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Identical expressions
dx/(four - nine *x^ two)
dx divide by (4 minus 9 multiply by x squared )
dx divide by (four minus nine multiply by x to the power of two)
dx/(4-9*x2)
dx/4-9*x2
dx/(4-9*x²)
dx/(4-9*x to the power of 2)
dx/(4-9x^2)
dx/(4-9x2)
dx/4-9x2
dx/4-9x^2
dx divide by (4-9*x^2)
Similar expressions
dx/(4+9*x^2)

Solving integrals/ dx/(4-9*x^2)

Integral of dx/(4-9*x^2) dx

The solution

You have entered [src]

  1            
  /            
 |             
 |     1       
 |  -------- dx
 |         2   
 |  4 - 9*x    
 |             
/              
0

$$\int\limits_{0}^{1} \frac{1}{4 - 9 x^{2}}\, dx$$

Integral(1/(4 - 9*x^2), (x, 0, 1))

Detail solution

PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=-9, c=4, context=1/(4 - 9*x**2), symbol=x), False), (ArccothRule(a=1, b=-9, c=4, context=1/(4 - 9*x**2), symbol=x), x**2 > 4/9), (ArctanhRule(a=1, b=-9, c=4, context=1/(4 - 9*x**2), symbol=x), x**2 < 4/9)], context=1/(4 - 9*x**2), symbol=x)

Add the constant of integration:

$\begin{cases} \frac{\operatorname{acoth}{\left(\frac{3 x}{2} \right)}}{6} & \text{for}\: x^{2} > \frac{4}{9} \\\frac{\operatorname{atanh}{\left(\frac{3 x}{2} \right)}}{6} & \text{for}\: x^{2} < \frac{4}{9} \end{cases}+ \mathrm{constant}$

The answer is:

$\begin{cases} \frac{\operatorname{acoth}{\left(\frac{3 x}{2} \right)}}{6} & \text{for}\: x^{2} > \frac{4}{9} \\\frac{\operatorname{atanh}{\left(\frac{3 x}{2} \right)}}{6} & \text{for}\: x^{2} < \frac{4}{9} \end{cases}+ \mathrm{constant}$

The answer (Indefinite) [src]

                     //     /3*x\              \
                     ||acoth|---|              |
  /                  ||     \ 2 /       2      |
 |                   ||----------  for x  > 4/9|
 |    1              ||    6                   |
 | -------- dx = C + |<                        |
 |        2          ||     /3*x\              |
 | 4 - 9*x           ||atanh|---|              |
 |                   ||     \ 2 /       2      |
/                    ||----------  for x  < 4/9|
                     \\    6                   /

$$\int \frac{1}{4 - 9 x^{2}}\, dx = C + \begin{cases} \frac{\operatorname{acoth}{\left(\frac{3 x}{2} \right)}}{6} & \text{for}\: x^{2} > \frac{4}{9} \\\frac{\operatorname{atanh}{\left(\frac{3 x}{2} \right)}}{6} & \text{for}\: x^{2} < \frac{4}{9} \end{cases}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

nan

$$\text{NaN}$$

nan

$$\text{NaN}$$

nan

Numerical answer [src]

9.87634846831445

9.87634846831445

The graph

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

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Identical expressions

Similar expressions

Integral of dx/(4-9*x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution