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Integral of (3-4x)/(2x^2-3x+1) dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src]
  1                  
  /                  
 |                   
 |     3 - 4*x       
 |  -------------- dx
 |     2             
 |  2*x  - 3*x + 1   
 |                   
/                    
0                    
$$\int\limits_{0}^{1} \frac{3 - 4 x}{2 x^{2} - 3 x + 1}\, dx$$
Integral((3 - 4*x)/(2*x^2 - 3*x + 1), (x, 0, 1))
Detail solution
We have the integral:
  /                   
 |                    
 |      3 - 4*x       
 | 1*-------------- dx
 |      2             
 |   2*x  - 3*x + 1   
 |                    
/                     
Rewrite the integrand
   3 - 4*x           2*2*x - 3   
-------------- = - --------------
   2                  2          
2*x  - 3*x + 1     2*x  - 3*x + 1
or
  /                     
 |                      
 |      3 - 4*x         
 | 1*-------------- dx  
 |      2              =
 |   2*x  - 3*x + 1     
 |                      
/                       
  
   /                 
  |                  
  |   2*2*x - 3      
- | -------------- dx
  |    2             
  | 2*x  - 3*x + 1   
  |                  
 /                   
In the integral
   /                 
  |                  
  |   2*2*x - 3      
- | -------------- dx
  |    2             
  | 2*x  - 3*x + 1   
  |                  
 /                   
do replacement
              2
u = -3*x + 2*x 
then
the integral =
   /                      
  |                       
  |   1                   
- | ----- du = -log(1 + u)
  | 1 + u                 
  |                       
 /                        
do backward replacement
   /                                        
  |                                         
  |   2*2*x - 3             /             2\
- | -------------- dx = -log\1 - 3*x + 2*x /
  |    2                                    
  | 2*x  - 3*x + 1                          
  |                                         
 /                                          
Solution is:
       /             2\
C - log\1 - 3*x + 2*x /
The answer (Indefinite) [src]
  /                                           
 |                                            
 |    3 - 4*x                 /   2          \
 | -------------- dx = C - log\2*x  - 3*x + 1/
 |    2                                       
 | 2*x  - 3*x + 1                             
 |                                            
/                                             
$$-\log \left(2\,x^2-3\,x+1\right)$$
The answer [src]
nan
$${\it \%a}$$
=
=
nan
$$\text{NaN}$$

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