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3/(x^2-4)

Integral of 3/(x^2-4) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |    3      
 |  ------ dx
 |   2       
 |  x  - 4   
 |           
/            
0            
$$\int\limits_{0}^{1} \frac{3}{x^{2} - 4}\, dx$$
Integral(3/(x^2 - 1*4), (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Rewrite the integrand:

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

      1. Integrate term-by-term:

        1. The integral of is .

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

          1. The integral of is .

          So, the result is:

        The result is:

      So, the result is:

    So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                            
 |                                             
 |   3             3*log(2 + x)   3*log(-2 + x)
 | ------ dx = C - ------------ + -------------
 |  2                   4               4      
 | x  - 4                                      
 |                                             
/                                              
$$\int \frac{3}{x^{2} - 4}\, dx = C + \frac{3 \log{\left(x - 2 \right)}}{4} - \frac{3 \log{\left(x + 2 \right)}}{4}$$
The graph
The answer [src]
-3*log(3)
---------
    4    
$$- \frac{3 \log{\left(3 \right)}}{4}$$
=
=
-3*log(3)
---------
    4    
$$- \frac{3 \log{\left(3 \right)}}{4}$$
Numerical answer [src]
-0.823959216501082
-0.823959216501082
The graph
Integral of 3/(x^2-4) dx

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