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Identical expressions
dx/(nine *x^ two - one)
dx divide by (9 multiply by x squared minus 1)
dx divide by (nine multiply by x to the power of two minus one)
dx/(9*x2-1)
dx/9*x2-1
dx/(9*x²-1)
dx/(9*x to the power of 2-1)
dx/(9x^2-1)
dx/(9x2-1)
dx/9x2-1
dx/9x^2-1
dx divide by (9*x^2-1)
Similar expressions
dx/(9*x^2+1)

Solving integrals/ dx/(9*x^2-1)

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

The solution

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  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

Rewrite the integrand:

$1 \cdot \frac{1}{9 x^{2} - 1} = \frac{- \frac{1}{x + \frac{1}{3}} + \frac{1}{x - \frac{1}{3}}}{6}$
The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{- \frac{1}{x + \frac{1}{3}} + \frac{1}{x - \frac{1}{3}}}{6}\, dx = \frac{\int \left(- \frac{1}{x + \frac{1}{3}} + \frac{1}{x - \frac{1}{3}}\right)\, dx}{6}$
1. Integrate term-by-term:
  1. The integral of $\frac{1}{x - \frac{1}{3}}$ is $\log{\left(x - \frac{1}{3} \right)}$ .
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{1}{x + \frac{1}{3}}\right)\, dx = - \int \frac{1}{x + \frac{1}{3}}\, dx$
    1. The integral of $\frac{1}{x + \frac{1}{3}}$ is $\log{\left(x + \frac{1}{3} \right)}$ .
    So, the result is: $- \log{\left(x + \frac{1}{3} \right)}$
  The result is: $\log{\left(x - \frac{1}{3} \right)} - \log{\left(x + \frac{1}{3} \right)}$
So, the result is: $\frac{\log{\left(x - \frac{1}{3} \right)}}{6} - \frac{\log{\left(x + \frac{1}{3} \right)}}{6}$
Add the constant of integration:

$\frac{\log{\left(x - \frac{1}{3} \right)}}{6} - \frac{\log{\left(x + \frac{1}{3} \right)}}{6}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(x - \frac{1}{3} \right)}}{6} - \frac{\log{\left(x + \frac{1}{3} \right)}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                
 |                                                 
 |      1              log(1/3 + x)   log(-1/3 + x)
 | 1*-------- dx = C - ------------ + -------------
 |      2                   6               6      
 |   9*x  - 1                                      
 |                                                 
/

$${{\log \left(3\,x-1\right)}\over{6}}-{{\log \left(3\,x+1\right) }\over{6}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

nan

$${{\log 2}\over{6}}-{{\log 4}\over{6}}$$

nan

$$\text{NaN}$$

Упростить

Numerical answer [src]

19.3689327544632

19.3689327544632

The graph

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

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

Limits of integration:

The graph:

Piecewise:

The solution