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Solving integrals/ (2x-5)/(x^2-5x+4)

Integral of (2x-5)/(x^2-5x+4) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |    2*x - 5      
 |  ------------ dx
 |   2             
 |  x  - 5*x + 4   
 |                 
/                  
0
$$\int\limits_{0}^{1} \frac{2 x - 5}{\left(x^{2} - 5 x\right) + 4}\, dx$$ 
Integral((2*x - 5)/(x^2 - 5*x + 4), (x, 0, 1))
Detail solution
We have the integral:
  /               
 |                
 |   2*x - 5      
 | ------------ dx
 |  2             
 | x  - 5*x + 4   
 |                
/
Rewrite the integrand
True
or
  /                 
 |                  
 |   2*x - 5        
 | ------------ dx  
 |  2              =
 | x  - 5*x + 4     
 |                  
/                   
  
  /               
 |                
 |   2*x - 5      
 | ------------ dx
 |  2             
 | x  - 5*x + 4   
 |                
/
In the integral
  /               
 |                
 |   2*x - 5      
 | ------------ dx
 |  2             
 | x  - 5*x + 4   
 |                
/
do replacement
     2      
u = x  - 5*x
then
the integral =
  /                     
 |                      
 |   1                  
 | ----- du = log(4 + u)
 | 4 + u                
 |                      
/
do backward replacement
  /                                   
 |                                    
 |   2*x - 5            /     2      \
 | ------------ dx = log\4 + x  - 5*x/
 |  2                                 
 | x  - 5*x + 4                       
 |                                    
/
Solution is:
       /     2      \
C + log\4 + x  - 5*x/
The answer (Indefinite) [src] 
  /                                       
 |                                        
 |   2*x - 5                / 2          \
 | ------------ dx = C + log\x  - 5*x + 4/
 |  2                                     
 | x  - 5*x + 4                           
 |                                        
/
$$\int \frac{2 x - 5}{\left(x^{2} - 5 x\right) + 4}\, dx = C + \log{\left(\left(x^{2} - 5 x\right) + 4 \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
-oo
$$-\infty$$ 
=
= 
-oo
$$-\infty$$ 
-oo
Numerical answer [src] 
-44.378726946325
-44.378726946325

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

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