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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  0               
  /               
 |                
 |       1        
 |  ----------- dx
 |    _________   
 |  \/ 1 - 2*x    
 |                
/                 
-oo
∫−∞011−2x dx\int\limits_{-\infty}^{0} \frac{1}{\sqrt{1 - 2 x}}\, dx 
Integral(1/(sqrt(1 - 2*x)), (x, -oo, 0))
Detail solution

  1. Let u=1−2xu = \sqrt{1 - 2 x}.

    Then let du=−dx1−2xdu = - \frac{dx}{\sqrt{1 - 2 x}} and substitute −du- du:

    ∫(−1) du\int \left(-1\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: −u- u

    Now substitute uu back in:

    −1−2x- \sqrt{1 - 2 x}

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                                
 |                                 
 |      1                 _________
 | ----------- dx = C - \/ 1 - 2*x 
 |   _________                     
 | \/ 1 - 2*x                      
 |                                 
/
∫11−2x dx=C−1−2x\int \frac{1}{\sqrt{1 - 2 x}}\, dx = C - \sqrt{1 - 2 x}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
oo
∞\infty 
=
= 
oo
∞\infty 
oo

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

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