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Integral of ln^3(1-x)/x-1 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1                     
  /                     
 |                      
 |  /   3           \   
 |  |log (1 - x)    |   
 |  |----------- - 1| dx
 |  \     x         /   
 |                      
/                       
0                       
$$\int\limits_{0}^{1} \left(-1 + \frac{\log{\left(1 - x \right)}^{3}}{x}\right)\, dx$$
Integral(log(1 - x)^3/x - 1, (x, 0, 1))
The answer (Indefinite) [src]
  /                                 /              
 |                                 |               
 | /   3           \               |    3          
 | |log (1 - x)    |               | log (1 - x)   
 | |----------- - 1| dx = C - x +  | ----------- dx
 | \     x         /               |      x        
 |                                 |               
/                                 /                
$$\int \left(-1 + \frac{\log{\left(1 - x \right)}^{3}}{x}\right)\, dx = C - x + \int \frac{\log{\left(1 - x \right)}^{3}}{x}\, dx$$
The answer [src]
               1                 
               /                 
    1         |                  
    /         |      3           
   |          |  -log (1 - x)    
-  |  1 dx -  |  ------------- dx
   |          |        x         
  /           |                  
  0          /                   
             0                   
$$- \int\limits_{0}^{1} 1\, dx - \int\limits_{0}^{1} \left(- \frac{\log{\left(1 - x \right)}^{3}}{x}\right)\, dx$$
=
=
               1                 
               /                 
    1         |                  
    /         |      3           
   |          |  -log (1 - x)    
-  |  1 dx -  |  ------------- dx
   |          |        x         
  /           |                  
  0          /                   
             0                   
$$- \int\limits_{0}^{1} 1\, dx - \int\limits_{0}^{1} \left(- \frac{\log{\left(1 - x \right)}^{3}}{x}\right)\, dx$$
-Integral(1, (x, 0, 1)) - Integral(-log(1 - x)^3/x, (x, 0, 1))
Numerical answer [src]
-7.49393940226682
-7.49393940226682

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