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1/sqrt(1-x)
Solving integrals/ 1/sqrt(1-x)

Integral of 1/sqrt(1-x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Let u=1−xu = \sqrt{1 - x}.

    Then let du=−dx21−xdu = - \frac{dx}{2 \sqrt{1 - x}} and substitute −2du- 2 du:

    ∫(−2) du\int \left(-2\right)\, du

    1. The integral of a constant times a function is the constant times the integral of the function:

      False\text{False}

      1. The integral of a constant is the constant times the variable of integration:

        ∫1 du=u\int 1\, du = u

      So, the result is: −2u- 2 u

    Now substitute uu back in:

    −21−x- 2 \sqrt{1 - x}

  2. Add the constant of integration:

    −21−x+constant- 2 \sqrt{1 - x}+ \mathrm{constant}

The answer is:

−21−x+constant- 2 \sqrt{1 - x}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                              
 |                               
 |     1                  _______
 | --------- dx = C - 2*\/ 1 - x 
 |   _______                     
 | \/ 1 - x                      
 |                               
/
∫11−x dx=C−21−x\int \frac{1}{\sqrt{1 - x}}\, dx = C - 2 \sqrt{1 - x}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90200-100
Plot the graph f(x)
The answer [src] 
2
22 
=
= 
2
22 
2
Numerical answer [src] 
1.99999999946952
1.99999999946952
The graph
Integral of 1/sqrt(1-x) dx

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

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