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x/(x^2-9)
Solving integrals/ x/(x^2-9)

Integral of x/(x^2-9) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |    x      
 |  ------ dx
 |   2       
 |  x  - 9   
 |           
/            
0
$$\int\limits_{0}^{1} \frac{x}{x^{2} - 9}\, dx$$ 
Integral(x/(x^2 - 9), (x, 0, 1))
Detail solution
We have the integral:
  /         
 |          
 |   x      
 | ------ dx
 |  2       
 | x  - 9   
 |          
/
Rewrite the integrand
         /    2*x     \
         |------------|
         | 2          |
  x      \x  + 0*x - 9/
------ = --------------
 2             2       
x  - 9
or
  /           
 |            
 |   x        
 | ------ dx  
 |  2        =
 | x  - 9     
 |            
/             
  
  /               
 |                
 |     2*x        
 | ------------ dx
 |  2             
 | x  + 0*x - 9   
 |                
/                 
------------------
        2
In the integral
  /               
 |                
 |     2*x        
 | ------------ dx
 |  2             
 | x  + 0*x - 9   
 |                
/                 
------------------
        2
do replacement
     2
u = x
then
the integral =
  /                       
 |                        
 |   1                    
 | ------ du              
 | -9 + u                 
 |                        
/              log(-9 + u)
------------ = -----------
     2              2
do backward replacement
  /                              
 |                               
 |     2*x                       
 | ------------ dx               
 |  2                            
 | x  + 0*x - 9                  
 |                      /      2\
/                    log\-9 + x /
------------------ = ------------
        2                 2
Solution is:
       /      2\
    log\-9 + x /
C + ------------
         2
The answer (Indefinite) [src] 
  /                            
 |                    /      2\
 |   x             log\-9 + x /
 | ------ dx = C + ------------
 |  2                   2      
 | x  - 9                      
 |                             
/
$$\int \frac{x}{x^{2} - 9}\, dx = C + \frac{\log{\left(x^{2} - 9 \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
log(8)   log(9)
------ - ------
  2        2
$$- \frac{\log{\left(9 \right)}}{2} + \frac{\log{\left(8 \right)}}{2}$$ 
=
= 
log(8)   log(9)
------ - ------
  2        2
$$- \frac{\log{\left(9 \right)}}{2} + \frac{\log{\left(8 \right)}}{2}$$ 
log(8)/2 - log(9)/2
Numerical answer [src] 
-0.0588915178281917
-0.0588915178281917
The graph
Integral of x/(x^2-9) dx

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

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