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

The solution

You have entered [src]

  3               
  /               
 |                
 |       1        
 |  ----------- dx
 |    _________   
 |  \/ 2*x - 1    
 |                
/                 
-2

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

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

Detail solution

Let $u = \sqrt{2 x - 1}$ .

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

$\int 1\, du$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, du = u$
Now substitute $u$ back in:

$\sqrt{2 x - 1}$
Now simplify:

$\sqrt{2 x - 1}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

  ___       ___
\/ 5  - I*\/ 5

$$\sqrt{5} - \sqrt{5} i$$

  ___       ___
\/ 5  - I*\/ 5

$$\sqrt{5} - \sqrt{5} i$$

sqrt(5) - i*sqrt(5)

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

Other calculators

How to use it?

Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution