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Solving integrals/ ln|x|

Integral of ln|x| dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
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 |  log(|x|) dx
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$$\int\limits_{0}^{1} \log{\left(\left|{x}\right| \right)}\, dx$$ 
Integral(log(|x|), (x, 0, 1))
The answer (Indefinite) [src] 
                       /                               /                                       
                      |                               |                                        
                      | d                             | d                                      
  /                   | --(im(x))*im(x)*sign(x)       | --(re(x))*re(x)*sign(x)                
 |                    | dx                            | dx                                     
 | log(|x|) dx = C -  | ----------------------- dx -  | ----------------------- dx + x*log(|x|)
 |                    |           |x|                 |           |x|                          
/                     |                               |                                        
                     /                               /
$$\int \log{\left(\left|{x}\right| \right)}\, dx = C + x \log{\left(\left|{x}\right| \right)} - \int \frac{\operatorname{re}{\left(x\right)} \operatorname{sign}{\left(x \right)} \frac{d}{d x} \operatorname{re}{\left(x\right)}}{\left|{x}\right|}\, dx - \int \frac{\operatorname{im}{\left(x\right)} \operatorname{sign}{\left(x \right)} \frac{d}{d x} \operatorname{im}{\left(x\right)}}{\left|{x}\right|}\, dx$$
Simplify
Numerical answer [src] 
-1.0
-1.0

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

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