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x/(x-1)
Solving integrals/ x/(x-1)

Integral of x/(x-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1         
  /         
 |          
 |    x     
 |  ----- dx
 |  x - 1   
 |          
/           
0
$$\int\limits_{0}^{1} \frac{x}{x - 1}\, dx$$ 
Integral(x/(x - 1), (x, 0, 1))
Detail solution

  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:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                              
 |                               
 |   x                           
 | ----- dx = C + x + log(-1 + x)
 | x - 1                         
 |                               
/
$$\int \frac{x}{x - 1}\, dx = C + x + \log{\left(x - 1 \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
-oo - pi*I
$$-\infty - i \pi$$ 
=
= 
-oo - pi*I
$$-\infty - i \pi$$ 
-oo - pi*i
Numerical answer [src] 
-43.0909567862195
-43.0909567862195
The graph
Integral of x/(x-1) dx

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

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