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1/sqrt(2-(5x)^2)
Solving integrals/ 1/sqrt(2-(5x)^2)

Integral of 1/sqrt(2-(5x)^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    
 |  \/  2 - (5*x)     
 |                    
/                     
0
∫0112−(5x)2 dx\int\limits_{0}^{1} \frac{1}{\sqrt{2 - \left(5 x\right)^{2}}}\, dx 
Integral(1/(sqrt(2 - (5*x)^2)), (x, 0, 1))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=sqrt(2)*sin(_theta)/5, rewritten=1/5, substep=ConstantRule(constant=1/5, context=1/5, symbol=_theta), restriction=(x > -sqrt(2)/5) & (x < sqrt(2)/5), context=1/(sqrt(2 - (5*x)**2)), symbol=x)

  1. Add the constant of integration:

    {asin⁡(52x2)5for x>−25∧x<25+constant\begin{cases} \frac{\operatorname{asin}{\left(\frac{5 \sqrt{2} x}{2} \right)}}{5} & \text{for}\: x > - \frac{\sqrt{2}}{5} \wedge x < \frac{\sqrt{2}}{5} \end{cases}+ \mathrm{constant}

The answer is:

{asin⁡(52x2)5for x>−25∧x<25+constant\begin{cases} \frac{\operatorname{asin}{\left(\frac{5 \sqrt{2} x}{2} \right)}}{5} & \text{for}\: x > - \frac{\sqrt{2}}{5} \wedge x < \frac{\sqrt{2}}{5} \end{cases}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                         //    /      ___\                                 \
 |                          ||    |5*x*\/ 2 |                                 |
 |        1                 ||asin|---------|         /       ___         ___\|
 | --------------- dx = C + |<    \    2    /         |    -\/ 2        \/ 2 ||
 |    ____________          ||---------------  for And|x > -------, x < -----||
 |   /          2           ||       5                \       5           5  /|
 | \/  2 - (5*x)            \\                                                /
 |                                                                             
/
∫12−(5x)2 dx=C+{asin⁡(52x2)5for x>−25∧x<25\int \frac{1}{\sqrt{2 - \left(5 x\right)^{2}}}\, dx = C + \begin{cases} \frac{\operatorname{asin}{\left(\frac{5 \sqrt{2} x}{2} \right)}}{5} & \text{for}\: x > - \frac{\sqrt{2}}{5} \wedge x < \frac{\sqrt{2}}{5} \end{cases}
Simplify
The graph
0.0000.0250.0500.0750.1000.1250.1500.1750.2000.2250.2500.275050
Plot the graph f(x)
The answer [src] 
    /    ___\
    |5*\/ 2 |
asin|-------|
    \   2   /
-------------
      5
asin⁡(522)5\frac{\operatorname{asin}{\left(\frac{5 \sqrt{2}}{2} \right)}}{5} 
=
= 
    /    ___\
    |5*\/ 2 |
asin|-------|
    \   2   /
-------------
      5
asin⁡(522)5\frac{\operatorname{asin}{\left(\frac{5 \sqrt{2}}{2} \right)}}{5} 
asin(5*sqrt(2)/2)/5
Numerical answer [src] 
(0.313073650498126 - 0.36029517896484j)
(0.313073650498126 - 0.36029517896484j)
The graph
Integral of 1/sqrt(2-(5x)^2) dx

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

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