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(x-2)/(x^2-4x+7)

Integral of (x-2)/(x^2-4x+7) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                
  /                
 |                 
 |     x - 2       
 |  ------------ dx
 |   2             
 |  x  - 4*x + 7   
 |                 
/                  
0                  
$$\int\limits_{0}^{1} \frac{x - 2}{\left(x^{2} - 4 x\right) + 7}\, dx$$
Integral((x - 2)/(x^2 - 4*x + 7), (x, 0, 1))
Detail solution
We have the integral:
  /               
 |                
 |    x - 2       
 | ------------ dx
 |  2             
 | x  - 4*x + 7   
 |                
/                 
Rewrite the integrand
               /  2*x - 4   \                             
               |------------|              /0\            
               | 2          |              |-|            
   x - 2       \x  - 4*x + 7/              \3/            
------------ = -------------- + --------------------------
 2                   2                               2    
x  - 4*x + 7                    /   ___          ___\     
                                |-\/ 3       2*\/ 3 |     
                                |-------*x + -------|  + 1
                                \   3           3   /     
or
  /                 
 |                  
 |    x - 2         
 | ------------ dx  
 |  2              =
 | x  - 4*x + 7     
 |                  
/                   
  
  /               
 |                
 |   2*x - 4      
 | ------------ dx
 |  2             
 | x  - 4*x + 7   
 |                
/                 
------------------
        2         
In the integral
  /               
 |                
 |   2*x - 4      
 | ------------ dx
 |  2             
 | x  - 4*x + 7   
 |                
/                 
------------------
        2         
do replacement
     2      
u = x  - 4*x
then
the integral =
  /                     
 |                      
 |   1                  
 | ----- du             
 | 7 + u                
 |                      
/             log(7 + u)
----------- = ----------
     2            2     
do backward replacement
  /                                   
 |                                    
 |   2*x - 4                          
 | ------------ dx                    
 |  2                                 
 | x  - 4*x + 7                       
 |                      /     2      \
/                    log\7 + x  - 4*x/
------------------ = -----------------
        2                    2        
In the integral
0
do replacement
        ___       ___
    2*\/ 3    x*\/ 3 
v = ------- - -------
       3         3   
then
the integral =
True
do backward replacement
True
Solution is:
       /     2      \
    log\7 + x  - 4*x/
C + -----------------
            2        
The answer (Indefinite) [src]
  /                                       
 |                          / 2          \
 |    x - 2              log\x  - 4*x + 7/
 | ------------ dx = C + -----------------
 |  2                            2        
 | x  - 4*x + 7                           
 |                                        
/                                         
$$\int \frac{x - 2}{\left(x^{2} - 4 x\right) + 7}\, dx = C + \frac{\log{\left(\left(x^{2} - 4 x\right) + 7 \right)}}{2}$$
The graph
The answer [src]
log(4)   log(7)
------ - ------
  2        2   
$$- \frac{\log{\left(7 \right)}}{2} + \frac{\log{\left(4 \right)}}{2}$$
=
=
log(4)   log(7)
------ - ------
  2        2   
$$- \frac{\log{\left(7 \right)}}{2} + \frac{\log{\left(4 \right)}}{2}$$
log(4)/2 - log(7)/2
Numerical answer [src]
-0.279807893967711
-0.279807893967711
The graph
Integral of (x-2)/(x^2-4x+7) dx

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