 1 \right)}$$
The graph
The answer [src]
oo + pi*I
$$\infty + i \pi$$
=
=
oo + pi*I
$$\infty + i \pi$$
oo + pi*i
Numerical answer [src]
43.5909567862195
43.5909567862195
The graph
Integral of xdx/(x-1)(x-2) dx

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