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1/(x^2+9x+20)

Integral of 1/(x^2+9x+20) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 oo                   
  /                   
 |                    
 |          1         
 |  1*------------- dx
 |     2              
 |    x  + 9*x + 20   
 |                    
/                     
7                     
$$\int\limits_{7}^{\infty} 1 \cdot \frac{1}{x^{2} + 9 x + 20}\, dx$$
Detail solution
  1. Rewrite the integrand:

  2. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. Let .

        Then let and substitute :

        1. The integral of is .

        Now substitute back in:

      So, the result is:

    1. Let .

      Then let and substitute :

      1. The integral of is .

      Now substitute back in:

    The result is:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                
 |                                                 
 |         1                                       
 | 1*------------- dx = C - log(5 + x) + log(4 + x)
 |    2                                            
 |   x  + 9*x + 20                                 
 |                                                 
/                                                  
$$\log \left(x+4\right)-\log \left(x+5\right)$$
The graph
The answer [src]
-log(11) + log(12)
$$- \log{\left(11 \right)} + \log{\left(12 \right)}$$
=
=
-log(11) + log(12)
$$- \log{\left(11 \right)} + \log{\left(12 \right)}$$
The graph
Integral of 1/(x^2+9x+20) dx

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