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Integral of d*x/sqrt(x-1) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src]
 10             
  /             
 |              
 |     d*x      
 |  --------- dx
 |    _______   
 |  \/ x - 1    
 |              
/               
5               
$$\int\limits_{5}^{10} \frac{d x}{\sqrt{x - 1}}\, dx$$
Integral((d*x)/sqrt(x - 1), (x, 5, 10))
Detail solution
  1. Let .

    Then let and substitute :

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

      1. Integrate term-by-term:

        1. The integral of is when :

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

        The result is:

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                               
 |                        /                   3/2\
 |    d*x                 |  _______   (x - 1)   |
 | --------- dx = C + 2*d*|\/ x - 1  + ----------|
 |   _______              \                3     /
 | \/ x - 1                                       
 |                                                
/                                                 
$$\int \frac{d x}{\sqrt{x - 1}}\, dx = C + 2 d \left(\frac{\left(x - 1\right)^{\frac{3}{2}}}{3} + \sqrt{x - 1}\right)$$
The answer [src]
44*d
----
 3  
$$\frac{44 d}{3}$$
=
=
44*d
----
 3  
$$\frac{44 d}{3}$$
44*d/3

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