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1/(x^2-4x+5)

Integral of 1/(x^2-4x+5) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 oo                  
  /                  
 |                   
 |         1         
 |  1*------------ dx
 |     2             
 |    x  - 4*x + 5   
 |                   
/                    
-oo                  
$$\int\limits_{-\infty}^{\infty} 1 \cdot \frac{1}{x^{2} - 4 x + 5}\, dx$$
Integral(1/(x^2 - 4*x + 5), (x, -oo, oo))
Detail solution
We have the integral:
  /                   
 |                    
 |          1         
 | 1*1*------------ dx
 |      2             
 |     x  - 4*x + 5   
 |                    
/                     
Rewrite the integrand
       1                 1        
1*------------ = -----------------
   2               /        2    \
  x  - 4*x + 5   1*\(-x + 2)  + 1/
or
  /                     
 |                      
 |          1           
 | 1*1*------------ dx  
 |      2              =
 |     x  - 4*x + 5     
 |                      
/                       
  
  /                
 |                 
 |       1         
 | ------------- dx
 |         2       
 | (-x + 2)  + 1   
 |                 
/                  
In the integral
  /                
 |                 
 |       1         
 | ------------- dx
 |         2       
 | (-x + 2)  + 1   
 |                 
/                  
do replacement
v = 2 - x
then
the integral =
  /                   
 |                    
 |   1                
 | ------ dv = atan(v)
 |      2             
 | 1 + v              
 |                    
/                     
do backward replacement
  /                               
 |                                
 |       1                        
 | ------------- dx = atan(-2 + x)
 |         2                      
 | (-x + 2)  + 1                  
 |                                
/                                 
Solution is:
C + atan(-2 + x)
The answer (Indefinite) [src]
  /                                    
 |                                     
 |        1                            
 | 1*------------ dx = C + atan(-2 + x)
 |    2                                
 |   x  - 4*x + 5                      
 |                                     
/                                      
$$\int 1 \cdot \frac{1}{x^{2} - 4 x + 5}\, dx = C + \operatorname{atan}{\left(x - 2 \right)}$$
The graph
The answer [src]
pi
$$\pi$$
=
=
pi
$$\pi$$
Numerical answer [src]
3.14159265358979
3.14159265358979
The graph
Integral of 1/(x^2-4x+5) dx

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