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dx/(9*x^2-1)

Integral of dx/(9*x^2-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1              
  /              
 |               
 |       1       
 |  1*-------- dx
 |       2       
 |    9*x  - 1   
 |               
/                
0                
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{9 x^{2} - 1}\, dx$$
Integral(1/(9*x^2 - 1*1), (x, 0, 1))
Detail solution
  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:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                
 |                                                 
 |      1              log(1/3 + x)   log(-1/3 + x)
 | 1*-------- dx = C - ------------ + -------------
 |      2                   6               6      
 |   9*x  - 1                                      
 |                                                 
/                                                  
$${{\log \left(3\,x-1\right)}\over{6}}-{{\log \left(3\,x+1\right) }\over{6}}$$
The graph
The answer [src]
nan
$${{\log 2}\over{6}}-{{\log 4}\over{6}}$$
=
=
nan
$$\text{NaN}$$
Numerical answer [src]
19.3689327544632
19.3689327544632
The graph
Integral of dx/(9*x^2-1) dx

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