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

The solution

You have entered [src]

  1               
  /               
 |                
 |  /1     2  \   
 |  |- + -----| dx
 |  \x   x - 1/   
 |                
/                 
0

$$\int\limits_{0}^{1} \left(\frac{2}{x - 1} + \frac{1}{x}\right)\, dx$$

Integral(1/x + 2/(x - 1), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{2}{x - 1}\, dx = 2 \int \frac{1}{x - 1}\, dx$
  1. Let $u = x - 1$ .
    
    Then let $du = dx$ and substitute $du$ :
    
    $\int \frac{1}{u}\, du$
    1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
    Now substitute $u$ back in:
    
    $\log{\left(x - 1 \right)}$
  So, the result is: $2 \log{\left(x - 1 \right)}$
1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
The result is: $\log{\left(x \right)} + 2 \log{\left(x - 1 \right)}$
Now simplify:

$\log{\left(x \right)} + 2 \log{\left(x - 1 \right)}$
Add the constant of integration:

$\log{\left(x \right)} + 2 \log{\left(x - 1 \right)}+ \mathrm{constant}$

The answer is:

$\log{\left(x \right)} + 2 \log{\left(x - 1 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                          
 |                                           
 | /1     2  \                               
 | |- + -----| dx = C + 2*log(x - 1) + log(x)
 | \x   x - 1/                               
 |                                           
/

$$\int \left(\frac{2}{x - 1} + \frac{1}{x}\right)\, dx = C + \log{\left(x \right)} + 2 \log{\left(x - 1 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

nan

$$\text{NaN}$$

nan

$$\text{NaN}$$

nan

Numerical answer [src]

-44.0914674384461

-44.0914674384461

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution