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dx/(x^2-8x+17)

Integral of dx/(x^2-8x+17) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 oo                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |   2              
 |  x  - 8*x + 17   
 |                  
/                   
5                   
$$\int\limits_{5}^{\infty} \frac{1}{\left(x^{2} - 8 x\right) + 17}\, dx$$
Integral(1/(x^2 - 8*x + 17), (x, 5, oo))
Detail solution
We have the integral:
  /                
 |                 
 |       1         
 | ------------- dx
 |  2              
 | x  - 8*x + 17   
 |                 
/                  
Rewrite the integrand
      1                 1        
------------- = -----------------
 2                /        2    \
x  - 8*x + 17   1*\(-x + 4)  + 1/
or
  /                  
 |                   
 |       1           
 | ------------- dx  
 |  2               =
 | x  - 8*x + 17     
 |                   
/                    
  
  /                
 |                 
 |       1         
 | ------------- dx
 |         2       
 | (-x + 4)  + 1   
 |                 
/                  
In the integral
  /                
 |                 
 |       1         
 | ------------- dx
 |         2       
 | (-x + 4)  + 1   
 |                 
/                  
do replacement
v = 4 - x
then
the integral =
  /                   
 |                    
 |   1                
 | ------ dv = atan(v)
 |      2             
 | 1 + v              
 |                    
/                     
do backward replacement
  /                               
 |                                
 |       1                        
 | ------------- dx = atan(-4 + x)
 |         2                      
 | (-x + 4)  + 1                  
 |                                
/                                 
Solution is:
C + atan(-4 + x)
The answer (Indefinite) [src]
  /                                   
 |                                    
 |       1                            
 | ------------- dx = C + atan(-4 + x)
 |  2                                 
 | x  - 8*x + 17                      
 |                                    
/                                     
$$\int \frac{1}{\left(x^{2} - 8 x\right) + 17}\, dx = C + \operatorname{atan}{\left(x - 4 \right)}$$
The graph
The answer [src]
pi
--
4 
$$\frac{\pi}{4}$$
=
=
pi
--
4 
$$\frac{\pi}{4}$$
pi/4
The graph
Integral of dx/(x^2-8x+17) dx

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