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(x^2-81)/(x+9)

Integral of (x^2-81)/(x+9) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1           
  /           
 |            
 |   2        
 |  x  - 81   
 |  ------- dx
 |   x + 9    
 |            
/             
0             
$$\int\limits_{0}^{1} \frac{x^{2} - 81}{x + 9}\, dx$$
Integral((x^2 - 81)/(x + 9), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. The integral of is when :

      1. The integral of a constant is the constant times the variable of integration:

      The result is:

    Method #2

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. Rewrite the integrand:

      2. Integrate term-by-term:

        1. The integral of is when :

        1. The integral of a constant is the constant times the variable of integration:

        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:

        The result is:

      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:

      The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                         
 |                          
 |  2                2      
 | x  - 81          x       
 | ------- dx = C + -- - 9*x
 |  x + 9           2       
 |                          
/                           
$$\int \frac{x^{2} - 81}{x + 9}\, dx = C + \frac{x^{2}}{2} - 9 x$$
The graph
The answer [src]
-17/2
$$- \frac{17}{2}$$
=
=
-17/2
$$- \frac{17}{2}$$
-17/2
Numerical answer [src]
-8.5
-8.5
The graph
Integral of (x^2-81)/(x+9) dx

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