Mister Exam

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Identical expressions
dx/sqrt(five -x)
dx divide by square root of (5 minus x)
dx divide by square root of (five minus x)
dx/√(5-x)
dx/sqrt5-x
dx divide by sqrt(5-x)
Similar expressions
dx/sqrt(5+x)
dx/sqrt(5-x^3)
(dx)/(sqrt(5-x^2))
dx/((sqrt5-x^2)-4x)

Integral of dx/sqrt(5-x) dx

The solution

You have entered [src]

  5             
  /             
 |              
 |      1       
 |  --------- dx
 |    _______   
 |  \/ 5 - x    
 |              
/               
1

$$\int\limits_{1}^{5} \frac{1}{\sqrt{5 - x}}\, dx$$

Integral(1/(sqrt(5 - x)), (x, 1, 5))

Detail solution

Let $u = \sqrt{5 - x}$ .

Then let $du = - \frac{dx}{2 \sqrt{5 - x}}$ and substitute $- 2 du$ :

$\int \left(-2\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\text{False}$
  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:

$- 2 \sqrt{5 - x}$
Add the constant of integration:

$- 2 \sqrt{5 - x}+ \mathrm{constant}$

The answer is:

$- 2 \sqrt{5 - x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                               
 |     1                  _______
 | --------- dx = C - 2*\/ 5 - x 
 |   _______                     
 | \/ 5 - x                      
 |                               
/

$$\int \frac{1}{\sqrt{5 - x}}\, dx = C - 2 \sqrt{5 - x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$4$$

Numerical answer [src]

3.99999999893904

3.99999999893904

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

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Integral of dx/sqrt(5-x) dx

Limits of integration:

The graph:

Piecewise:

The solution