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Identical expressions
three /(x^ two - four)
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three divide by (x to the power of two minus four)
3/(x2-4)
3/x2-4
3/(x²-4)
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3/x^2-4
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3/(x^2-4)dx
Similar expressions
3/(x^2+4)

Solving integrals/ 3/(x^2-4)

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

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

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

$\int \frac{3}{x^{2} - 4}\, dx = 3 \int \frac{1}{x^{2} - 4}\, dx$
1. Rewrite the integrand:
  
  $\frac{1}{x^{2} - 4} = \frac{- \frac{1}{x + 2} + \frac{1}{x - 2}}{4}$
2. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{- \frac{1}{x + 2} + \frac{1}{x - 2}}{4}\, dx = \frac{\int \left(- \frac{1}{x + 2} + \frac{1}{x - 2}\right)\, dx}{4}$
  1. Integrate term-by-term:
    1. The integral of $\frac{1}{x - 2}$ is $\log{\left(x - 2 \right)}$ .
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \left(- \frac{1}{x + 2}\right)\, dx = - \int \frac{1}{x + 2}\, dx$
      1. The integral of $\frac{1}{x + 2}$ is $\log{\left(x + 2 \right)}$ .
      So, the result is: $- \log{\left(x + 2 \right)}$
    The result is: $\log{\left(x - 2 \right)} - \log{\left(x + 2 \right)}$
  So, the result is: $\frac{\log{\left(x - 2 \right)}}{4} - \frac{\log{\left(x + 2 \right)}}{4}$
So, the result is: $\frac{3 \log{\left(x - 2 \right)}}{4} - \frac{3 \log{\left(x + 2 \right)}}{4}$
Add the constant of integration:

$\frac{3 \log{\left(x - 2 \right)}}{4} - \frac{3 \log{\left(x + 2 \right)}}{4}+ \mathrm{constant}$

The answer is:

\frac{3 \log{\left(x - 2 \right)}}{4} - \frac{3 \log{\left(x + 2 \right)}}{4}+ \mathrm{constant}

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}

Simplify

The graph

Plot the graph f(x)

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}

Упростить

Numerical answer [src]

-0.823959216501082

-0.823959216501082

The graph

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

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

Limits of integration:

The graph:

Piecewise:

The solution