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Solving integrals/ dx/sqrt(1-8x^2)

Integral of dx/sqrt(1-8x^2) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |     __________   
 |    /        2    
 |  \/  1 - 8*x     
 |                  
/                   
0
∫0111−8x2 dx\int\limits_{0}^{1} \frac{1}{\sqrt{1 - 8 x^{2}}}\, dx 
Integral(1/(sqrt(1 - 8*x^2)), (x, 0, 1))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=sqrt(2)*sin(_theta)/4, rewritten=sqrt(2)/4, substep=ConstantRule(constant=sqrt(2)/4, context=sqrt(2)/4, symbol=_theta), restriction=(x > -sqrt(2)/4) & (x < sqrt(2)/4), context=1/(sqrt(1 - 8*x**2)), symbol=x)

  1. Add the constant of integration:

    {2asin⁡(22x)4for x>−24∧x<24+constant\begin{cases} \frac{\sqrt{2} \operatorname{asin}{\left(2 \sqrt{2} x \right)}}{4} & \text{for}\: x > - \frac{\sqrt{2}}{4} \wedge x < \frac{\sqrt{2}}{4} \end{cases}+ \mathrm{constant}

The answer is:

{2asin⁡(22x)4for x>−24∧x<24+constant\begin{cases} \frac{\sqrt{2} \operatorname{asin}{\left(2 \sqrt{2} x \right)}}{4} & \text{for}\: x > - \frac{\sqrt{2}}{4} \wedge x < \frac{\sqrt{2}}{4} \end{cases}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                                                
 |                        //  ___     /      ___\         /       ___         ___\\
 |       1                ||\/ 2 *asin\2*x*\/ 2 /         |    -\/ 2        \/ 2 ||
 | ------------- dx = C + |<---------------------  for And|x > -------, x < -----||
 |    __________          ||          4                   \       4           4  /|
 |   /        2           \\                                                      /
 | \/  1 - 8*x                                                                     
 |                                                                                 
/
∫11−8x2 dx=C+{2asin⁡(22x)4for x>−24∧x<24\int \frac{1}{\sqrt{1 - 8 x^{2}}}\, dx = C + \begin{cases} \frac{\sqrt{2} \operatorname{asin}{\left(2 \sqrt{2} x \right)}}{4} & \text{for}\: x > - \frac{\sqrt{2}}{4} \wedge x < \frac{\sqrt{2}}{4} \end{cases}
Simplify
The graph
0.000.050.100.150.200.250.300.350100
Plot the graph f(x)
The answer [src] 
  ___     /    ___\
\/ 2 *asin\2*\/ 2 /
-------------------
         4
2asin⁡(22)4\frac{\sqrt{2} \operatorname{asin}{\left(2 \sqrt{2} \right)}}{4} 
=
= 
  ___     /    ___\
\/ 2 *asin\2*\/ 2 /
-------------------
         4
2asin⁡(22)4\frac{\sqrt{2} \operatorname{asin}{\left(2 \sqrt{2} \right)}}{4} 
sqrt(2)*asin(2*sqrt(2))/4
Numerical answer [src] 
(0.503887140518608 - 0.619511988515451j)
(0.503887140518608 - 0.619511988515451j)

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

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