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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                    
  /                    
 |                     
 |          1          
 |  1*-------------- dx
 |       2             
 |    4*x  - 4*x + 5   
 |                     
/                      
0
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{4 x^{2} - 4 x + 5}\, dx$$ 
Integral(1/(4*x^2 - 4*x + 5), (x, 0, 1))
Detail solution
We have the integral:
  /                     
 |                      
 |           1          
 | 1*1*-------------- dx
 |        2             
 |     4*x  - 4*x + 5   
 |                      
/
Rewrite the integrand
        1                   1         
1*-------------- = -------------------
     2               /          2    \
  4*x  - 4*x + 5   4*\(-x + 1/2)  + 1/
or
  /                       
 |                        
 |           1            
 | 1*1*-------------- dx  
 |        2              =
 |     4*x  - 4*x + 5     
 |                        
/                         
  
  /                  
 |                   
 |        1          
 | --------------- dx
 |           2       
 | (-x + 1/2)  + 1   
 |                   
/                    
---------------------
          4
In the integral
  /                  
 |                   
 |        1          
 | --------------- dx
 |           2       
 | (-x + 1/2)  + 1   
 |                   
/                    
---------------------
          4
do replacement
v = 1/2 - x
then
the integral =
  /                   
 |                    
 |   1                
 | ------ dv          
 |      2             
 | 1 + v              
 |                    
/              atan(v)
------------ = -------
     4            4
do backward replacement
  /                                   
 |                                    
 |        1                           
 | --------------- dx                 
 |           2                        
 | (-x + 1/2)  + 1                    
 |                                    
/                       atan(-1/2 + x)
--------------------- = --------------
          4                   4
Solution is:
    atan(-1/2 + x)
C + --------------
          4
The answer (Indefinite) [src] 
  /                                        
 |                                         
 |         1                 atan(-1/2 + x)
 | 1*-------------- dx = C + --------------
 |      2                          4       
 |   4*x  - 4*x + 5                        
 |                                         
/
$${{\arctan \left({{8\,x-4}\over{8}}\right)}\over{4}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
atan(1/2)
---------
    2
$${{\arctan \left({{1}\over{2}}\right)}\over{2}}$$ 
=
= 
atan(1/2)
---------
    2
$$\frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{2}$$
Упростить
Numerical answer [src] 
0.231823804500403
0.231823804500403
The graph
Integral of 1/(4x^2-4x+5) dx

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

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