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Solving integrals/ (sqrt(x^2+6x+4))/(x^2+6x+9)

Integral of (sqrt(x^2+6x+4))/(x^2+6x+9) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                     
  /                     
 |                      
 |     ______________   
 |    /  2              
 |  \/  x  + 6*x + 4    
 |  ----------------- dx
 |      2               
 |     x  + 6*x + 9     
 |                      
/                       
0
$$\int\limits_{0}^{1} \frac{\sqrt{\left(x^{2} + 6 x\right) + 4}}{\left(x^{2} + 6 x\right) + 9}\, dx$$ 
Integral(sqrt(x^2 + 6*x + 4)/(x^2 + 6*x + 9), (x, 0, 1))
The answer (Indefinite) [src] 
  /                             /                    
 |                             |                     
 |    ______________           |    ______________   
 |   /  2                      |   /      2          
 | \/  x  + 6*x + 4            | \/  4 + x  + 6*x    
 | ----------------- dx = C +  | ----------------- dx
 |     2                       |             2       
 |    x  + 6*x + 9             |      (3 + x)        
 |                             |                     
/                             /
$$\int \frac{\sqrt{\left(x^{2} + 6 x\right) + 4}}{\left(x^{2} + 6 x\right) + 9}\, dx = C + \int \frac{\sqrt{x^{2} + 6 x + 4}}{\left(x + 3\right)^{2}}\, dx$$
Simplify
The answer [src] 
  1                     
  /                     
 |                      
 |     ______________   
 |    /      2          
 |  \/  4 + x  + 6*x    
 |  ----------------- dx
 |              2       
 |       (3 + x)        
 |                      
/                       
0
$$\int\limits_{0}^{1} \frac{\sqrt{x^{2} + 6 x + 4}}{\left(x + 3\right)^{2}}\, dx$$ 
=
= 
  1                     
  /                     
 |                      
 |     ______________   
 |    /      2          
 |  \/  4 + x  + 6*x    
 |  ----------------- dx
 |              2       
 |       (3 + x)        
 |                      
/                       
0
$$\int\limits_{0}^{1} \frac{\sqrt{x^{2} + 6 x + 4}}{\left(x + 3\right)^{2}}\, dx$$ 
Integral(sqrt(4 + x^2 + 6*x)/(3 + x)^2, (x, 0, 1))
Numerical answer [src] 
0.218221684066568
0.218221684066568

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

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