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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

    PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=9, c=-1, context=1/(9*x**2 - 1), symbol=x), False), (ArccothRule(a=1, b=9, c=-1, context=1/(9*x**2 - 1), symbol=x), x**2 > 1/9), (ArctanhRule(a=1, b=9, c=-1, context=1/(9*x**2 - 1), symbol=x), x**2 < 1/9)], context=1/(9*x**2 - 1), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                  //-acoth(3*x)        2      \
 |                   ||------------  for x  > 1/9|
 |    1              ||     3                    |
 | -------- dx = C + |<                          |
 |    2              ||-atanh(3*x)        2      |
 | 9*x  - 1          ||------------  for x  < 1/9|
 |                   \\     3                    /
/
$$\int \frac{1}{9 x^{2} - 1}\, dx = C + \begin{cases} - \frac{\operatorname{acoth}{\left(3 x \right)}}{3} & \text{for}\: x^{2} > \frac{1}{9} \\- \frac{\operatorname{atanh}{\left(3 x \right)}}{3} & \text{for}\: x^{2} < \frac{1}{9} \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
nan
$$\text{NaN}$$ 
=
= 
nan
$$\text{NaN}$$ 
nan
Numerical answer [src] 
19.3689327544632
19.3689327544632

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

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