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  • Identical expressions

  • dx/(sqrt(four - five *x^ two))
  • dx divide by ( square root of (4 minus 5 multiply by x squared ))
  • dx divide by ( square root of (four minus five multiply by x to the power of two))
  • dx/(√(4-5*x^2))
  • dx/(sqrt(4-5*x2))
  • dx/sqrt4-5*x2
  • dx/(sqrt(4-5*x²))
  • dx/(sqrt(4-5*x to the power of 2))
  • dx/(sqrt(4-5x^2))
  • dx/(sqrt(4-5x2))
  • dx/sqrt4-5x2
  • dx/sqrt4-5x^2
  • dx divide by (sqrt(4-5*x^2))

  • Similar expressions

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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                       //          /    ___\                                    \
 |                        ||  ___     |x*\/ 5 |                                    |
 |       1                ||\/ 5 *asin|-------|         /         ___          ___\|
 | ------------- dx = C + |<          \   2   /         |    -2*\/ 5       2*\/ 5 ||
 |    __________          ||-------------------  for And|x > --------, x < -------||
 |   /        2           ||         5                  \       5             5   /|
 | \/  4 - 5*x            \\                                                       /
 |                                                                                  
/
$$\int \frac{1}{\sqrt{4 - 5 x^{2}}}\, dx = C + \begin{cases} \frac{\sqrt{5} \operatorname{asin}{\left(\frac{\sqrt{5} x}{2} \right)}}{5} & \text{for}\: x > - \frac{2 \sqrt{5}}{5} \wedge x < \frac{2 \sqrt{5}}{5} \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
          /  ___\
  ___     |\/ 5 |
\/ 5 *asin|-----|
          \  2  /
-----------------
        5
$$\frac{\sqrt{5} \operatorname{asin}{\left(\frac{\sqrt{5}}{2} \right)}}{5}$$ 
=
= 
          /  ___\
  ___     |\/ 5 |
\/ 5 *asin|-----|
          \  2  /
-----------------
        5
$$\frac{\sqrt{5} \operatorname{asin}{\left(\frac{\sqrt{5}}{2} \right)}}{5}$$ 
sqrt(5)*asin(sqrt(5)/2)/5
Numerical answer [src] 
(0.676056261612884 - 0.21818552482013j)
(0.676056261612884 - 0.21818552482013j)

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

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