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Solving integrals/ 1/√(1-4x^2)

Integral of 1/√(1-4x^2) dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |     __________   
 |    /        2    
 |  \/  1 - 4*x     
 |                  
/                   
0

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

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

Detail solution

TrigSubstitutionRule(theta=_theta, func=sin(_theta)/2, rewritten=1/2, substep=ConstantRule(constant=1/2, context=1/2, symbol=_theta), restriction=(x > -1/2) & (x < 1/2), context=1/(sqrt(1 - 4*x**2)), symbol=x)

Add the constant of integration:

$\begin{cases} \frac{\operatorname{asin}{\left(2 x \right)}}{2} & \text{for}\: x > - \frac{1}{2} \wedge x < \frac{1}{2} \end{cases}+ \mathrm{constant}$

The answer is:

$\begin{cases} \frac{\operatorname{asin}{\left(2 x \right)}}{2} & \text{for}\: x > - \frac{1}{2} \wedge x < \frac{1}{2} \end{cases}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                               
 |                                                                
 |       1                //asin(2*x)                            \
 | ------------- dx = C + |<---------  for And(x > -1/2, x < 1/2)|
 |    __________          \\    2                                /
 |   /        2                                                   
 | \/  1 - 4*x                                                    
 |                                                                
/

$$\int \frac{1}{\sqrt{1 - 4 x^{2}}}\, dx = C + \begin{cases} \frac{\operatorname{asin}{\left(2 x \right)}}{2} & \text{for}\: x > - \frac{1}{2} \wedge x < \frac{1}{2} \end{cases}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

asin(2)
-------
   2

$$\frac{\operatorname{asin}{\left(2 \right)}}{2}$$

asin(2)
-------
   2

$$\frac{\operatorname{asin}{\left(2 \right)}}{2}$$

asin(2)/2

The graph

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

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Identical expressions

Similar expressions

Integral of 1/√(1-4x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution