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

The solution

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 oo             
  /             
 |              
 |      1       
 |  --------- dx
 |    _______   
 |  \/ x - 2    
 |              
/               
3

$$\int\limits_{3}^{\infty} \frac{1}{\sqrt{x - 2}}\, dx$$

Integral(1/(sqrt(x - 2)), (x, 3, oo))

Detail solution

Let $u = \sqrt{x - 2}$ .

Then let $du = \frac{dx}{2 \sqrt{x - 2}}$ and substitute $2 du$ :

$\int 2\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\text{False}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, du = u$
  So, the result is: $2 u$
Now substitute $u$ back in:

$2 \sqrt{x - 2}$
Now simplify:

$2 \sqrt{x - 2}$
Add the constant of integration:

$2 \sqrt{x - 2}+ \mathrm{constant}$

The answer is:

$2 \sqrt{x - 2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                               
 |     1                  _______
 | --------- dx = C + 2*\/ x - 2 
 |   _______                     
 | \/ x - 2                      
 |                               
/

$$\int \frac{1}{\sqrt{x - 2}}\, dx = C + 2 \sqrt{x - 2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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$$\infty$$

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

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

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