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Solving integrals/ dx/(x^2-2*x+10)

Integral of dx/(x^2-2*x+10) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  4                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |   2              
 |  x  - 2*x + 10   
 |                  
/                   
1
$$\int\limits_{1}^{4} \frac{1}{\left(x^{2} - 2 x\right) + 10}\, dx$$ 
Integral(1/(x^2 - 2*x + 10), (x, 1, 4))
Detail solution
We have the integral:
  /                
 |                 
 |       1         
 | ------------- dx
 |  2              
 | x  - 2*x + 10   
 |                 
/
Rewrite the integrand
      1                 1         
------------- = ------------------
 2                /         2    \
x  - 2*x + 10     |/  x   1\     |
                9*||- - + -|  + 1|
                  \\  3   3/     /
or
  /                  
 |                   
 |       1           
 | ------------- dx  
 |  2               =
 | x  - 2*x + 10     
 |                   
/                    
  
  /                 
 |                  
 |       1          
 | -------------- dx
 |          2       
 | /  x   1\        
 | |- - + -|  + 1   
 | \  3   3/        
 |                  
/                   
--------------------
         9
In the integral
  /                 
 |                  
 |       1          
 | -------------- dx
 |          2       
 | /  x   1\        
 | |- - + -|  + 1   
 | \  3   3/        
 |                  
/                   
--------------------
         9
do replacement
    1   x
v = - - -
    3   3
then
the integral =
  /                   
 |                    
 |   1                
 | ------ dv          
 |      2             
 | 1 + v              
 |                    
/              atan(v)
------------ = -------
     9            9
do backward replacement
  /                                 
 |                                  
 |       1                          
 | -------------- dx                
 |          2                       
 | /  x   1\                        
 | |- - + -|  + 1                   
 | \  3   3/               /  1   x\
 |                     atan|- - + -|
/                          \  3   3/
-------------------- = -------------
         9                   3
Solution is:
        /  1   x\
    atan|- - + -|
        \  3   3/
C + -------------
          3
The answer (Indefinite) [src] 
  /                           /  1   x\
 |                        atan|- - + -|
 |       1                    \  3   3/
 | ------------- dx = C + -------------
 |  2                           3      
 | x  - 2*x + 10                       
 |                                     
/
$$\int \frac{1}{\left(x^{2} - 2 x\right) + 10}\, dx = C + \frac{\operatorname{atan}{\left(\frac{x}{3} - \frac{1}{3} \right)}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
pi
--
12
$$\frac{\pi}{12}$$ 
=
= 
pi
--
12
$$\frac{\pi}{12}$$ 
pi/12
Numerical answer [src] 
0.261799387799149
0.261799387799149

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

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