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Similar expressions
1/(sqrt(2x+1))^3

Integral of 1/(sqrt(2x-1))^3 dx

The solution

You have entered [src]

 1/2               
  /                
 |                 
 |       1         
 |  ------------ dx
 |             3   
 |    _________    
 |  \/ 2*x - 1     
 |                 
/                  
0

$$\int\limits_{0}^{\frac{1}{2}} \frac{1}{\left(\sqrt{2 x - 1}\right)^{3}}\, dx$$

Integral(1/((sqrt(2*x - 1))^3), (x, 0, 1/2))

Detail solution

There are multiple ways to do this integral.
Method #1
1. Rewrite the integrand:
  
  $\frac{1}{\left(\sqrt{2 x - 1}\right)^{3}} = \frac{1}{2 x \sqrt{2 x - 1} - \sqrt{2 x - 1}}$
2. Let $u = \sqrt{2 x - 1}$ .
  
  Then let $du = \frac{dx}{\sqrt{2 x - 1}}$ and substitute $du$ :
  
  $\int \frac{1}{u^{2}}\, du$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \frac{1}{u^{2}}\, du = - \frac{1}{u}$
  Now substitute $u$ back in:
  
  $- \frac{1}{\sqrt{2 x - 1}}$
Method #2
1. Rewrite the integrand:
  
  $\frac{1}{\left(\sqrt{2 x - 1}\right)^{3}} = \frac{1}{2 x \sqrt{2 x - 1} - \sqrt{2 x - 1}}$
2. Let $u = \sqrt{2 x - 1}$ .
  
  Then let $du = \frac{dx}{\sqrt{2 x - 1}}$ and substitute $du$ :
  
  $\int \frac{1}{u^{2}}\, du$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \frac{1}{u^{2}}\, du = - \frac{1}{u}$
  Now substitute $u$ back in:
  
  $- \frac{1}{\sqrt{2 x - 1}}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                  
 |                                   
 |      1                     1      
 | ------------ dx = C - ------------
 |            3            __________
 |   _________           \/ -1 + 2*x 
 | \/ 2*x - 1                        
 |                                   
/

$$\int \frac{1}{\left(\sqrt{2 x - 1}\right)^{3}}\, dx = C - \frac{1}{\sqrt{2 x - 1}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo*I

$$\infty i$$

oo*I

$$\infty i$$

oo*i

Numerical answer [src]

(0.0 + 3733323237.08344j)

(0.0 + 3733323237.08344j)

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

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Identical expressions

Similar expressions

Integral of 1/(sqrt(2x-1))^3 dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2