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  • Identical expressions

  • one *dx/(sqrt(five - four *x^ two))
  • 1 multiply by dx divide by ( square root of (5 minus 4 multiply by x squared ))
  • one multiply by dx divide by ( square root of (five minus four multiply by x to the power of two))
  • 1*dx/(√(5-4*x^2))
  • 1*dx/(sqrt(5-4*x2))
  • 1*dx/sqrt5-4*x2
  • 1*dx/(sqrt(5-4*x²))
  • 1*dx/(sqrt(5-4*x to the power of 2))
  • 1dx/(sqrt(5-4x^2))
  • 1dx/(sqrt(5-4x2))
  • 1dx/sqrt5-4x2
  • 1dx/sqrt5-4x^2
  • 1*dx divide by (sqrt(5-4*x^2))

  • Similar expressions

  • 1*dx/(sqrt(5+4*x^2))
Solving integrals/ 1*dx/(sqrt(5-4*x^2))

Integral of 1*dx/(sqrt(5-4*x^2)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |     __________   
 |    /        2    
 |  \/  5 - 4*x     
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{5 - 4 x^{2}}}\, dx$$ 
Integral(1/(sqrt(5 - 4*x^2)), (x, 0, 1))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=sqrt(5)*sin(_theta)/2, rewritten=1/2, substep=ConstantRule(constant=1/2, context=1/2, symbol=_theta), restriction=(x > -sqrt(5)/2) & (x < sqrt(5)/2), context=1/(sqrt(5 - 4*x**2)), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                       //    /      ___\                                 \
 |                        ||    |2*x*\/ 5 |                                 |
 |       1                ||asin|---------|         /       ___         ___\|
 | ------------- dx = C + |<    \    5    /         |    -\/ 5        \/ 5 ||
 |    __________          ||---------------  for And|x > -------, x < -----||
 |   /        2           ||       2                \       2           2  /|
 | \/  5 - 4*x            \\                                                /
 |                                                                           
/
$$\int \frac{1}{\sqrt{5 - 4 x^{2}}}\, dx = C + \begin{cases} \frac{\operatorname{asin}{\left(\frac{2 \sqrt{5} x}{5} \right)}}{2} & \text{for}\: x > - \frac{\sqrt{5}}{2} \wedge x < \frac{\sqrt{5}}{2} \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
    /    ___\
    |2*\/ 5 |
asin|-------|
    \   5   /
-------------
      2
$$\frac{\operatorname{asin}{\left(\frac{2 \sqrt{5}}{5} \right)}}{2}$$ 
=
= 
    /    ___\
    |2*\/ 5 |
asin|-------|
    \   5   /
-------------
      2
$$\frac{\operatorname{asin}{\left(\frac{2 \sqrt{5}}{5} \right)}}{2}$$ 
asin(2*sqrt(5)/5)/2
Numerical answer [src] 
0.553574358897045
0.553574358897045

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

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