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1/(2x^2-12x+26)

Integral of 1/(2x^2-12x+26) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                      
  /                      
 |                       
 |           1           
 |  1*---------------- dx
 |       2               
 |    2*x  - 12*x + 26   
 |                       
/                        
0                        
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{2 x^{2} - 12 x + 26}\, dx$$
Integral(1/(2*x^2 - 12*x + 26), (x, 0, 1))
Detail solution
We have the integral:
  /                       
 |                        
 |            1           
 | 1*1*---------------- dx
 |        2               
 |     2*x  - 12*x + 26   
 |                        
/                         
Rewrite the integrand
         1                   1         
1*---------------- = ------------------
     2                 /         2    \
  2*x  - 12*x + 26     |/  x   3\     |
                     8*||- - + -|  + 1|
                       \\  2   2/     /
or
  /                         
 |                          
 |            1             
 | 1*1*---------------- dx  
 |        2                =
 |     2*x  - 12*x + 26     
 |                          
/                           
  
  /                 
 |                  
 |       1          
 | -------------- dx
 |          2       
 | /  x   3\        
 | |- - + -|  + 1   
 | \  2   2/        
 |                  
/                   
--------------------
         8          
In the integral
  /                 
 |                  
 |       1          
 | -------------- dx
 |          2       
 | /  x   3\        
 | |- - + -|  + 1   
 | \  2   2/        
 |                  
/                   
--------------------
         8          
do replacement
    3   x
v = - - -
    2   2
then
the integral =
  /                   
 |                    
 |   1                
 | ------ dv          
 |      2             
 | 1 + v              
 |                    
/              atan(v)
------------ = -------
     8            8   
do backward replacement
  /                                 
 |                                  
 |       1                          
 | -------------- dx                
 |          2                       
 | /  x   3\                        
 | |- - + -|  + 1                   
 | \  2   2/               /  3   x\
 |                     atan|- - + -|
/                          \  2   2/
-------------------- = -------------
         8                   4      
Solution is:
        /  3   x\
    atan|- - + -|
        \  2   2/
C + -------------
          4      
The answer (Indefinite) [src]
  /                                /  3   x\
 |                             atan|- - + -|
 |          1                      \  2   2/
 | 1*---------------- dx = C + -------------
 |      2                            4      
 |   2*x  - 12*x + 26                       
 |                                          
/                                           
$${{\arctan \left({{2\,x-6}\over{4}}\right)}\over{4}}$$
The graph
The answer [src]
  pi   atan(3/2)
- -- + ---------
  16       4    
$${{\arctan \left({{3}\over{2}}\right)}\over{4}}-{{\pi}\over{16}}$$
=
=
  pi   atan(3/2)
- -- + ---------
  16       4    
$$- \frac{\pi}{16} + \frac{\operatorname{atan}{\left(\frac{3}{2} \right)}}{4}$$
Numerical answer [src]
0.0493488899624702
0.0493488899624702
The graph
Integral of 1/(2x^2-12x+26) dx

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