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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |    1      
 |  ------ dx
 |       2   
 |  9 - x    
 |           
/            
0
∫0119−x2 dx\int\limits_{0}^{1} \frac{1}{9 - x^{2}}\, dx 
Integral(1/(9 - x^2), (x, 0, 1))
Detail solution

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

  1. Add the constant of integration:

    {acoth⁡(x3)3for x2>9atanh⁡(x3)3for x2<9+constant\begin{cases} \frac{\operatorname{acoth}{\left(\frac{x}{3} \right)}}{3} & \text{for}\: x^{2} > 9 \\\frac{\operatorname{atanh}{\left(\frac{x}{3} \right)}}{3} & \text{for}\: x^{2} < 9 \end{cases}+ \mathrm{constant}

The answer is:

{acoth⁡(x3)3for x2>9atanh⁡(x3)3for x2<9+constant\begin{cases} \frac{\operatorname{acoth}{\left(\frac{x}{3} \right)}}{3} & \text{for}\: x^{2} > 9 \\\frac{\operatorname{atanh}{\left(\frac{x}{3} \right)}}{3} & \text{for}\: x^{2} < 9 \end{cases}+ \mathrm{constant}

The answer (Indefinite) [src] 
                   //     /x\            \
                   ||acoth|-|            |
  /                ||     \3/       2    |
 |                 ||--------  for x  > 9|
 |   1             ||   3                |
 | ------ dx = C + |<                    |
 |      2          ||     /x\            |
 | 9 - x           ||atanh|-|            |
 |                 ||     \3/       2    |
/                  ||--------  for x  < 9|
                   \\   3                /
∫19−x2 dx=C+{acoth⁡(x3)3for x2>9atanh⁡(x3)3for x2<9\int \frac{1}{9 - x^{2}}\, dx = C + \begin{cases} \frac{\operatorname{acoth}{\left(\frac{x}{3} \right)}}{3} & \text{for}\: x^{2} > 9 \\\frac{\operatorname{atanh}{\left(\frac{x}{3} \right)}}{3} & \text{for}\: x^{2} < 9 \end{cases}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.100.14
Plot the graph f(x)
The answer [src] 
  log(2)   log(4)
- ------ + ------
    6        6
−log⁡(2)6+log⁡(4)6- \frac{\log{\left(2 \right)}}{6} + \frac{\log{\left(4 \right)}}{6} 
=
= 
  log(2)   log(4)
- ------ + ------
    6        6
−log⁡(2)6+log⁡(4)6- \frac{\log{\left(2 \right)}}{6} + \frac{\log{\left(4 \right)}}{6} 
-log(2)/6 + log(4)/6
Numerical answer [src] 
0.115524530093324
0.115524530093324
The graph
Integral of 1/(9-x^2) dx

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

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