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dx/(1-4*x^2)
Solving integrals/ dx/(1-4*x^2)

Integral of dx/(1-4*x^2) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |     1       
 |  -------- dx
 |         2   
 |  1 - 4*x    
 |             
/              
0
∫0111−4x2 dx\int\limits_{0}^{1} \frac{1}{1 - 4 x^{2}}\, dx 
Integral(1/(1 - 4*x^2), (x, 0, 1))
Detail solution

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

  1. Add the constant of integration:

    {acoth⁡(2x)2for x2>14atanh⁡(2x)2for x2<14+constant\begin{cases} \frac{\operatorname{acoth}{\left(2 x \right)}}{2} & \text{for}\: x^{2} > \frac{1}{4} \\\frac{\operatorname{atanh}{\left(2 x \right)}}{2} & \text{for}\: x^{2} < \frac{1}{4} \end{cases}+ \mathrm{constant}

The answer is:

{acoth⁡(2x)2for x2>14atanh⁡(2x)2for x2<14+constant\begin{cases} \frac{\operatorname{acoth}{\left(2 x \right)}}{2} & \text{for}\: x^{2} > \frac{1}{4} \\\frac{\operatorname{atanh}{\left(2 x \right)}}{2} & \text{for}\: x^{2} < \frac{1}{4} \end{cases}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  //acoth(2*x)       2      \
 |                   ||----------  for x  > 1/4|
 |    1              ||    2                   |
 | -------- dx = C + |<                        |
 |        2          ||atanh(2*x)       2      |
 | 1 - 4*x           ||----------  for x  < 1/4|
 |                   \\    2                   /
/
∫11−4x2 dx=C+{acoth⁡(2x)2for x2>14atanh⁡(2x)2for x2<14\int \frac{1}{1 - 4 x^{2}}\, dx = C + \begin{cases} \frac{\operatorname{acoth}{\left(2 x \right)}}{2} & \text{for}\: x^{2} > \frac{1}{4} \\\frac{\operatorname{atanh}{\left(2 x \right)}}{2} & \text{for}\: x^{2} < \frac{1}{4} \end{cases}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-1000010000
Plot the graph f(x)
The answer [src] 
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The graph
Integral of dx/(1-4*x^2) dx

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

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